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children ::: Math (facts), Math (formulas)
branches ::: Math, Savitri maths

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object:Math
class:subject
class:Language

MATH TRICKS
percentages are reversable.
8% of 25 = 2
25% of 8 = 2

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now begins generated list of local instances, definitions, quotes, instances in chapters, wordnet info if available and instances among weblinks


OBJECT INSTANCES [2] - TOPICS - AUTHORS - BOOKS - CHAPTERS - CLASSES - SEE ALSO - SIMILAR TITLES

TOPICS
Math_(facts)
Math_(formulas)
SEE ALSO


AUTH
Eratosthenes
Gottfried_Wilhelm_Leibniz
Hemachandra
Johannes_Kepler
Lalla
Lewis_Carroll
Niels_Bohr
Norbert_Wiener
Omar_Khayyam
Plato
Sir_Roger_Penrose
Thomas_Carlyle
Wang_Zhenyi

BOOKS
Al-Fihrist
Full_Circle
Heart_of_Matter
How_to_Practice_Shamatha_Meditation__The_Cultivation_of_Meditative_Quiescene
Infinite_Library
Liber_157_-_The_Tao_Teh_King
Life_without_Death
Modern_Man_in_Search_of_a_Soul
Moral_Disengagement__How_Good_People_Can_Do_Harm_and_Feel_Good_About_Themselves
My_Burning_Heart
Mysticism_and_Logic
Plotinus_-_Complete_Works_Vol_01
Process_and_Reality
Savitri
Synergetics_-_Explorations_in_the_Geometry_of_Thinking
The_Act_of_Creation
The_Ever-Present_Origin
The_Principia__Mathematical_Principles_of_Natural_Philosophy
The_Principles_of_Mathematics
The_Republic
The_Use_and_Abuse_of_History
The_Wit_and_Wisdom_of_Alfred_North_Whitehead
The_World_as_Will_and_Idea
The_Yoga_Sutras
Three_Books_on_Occult_Philosophy
Toward_the_Future
Vishnu_Purana

IN CHAPTERS TITLE
1.jk_-_To_George_Felton_Mathew

IN CHAPTERS CLASSNAME

IN CHAPTERS TEXT
0_0.01_-_Introduction
00.01_-_The_Approach_to_Mysticism
000_-_Humans_in_Universe
0.00_-_INTRODUCTION
0.00_-_The_Book_of_Lies_Text
0.00_-_THE_GOSPEL_PREFACE
0.00_-_The_Wellspring_of_Reality
0.06_-_INTRODUCTION
01.07_-_Blaise_Pascal_(1623-1662)
01.08_-_Walter_Hilton:_The_Scale_of_Perfection
0.10_-_Letters_to_a_Young_Captain
0_1958-05-01
0_1958-11-08
0_1961-01-31
0_1961-02-11
0_1961-04-29
0_1962-02-13
0_1962-05-15
0_1962-06-09
0_1962-07-21
0_1963-02-23
0_1963-05-11
0_1964-01-04
0_1964-08-08
0_1965-07-21
0_1966-12-17
0_1967-02-18
0_1967-07-26
0_1969-05-21
0_1969-11-29
0_1971-05-15
0_1971-05-26
0_1971-10-06
02.02_-_Lines_of_the_Descent_of_Consciousness
02.05_-_The_Godheads_of_the_Little_Life
02.07_-_India_One_and_Indivisable
02.10_-_The_Kingdoms_and_Godheads_of_the_Little_Mind
02.11_-_The_Kingdoms_and_Godheads_of_the_Greater_Mind
03.02_-_The_Gradations_of_Consciousness__The_Gradation_of_Planes
03.05_-_Some_Conceptions_and_Misconceptions
03.09_-_Buddhism_and_Hinduism
03.14_-_Mater_Dolorosa
03.15_-_Towards_the_Future
04.02_-_Human_Progress
04.07_-_Matter_Aspires
05.05_-_In_Quest_of_Reality
05.06_-_Physics_or_philosophy
05.07_-_The_Observer_and_the_Observed
05.08_-_An_Age_of_Revolution
05.09_-_The_Changed_Scientific_Outlook
05.12_-_The_Soul_and_its_Journey
05.28_-_God_Protects
05.31_-_Divine_Intervention
09.11_-_The_Supramental_Manifestation_and_World_Change
09.13_-_On_Teachers_and_Teaching
100.00_-_Synergy
1.00a_-_Introduction
1.00d_-_Introduction
1.00_-_Preface
10.17_-_Miracles:_Their_True_Significance
1.01_-_Adam_Kadmon_and_the_Evolution
1.01_-_Archetypes_of_the_Collective_Unconscious
1.01_-_Economy
1.01_-_Historical_Survey
1.01_-_Introduction
1.01_-_MAPS_OF_EXPERIENCE_-_OBJECT_AND_MEANING
1.01_-_MASTER_AND_DISCIPLE
1.01_-_Newtonian_and_Bergsonian_Time
1.01_-_THE_STUFF_OF_THE_UNIVERSE
1.01_-_What_is_Magick?
1.024_-_Affiliation_With_Larger_Wholes
1.025_-_Sadhana_-_Intensifying_a_Lighted_Flame
1.02_-_Groups_and_Statistical_Mechanics
1.02_-_In_the_Beginning
1.02_-_IN_THE_COMPANY_OF_DEVOTEES
1.02_-_THE_NATURE_OF_THE_GROUND
1.02_-_The_Pit
1.02_-_The_Three_European_Worlds
1.02_-_THE_WITHIN_OF_THINGS
10.32_-_The_Mystery_of_the_Five_Elements
10.37_-_The_Golden_Bridge
1.03_-_Hieroglypics__Life_and_Language_Necessarily_Symbolic
1.03_-_Preparing_for_the_Miraculous
1.03_-_.REASON._IN_PHILOSOPHY
1.03_-_THE_GRAND_OPTION
1.03_-_The_House_Of_The_Lord
1.03_-_The_Phenomenon_of_Man
1.03_-_The_Sephiros
1.03_-_Time_Series,_Information,_and_Communication
1.04_-_ADVICE_TO_HOUSEHOLDERS
1.04_-_Feedback_and_Oscillation
1.04_-_Religion_and_Occultism
1.04_-_SOME_REFLECTIONS_ON_PROGRESS
1.04_-_The_Conditions_of_Esoteric_Training
1.04_-_The_Paths
1.04_-_The_Qabalah__The_Best_Training_for_Memory
1.05_-_BOOK_THE_FIFTH
1.05_-_Computing_Machines_and_the_Nervous_System
1.05_-_Problems_of_Modern_Psycho_therapy
1.05_-_Qualifications_of_the_Aspirant_and_the_Teacher
1.05_-_THE_HOSTILE_BROTHERS_-_ARCHETYPES_OF_RESPONSE_TO_THE_UNKNOWN
1.05_-_The_Universe__The_0_=_2_Equation
1.05_-_War_And_Politics
1.060_-_Tracing_the_Ultimate_Cause_of_Any_Experience
1.06_-_Being_Human_and_the_Copernican_Principle
1.06_-_Dhyana
1.06_-_Quieting_the_Vital
1.06_-_The_Literal_Qabalah
1.06_-_THE_MASTER_WITH_THE_BRAHMO_DEVOTEES
1.06_-_The_Three_Schools_of_Magick_1
1.07_-_A_Song_of_Longing_for_Tara,_the_Infallible
1.07_-_On_Our_Knowledge_of_General_Principles
1.07_-_The_Farther_Reaches_of_Human_Nature
1.081_-_The_Application_of_Pratyahara
1.08a_-_The_Ladder
1.08_-_SOME_REFLECTIONS_ON_THE_SPIRITUAL_REPERCUSSIONS_OF_THE_ATOM_BOMB
1.08_-_The_Change_of_Vision
1.09_-_Sri_Aurobindo_and_the_Big_Bang
1.09_-_The_Secret_Chiefs
11.05_-_The_Ladder_of_Unconsciousness
1.10_-_Aesthetic_and_Ethical_Culture
1.10_-_BOOK_THE_TENTH
1.10_-_Harmony
1.10_-_On_our_Knowledge_of_Universals
1.10_-_The_descendants_of_the_daughters_of_Daksa_married_to_the_Rsis
1.10_-_THE_MASTER_WITH_THE_BRAHMO_DEVOTEES_(II)
11.15_-_Sri_Aurobindo
1.11_-_BOOK_THE_ELEVENTH
1.11_-_FAITH_IN_MAN
1.11_-_On_Intuitive_Knowledge
1.11_-_WITH_THE_DEVOTEES_AT_DAKSHINEWAR
1.11_-_Woolly_Pomposities_of_the_Pious_Teacher
1.12_-_Dhruva_commences_a_course_of_religious_austerities
1.12_-_God_Departs
1.12_-_The_Superconscient
1.12_-_Truth_and_Knowledge
1.13_-_Under_the_Auspices_of_the_Gods
1.14_-_INSTRUCTION_TO_VAISHNAVS_AND_BRHMOS
1.14_-_The_Limits_of_Philosophical_Knowledge
1.14_-_The_Structure_and_Dynamics_of_the_Self
1.15_-_Index
1.15_-_LAST_VISIT_TO_KESHAB
1.15_-_The_Supramental_Consciousness
1.15_-_The_Suprarational_Good
1.15_-_The_Value_of_Philosophy
1.16_-_WITH_THE_DEVOTEES_AT_DAKSHINESWAR
1.17_-_M._AT_DAKSHINEWAR
1.18_-_FAITH
1.18_-_M._AT_DAKSHINESWAR
1.18_-_Mind_and_Supermind
1.19_-_ON_THE_PROBABLE_EXISTENCE_AHEAD_OF_US_OF_AN_ULTRA-HUMAN
1.19_-_THE_MASTER_AND_HIS_INJURED_ARM
1.201_-_Socrates
12.01_-_This_Great_Earth_Our_Mother
12.02_-_The_Stress_of_the_Spirit
1.21_-_A_DAY_AT_DAKSHINESWAR
1.22_-_ADVICE_TO_AN_ACTOR
1.22_-_Tabooed_Words
1.22_-_THE_END_OF_THE_SPECIES
1.23_-_FESTIVAL_AT_SURENDRAS_HOUSE
1.25_-_ADVICE_TO_PUNDIT_SHASHADHAR
1.26_-_FESTIVAL_AT_ADHARS_HOUSE
1.27_-_AT_DAKSHINESWAR
1.29_-_What_is_Certainty?
13.05_-_A_Dream_Of_Surreal_Science
1.31_-_Adonis_in_Cyprus
1.32_-_How_can_a_Yogi_ever_be_Worried?
1.39_-_Prophecy
1.40_-_Coincidence
1.42_-_This_Self_Introversion
1.44_-_Serious_Style_of_A.C.,_or_the_Apparent_Frivolity_of_Some_of_my_Remarks
1.49_-_Ancient_Deities_of_Vegetation_as_Animals
1.49_-_Thelemic_Morality
15.08_-_Ashram_-_Inner_and_Outer
1.53_-_The_Propitation_of_Wild_Animals_By_Hunters
1.58_-_Do_Angels_Ever_Cut_Themselves_Shaving?
1.65_-_Man
1.66_-_Vampires
1.72_-_Education
1.77_-_Work_Worthwhile_-_Why?
1.83_-_Epistola_Ultima
1917_03_27p
1951-03-12_-_Mental_forms_-_learning_difficult_subjects_-_Mental_fortress_-_thought_-_Training_the_mind_-_Helping_the_vital_being_after_death_-_ceremonies_-_Human_stupidities
1953-06-24
1953-07-22
1953-09-30
1954-06-02_-_Learning_how_to_live_-_Work,_studies_and_sadhana_-_Waste_of_the_Energy_and_Consciousness
1954-10-20_-_Stand_back_-_Asking_questions_to_Mother_-_Seeing_images_in_meditation_-_Berlioz_-Music_-_Mothers_organ_music_-_Destiny
1955-03-23_-_Procedure_for_rejection_and_transformation_-_Learning_by_heart,_true_understanding_-_Vibrations,_movements_of_the_species_-_A_cat_and_a_Russian_peasant_woman_-_A_cat_doing_yoga
1955-08-03_-_Nothing_is_impossible_in_principle_-_Psychic_contact_and_psychic_influence_-_Occult_powers,_adverse_influences;_magic_-_Magic,_occultism_and_Yogic_powers_-Hypnotism_and_its_effects
1955-12-07_-_Emotional_impulse_of_self-giving_-_A_young_dancer_in_France_-_The_heart_has_wings,_not_the_head_-_Only_joy_can_conquer_the_Adversary
1956-01-04_-_Integral_idea_of_the_Divine_-_All_things_attracted_by_the_Divine_-_Bad_things_not_in_place_-_Integral_yoga_-_Moving_idea-force,_ideas_-_Consequences_of_manifestation_-_Work_of_Spirit_via_Nature_-_Change_consciousness,_change_world
1956-10-03_-_The_Mothers_different_ways_of_speaking_-_new_manifestation_-_new_element,_possibilities_-_child_prodigies_-_Laws_of_Nature,_supramental_-_Logic_of_the_unforeseen_-_Creative_writers,_hands_of_musicians_-_Prodigious_children,_men
1956-11-14_-_Conquering_the_desire_to_appear_good_-_Self-control_and_control_of_the_life_around_-_Power_of_mastery_-_Be_a_great_yogi_to_be_a_good_teacher_-_Organisation_of_the_Ashram_school_-_Elementary_discipline_of_regularity
1956-11-21_-_Knowings_and_Knowledge_-_Reason,_summit_of_mans_mental_activities_-_Willings_and_the_true_will_-_Personal_effort_-_First_step_to_have_knowledge_-_Relativity_of_medical_knowledge_-_Mental_gymnastics_make_the_mind_supple
1956-12-12_-_paradoxes_-_Nothing_impossible_-_unfolding_universe,_the_Eternal_-_Attention,_concentration,_effort_-_growth_capacity_almost_unlimited_-_Why_things_are_not_the_same_-_will_and_willings_-_Suggestions,_formations_-_vital_world
1957-01-02_-_Can_one_go_out_of_time_and_space?_-_Not_a_crucified_but_a_glorified_body_-_Individual_effort_and_the_new_force
1958-09-24_-_Living_the_truth_-_Words_and_experience
1958-11-05_-_Knowing_how_to_be_silent
1960_06_29
1969_09_17
1.bs_-_Love_Springs_Eternal
1f.lovecraft_-_At_the_Mountains_of_Madness
1f.lovecraft_-_Deaf,_Dumb,_and_Blind
1f.lovecraft_-_In_the_Walls_of_Eryx
1f.lovecraft_-_Pickmans_Model
1f.lovecraft_-_Poetry_and_the_Gods
1f.lovecraft_-_The_Case_of_Charles_Dexter_Ward
1f.lovecraft_-_The_Colour_out_of_Space
1f.lovecraft_-_The_Descendant
1f.lovecraft_-_The_Dreams_in_the_Witch_House
1f.lovecraft_-_The_Electric_Executioner
1f.lovecraft_-_The_Haunter_of_the_Dark
1f.lovecraft_-_The_Horror_in_the_Museum
1f.lovecraft_-_The_Last_Test
1f.lovecraft_-_The_Little_Glass_Bottle
1f.lovecraft_-_The_Loved_Dead
1f.lovecraft_-_The_Lurking_Fear
1f.lovecraft_-_The_Picture_in_the_House
1f.lovecraft_-_The_Secret_Cave
1f.lovecraft_-_The_Shadow_out_of_Time
1f.lovecraft_-_The_Shadow_over_Innsmouth
1f.lovecraft_-_The_Thing_on_the_Doorstep
1f.lovecraft_-_The_Trap
1f.lovecraft_-_The_Unnamable
1f.lovecraft_-_The_Whisperer_in_Darkness
1f.lovecraft_-_Through_the_Gates_of_the_Silver_Key
1f.lovecraft_-_Till_A_the_Seas
1.fs_-_The_Gods_Of_Greece
1.jk_-_To_George_Felton_Mathew
1.jr_-_God_is_what_is_nearer_to_you_than_your_neck-vein,
1.jr_-_I_regard_not_the_outside_and_the_words
1.jr_-_Rise,_Lovers
1.kbr_-_I_Burst_Into_Laughter
1.kbr_-_I_burst_into_laughter
1.lb_-_Exile's_Letter
1.lb_-_Lament_of_the_Frontier_Guard
1.lb_-_Leave-Taking_Near_Shoku
1.lb_-_Poem_by_The_Bridge_at_Ten-Shin
1.lb_-_South-Folk_in_Cold_Country
1.lb_-_Taking_Leave_of_a_Friend_by_Li_Po_Tr._by_Ezra_Pound
1.lb_-_The_City_of_Choan
1.lb_-_The_River_Song
1.lovecraft_-_Fungi_From_Yuggoth
1.pbs_-_Letter_To_Maria_Gisborne
1.poe_-_Eureka_-_A_Prose_Poem
1.poe_-_The_Power_Of_Words_Oinos.
1.rb_-_A_Toccata_Of_Galuppi's
1.rwe_-_Seashore
1.wby_-_Blood_And_The_Moon
1.whitman_-_Eidolons
1.whitman_-_Song_of_Myself
1.whitman_-_Song_Of_Myself-_XXIII
1.whitman_-_Song_Of_The_Redwood-Tree
1.ww_-_The_Excursion-_VII-_Book_Sixth-_The_Churchyard_Among_the_Mountains
2.01_-_AT_THE_STAR_THEATRE
2.01_-_Indeterminates,_Cosmic_Determinations_and_the_Indeterminable
2.01_-_On_Books
2.01_-_THE_ADVENT_OF_LIFE
2.01_-_The_Therapeutic_value_of_Abreaction
2.01_-_The_Yoga_and_Its_Objects
2.02_-_Brahman,_Purusha,_Ishwara_-_Maya,_Prakriti,_Shakti
2.02_-_Habit_2__Begin_with_the_End_in_Mind
2.02_-_On_Letters
2.03_-_On_Medicine
2.03_-_THE_ENIGMA_OF_BOLOGNA
2.04_-_ADVICE_TO_ISHAN
2.05_-_Apotheosis
2.06_-_WITH_VARIOUS_DEVOTEES
2.07_-_On_Congress_and_Politics
2.07_-_The_Cup
2.08_-_ALICE_IN_WONDERLAND
2.09_-_On_Sadhana
2.09_-_SEVEN_REASONS_WHY_A_SCIENTIST_BELIEVES_IN_GOD
2.09_-_The_Pantacle
2.0_-_THE_ANTICHRIST
2.1.03_-_Man_and_Superman
2.10_-_THE_MASTER_AND_NARENDRA
2.11_-_WITH_THE_DEVOTEES_IN_CALCUTTA
2.12_-_THE_MASTERS_REMINISCENCES
2.12_-_The_Origin_of_the_Ignorance
2.13_-_On_Psychology
2.13_-_THE_MASTER_AT_THE_HOUSES_OF_BALARM_AND_GIRISH
2.1.4.2_-_Teaching
2.1.4.4_-_Homework
2.14_-_AT_RAMS_HOUSE
2.14_-_The_Unpacking_of_God
2.1.5.5_-_Other_Subjects
2.15_-_CAR_FESTIVAL_AT_BALARMS_HOUSE
2.15_-_On_the_Gods_and_Asuras
2.15_-_Reality_and_the_Integral_Knowledge
2.17_-_December_1938
2.17_-_THE_MASTER_ON_HIMSELF_AND_HIS_EXPERIENCES
2.18_-_January_1939
2.18_-_SRI_RAMAKRISHNA_AT_SYAMPUKUR
2.19_-_THE_MASTER_AND_DR._SARKAR
2.2.01_-_Work_and_Yoga
2.20_-_THE_MASTERS_TRAINING_OF_HIS_DISCIPLES
2.21_-_IN_THE_COMPANY_OF_DEVOTEES_AT_SYAMPUKUR
2.22_-_Rebirth_and_Other_Worlds;_Karma,_the_Soul_and_Immortality
2.22_-_THE_MASTER_AT_COSSIPORE
2.23_-_THE_MASTER_AND_BUDDHA
2.24_-_The_Evolution_of_the_Spiritual_Man
2.25_-_AFTER_THE_PASSING_AWAY
2.3.01_-_The_Planes_or_Worlds_of_Consciousness
23.10_-_Observations_II
24.03_-_Notes_on_Savitri_II
24.05_-_Vision_of_Dante
29.03_-_In_Her_Company
3.00_-_Introduction
3.00_-_The_Magical_Theory_of_the_Universe
3.01_-_THE_BIRTH_OF_THOUGHT
3.03_-_THE_MODERN_EARTH
3.04_-_LUNA
3.07_-_The_Formula_of_the_Holy_Grail
3.08_-_Of_Equilibrium
3.09_-_Of_Silence_and_Secrecy
31.06_-_Jagadish_Chandra_Bose
3.10_-_The_New_Birth
3.12_-_Of_the_Bloody_Sacrifice
3.18_-_Of_Clairvoyance_and_the_Body_of_Light
32.07_-_The_God_of_the_Scientist
3.2.08_-_Bhakti_Yoga_and_Vaishnavism
3.21_-_Of_Black_Magic
33.01_-_The_Initiation_of_Swadeshi
33.03_-_Muraripukur_-_I
33.07_-_Alipore_Jail
33.08_-_I_Tried_Sannyas
3.4.03_-_Materialism
3.5.01_-_Aphorisms
3-5_Full_Circle
37.05_-_Narada_-_Sanatkumara_(Chhandogya_Upanishad)
3.7.1.01_-_Rebirth
3.7.1.12_-_Karma_and_Justice
3.7.2.01_-_The_Foundation
3.7.2.03_-_Mind_Nature_and_Law_of_Karma
3_-_Commentaries_and_Annotated_Translations
4.01_-_THE_COLLECTIVE_ISSUE
4.01_-_The_Presence_of_God_in_the_World
4.02_-_BEYOND_THE_COLLECTIVE_-_THE_HYPER-PERSONAL
4.02_-_Humanity_in_Progress
4.0_-_The_Path_of_Knowledge
41.03_-_Bengali_Poems_of_Sri_Aurobindo
4.1_-_Jnana
5.01_-_ADAM_AS_THE_ARCANE_SUBSTANCE
5.1.03_-_The_Hostile_Forces_and_Hostile_Beings
5.4.01_-_Notes_on_Root-Sounds
5.4.01_-_Occult_Knowledge
6.0_-_Conscious,_Unconscious,_and_Individuation
7.08_-_Sincerity
7.10_-_Order
7_-_Yoga_of_Sri_Aurobindo
9.99_-_Glossary
Aeneid
APPENDIX_I_-_Curriculum_of_A._A.
Avatars_of_the_Tortoise
Blazing_P3_-_Explore_the_Stages_of_Postconventional_Consciousness
BOOK_III._-_The_external_calamities_of_Rome
BOOK_II._--_PART_I._ANTHROPOGENESIS.
BOOK_II._--_PART_III._ADDENDA._SCIENCE_AND_THE_SECRET_DOCTRINE_CONTRASTED
BOOK_II._--_PART_II._THE_ARCHAIC_SYMBOLISM_OF_THE_WORLD-RELIGIONS
BOOK_I._--_PART_I._COSMIC_EVOLUTION
BOOK_I._--_PART_III._SCIENCE_AND_THE_SECRET_DOCTRINE_CONTRASTED
BOOK_I._--_PART_II._THE_EVOLUTION_OF_SYMBOLISM_IN_ITS_APPROXIMATE_ORDER
Book_of_Genesis
BOOK_V._-_Of_fate,_freewill,_and_God's_prescience,_and_of_the_source_of_the_virtues_of_the_ancient_Romans
BOOK_XXI._-_Of_the_eternal_punishment_of_the_wicked_in_hell,_and_of_the_various_objections_urged_against_it
BS_1_-_Introduction_to_the_Idea_of_God
Conversations_with_Sri_Aurobindo
COSA_-_BOOK_IV
Cratylus
ENNEAD_01.03_-_Of_Dialectic,_or_the_Means_of_Raising_the_Soul_to_the_Intelligible_World.
ENNEAD_02.01_-_Of_the_Heaven.
ENNEAD_02.09_-_Against_the_Gnostics;_or,_That_the_Creator_and_the_World_are_Not_Evil.
ENNEAD_03.01_-_Concerning_Fate.
ENNEAD_03.07_-_Of_Time_and_Eternity.
ENNEAD_04.02_-_How_the_Soul_Mediates_Between_Indivisible_and_Divisible_Essence.
ENNEAD_04.03_-_Psychological_Questions.
ENNEAD_06.01_-_Of_the_Ten_Aristotelian_and_Four_Stoic_Categories.
ENNEAD_06.02_-_The_Categories_of_Plotinos.
ENNEAD_06.05_-_The_One_and_Identical_Being_is_Everywhere_Present_In_Its_Entirety.345
Gorgias
Jaap_Sahib_Text_(Guru_Gobind_Singh)
Liber
Liber_111_-_The_Book_of_Wisdom_-_LIBER_ALEPH_VEL_CXI
Liber_46_-_The_Key_of_the_Mysteries
Liber_71_-_The_Voice_of_the_Silence_-_The_Two_Paths_-_The_Seven_Portals
LUX.06_-_DIVINATION
Meno
MoM_References
Phaedo
r1912_07_19
r1913_11_18
r1914_03_26
r1914_07_28
r1914_08_20
r1915_01_10
r1915_05_21
Sayings_of_Sri_Ramakrishna_(text)
Sophist
Symposium_translated_by_B_Jowett
Tablets_of_Baha_u_llah_text
Talks_With_Sri_Aurobindo_1
Talks_With_Sri_Aurobindo_2
The_Act_of_Creation_text
Theaetetus
The_Anapanasati_Sutta__A_Practical_Guide_to_Mindfullness_of_Breathing_and_Tranquil_Wisdom_Meditation
The_Book_of_Job
The_Book_of_Joshua
The_Book_of_the_Prophet_Isaiah
The_Dwellings_of_the_Philosophers
The_Gospel_According_to_John
The_Gospel_According_to_Luke
The_Gospel_According_to_Mark
The_Gospel_According_to_Matthew
The_Logomachy_of_Zos
The_Lottery_in_Babylon
The_Monadology
The_Riddle_of_this_World
The_Shadow_Out_Of_Time
Timaeus
Verses_of_Vemana

PRIMARY CLASS

Language
Math
subject
SIMILAR TITLES
God and MATHEMATICS
How to Practice Shamatha Meditation The Cultivation of Meditative Quiescene
Math
Math (facts)
Math (formulas)
Savitri maths
The Principia Mathematical Principles of Natural Philosophy
The Principles of Mathematics

DEFINITIONS


TERMS STARTING WITH

Mathadhipati (Sanskrit) Maṭhādhipati [from maṭha a seat of learning, instruction, or training + adhipati chief or ruler] The head or chief of a center of mystical instruction and training; hence also the principal of a college.

Mathakasa: Space bounded by a temple or a house or a room.

Matha (Sanskrit) Maṭha A seat of learning or instruction and training, especially for young Brahmins; or occasionally a temple. Also a hut or cottage, particularly of an ascetic, as a center of mystical training.

Mathcad ::: A symbolic mathematics environment.

Mathcad A {symbolic mathematics} environment.

Mathematical Analysis without Programming (MAP) An On-line system for mathematics under {CTSS}. [Sammet 1969, p. 240]. (1995-02-10)

Mathematical Analysis without Programming ::: (MAP) An On-line system for mathematics under CTSS.[Sammet 1969, p. 240]. (1995-02-10)

Mathematical Analyzer, Numerical Integrator and Computer "computer, history" (MANIAC, Or "Mathematical Analyzer, Numerator, Integrator, and Computer") An early computer, built for the {Los Alamos Scientific Laboratory}. MANIAC began operation in March 1952. Typical of early computers, it ran its own propriatery language. It was succeeded by {MANIAC II} in 1957. A {MANIAC III} was built at the University of Chicago in 1964. Contrary to legend, MANIAC did not run {MAD} ({Michigan Algorithm Decoder}), which was not invented until 1959. (2013-05-05)

Mathematical Point. See POINT; PRIMORDIAL POINT

Mathematica "tool, mathematics" A popular {symbolic mathematics} and graphics system, developed in 1988 by Stephen Wolfram and sold by {Wolfram Research}. The language emphasises rules and {pattern-matching}. The name was suggested by {Steve Jobs}. {(http://wri.com/mathematica/)}. {Stanford FTP (ftp://otter.stanford.edu/)}, {NCSA FTP (ftp://ftp.ncsa.uiuc.edu/)}. Mailing list: mathgroup-request@yoda.ncsa.uiuc.edu. {Usenet} newsgroup: {news:comp.soft-sys.math.mathematica}. ["Mathematica: A System for Doing Mathematics by Computer", Stephen Wolfram, A-W 1988]. (1995-05-01)

Mathematica ::: (tool, mathematics) A popular symbolic mathematics and graphics system, developed in 1988 by Stephen Wolfram and sold by Wolfram Research. The language emphasises rules and pattern-matching. The name was suggested by Steve Jobs. . .Mailing list: Usenet newsgroup: comp.soft-sys.math.mathematica.[Mathematica: A System for Doing Mathematics by Computer, Stephen Wolfram, A-W 1988]. (1995-05-01)

Mathematics in Recognizable Form Automatically Compiled "language" (MIRFAC) An early interactive system resembling {BASIC} using typewriter output with special mathematical symbols. [Sammet 1969, pp. 281-284]. (1997-08-01)

Mathematics in Recognizable Form Automatically Compiled ::: (language) (MIRFAC) An early interactive system resembling BASIC using typewriter output with special mathematical symbols.[Sammet 1969, pp. 281-284]. (1997-08-01)

Mathematics: The traditional definition of mathematics as "the science of quantity" or "the science of discrete and continuous magnitude" is today inadequate, in that modern mathematics, while clearly in some sense a single connected whole, includes many branches which do not come under this head. Contemporary accounts of the nature of mathematics tend to characterize it rather by its method than by its subject matter.

Mathers. [Rf. Westcott, The Study of the Kabalah,

Mathers, S. L. MacGregor (ed.). The Almadel of Solomon

Mathers, The Greater Key of Solomon; also the

Mathers, The Greater Key of Solomon, p. 112, and

Mathers, The Greater Key of Solomon, p. 63. In

Mathers, The Greater Key of Solomon, p. 80.]

Mathers, The Greater Key of Solomon .]

Mathers, The Greater Key of Solomon.

Mathers, The Greater Key of Solomon.]

Mathers, The Greater Key of Solomon .] Yahel is also

Mathers, The Kabbalah Unveiled.] In the tables

Mathers was published in London, 1887, by George

Mathey, then the presiding spirit is Sammael.

Math fab Mathonwy was a famous enchanter; in the mabinogi he is the teacher of Gwydion. Men are “enchanted by Math before” they “become immortal,” then by Gwydion the Initiator.

Mathiel— in de Abano, The Heptameron,

Mathiel is an angel serving in the 5th Heaven. He

MathJax "mathematics, web" A {JavaScript} {library} for rendering {mathematical symbols} in {web browsers} using {CSS} with {web fonts} or {SVG}. Input can be in {MathML}, {TeX} or {ASCIImath}. {MathJax Home (https://www.mathjax.org/)}. (2019-01-27)

Mathlai is a resident of the 2nd Heaven, and in¬

Mathlai —one of the spirits of the planet

Mathurā. [alt. Madhurā] (T. Bcom rlag; C. Motouluo; J. Machura; K. Mat'ura 摩偸羅). North central Indian city on the Yamunā River, located approximately thirty miles (fifty kms.) north of Agra, and renowned as the birthplace of Kṛsna. During the time of the Buddha, it was the capital of surasena and was ruled by King Avantiputra. The Buddha seems to have visited the city but did not preach there. Indeed, he seems to have disliked it; in the Madhurasutta, he enumerates its five disadvantages: uneven ground, excessive dust, fierce dogs, bestial spirits (YAKsA), and difficulty in obtaining alms. Buddhism gained favor there in later years, and Mathurā became one of the major scholastic centers of the SARVĀSTIVĀDA and/or MuLASARVĀSTIVĀDA school; both FAXIAN and XUANZANG describe it as a flourishing Buddhist city.

Mathura ::: [a town near Agra in North India, the birth-place of Krsna].

Mathura (Sanskrit) Mathurā The birthplace of Krishna, situated in the province of Agra on the right bank of the Yamuna River.

Mathurā

MathWorks {The MathWorks, Inc.}

matha ::: [monastery, hermitage].

mathematical ::: a. --> Of or pertaining to mathematics; according to mathematics; hence, theoretically precise; accurate; as, mathematical geography; mathematical instruments; mathematical exactness.

mathematical equations, to wit: Haniel = Anael = Anfiel = Aniyel = Anafiel = Onoel =

mathematical optimization

mathematic ::: a. --> See Mathematical.

mathematician ::: n. --> One versed in mathematics.

mathematics and can make men invisible. He

mathematics. He can render people invisible;

mathematics ::: n. --> That science, or class of sciences, which treats of the exact relations existing between quantities or magnitudes, and of the methods by which, in accordance with these relations, quantities sought are deducible from other quantities known or supposed; the science of spatial and quantitative relations.

mathematises ::: to reduce to or as if to mathematical formulas.

mather ::: n. --> See Madder.

mathesis ::: n. --> Learning; especially, mathematics.

mathes ::: n. --> The mayweed. Cf. Maghet.

MATHLAB ::: Symbolic math system, MITRE, 1964. Later version: MATHLAB 68 (PDP-6, 1967).[The Legacy of MATHLAB 68, C. Engelman, Proc 2nd Symp on Symbolic and Algebraic Manip, ACM (Mar 1971)].[Sammet 1969, p. 498].

MATHLAB Symbolic math system, MITRE, 1964. Later version: MATHLAB 68 (PDP-6, 1967). ["The Legacy of MATHLAB 68", C. Engelman, Proc 2nd Symp on Symbolic and Algebraic Manip, ACM (Mar 1971)]. [Sammet 1969, p. 498].

MATH-MATIC or MATHMATIC ::: Alternate name for AT-3. Early, pre-Fortran language for UNIVAC I or II. Sammet 1969.

MATH-MATIC or MATHMATIC Alternate name for AT-3. Early, pre-Fortran language for UNIVAC I or II. Sammet 1969.

math ::: n. --> A mowing, or that which is gathered by mowing; -- chiefly used in composition; as, an aftermath.

math-out (Possibly from "white-out", the blizzard variety) A paper or presentation so encrusted with mathematical or other formal notation as to be incomprehensible. This may be a device for concealing the fact that it is actually {content-free}. See also {numbers}, {social science number}. [{Jargon File}] (1994-12-14)

math-out ::: (Possibly from white-out, the blizzard variety) A paper or presentation so encrusted with mathematical or other formal notation as to be incomprehensible. This may be a device for concealing the fact that it is actually content-free.See also numbers, social science number.[Jargon File] (1994-12-14)

math&

mathurin ::: n. --> See Trinitarian.

mathusian ::: n. --> A follower of Malthus.


TERMS ANYWHERE

1-p ::: 1. A notation in Integral Mathematics that represents a first-person mode or perspective. 2. The inside view of any holon.

1p ::: A notation in Integral Mathematics that represents an actual but nonspecific first person.

2. A mathematical expectation is the value of any chance which depends upon some contingent event. Thus, if a person is to receive an amount of money upon the occurrence of an event which has an equal chance of happening or failing, the expectation is worth half that amount. The mathematical expectation of life is the average duration of life (of an individual or a group) after a given age, as determined by computation from the mortality tables.

2. In Logic and Mathematics, a collection, a manifold, a multiplicity, a set, an ensemble, an assemblage, a totality of elements (usually numbers or points) satisfying a given condition or subjected to definite operational laws. According to Cantor, an aggregate is any collection of separate objects of thought gathered into a whole; or again, any multiplicity which can be thought as one; or better, any totality of definite elements bound up into a whole by means of a law. Aggregates have several properties: for example, they have the "same power" when their respective elements can be brought into one-to-one correspondence; and they are "enumerable" when they have the same power as the aggregate of natural numbers. Aggregates may be finite or infinite; and the laws applying to each type are different and often incompatible, thus raising difficult philosophical problems. See One-One; Cardinal Number; Enumerable. Hence the practice to isolate the mathematical notion of the aggregate from its metaphysical implications and to consider such collections as symbols of a certain kind which are to facilitate mathematical calculations in much the same way as numbers do. In spite of the controversial nature of infinite sets great progress has been made in mathematics by the introduction of the Theory of Aggregates in arithmetic, geometry and the theory of functions. (German, Mannigfaltigkeit, Menge; French, Ensemble).

2p ::: A notation in Integral Mathematics that represents an actual but nonspecific second person.

2-p ::: A notation in Integral Mathematics that represents a second-person mode or perspective.

(3) In any proposition of form 'aRb', where R is a propositional function of two variables, a is termed the referent by contrast with the relatum b. (Due to Whitehead and Russell, Principia Mathematica). -- M.B.

3. In mathematical theory, prediction is an inference regarding an unknown or future event, from calculations involving probabilities and in particular the computation of correlations. Statistical predictions are usually made by means of regression coefficients and regression lines, which indicate the amount of change of one variable which accompanies a given amount of change in the other variable. The process of predicting values within the range of known data is called interpolation, and the process of predicting values beyond the range of known data is called extrapolation. The reliability of these predictions varies on the basis of the known variables, and of their limits. -- T.G.

3-p ::: 1. A notation in Integral Mathematics that represents a third-person mode or perspective. 2. The outside view of any holon.

3p ::: A notation in Integral Mathematics that represents an actual but nonspecific third person.

3. Syntactics. Theory of the formal relations (see Formal 2) among signs. Logical Syntax is syntactics applied to theoretical language (language of science); it contains the theory of formal calculi (q.v.), including formalized logic. Compare C. W. Morris, Foundations of the Theory or Signs, 1938; R. Carnap, Foundations of Logic and Mathematics, 1939. -- R.C.

A-0 "language" (Or A0) A language for the {UNIVAC I} or II, using {three-address code} instructions for solving mathematical problems. A-0 was the first language for which a {compiler} was developed. It was produced by {Grace Hopper}'s team at {Remington Rand} in 1952. Later internal versions were A-1, A-2, A-3, AT-3. AT-3 was released as {MATH-MATIC}. ["The A-2 Compiler System", Rem Rand, 1955]. [Sammet 1969, p. 12]. (1995-12-03)

ABC ALGOL "language" An extension of {ALGOL 60} with arbitrary data structures and user-defined operators, for {symbolic mathematics}. ["ABC ALGOL, A Portable Language for Formula Manipulation Systems", R.P. van de Riet, Amsterdam Math Centrum 1973]. (1994-10-28)

AberMUD "games" The first popular {open source} {MUD}. The first version of AberMUD, named after Aberystwyth, UK, was written in {B} by Alan Cox, Richard Acott, Jim Finnis, and Leon Thrane, at University of Wales, Aberystwyth for an old {Honeywell} {mainframe} and opened in 1987. The gameplay was heavily influenced by {MUD1}, written by Roy Trubshaw and Richard Bartle, which Alan Cox had played at the University of Essex. In late 1988, Alan Cox ported AberMUD to {C} so it could run under {UNIX} on Southampton University's Maths machines. This version was named AberMUD2. Various other versions followed. (2008-11-24)

abscissa "mathematics" The horizontal or x coordinate on an (x, y) graph; the input of a function against which the output is plotted. The vertical or y coordinate is the "{ordinate}". See {Cartesian coordinates}. (1997-07-08)

Abstract Machine Notation "language" (AMN) A language for specifying {abstract machines} in the {B-Method}, based on the mathematical theory of {Generalised Substitutions}. (1995-03-13)

aca-pramatha (pisacha-pramatha; pisacha pramatha; pisachopramatha) ::: the combination of pisaca and pramatha, which evolves in the asura type in the third manvantara of the sixth pratikalpa.

According to a view which is widely held by mathematicians, it is characteristic of a mathematical discipline that it begins with a set of undefined elements, properties, functions, and relations, and a set of unproved propositions (called axioms or postulates) involving them; and that from these all other propositions (called theorems) of the discipline are to be derived by the methods of formal logic. On its face, as thus stated, this view would identify mathematics with applied logic. It is usually added, however, that the undefined terms, which appear in the role of names of undefined elements, etc., are not really names of particulars at all but are variables, and that the theorems are to be regarded as proved for any values of these variables which render the postulates true. If then each theorem is replaced by the proposition embodying the implication from the conjunction of the postulates to the theorem in question, we have a reduction of mathematics to pure logic. (For a particular example of a set of postulates for a mathematical discipline see the article Arithmetic, foundations of.)

accuracy "mathematics" How close to the real value a measurement is. Compare {precision}. (1998-04-19)

A. Church, review of the preceding, Bulletin of the American Mathematical Society, vol. 4l (1935), pp. 498-603.

A consistency proof evidently loses much of its significance unless the methods employed in the proof are in some sense less than, or less dubitable than, the methods of proof which the logistic system is intended to formalize. Hilbert required that the methods employed in a consistency proof should be finitary -- a condition more stringent than that of intuitionistic acceptability. See Intuitionism (mathematical).

Active Language I "tool, mathematics" An early interactive mathematics system for the {XDS 930} at the {University of California at Berkeley}. ["Active Language I", R. de Vogelaere in Interactive Systems for Experimental Applied Mathematics, A-P 1968]. (1994-11-08)

additive "mathematics" A function f : X -" Y is additive if for all Z "= X f (lub Z) = lub { f z : z in Z } (f "preserves {lubs}"). All additive functions defined over {cpos} are {continuous}. (""=" is written in {LaTeX} as {\subseteq}, "lub" as \sqcup ). (1995-02-03)

affine transformation "mathematics" A {linear transformation} followed by a {translation}. Given a {matrix} M and a {vector} v, A(x) = Mx + v is a typical affine transformation. (1995-04-10)

aftergrass ::: n. --> The grass that grows after the first crop has been mown; aftermath.

aftermath ::: n. --> A second moving; the grass which grows after the first crop of hay in the same season; rowen.

Aftermath of descent: Whenever there .is a descent of the higher consciousness in the adhara: (1) Part of it is stored up in the frontal consdousness and remains there. (2) Part of it goes behind and remains as a support to the active part of the being. (3) Part flows out into the universal Nature. (4) Part is" absorbed by the inconsdent and lost to the individual cons- dousness and its action.

Agner Krarup Erlang "person" (1878-1929) A Danish mathematician. {Erlang} the language and unit were named after him. Interested in the theory of {probability}, in 1908 Erlang joined the Copenhagen Telephone Company where he studied the problem of waiting times for telephone calls. He worked out how to calculate the fraction of callers who must wait due to all the lines of an exchange being in use. His formula for loss and waiting time was published in 1917. It is now known as the "Erlang formula" and is still in use today. {Biography (http://www-history.mcs.st-andrews.ac.uk/~history/Mathematicians/Erlang.html)}, {Biography (http://pass.maths.org.uk/issue2/erlang/index.html)}. (2005-02-26)

A. Heyting, Mathematische Grundlagen-forschung, Intuitionismus, Beweistheorie, Berlin, 1934. Intuitionism (philosophical):

A. Heyting, Mathematische Grundlagenforschung, Intuitionismus, Beweistheorie, Berlin, 1934.

A. Heyting, Die intuitionistische Grundlegung der Mathematik. ibid., pp. 106-115.

aks.asa (pramatha-rakshasa) ::: the combination of pramatha and raks.asa, which evolves in the asura type in the fifth manvantara of the sixth pratikalpa.

ALADIN 1. "language" {A Language for Attributed Definitions}. 2. "tool" An interactive mathematics system for the {IBM 360}. ["A Conversational System for Engineering Assistance: ALADIN", Y. Siret, Proc Second Symp Symb Algebraic Math, ACM Mar 1971]. (1995-04-13)

ALAM "language" A language for {symbolic mathematics}, especially General Relativity. See also {CLAM}. ["ALAM Programmer's Manual", Ray D'Inverno, 1970]. (1994-10-28)

Alan Turing "person" Alan M. Turing, 1912-06-22/3? - 1954-06-07. A British mathematician, inventor of the {Turing Machine}. Turing also proposed the {Turing test}. Turing's work was fundamental in the theoretical foundations of computer science. Turing was a student and fellow of {King's College Cambridge} and was a graduate student at {Princeton University} from 1936 to 1938. While at Princeton Turing published "On Computable Numbers", a paper in which he conceived an {abstract machine}, now called a {Turing Machine}. Turing returned to England in 1938 and during World War II, he worked in the British Foreign Office. He masterminded operations at {Bletchley Park}, UK which were highly successful in cracking the Nazis "Enigma" codes during World War II. Some of his early advances in computer design were inspired by the need to perform many repetitive symbolic manipulations quickly. Before the building of the {Colossus} computer this work was done by a roomful of women. In 1945 he joined the {National Physical Laboratory} in London and worked on the design and construction of a large computer, named {Automatic Computing Engine} (ACE). In 1949 Turing became deputy director of the Computing Laboratory at Manchester where the {Manchester Automatic Digital Machine}, the worlds largest memory computer, was being built. He also worked on theories of {artificial intelligence}, and on the application of mathematical theory to biological forms. In 1952 he published the first part of his theoretical study of morphogenesis, the development of pattern and form in living organisms. Turing was gay, and died rather young under mysterious circumstances. He was arrested for violation of British homosexuality statutes in 1952. He died of potassium cyanide poisoning while conducting electrolysis experiments. An inquest concluded that it was self-administered but it is now thought by some to have been an accident. There is an excellent biography of Turing by Andrew Hodges, subtitled "The Enigma of Intelligence" and a play based on it called "Breaking the Code". There was also a popular summary of his work in Douglas Hofstadter's book "Gödel, Escher, Bach". {(http://AlanTuring.net/)}. (2001-10-09)

aleph 0 "mathematics" The {cardinality} of the first {infinite} {ordinal}, {omega} (the number of {natural numbers}). Aleph 1 is the cardinality of the smallest {ordinal} whose cardinality is greater than aleph 0, and so on up to aleph omega and beyond. These are all kinds of {infinity}. The {Axiom of Choice} (AC) implies that every set can be {well-ordered}, so every {infinite} {cardinality} is an aleph; but in the absence of AC there may be sets that can't be well-ordered (don't posses a {bijection} with any {ordinal}) and therefore have cardinality which is not an aleph. These sets don't in some way sit between two alephs; they just float around in an annoying way, and can't be compared to the alephs at all. No {ordinal} possesses a {surjection} onto such a set, but it doesn't surject onto any sufficiently large ordinal either. (1995-03-29)

Algebraic Manipulation Package "mathematics, tool" (AMP) A {symbolic mathematics} program written in {Modula-2}, seen on {CompuServe}. (1994-10-19)

algebraic structure "mathematics" Any formal mathematical system consisting of a set of objects and operations on those objects. Examples are {Boolean algebra}, numerical algebra, set algebra and matrix algebra. [Is this the most common name for this concept?] (1997-02-25)

algebra "mathematics, logic" 1. A loose term for an {algebraic structure}. 2. A {vector space} that is also a {ring}, where the vector space and the ring share the same addition operation and are related in certain other ways. An example algebra is the set of 2x2 {matrices} with {real numbers} as entries, with the usual operations of addition and matrix multiplication, and the usual {scalar} multiplication. Another example is the set of all {polynomials} with real coefficients, with the usual operations. In more detail, we have: (1) an underlying {set}, (2) a {field} of {scalars}, (3) an operation of scalar multiplication, whose input is a scalar and a member of the underlying set and whose output is a member of the underlying set, just as in a {vector space}, (4) an operation of addition of members of the underlying set, whose input is an {ordered pair} of such members and whose output is one such member, just as in a vector space or a ring, (5) an operation of multiplication of members of the underlying set, whose input is an ordered pair of such members and whose output is one such member, just as in a ring. This whole thing constitutes an `algebra' iff: (1) it is a vector space if you discard item (5) and (2) it is a ring if you discard (2) and (3) and (3) for any scalar r and any two members A, B of the underlying set we have r(AB) = (rA)B = A(rB). In other words it doesn't matter whether you multiply members of the algebra first and then multiply by the scalar, or multiply one of them by the scalar first and then multiply the two members of the algebra. Note that the A comes before the B because the multiplication is in some cases not commutative, e.g. the matrix example. Another example (an example of a {Banach algebra}) is the set of all {bounded} {linear operators} on a {Hilbert space}, with the usual {norm}. The multiplication is the operation of {composition} of operators, and the addition and scalar multiplication are just what you would expect. Two other examples are {tensor algebras} and {Clifford algebras}. [I. N. Herstein, "Topics in Algebra"]. (1999-07-14)

algebra ::: n. --> That branch of mathematics which treats of the relations and properties of quantity by means of letters and other symbols. It is applicable to those relations that are true of every kind of magnitude.
A treatise on this science.


algebra ::: the branch of mathematics that deals with general statements of relations, utilizing letters and other symbols to represent specific sets of numbers, values, vectors, etc., in the description of such relations. 2. Any special system of notation adapted to the study of a special system of relationship.

algorithm "algorithm, programming" A detailed sequence of actions to perform to accomplish some task. Named after the Iranian, Islamic mathematician, astronomer, astrologer and geographer, {Muhammad ibn Musa al-Khwarizmi}. Technically, an algorithm must reach a result after a {finite} number of steps, thus ruling out {brute force} search methods for certain problems, though some might claim that brute force search was also a valid (generic) algorithm. The term is also used loosely for any sequence of actions (which may or may not terminate). {Paul E. Black's Dictionary of Algorithms, Data Structures, and Problems (http://nist.gov/dads/)}. (2002-02-05)

ALgorIthmic ASsembly language "language" (ALIAS) A machine oriented variant of {BLISS}. ALIAS was implemented in {BCPL} for the {PDP-9}. ["ALIAS", H.E. Barreveld, Int Rep, Math Dept, Delft U Tech, Netherlands, 1973]. (1997-03-13)

Algorithmic Model "programming" A method of estimating software cost using mathematical {algorithms} based on the parameters which are considered to be the major cost drivers. These estimate of effort or cost are based primarily on the size of the software or {Delivered Source Instructions} (DSI)s, and other productivity factors known as {Cost Driver Attributes}. See also {Parametric Model}. (1996-05-28)

Algorithm (or, less commonly, but etymologlcally more correctly, algorism): In its original usage, this word referred to the Arabic system of notation for numbers and to the elementary operations of arithmetic as performed in this notation. In mathematics, the word is used for a method or process of calculation with symbols (often, but not necessarily, numerical symbols) according to fixed rules which yields effectively the, solution of any given problem of some class of problems. -- A.C. Al

ALGY "language" An early language for {symbolic mathematics}. [Sammet 1969, p. 520]. (1995-04-12)

A like result may be obtained for the functional calculus of order omega (theory of types) by utilizing a representation of it within the Zermelo set theory. It is thus in a certain sense impossible to postulate the non-enumerable infinite: any set of postulates designed to do so will have an unintended interpretation within the enumerable. Usual sets of mathematical postulates for the real number system (see number) have an appearance to the contrary only because they are incompletely formalized (i.e., the mathematical concepts are formalized, while the underlying logic remains unformalized and indefinite).

Alonzo Church "person" A twentieth century mathematician and logician, and one of the founders of computer science. Church invented the {lambda-calculus} and posited a version of the {Church-Turing thesis}. (1995-03-25)

ALPS "language" 1. An interpreted {algebraic language} for the {Bendix G15} developed by Dr. Richard V. Andree (? - 1987), Joel C. Ewing and others of the {University of Oklahoma} from Spring 1966 (possibly 1965). Dale Peters "dpeters@theshop.net" reports that in the summer of 1966 he attended the second year of an {NSF}-sponsored summer institute in mathematics and computing at the University of Oklahoma. Dr. Andree's computing class mostly used the language GO-GO, later renamed ALPS. The language changed frequently during the class, which was occasionally disorienting. Dale believes it was also used in Summer 1965 and that it was about this time that {John G. Kemeny} (one of the designers of {Dartmouth BASIC}, 1963) saw it during a visit. Dr. Andree's January 1967 class mimeo notes on ALPS begin: "ALPS is a new programming language designed and perfected by Mr. Harold Bradbury, Mr. Joel Ewing and Mr. Harold Wiebe, members of the O.U. Mathematics Computer Consultants Group under the direction of Dr. Richard V. Andree. ALPS is designed to be used with a minimum of training to solve numerical problems on a computer with typewriter stations and using man-computer cooperation by persons who have little familiarity with advanced mathematics." The initial version of what evolved into ALPS was designed and implemented by Joel Ewing (a pre-senior undergrad) in G15 {machine language} out of frustration with the lack of applications to use the G15's dual-case alphanumeric I/O capabilities. Harold Wiebe also worked on the code. Others, including Ralph Howenstine, a member of the O.U. Math Computer Consultants Group, contributed to the design of extensions and Dr. Andree authored all the instructional materials, made the outside world aware of the language and encouraged work on the language. (2006-10-10) 2. A parallel {logic language}. ["Synchronization and Scheduling in ALPS Objects", P. Vishnubhotia, Proc 8th Intl Conf Distrib Com Sys, IEEE 1988, pp. 256-264]. (1994-11-24)

AM 1. "communications" {Amplitude Modulation}. 2. "artificial intelligence" A program by {Doug Lenat} to discover concepts in elementary mathematics. AM was written in 1976 in {Interlisp}. From 100 fundamental concepts and about 250 {heuristics} it discovered several important mathematical concepts including subsets, disjoint sets, sets with the same number of elements, and numbers. It worked by filling slots in {frames} maintaining an agenda of resource-limited prioritised tasks. AM's successor was {Eurisko}. {(http://homepages.enterprise.net/hibou/aicourse/lenat.txt)}. (1999-04-19)

AMBIT/G "language" {AMBIT} for graphs. ["An Example of the Manipulation of Directed Graphs in the AMBIT/G Programming Language", C. Christensen, in Interactive Systems for Experimental Applied Mathematics, M. Klerer et al, eds, Academic Press 1968, pp. 423-435]. (1994-12-08)

AMP 1. "mathematics, tool" {Algebraic Manipulation Package}. 2. "networking, tool" {Active Measurement Project}.

AMTRAN {Automatic Mathematical TRANslation}

A. M. Turing, On computable numbers, with an application to the Entscheidungsproblem, Proceedings of the London Mathematical Society, ser. 2 vol. 42 (1937), pp. 230-265, and Correction, ibid., ser. 2 vol. 43 (1937), pp. 544-546.

Analogy: Originally a mathematical term, Analogia, meaning equality of ratios (Euclid VII Df. 20, V. Dfs. 5, 6), which entered Plato's philosophy (Republic 534a6), where it also expressed the epistemological doctrine that sensed things are related as their mathematical and ideal correlates. In modern usage analogy was identified with a weak form of reasoning in which "from the similarity of two things in certain particulars, their similarity in other particulars is inferred." (Century Dic.) Recently, the analysis of scientific method has given the term new significance. The observable data of science are denoted by concepts by inspection, whose complete meaning is given by something immediately apprehendable; its verified theory designating unobservable scientific objects is expressed by concepts by postulation, whose complete meaning is prescribed for them by the postulates of the deductive theory in which they occur. To verify such theory relations, termed epistemic correlations (J. Un. Sc. IX: 125-128), are required. When these are one-one, analogy exists in a very precise sense, since the concepts by inspection denoting observable data are then related as are the correlated concepts by postulation designating unobservable scientific objects. -- F.S.C.N. Analogy of Pythagoras: (Gr. analogia) The equality of ratios, or proportion, between the lengths of the strings producing the consonant notes of the musical scale. The discovery of these ratios is credited to Pythagoras, who is also said to have applied the principle of mathematical proportion to the other arts, and hence to have discovered, in his analogy, the secret of beauty in all its forms. -- G.R.M.

Analysis (mathematical): The theory of real numbers, of complex numbers, and of functions of real and complex numbers. See number; continuity; limit. -- A. C.

Andrei Markov "person" 1856-1922. The Russian mathematician, after who {Markov chains} were named. {Biography (http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Markov.html)}. [Other contributions?] (1995-10-06)

An expression A introduced by contextual definition -- i.e., by a definition which construes particular kinds of expressions containing A, as abbreviations or substitutes for certain expressions not containing A, but provides no such construction for A itself -- is an incomplete symbol in this sense. In Principia Mathematica, notations for classes, and descriptions (more correctly, notations which serve some of the purposes that would be served by notations for classes and by descriptions) are introduced in this way by contextual definition. -- A. C.

An important mathematical example of continuous order is afforded by the real numbers, ordered by the relation not greater than. According to usual geometric postulates, the points on a straight line also have continuous order, and, indeed, have the same order type as the real numbers.

antichain "mathematics" A subset S of a {partially ordered set} P is an antichain if, for all x, y in S, x "= y =" x = y I.e. no two different elements are related. (""=" is written in {LaTeX} as {\subseteq}). (1995-02-03)

antisymmetric "mathematics" A {relation} R is antisymmetric if, for all x and y, x R y and y R x =" x == y. I.e. no two different elements are mutually related. {Partial orders} and {total orders} are antisymmetric. If R is also {symmetric}, i.e. x R y =" y R x then x R y =" x == y I.e. different elements are not related. (1995-04-18)

A. N. Whitehead. An Introduction to Mathematics, London, 1911, and New York, 1911.

a person who is practised in or who studies geometry, the branch of mathematics that deals with the deduction of the properties, measurement, and relationships of points, lines, angles, and figures in space from their defining conditions by means of certain assumed properties of space. World-Geometer"s.

apple-touch-icon-precomposed "programming" An alternative form of {apple-touch-icon} that is not subject to automatic modification (rounding, drop-shadow, reflective shine) as applied by {iOS} versions prior to iOS 7. A {web page} specifies a pre-composed icon by including an element in the "head" like: "link rel="apple-touch-icon-precomposed" href="apple-touch-icon-precomposed.png"" The icon can be provided in various different resolutions for different screen sizes and resolutions, e.g. apple-touch-icon-152x152-precomposed.png for {retina iPad} with {iOS7}. {Everything you always wanted to know about touch icons (https://mathiasbynens.be/notes/touch-icons)}. (2018-08-19)

A Programming Language "language" (APL) A programming language designed originally by Ken Iverson at Harvard University in 1957-1960 as a notation for the concise expression of mathematical {algorithms}. It went unnamed (or just called Iverson's Language) and unimplemented for many years. Finally a subset, APL\360, was implemented in 1964. APL is an interactive array-oriented language and programming environment with many innovative features. It was originally written using a non-standard {character set}. It is {dynamically typed} with {dynamic scope}. APL introduced several functional forms but is not {purely functional}. Dyalog APL/W and Visual APL are recognized .{NET} languages. Dyalog APL/W, APLX and APL2000 all offer {object-oriented} extensions to the language. ISO 8485 is the 1989 standard defining the language. Commercial versions: APL SV, VS APL, Sharp APL, Sharp APL/PC, APL*PLUS, APL*PLUS/PC, APL*PLUS/PC II, MCM APL, Honeyapple, DEC APL, {APL+Win, APL+Linux, APL+Unix and VisualAPL (http://www.apl2000.com/)}, {Dyalog APL (http://www.dyalog.com/)}, {IBM APL2 (http://www-306.ibm.com/software/awdtools/apl/)}, {APLX (http://www.microapl.co.uk/apl/)}, {Sharp APL (http://www.soliton.com/services_sharp.html)} Open source version: {NARS2000 (http://www.nars2000.org/)}. {APL wiki (http://aplwiki.com/)}. See also {Kamin's interpreters}. {APLWEB (http://www.microapl.co.uk/apl/)} translates {WEB} to APL. ["A Programming Language", Kenneth E. Iverson, Wiley, 1962]. ["APL: An Interactive Approach", 1976]. (2009-08-11)

arc 1. "file format, tool" An old {archive} format for {IBM PC}. The format is now so obscure that it is only likely to be supported by jack-of-all-trades decompression programs such as {WINZIP}. 2. "mathematics, data" An {edge} in a {tree}. "{branch}" is a generally more common synonym. (1998-12-29)

argument "programming" (Or "arg") A value or reference passed to a {function}, {procedure}, {subroutine}, command or program, by the caller. For example, in the function definition square(x) = x * x x is the {formal argument} or "parameter", and in the call y = square(3+4) 3+4 is the {actual argument}. This will execute the function square with x having the value 7 and return the result 49. There are many different conventions for passing arguments to functions and procedures including {call-by-value}, {call-by-name}, {call-by-reference}, {call-by-need}. These affect whether the value of the argument is computed by the caller or the callee (the function) and whether the callee can modify the value of the argument as seen by the caller (if it is a variable). Arguments to functions are usually, following mathematical notation, written in parentheses after the function name, separated by commas (but see {curried function}). Arguments to a program are usually given after the command name, separated by spaces, e.g.: cat myfile yourfile hisfile Here "cat" is the command and "myfile", "yourfile", and "hisfile" are the arguments. (2006-05-27)

Aristotle's Illusion: See Aristotle's Experiment. Arithmetic, foundations of: Arithmetic (i.e., the mathematical theory of the non-negative integers, 0, 1, 2, . . .) may be based on the five following postulates, which are due to Peano (and Dedekind, from whom Peano's ideas were partly derived): N(0) N(x) ⊃x N(S(x)). N(x) ⊃x [N(y) ⊃y [[S(x) = S(y)] ⊃x [x = y]]]. N(x) ⊃x ∼[S(x) = 0]. F(0)[N(x)F(x) ⊃x F(S(x))] ⊃F [N(x) ⊃x F(x)] The undefined terms are here 0, N, S, which may be interpreted as denoting, respectively, the non-negative integer 0, the propositional function to be a non-negative integer, and the function +1 (so that S(x) is x+l). The underlying logic may be taken to be the functional calculus of second order (Logic, formal, § 6), with the addition of notations for descriptions and for functions from individuals to individuals, and the individual constant 0, together with appropriate modifications and additions to the primitive formulas and primitive rules of inference (the axiom of infinity is not needed because the Peano postulates take its place). By adding the five postulates of Peano as primitive formulas to this underlying logic, a logistic system is obtained which is adequate to extant elementary number theory (arithmetic) and to all methods of proof which have found actual employment in elementary number theory (and are normally considered to belong to elementary number theory). But of course, the system, if consistent, is incomplete in the sense of Gödel's theorem (Logic, formal, § 6).

arithmetic mean "mathematics" The {mean} of a list of N numbers calculated by dividing their sum by N. The arithmetic mean is appropriate for sets of numbers that are added together or that form an {arithmetic series}. If all the numbers in the list were changed to their arithmetic mean then their total would stay the same. For sets of numbers that are multiplied together, the {geometric mean} is more appropriate. (2007-03-20)

Ars Combinatoria: (Leibniz) An art or technique of deriving or inventing complex concepts by a combination of a relatively few simple ones taken as primitive. This technique was proposed as a valuable subject for study by Leibniz in De Arte Combinatoria (1666) but was never greatly developed by him. Leibniz's program for logic consisted of two main projects: (1) the development of a universal characteristic (characteristica universalis), and (2) the development of a universal mathematics (mathesis universalis (q.v.). The universal characteristic was to be a universal language for scientists and philosophers. With a relatively few basic symbols for the ultimately simple ideas, and a suitable technique for constructing compound ideas out of the simple ones, Leibniz thought that a language could be constructed which would be much more efficient for reasoning and for communication than the vague, complicated, and more or less parochial languages then available. This language would be completely universal in the sense that all scientific and philosophical concepts could be expressed in it, and also in that it would enable scholars m all countries to communicate over the barriers of their vernacular tongues. Leibniz's proposals in this matter, and what work he did on it, are the grand predecessors of a vast amount of research which has been done in the last hundred years on the techniques of language construction, and specifically on the invention of formal rules and procedures for introducing new terms into a language on the basis of terms already present, the general project of constructing a unified language for science and philosophy. L. Couturat, La Logique de Leibniz, Paris, 1901; C. I. Lewis, A Survey of Symbolic Logic, Berkeley, 1918. -- F.L.W.

Ars magna Raymundi: A device by which Raymundus Lullus, Ramon Lul, thought to arrive at all possible conclusions from certain given principles or notions. A very imperfect precursor of Leibniz's mathesis universalis. See Lullic art. -- R.A.

artificial neural network "artificial intelligence" (ANN, commonly just "neural network" or "neural net") A network of many very simple processors ("units" or "neurons"), each possibly having a (small amount of) local memory. The units are connected by unidirectional communication channels ("connections"), which carry numeric (as opposed to symbolic) data. The units operate only on their local data and on the inputs they receive via the connections. A neural network is a processing device, either an {algorithm}, or actual hardware, whose design was inspired by the design and functioning of animal brains and components thereof. Most neural networks have some sort of "training" rule whereby the weights of connections are adjusted on the basis of presented patterns. In other words, neural networks "learn" from examples, just like children learn to recognise dogs from examples of dogs, and exhibit some structural capability for generalisation. Neurons are often elementary non-linear signal processors (in the limit they are simple threshold discriminators). Another feature of NNs which distinguishes them from other computing devices is a high degree of interconnection which allows a high degree of parallelism. Further, there is no idle memory containing data and programs, but rather each neuron is pre-programmed and continuously active. The term "neural net" should logically, but in common usage never does, also include biological neural networks, whose elementary structures are far more complicated than the mathematical models used for ANNs. See {Aspirin}, {Hopfield network}, {McCulloch-Pitts neuron}. {Usenet} newsgroup: {news:comp.ai.neural-nets}. (1997-10-13)

Ashmedai "tool" A {symbolic mathematics} package by Michael Levine "levine@cpwsca.psc.edu" that influenced {SMP} and {FORM}. There are versions for the {Univac 1108} and {VAX}/{VMS}. (1995-03-21)

A

assignment problem "mathematics, algorithm" (Or "linear assignment") Any problem involving minimising the sum of C(a, b) over a set P of pairs (a, b) where a is an element of some set A and b is an element of set B, and C is some function, under constraints such as "each element of A must appear exactly once in P" or similarly for B, or both. For example, the a's could be workers and the b's projects. The problem is "linear" because the "cost function" C() depends only on the particular pairing (a, b) and is independent of all other pairings. {(http://forum.swarthmore.edu/epigone/comp.soft-sys.matlab/bringhyclu)}. {(http://soci.swt.edu/capps/prob.htm)}. {(http://mat.gsia.cmu.edu/GROUP95/0577.html)}. {(http://informs.org/Conf/WA96/TALKS/SB24.3.html)}. [Algorithms?] (1999-07-12)

assignment "programming" Storing the value of an expression in a {variable}. This is commonly written in the form "v = e". In {Algol} the assignment operator was ":=" (pronounced "becomes") to avoid mathematicians qualms about writing statements like x = x+1. Assignment is not allowed in {functional languages}, where an {identifier} always has the same value. See also {referential transparency}, {single assignment}, {zero assignment}. (1996-08-19)

Association for Computing "body" (ACM, before 1997 - "Association for Computing Machinery") The largest and oldest international scientific and educational computer society in the industry. Founded in 1947, only a year after the unveiling of {ENIAC}, ACM was established by mathematicians and electrical engineers to advance the science and application of {Information Technology}. {John Mauchly}, co-inventor of the ENIAC, was one of ACM's founders. Since its inception ACM has provided its members and the world of computer science a forum for the sharing of knowledge on developments and achievements necessary to the fruitful interchange of ideas. ACM has 90,000 members - educators, researchers, practitioners, managers, and engineers - who drive the Association's major programs and services - publications, special interest groups, chapters, conferences, awards, and special activities. The ACM Press publishes journals (notably {CACM}), book series, conference proceedings, {CD-ROM}, {hypertext}, {video}, and specialized publications such as curricula recommendations and self-assessment procedures. {(http://info.acm.org/)}. (1998-02-24)

Assumption: A proposition which is taken or posed in order to draw inferences from it; or the act of so taking, posing, or assuming a proposition. The motive for an assumption may be (but need not necessarily be) a belief in the truth, or possible truth, of the proposition assumed; or the motive may be an attempt to refute the proposition by reductio ad absurdum (q.v.). The word assumption has also sometimes been used as a synonym of axiom, or postulate (see the article Mathematics). -- A.C.

AT-3 "language" The original name of {MATH-MATIC}. [Sammet 1969, p. 135]. (2000-02-24)

Atanasoff-Berry Computer "computer" (ABC) An early design for a binary calculator, one of the predecessors of the {digital computer}. The ABC was partially constructed between 1937 and 1942 by Dr. {John Vincent Atanasoff} and Clifford Berry at {Iowa State College}. As well as {binary} arithmetic, it incorporated {regenerative memory}, {parallel processing}, and separation of memory and computing functions. The electronic parts were mounted on a rotating drum, making it hybrid electronic/electromechanical. It was designed to handle only a single type of mathematical problem and was not automated. The results of a single calculation cycle had to be retrieved by a human operator, and fed back into the machine with all new instructions, to perform complex operations. It lacked any serious form of logical control or {conditional} statements. Atanasoff's patent application was denied because he never have a completed, working product. Ideas from the ABC were used in the design of {ENIAC} (1943-1946). {(http://cs.iastate.edu/jva/jva-archive.shtml)}. (2003-09-28)

A. Tarski, Einige Betrachtungen uber die Begriffe der ω-Widerspruchsfreiheit und der ω-Vollstandigkeit, Monatshefte für Mathematik und Physik, vol. 40 (1933), pp. 97-112.

Aufklärung: In general, this German word and its English equivalent Enlightenment denote the self-emancipation of man from mere authority, prejudice, convention and tradition, with an insistence on freer thinking about problems uncritically referred to these other agencies. According to Kant's famous definition "Enlightenment is the liberation of man from his self-caused state of minority, which is the incapacity of using one's understanding without the direction of another. This state of minority is caused when its source lies not in the lack of understanding, but in the lack of determination and courage to use it without the assistance of another" (Was ist Aufklärung? 1784). In its historical perspective, the Aufklärung refers to the cultural atmosphere and contrlbutions of the 18th century, especially in Germany, France and England [which affected also American thought with B. Franklin, T. Paine and the leaders of the Revolution]. It crystallized tendencies emphasized by the Renaissance, and quickened by modern scepticism and empiricism, and by the great scientific discoveries of the 17th century. This movement, which was represented by men of varying tendencies, gave an impetus to general learning, a more popular philosophy, empirical science, scriptural criticism, social and political thought. More especially, the word Aufklärung is applied to the German contributions to 18th century culture. In philosophy, its principal representatives are G. E. Lessing (1729-81) who believed in free speech and in a methodical criticism of religion, without being a free-thinker; H. S. Reimarus (1694-1768) who expounded a naturalistic philosophy and denied the supernatural origin of Christianity; Moses Mendelssohn (1729-86) who endeavoured to mitigate prejudices and developed a popular common-sense philosophy; Chr. Wolff (1679-1754), J. A. Eberhard (1739-1809) who followed the Leibnizian rationalism and criticized unsuccessfully Kant and Fichte; and J. G. Herder (1744-1803) who was best as an interpreter of others, but whose intuitional suggestions have borne fruit in the organic correlation of the sciences, and in questions of language in relation to human nature and to national character. The works of Kant and Goethe mark the culmination of the German Enlightenment. Cf. J. G. Hibben, Philosophy of the Enlightenment, 1910. --T.G. Augustinianism: The thought of St. Augustine of Hippo, and of his followers. Born in 354 at Tagaste in N. Africa, A. studied rhetoric in Carthage, taught that subject there and in Rome and Milan. Attracted successively to Manicheanism, Scepticism, and Neo-Platontsm, A. eventually found intellectual and moral peace with his conversion to Christianity in his thirty-fourth year. Returning to Africa, he established numerous monasteries, became a priest in 391, Bishop of Hippo in 395. Augustine wrote much: On Free Choice, Confessions, Literal Commentary on Genesis, On the Trinity, and City of God, are his most noted works. He died in 430.   St. Augustine's characteristic method, an inward empiricism which has little in common with later variants, starts from things without, proceeds within to the self, and moves upwards to God. These three poles of the Augustinian dialectic are polarized by his doctrine of moderate illuminism. An ontological illumination is required to explain the metaphysical structure of things. The truth of judgment demands a noetic illumination. A moral illumination is necessary in the order of willing; and so, too, an lllumination of art in the aesthetic order. Other illuminations which transcend the natural order do not come within the scope of philosophy; they provide the wisdoms of theology and mysticism. Every being is illuminated ontologically by number, form, unity and its derivatives, and order. A thing is what it is, in so far as it is more or less flooded by the light of these ontological constituents.   Sensation is necessary in order to know material substances. There is certainly an action of the external object on the body and a corresponding passion of the body, but, as the soul is superior to the body and can suffer nothing from its inferior, sensation must be an action, not a passion, of the soul. Sensation takes place only when the observing soul, dynamically on guard throughout the body, is vitally attentive to the changes suffered by the body. However, an adequate basis for the knowledge of intellectual truth is not found in sensation alone. In order to know, for example, that a body is multiple, the idea of unity must be present already, otherwise its multiplicity could not be recognized. If numbers are not drawn in by the bodily senses which perceive only the contingent and passing, is the mind the source of the unchanging and necessary truth of numbers? The mind of man is also contingent and mutable, and cannot give what it does not possess. As ideas are not innate, nor remembered from a previous existence of the soul, they can be accounted for only by an immutable source higher than the soul. In so far as man is endowed with an intellect, he is a being naturally illuminated by God, Who may be compared to an intelligible sun. The human intellect does not create the laws of thought; it finds them and submits to them. The immediate intuition of these normative rules does not carry any content, thus any trace of ontologism is avoided.   Things have forms because they have numbers, and they have being in so far as they possess form. The sufficient explanation of all formable, and hence changeable, things is an immutable and eternal form which is unrestricted in time and space. The forms or ideas of all things actually existing in the world are in the things themselves (as rationes seminales) and in the Divine Mind (as rationes aeternae). Nothing could exist without unity, for to be is no other than to be one. There is a unity proper to each level of being, a unity of the material individual and species, of the soul, and of that union of souls in the love of the same good, which union constitutes the city. Order, also, is ontologically imbibed by all beings. To tend to being is to tend to order; order secures being, disorder leads to non-being. Order is the distribution which allots things equal and unequal each to its own place and integrates an ensemble of parts in accordance with an end. Hence, peace is defined as the tranquillity of order. Just as things have their being from their forms, the order of parts, and their numerical relations, so too their beauty is not something superadded, but the shining out of all their intelligible co-ingredients.   S. Aurelii Augustini, Opera Omnia, Migne, PL 32-47; (a critical edition of some works will be found in the Corpus Scriptorum Ecclesiasticorum Latinorum, Vienna). Gilson, E., Introd. a l'etude de s. Augustin, (Paris, 1931) contains very good bibliography up to 1927, pp. 309-331. Pope, H., St. Augustine of Hippo, (London, 1937). Chapman, E., St. Augustine's Philos. of Beauty, (N. Y., 1939). Figgis, J. N., The Political Aspects of St. Augustine's "City of God", (London, 1921). --E.C. Authenticity: In a general sense, genuineness, truth according to its title. It involves sometimes a direct and personal characteristic (Whitehead speaks of "authentic feelings").   This word also refers to problems of fundamental criticism involving title, tradition, authorship and evidence. These problems are vital in theology, and basic in scholarship with regard to the interpretation of texts and doctrines. --T.G. Authoritarianism: That theory of knowledge which maintains that the truth of any proposition is determined by the fact of its having been asserted by a certain esteemed individual or group of individuals. Cf. H. Newman, Grammar of Assent; C. S. Peirce, "Fixation of Belief," in Chance, Love and Logic, ed. M. R. Cohen. --A.C.B. Autistic thinking: Absorption in fanciful or wishful thinking without proper control by objective or factual material; day dreaming; undisciplined imagination. --A.C.B. Automaton Theory: Theory that a living organism may be considered a mere machine. See Automatism. Automatism: (Gr. automatos, self-moving) (a) In metaphysics: Theory that animal and human organisms are automata, that is to say, are machines governed by the laws of physics and mechanics. Automatism, as propounded by Descartes, considered the lower animals to be pure automata (Letter to Henry More, 1649) and man a machine controlled by a rational soul (Treatise on Man). Pure automatism for man as well as animals is advocated by La Mettrie (Man, a Machine, 1748). During the Nineteenth century, automatism, combined with epiphenomenalism, was advanced by Hodgson, Huxley and Clifford. (Cf. W. James, The Principles of Psychology, Vol. I, ch. V.) Behaviorism, of the extreme sort, is the most recent version of automatism (See Behaviorism).   (b) In psychology: Psychological automatism is the performance of apparently purposeful actions, like automatic writing without the superintendence of the conscious mind. L. C. Rosenfield, From Beast Machine to Man Machine, N. Y., 1941. --L.W. Automatism, Conscious: The automatism of Hodgson, Huxley, and Clifford which considers man a machine to which mind or consciousness is superadded; the mind of man is, however, causally ineffectual. See Automatism; Epiphenomenalism. --L.W. Autonomy: (Gr. autonomia, independence) Freedom consisting in self-determination and independence of all external constraint. See Freedom. Kant defines autonomy of the will as subjection of the will to its own law, the categorical imperative, in contrast to heteronomy, its subjection to a law or end outside the rational will. (Fundamental Principles of the Metaphysics of Morals, § 2.) --L.W. Autonomy of ethics: A doctrine, usually propounded by intuitionists, that ethics is not a part of, and cannot be derived from, either metaphysics or any of the natural or social sciences. See Intuitionism, Metaphysical ethics, Naturalistic ethics. --W.K.F. Autonomy of the will: (in Kant's ethics) The freedom of the rational will to legislate to itself, which constitutes the basis for the autonomy of the moral law. --P.A.S. Autonymy: In the terminology introduced by Carnap, a word (phrase, symbol, expression) is autonymous if it is used as a name for itself --for the geometric shape, sound, etc. which it exemplifies, or for the word as a historical and grammatical unit. Autonymy is thus the same as the Scholastic suppositio matertalis (q. v.), although the viewpoint is different. --A.C. Autotelic: (from Gr. autos, self, and telos, end) Said of any absorbing activity engaged in for its own sake (cf. German Selbstzweck), such as higher mathematics, chess, etc. In aesthetics, applied to creative art and play which lack any conscious reference to the accomplishment of something useful. In the view of some, it may constitute something beneficent in itself of which the person following his art impulse (q.v.) or playing is unaware, thus approaching a heterotelic (q.v.) conception. --K.F.L. Avenarius, Richard: (1843-1896) German philosopher who expressed his thought in an elaborate and novel terminology in the hope of constructing a symbolic language for philosophy, like that of mathematics --the consequence of his Spinoza studies. As the most influential apostle of pure experience, the posltivistic motive reaches in him an extreme position. Insisting on the biologic and economic function of thought, he thought the true method of science is to cure speculative excesses by a return to pure experience devoid of all assumptions. Philosophy is the scientific effort to exclude from knowledge all ideas not included in the given. Its task is to expel all extraneous elements in the given. His uncritical use of the category of the given and the nominalistic view that logical relations are created rather than discovered by thought, leads him to banish not only animism but also all of the categories, substance, causality, etc., as inventions of the mind. Explaining the evolution and devolution of the problematization and deproblematization of numerous ideas, and aiming to give the natural history of problems, Avenarius sought to show physiologically, psychologically and historically under what conditions they emerge, are challenged and are solved. He hypothesized a System C, a bodily and central nervous system upon which consciousness depends. R-values are the stimuli received from the world of objects. E-values are the statements of experience. The brain changes that continually oscillate about an ideal point of balance are termed Vitalerhaltungsmaximum. The E-values are differentiated into elements, to which the sense-perceptions or the content of experience belong, and characters, to which belongs everything which psychology describes as feelings and attitudes. Avenarius describes in symbolic form a series of states from balance to balance, termed vital series, all describing a series of changes in System C. Inequalities in the vital balance give rise to vital differences. According to his theory there are two vital series. It assumes a series of brain changes because parallel series of conscious states can be observed. The independent vital series are physical, and the dependent vital series are psychological. The two together are practically covariants. In the case of a process as a dependent vital series three stages can be noted: first, the appearance of the problem, expressed as strain, restlessness, desire, fear, doubt, pain, repentance, delusion; the second, the continued effort and struggle to solve the problem; and finally, the appearance of the solution, characterized by abating anxiety, a feeling of triumph and enjoyment.   Corresponding to these three stages of the dependent series are three stages of the independent series: the appearance of the vital difference and a departure from balance in the System C, the continuance with an approximate vital difference, and lastly, the reduction of the vital difference to zero, the return to stability. By making room for dependent and independent experiences, he showed that physics regards experience as independent of the experiencing indlvidual, and psychology views experience as dependent upon the individual. He greatly influenced Mach and James (q.v.). See Avenarius, Empirio-criticism, Experience, pure. Main works: Kritik der reinen Erfahrung; Der menschliche Weltbegriff. --H.H. Averroes: (Mohammed ibn Roshd) Known to the Scholastics as The Commentator, and mentioned as the author of il gran commento by Dante (Inf. IV. 68) he was born 1126 at Cordova (Spain), studied theology, law, medicine, mathematics, and philosophy, became after having been judge in Sevilla and Cordova, physician to the khalifah Jaqub Jusuf, and charged with writing a commentary on the works of Aristotle. Al-mansur, Jusuf's successor, deprived him of his place because of accusations of unorthodoxy. He died 1198 in Morocco. Averroes is not so much an original philosopher as the author of a minute commentary on the whole works of Aristotle. His procedure was imitated later by Aquinas. In his interpretation of Aristotelian metaphysics Averroes teaches the coeternity of a universe created ex nihilo. This doctrine formed together with the notion of a numerical unity of the active intellect became one of the controversial points in the discussions between the followers of Albert-Thomas and the Latin Averroists. Averroes assumed that man possesses only a disposition for receiving the intellect coming from without; he identifies this disposition with the possible intellect which thus is not truly intellectual by nature. The notion of one intellect common to all men does away with the doctrine of personal immortality. Another doctrine which probably was emphasized more by the Latin Averroists (and by the adversaries among Averroes' contemporaries) is the famous statement about "two-fold truth", viz. that a proposition may be theologically true and philosophically false and vice versa. Averroes taught that religion expresses the (higher) philosophical truth by means of religious imagery; the "two-truth notion" came apparently into the Latin text through a misinterpretation on the part of the translators. The works of Averroes were one of the main sources of medieval Aristotelianlsm, before and even after the original texts had been translated. The interpretation the Latin Averroists found in their texts of the "Commentator" spread in spite of opposition and condemnation. See Averroism, Latin. Averroes, Opera, Venetiis, 1553. M. Horten, Die Metaphysik des Averroes, 1912. P. Mandonnet, Siger de Brabant et l'Averroisme Latin, 2d ed., Louvain, 1911. --R.A. Averroism, Latin: The commentaries on Aristotle written by Averroes (Ibn Roshd) in the 12th century became known to the Western scholars in translations by Michael Scottus, Hermannus Alemannus, and others at the beginning of the 13th century. Many works of Aristotle were also known first by such translations from Arabian texts, though there existed translations from the Greek originals at the same time (Grabmann). The Averroistic interpretation of Aristotle was held to be the true one by many; but already Albert the Great pointed out several notions which he felt to be incompatible with the principles of Christian philosophy, although he relied for the rest on the "Commentator" and apparently hardly used any other text. Aquinas, basing his studies mostly on a translation from the Greek texts, procured for him by William of Moerbecke, criticized the Averroistic interpretation in many points. But the teachings of the Commentator became the foundation for a whole school of philosophers, represented first by the Faculty of Arts at Paris. The most prominent of these scholars was Siger of Brabant. The philosophy of these men was condemned on March 7th, 1277 by Stephen Tempier, Bishop of Paris, after a first condemnation of Aristotelianism in 1210 had gradually come to be neglected. The 219 theses condemned in 1277, however, contain also some of Aquinas which later were generally recognized an orthodox. The Averroistic propositions which aroused the criticism of the ecclesiastic authorities and which had been opposed with great energy by Albert and Thomas refer mostly to the following points: The co-eternity of the created word; the numerical identity of the intellect in all men, the so-called two-fold-truth theory stating that a proposition may be philosophically true although theologically false. Regarding the first point Thomas argued that there is no philosophical proof, either for the co-eternity or against it; creation is an article of faith. The unity of intellect was rejected as incompatible with the true notion of person and with personal immortality. It is doubtful whether Averroes himself held the two-truths theory; it was, however, taught by the Latin Averroists who, notwithstanding the opposition of the Church and the Thomistic philosophers, gained a great influence and soon dominated many universities, especially in Italy. Thomas and his followers were convinced that they interpreted Aristotle correctly and that the Averroists were wrong; one has, however, to admit that certain passages in Aristotle allow for the Averroistic interpretation, especially in regard to the theory of intellect.   Lit.: P. Mandonnet, Siger de Brabant et l'Averroisme Latin au XIIIe Siecle, 2d. ed. Louvain, 1911; M. Grabmann, Forschungen über die lateinischen Aristotelesübersetzungen des XIII. Jahrhunderts, Münster 1916 (Beitr. z. Gesch. Phil. d. MA. Vol. 17, H. 5-6). --R.A. Avesta: See Zendavesta. Avicehron: (or Avencebrol, Salomon ibn Gabirol) The first Jewish philosopher in Spain, born in Malaga 1020, died about 1070, poet, philosopher, and moralist. His main work, Fons vitae, became influential and was much quoted by the Scholastics. It has been preserved only in the Latin translation by Gundissalinus. His doctrine of a spiritual substance individualizing also the pure spirits or separate forms was opposed by Aquinas already in his first treatise De ente, but found favor with the medieval Augustinians also later in the 13th century. He also teaches the necessity of a mediator between God and the created world; such a mediator he finds in the Divine Will proceeding from God and creating, conserving, and moving the world. His cosmogony shows a definitely Neo-Platonic shade and assumes a series of emanations. Cl. Baeumker, Avencebrolis Fons vitae. Beitr. z. Gesch. d. Philos. d. MA. 1892-1895, Vol. I. Joh. Wittman, Die Stellung des hl. Thomas von Aquino zu Avencebrol, ibid. 1900. Vol. III. --R.A. Avicenna: (Abu Ali al Hosain ibn Abdallah ibn Sina) Born 980 in the country of Bocchara, began to write in young years, left more than 100 works, taught in Ispahan, was physician to several Persian princes, and died at Hamadan in 1037. His fame as physician survived his influence as philosopher in the Occident. His medical works were printed still in the 17th century. His philosophy is contained in 18 vols. of a comprehensive encyclopedia, following the tradition of Al Kindi and Al Farabi. Logic, Physics, Mathematics and Metaphysics form the parts of this work. His philosophy is Aristotelian with noticeable Neo-Platonic influences. His doctrine of the universal existing ante res in God, in rebus as the universal nature of the particulars, and post res in the human mind by way of abstraction became a fundamental thesis of medieval Aristotelianism. He sharply distinguished between the logical and the ontological universal, denying to the latter the true nature of form in the composite. The principle of individuation is matter, eternally existent. Latin translations attributed to Avicenna the notion that existence is an accident to essence (see e.g. Guilelmus Parisiensis, De Universo). The process adopted by Avicenna was one of paraphrasis of the Aristotelian texts with many original thoughts interspersed. His works were translated into Latin by Dominicus Gundissalinus (Gondisalvi) with the assistance of Avendeath ibn Daud. This translation started, when it became more generally known, the "revival of Aristotle" at the end of the 12th and the beginning of the 13th century. Albert the Great and Aquinas professed, notwithstanding their critical attitude, a great admiration for Avicenna whom the Arabs used to call the "third Aristotle". But in the Orient, Avicenna's influence declined soon, overcome by the opposition of the orthodox theologians. Avicenna, Opera, Venetiis, 1495; l508; 1546. M. Horten, Das Buch der Genesung der Seele, eine philosophische Enzyklopaedie Avicenna's; XIII. Teil: Die Metaphysik. Halle a. S. 1907-1909. R. de Vaux, Notes et textes sur l'Avicennisme Latin, Bibl. Thomiste XX, Paris, 1934. --R.A. Avidya: (Skr.) Nescience; ignorance; the state of mind unaware of true reality; an equivalent of maya (q.v.); also a condition of pure awareness prior to the universal process of evolution through gradual differentiation into the elements and factors of knowledge. --K.F.L. Avyakta: (Skr.) "Unmanifest", descriptive of or standing for brahman (q.v.) in one of its or "his" aspects, symbolizing the superabundance of the creative principle, or designating the condition of the universe not yet become phenomenal (aja, unborn). --K.F.L. Awareness: Consciousness considered in its aspect of act; an act of attentive awareness such as the sensing of a color patch or the feeling of pain is distinguished from the content attended to, the sensed color patch, the felt pain. The psychologlcal theory of intentional act was advanced by F. Brentano (Psychologie vom empirischen Standpunkte) and received its epistemological development by Meinong, Husserl, Moore, Laird and Broad. See Intentionalism. --L.W. Axiological: (Ger. axiologisch) In Husserl: Of or pertaining to value or theory of value (the latter term understood as including disvalue and value-indifference). --D.C. Axiological ethics: Any ethics which makes the theory of obligation entirely dependent on the theory of value, by making the determination of the rightness of an action wholly dependent on a consideration of the value or goodness of something, e.g. the action itself, its motive, or its consequences, actual or probable. Opposed to deontological ethics. See also teleological ethics. --W.K.F. Axiologic Realism: In metaphysics, theory that value as well as logic, qualities as well as relations, have their being and exist external to the mind and independently of it. Applicable to the philosophy of many though not all realists in the history of philosophy, from Plato to G. E. Moore, A. N. Whitehead, and N, Hartmann. --J.K.F. Axiology: (Gr. axios, of like value, worthy, and logos, account, reason, theory). Modern term for theory of value (the desired, preferred, good), investigation of its nature, criteria, and metaphysical status. Had its rise in Plato's theory of Forms or Ideas (Idea of the Good); was developed in Aristotle's Organon, Ethics, Poetics, and Metaphysics (Book Lambda). Stoics and Epicureans investigated the summum bonum. Christian philosophy (St. Thomas) built on Aristotle's identification of highest value with final cause in God as "a living being, eternal, most good."   In modern thought, apart from scholasticism and the system of Spinoza (Ethica, 1677), in which values are metaphysically grounded, the various values were investigated in separate sciences, until Kant's Critiques, in which the relations of knowledge to moral, aesthetic, and religious values were examined. In Hegel's idealism, morality, art, religion, and philosophy were made the capstone of his dialectic. R. H. Lotze "sought in that which should be the ground of that which is" (Metaphysik, 1879). Nineteenth century evolutionary theory, anthropology, sociology, psychology, and economics subjected value experience to empirical analysis, and stress was again laid on the diversity and relativity of value phenomena rather than on their unity and metaphysical nature. F. Nietzsche's Also Sprach Zarathustra (1883-1885) and Zur Genealogie der Moral (1887) aroused new interest in the nature of value. F. Brentano, Vom Ursprung sittlicher Erkenntnis (1889), identified value with love.   In the twentieth century the term axiology was apparently first applied by Paul Lapie (Logique de la volonte, 1902) and E. von Hartmann (Grundriss der Axiologie, 1908). Stimulated by Ehrenfels (System der Werttheorie, 1897), Meinong (Psychologisch-ethische Untersuchungen zur Werttheorie, 1894-1899), and Simmel (Philosophie des Geldes, 1900). W. M. Urban wrote the first systematic treatment of axiology in English (Valuation, 1909), phenomenological in method under J. M. Baldwin's influence. Meanwhile H. Münsterberg wrote a neo-Fichtean system of values (The Eternal Values, 1909).   Among important recent contributions are: B. Bosanquet, The Principle of Individuality and Value (1912), a free reinterpretation of Hegelianism; W. R. Sorley, Moral Values and the Idea of God (1918, 1921), defending a metaphysical theism; S. Alexander, Space, Time, and Deity (1920), realistic and naturalistic; N. Hartmann, Ethik (1926), detailed analysis of types and laws of value; R. B. Perry's magnum opus, General Theory of Value (1926), "its meaning and basic principles construed in terms of interest"; and J. Laird, The Idea of Value (1929), noteworthy for historical exposition. A naturalistic theory has been developed by J. Dewey (Theory of Valuation, 1939), for which "not only is science itself a value . . . but it is the supreme means of the valid determination of all valuations." A. J. Ayer, Language, Truth and Logic (1936) expounds the view of logical positivism that value is "nonsense." J. Hessen, Wertphilosophie (1937), provides an account of recent German axiology from a neo-scholastic standpoint.   The problems of axiology fall into four main groups, namely, those concerning (1) the nature of value, (2) the types of value, (3) the criterion of value, and (4) the metaphysical status of value.   (1) The nature of value experience. Is valuation fulfillment of desire (voluntarism: Spinoza, Ehrenfels), pleasure (hedonism: Epicurus, Bentham, Meinong), interest (Perry), preference (Martineau), pure rational will (formalism: Stoics, Kant, Royce), apprehension of tertiary qualities (Santayana), synoptic experience of the unity of personality (personalism: T. H. Green, Bowne), any experience that contributes to enhanced life (evolutionism: Nietzsche), or "the relation of things as means to the end or consequence actually reached" (pragmatism, instrumentalism: Dewey).   (2) The types of value. Most axiologists distinguish between intrinsic (consummatory) values (ends), prized for their own sake, and instrumental (contributory) values (means), which are causes (whether as economic goods or as natural events) of intrinsic values. Most intrinsic values are also instrumental to further value experience; some instrumental values are neutral or even disvaluable intrinsically. Commonly recognized as intrinsic values are the (morally) good, the true, the beautiful, and the holy. Values of play, of work, of association, and of bodily well-being are also acknowledged. Some (with Montague) question whether the true is properly to be regarded as a value, since some truth is disvaluable, some neutral; but love of truth, regardless of consequences, seems to establish the value of truth. There is disagreement about whether the holy (religious value) is a unique type (Schleiermacher, Otto), or an attitude toward other values (Kant, Höffding), or a combination of the two (Hocking). There is also disagreement about whether the variety of values is irreducible (pluralism) or whether all values are rationally related in a hierarchy or system (Plato, Hegel, Sorley), in which values interpenetrate or coalesce into a total experience.   (3) The criterion of value. The standard for testing values is influenced by both psychological and logical theory. Hedonists find the standard in the quantity of pleasure derived by the individual (Aristippus) or society (Bentham). Intuitionists appeal to an ultimate insight into preference (Martineau, Brentano). Some idealists recognize an objective system of rational norms or ideals as criterion (Plato, Windelband), while others lay more stress on rational wholeness and coherence (Hegel, Bosanquet, Paton) or inclusiveness (T. H. Green). Naturalists find biological survival or adjustment (Dewey) to be the standard. Despite differences, there is much in common in the results of the application of these criteria.   (4) The metaphysical status of value. What is the relation of values to the facts investigated by natural science (Koehler), of Sein to Sollen (Lotze, Rickert), of human experience of value to reality independent of man (Hegel, Pringle-Pattlson, Spaulding)? There are three main answers:   subjectivism (value is entirely dependent on and relative to human experience of it: so most hedonists, naturalists, positivists);   logical objectivism (values are logical essences or subsistences, independent of their being known, yet with no existential status or action in reality);   metaphysical objectivism (values   --or norms or ideals   --are integral, objective, and active constituents of the metaphysically real: so theists, absolutists, and certain realists and naturalists like S. Alexander and Wieman). --E.S.B. Axiom: See Mathematics. Axiomatic method: That method of constructing a deductive system consisting of deducing by specified rules all statements of the system save a given few from those given few, which are regarded as axioms or postulates of the system. See Mathematics. --C.A.B. Ayam atma brahma: (Skr.) "This self is brahman", famous quotation from Brhadaranyaka Upanishad 2.5.19, one of many alluding to the central theme of the Upanishads, i.e., the identity of the human and divine or cosmic. --K.F.L.

Austin Kyoto Common Lisp "language" (AKCL) A collection of ports, bug fixes, and performance improvements to {KCL} by William Schelter "wfs@cli.com", "wfs@math.utexas.edu", University of Texas. Version 1-615 includes ports to {Decstation} 3100, {HP9000}/300, {i386}/{Sys V}, {IBM-PS2}/{AIX}, {IBM-RT}/{AIX}, {SGI}, {Sun-3}/{Sunos} 3 or 4, {Sun-4}, {Sequent Symmetry}, {IBM370}/{AIX}, {VAX}/{BSD VAX}/{Ultrix}, {NeXT}. {(ftp://rascal.ics.utexas.edu/pub/akcl-1-609.tar.Z)}. (1992-04-29)

autodidact ::: n. --> One who is self-taught; an automath.

AUTOmated GRouPing system "tool, mathematics" (AUTOGRP) An interactive statistical analysis system, an extension of {CML}. ["AUTOGRP: An Interactive Computer System for the Analysis of Health Care Data", R.E. Mills et al, Medical Care 14(7), Jul 1976]. (1994-11-07)

AUTOMATH "language, mathematics" A very high level language for writing proofs, from Eindhoven, Netherlands. ["The Mathematical Language AUTOMATH, Its Usage and Some of its Extensions", N.G. deBruijn, in Symp on Automatic Demonstration, LNM 125, Springer 1970]. (2001-07-09)

automath ::: n. --> One who is self-taught.

Automatic Mathematical TRANslation "mathematics, tool" (AMTRAN) A system developed by NASA in Huntsville in 1966 for the {IBM 1620}, based on the {Culler-Fried} System. It required a special terminal. ["AMTRAN: An Interactive Computing System", J. Reinfelds, Proc FJCC 37:537- 542, AFIPS (Fall 1970)]. (1995-11-14)

automaton "robotics, mathematics, algorithm" (Plural automata) A machine, {robot}, or {formal system} designed to follow a precise sequence of instructions. Automata theory, the invention and study of automata, includes the study of the capabilities and limitations of computing processes, the manner in which systems receive input, process it, and produce output, and the relationships between behavioural theories and the operation and use of automated devices. See also {cellular automaton}, {finite state machine}. (1996-04-23)

A view of the nature of mathematics which is widely different from any of the above is held by the school of mathematical intuitionism (q. v.). According to this school, mathematics is "identical with the exact part of our thought." "No science, not even philosophy or logic, can be a presupposition for mathematics. It would be circular to apply any philosophical or logical theorem as a means of proof in mathematics, since such theorems already presuppose for their formulation the construction of mathematical concepts. If mathematics is to be in this sense presupposition-free, then there remains for it no other source than an intuition which presents mathematical concepts and inferences to us as immediately clear. . . . [This intuition] is nothing else than the ability to treat separately certain concepts and inferences which regularly occur in ordinary thinking." This is quoted in translation from Heyting, who, in the same connection, characterizes the intuitionittic doctrine as asserting the existence of mathematical objects (Gegenstände), which are immediately grasped by thought, are independent of experience, and give to mathematics more than a mere formal content. But to these mathematical objects no existence is to be ascribed independent of thought. Elsewhere Heyting speaks of a relationship to Kant in the apriority ascribed to the natural numbers, or rather to the underlying ideas of one and the process of adding one and the indefinite repetition of the latter. At least in his earlier writings, Brouwer traces the doctrine of intuitionism directly to Kant. In 1912 he speaks of "abandoning Kant's apriority of space but adhering the more resolutely to the apriority of time" and in the same paper explicitly reaffirms Kant's opinion that mathematical judgments are synthetic and a priori.

axiomatic set theory "theory" One of several approaches to {set theory}, consisting of a {formal language} for talking about sets and a collection of {axioms} describing how they behave. There are many different {axiomatisations} for set theory. Each takes a slightly different approach to the problem of finding a theory that captures as much as possible of the intuitive idea of what a set is, while avoiding the {paradoxes} that result from accepting all of it, the most famous being {Russell's paradox}. The main source of trouble in naive set theory is the idea that you can specify a set by saying whether each object in the universe is in the "set" or not. Accordingly, the most important differences between different axiomatisations of set theory concern the restrictions they place on this idea (known as "comprehension"). {Zermelo Fränkel set theory}, the most commonly used axiomatisation, gets round it by (in effect) saying that you can only use this principle to define subsets of existing sets. NBG (von Neumann-Bernays-Goedel) set theory sort of allows comprehension for all {formulae} without restriction, but distinguishes between two kinds of set, so that the sets produced by applying comprehension are only second-class sets. NBG is exactly as powerful as ZF, in the sense that any statement that can be formalised in both theories is a theorem of ZF if and only if it is a theorem of ZFC. MK (Morse-Kelley) set theory is a strengthened version of NBG, with a simpler axiom system. It is strictly stronger than NBG, and it is possible that NBG might be consistent but MK inconsistent. {NF (http://math.boisestate.edu/~holmes/holmes/nf.html)} ("New Foundations"), a theory developed by Willard Van Orman Quine, places a very different restriction on comprehension: it only works when the formula describing the membership condition for your putative set is "stratified", which means that it could be made to make sense if you worked in a system where every set had a level attached to it, so that a level-n set could only be a member of sets of level n+1. (This doesn't mean that there are actually levels attached to sets in NF). NF is very different from ZF; for instance, in NF the universe is a set (which it isn't in ZF, because the whole point of ZF is that it forbids sets that are "too large"), and it can be proved that the {Axiom of Choice} is false in NF! ML ("Modern Logic") is to NF as NBG is to ZF. (Its name derives from the title of the book in which Quine introduced an early, defective, form of it). It is stronger than ZF (it can prove things that ZF can't), but if NF is consistent then ML is too. (2003-09-21)

AXIOM "language" A commercially available subset of the {Scratchpad}, {symbolic mathematics} system from {IBM}. ["Axiom - The Scientific Computing System", R. Jenks et al, Springer 1992]. [Relationship with {AXIOM*}?] (1995-02-21)

AXIOM* "mathematics, tool" A {symbolic mathematics} system. {A

Axiom of Choice "logic" (AC, or "Choice") An {axiom} of {set theory}: If X is a set of sets, and S is the union of all the elements of X, then there exists a function f:X -" S such that for all non-empty x in X, f(x) is an element of x. In other words, we can always choose an element from each set in a set of sets, simultaneously. Function f is a "choice function" for X - for each x in X, it chooses an element of x. Most people's reaction to AC is: "But of course that's true! From each set, just take the element that's biggest, stupidest, closest to the North Pole, or whatever". Indeed, for any {finite} set of sets, we can simply consider each set in turn and pick an arbitrary element in some such way. We can also construct a choice function for most simple {infinite sets} of sets if they are generated in some regular way. However, there are some infinite sets for which the construction or specification of such a choice function would never end because we would have to consider an infinite number of separate cases. For example, if we express the {real number} line R as the union of many "copies" of the {rational numbers}, Q, namely Q, Q+a, Q+b, and infinitely (in fact uncountably) many more, where a, b, etc. are {irrational numbers} no two of which differ by a rational, and Q+a == {q+a : q in Q} we cannot pick an element of each of these "copies" without AC. An example of the use of AC is the theorem which states that the {countable} union of countable sets is countable. I.e. if X is countable and every element of X is countable (including the possibility that they're finite), then the sumset of X is countable. AC is required for this to be true in general. Even if one accepts the axiom, it doesn't tell you how to construct a choice function, only that one exists. Most mathematicians are quite happy to use AC if they need it, but those who are careful will, at least, draw attention to the fact that they have used it. There is something a little odd about Choice, and it has some alarming consequences, so results which actually "need" it are somehow a bit suspicious, e.g. the {Banach-Tarski paradox}. On the other side, consider {Russell's Attic}. AC is not a {theorem} of {Zermelo Fränkel set theory} (ZF). Gödel and Paul Cohen proved that AC is independent of ZF, i.e. if ZF is consistent, then so are ZFC (ZF with AC) and ZF(~C) (ZF with the negation of AC). This means that we cannot use ZF to prove or disprove AC. (2003-07-11)

back-propagation (Or "backpropagation") A learning {algorithm} for modifying a {feed-forward} {neural network} which minimises a continuous "{error function}" or "{objective function}." Back-propagation is a "{gradient descent}" method of training in that it uses gradient information to modify the network weights to decrease the value of the error function on subsequent tests of the inputs. Other gradient-based methods from {numerical analysis} can be used to train networks more efficiently. Back-propagation makes use of a mathematical trick when the network is simulated on a digital computer, yielding in just two traversals of the network (once forward, and once back) both the difference between the desired and actual output, and the derivatives of this difference with respect to the connection weights.

Bacon, Roger: (1214-1294) Franciscan. He recognized the significance of the deductive application of principles and the necessity for experimental verification of the results. He was keenly interested in mathematics. His most famous work was called Opus majus, a veritable encyclopaedia of the sciences of his day. -- L.E.D Baconian Method: The inductive method as advanced by Francis Bacon (1561-1626). The purpose of the method was to enable man to attain mastery over nature in order to exploit it for his benefit. The mind should pass from particular facts to a more general knowledge of forms, or generalized physical properties. They are laws according to which phenomena actually proceed. He demanded an exhaustive enumeration of positive instances of occurrences of phenomena, the recording of comparative instances, in which an event manifests itself with greater or lesser intensity, and the additional registration of negative instances. Then experiments should test the observations. See Mill's Methods. -- J.J.R.

Banach algebra "mathematics" An {algebra} in which the {vector space} is a {Banach space}. (1997-02-25)

Banach inverse mapping theorem "mathematics" In a {Banach space} the inverse to a {continuous} {linear mapping} is continuous. (1998-06-25)

Banach space "mathematics" A {complete} {normed} {vector space}. Metric is induced by the norm: d(x,y) = ||x-y||. Completeness means that every {Cauchy sequence} converges to an element of the space. All finite-dimensional {real} and {complex} normed vector spaces are complete and thus are Banach spaces. Using absolute value for the norm, the real numbers are a Banach space whereas the rationals are not. This is because there are sequences of rationals that converges to irrationals. Several theorems hold only in Banach spaces, e.g. the {Banach inverse mapping theorem}. All finite-dimensional real and complex vector spaces are Banach spaces. {Hilbert spaces}, spaces of {integrable functions}, and spaces of {absolutely convergent series} are examples of infinite-dimensional Banach spaces. Applications include {wavelets}, {signal processing}, and radar. [Robert E. Megginson, "An Introduction to Banach Space Theory", Graduate Texts in Mathematics, 183, Springer Verlag, September 1998]. (2000-03-10)

Banach-Tarski paradox "mathematics" It is possible to cut a solid ball into finitely many pieces (actually about half a dozen), and then put the pieces together again to get two solid balls, each the same size as the original. This {paradox} is a consequence of the {Axiom of Choice}. (1995-03-29)

barycentric "mathematics" Centre of gravity, {mean}. (2007-07-10)

base "mathematics" {radix}.

Basic Multilingual Plane "text, standard" (BMP) The first plane defined in {Unicode}/{ISO 10646}, designed to include all {scripts} in active modern use. The BMP currently includes the Latin, Greek, Cyrillic, Devangari, hiragana, katakana, and Cherokee scripts, among others, and a large body of mathematical, {APL}-related, and other miscellaneous {characters}. Most of the {Han} {ideographs} in current use are present in the BMP, but due to the large number of ideographs, many were placed in the {Supplementary Ideographic Plane}. {Unicode home (http://unicode.org)}. (2002-03-19)

Bernoulli principle (Or "air foil principle", after Swiss mathematician Daniel Bernoulli, 1700-1782) The law that pressure in a fluid decreases with the rate of flow. It has been applied to a class of {hard disk} drives. See {Bernoulli Box}. (1997-04-15)

Bertrand (Named after the British mathematician Bertrand Russell (1872-1970)). Wm. Leler. Rule-based specification language based on augmented term rewriting. Used to implement constraint languages. The user must explicitly specify the tree-search and the constraint propagation. {(ftp://nexus.yorku.ca/pub/scheme/scm/bevan.shar)}. ["Constraint Programming Languages - Their Specification and Generation", W. Leler, A-W 1988, ISBN 0-201-06243-7].

Bertrand Russell "person" (1872-1970) A British mathematician, the discoverer of {Russell's paradox}. (1995-03-27)

Besides the Zermelo set theory and the functional calculus (theory of types), there is a third method of obtaining a system adequate for mathematics and at the same time -- it is hoped -- consistent, proposed by Quine in his book cited below (1940). -- The last word on these matters has almost certainly not yet been said.

Bezier curve "graphics" A type of curve defined by mathematical formulae, used in {computer graphics}. A curve with coordinates P(u), where u varies from 0 at one end of the curve to 1 at the other, is defined by a set of n+1 "control points" (X(i), Y(i), Z(i)) for i = 0 to n. P(u) = Sum i=0..n [(X(i), Y(i), Z(i)) * B(i, n, u)] B(i, n, u) = C(n, i) * u^i * (1-u)^(n-i) C(n, i) = n!/i!/(n-i)! A Bezier curve (or surface) is defined by its control points, which makes it invariant under any {affine mapping} (translation, rotation, parallel projection), and thus even under a change in the axis system. You need only to transform the control points and then compute the new curve. The control polygon defined by the points is itself affine invariant. Bezier curves also have the variation-diminishing property. This makes them easier to split compared to other types of curve such as {Hermite} or {B-spline}. Other important properties are multiple values, global and local control, versatility, and order of continuity. [What do these properties mean?] (1996-06-12)

Bezier surface "graphics" A surface defined by mathematical formulae, used in {computer graphics}. A surface P(u, v), where u and v vary orthogonally from 0 to 1 from one edge of the surface to the other, is defined by a set of (n+1)*(m+1) "control points" (X(i, j), Y(i, j), Z(i, j)) for i = 0 to n, j = 0 to m. P(u, v) = Sum i=0..n {Sum j=0..m [ (X(i, j), Y(i, j), Z(i, j)) * B(i, n, u) * B(j, m, v)]} B(i, n, u) = C(n, i) * u^i * (1-u)^(n-i) C(n, i) = n!/i!/(n-i)! Bezier surfaces are an extension of the idea of {Bezier curves}, and share many of their properties. (1996-06-12)

Bibliography. The various theories outlined in this article do not exhaust the possible definitions and problems concerning probability, but they give an idea of the trend of the discussions. The following works are selected from a considerable literature of the subject. Laplace, Essai sur les Probabilites. Keynes, A Treatise on Probability. Jeffreys, Theory of Probability. Uspensky, Introduction to Mathematical Probability. Borel, Traite de Calcul des Probabilites (especially the last volume dealing with its philosophical aspects). Mises, Probability, Statistics and Truth. Reichenbach, Les Fondements Logiques du Calcul dcs Probabilites. Frechet, Recherches sur le Calcul des Probabilites. Ville, Essai sur la Theorie des Collectifs. Kolmogoroff, Grundbegriffe der Wahrscheinhchkeitsrechnung. Wald, Die Widerspruchsfreiheit des Kollektivbegriffes. Nagel, The Theory of Probability.

bijection "mathematics" A {function} is bijective or a bijection or a one-to-one correspondence if it is both {injective} (no two values map to the same value) and {surjective} (for every element of the {codomain} there is some element of the {domain} which maps to it). I.e. there is exactly one element of the domain which maps to each element of the codomain. For a general bijection f from the set A to the set B: f'(f(a)) = a where a is in A and f(f'(b)) = b where b is in B. A and B could be disjoint sets. See also {injection}, {surjection}, {isomorphism}, {permutation}. (2001-05-10)

binary 1. "mathematics" {Base} two. A number representation consisting of zeros and ones used by practically all computers because of its ease of implementation using digital electronics and {Boolean algebra}. 2. "file format" {binary file}. 3. "programming" A description of an {operator} which takes two {arguments}. See also {unary}, {ternary}. (2005-02-21)

binary relation "mathematics" A {relation} between two sets or between a set and itself. A {partial order} is a binary relation on a set that satisfies certain criteria. (2019-08-31)

Biometry: The scientific application of mathematical analysis to biological problems (also spoken of as "mathematical biophysics" and "mathematical biochemistry"). The journal Biometrtka was founded by Karl Pearson. -- W.M.M.

blackboard ::: n. --> A broad board painted black, or any black surface on which writing, drawing, or the working of mathematical problems can be done with chalk or crayons. It is much used in schools.

blow up 1. "mathematics" A description of a function that, as its input changes over a finite interval, its output goes from stable (steadily increasing or decreasing) to {unstable} (oscilating wildly between extreme values). The term might also be used for successive elements in a discrete sequence or stepwise approximation of a continuous function. Rather than becoming unstable, the value may simply tend to positive or negative {infinity}. When calculating such a function or sequence, a computer will typically suffer {overflow}. 2. {blow out}. [{Jargon File}] (2019-12-27)

Mathematics: The traditional definition of mathematics as "the science of quantity" or "the science of discrete and continuous magnitude" is today inadequate, in that modern mathematics, while clearly in some sense a single connected whole, includes many branches which do not come under this head. Contemporary accounts of the nature of mathematics tend to characterize it rather by its method than by its subject matter.

Mathura ::: [a town near Agra in North India, the birth-place of Krsna].

B-Method "programming, tool" A system for rigorous or formal development of software using the notion of {Abstract Machines} to specify and design software systems. The B-Method is supported by the {B-Toolkit}. Abstract Machines are specified using the Abstract Machine Notation (AMN) which is in turn based on the mathematical theory of {Generalised Substitutions}. (1995-03-13)

Bolzano, Bernard: (1781-1848) Austrian philosopher and mathematician. Professor of the philosophy of religion at Prague, 1805-1820, he was compelled to resign in the latter year because of his rationalistic tendencies in theology and afterwards held no academic position. His Wissenschaftslehre of 1837, while it is to be classed as a work on traditional logic, contains significant anticipations of many ideas which have since become important in symbolic logic and mathematics. In his posthumously published Paradoxien des Unendlitchen (1851) he appears as a forerunner in some respects of Cantor's theory of transfinite numbers. -- A.C.

Boodin, John Elof: American philosopher born in Sweden in 1869 who emigrated in 1886 to the United States. Studied at the Universities of Colorado, Minnesota, Brown and especially Harvard under Royce with whom he kept a life-long friendship though he was opposed to his idealism. His works (Time and Reality, 1904 -- Truth and Reality, 1912 -- A Realistic Universe, 1916 -- Cosmic Evolution, 1925 -- Three Interpretations of the Universe, 1934 -- God, 1935 -- The Social Mind, 1940) form practically a complete system. His philosophy takes the form of a cosmic idealism, though he was interested for a time in certain aspects of pragmatism. It grew gradually from his early studies when he developed a new concept of a real and non-serial time. The structure of the cosmos is that of a hierarchy of fields, as exemplified in physics, in organisms, in consciousness and in society. The interpenetration of the mental fields makes possible human knowledge and social intercourse. Reality as such possesses five attributes: being (the dynamic stuff of all complexes, the active energy), time (the ground of change and transformation), space (which accounts for extension), consciousness (active awareness which lights up reality in spots; it becomes the self when conative tendencies cooperate as one active group), and form (the ground of organization and structure which conditions selective direction). God is the spirit of the whole. -- T.G.J Boole, George: (1815-1864) English mathematician. Professor of mathematics at Queen's College, Cork, 1849-1864. While he made contributions to other branches of mathematics, he is now remembered primarily as the founder of the Nineteenth Century algebra of logic and through it of modern symbolic logic. His Mathematical Analysis of Logic appeared in 1847 and the fuller Laws of Thought in 1854. -- A.C.

Boolean algebra "logic" (After the logician {George Boole}) 1. Commonly, and especially in computer science and digital electronics, this term is used to mean {two-valued logic}. 2. This is in stark contrast with the definition used by pure mathematicians who in the 1960s introduced "Boolean-valued {models}" into logic precisely because a "Boolean-valued model" is an interpretation of a {theory} that allows more than two possible truth values! Strangely, a Boolean algebra (in the mathematical sense) is not strictly an {algebra}, but is in fact a {lattice}. A Boolean algebra is sometimes defined as a "complemented {distributive lattice}". Boole's work which inspired the mathematical definition concerned {algebras} of {sets}, involving the operations of intersection, union and complement on sets. Such algebras obey the following identities where the operators ^, V, - and constants 1 and 0 can be thought of either as set intersection, union, complement, universal, empty; or as two-valued logic AND, OR, NOT, TRUE, FALSE; or any other conforming system. a ^ b = b ^ a  a V b = b V a   (commutative laws) (a ^ b) ^ c = a ^ (b ^ c) (a V b) V c = a V (b V c)     (associative laws) a ^ (b V c) = (a ^ b) V (a ^ c) a V (b ^ c) = (a V b) ^ (a V c)  (distributive laws) a ^ a = a  a V a = a     (idempotence laws) --a = a -(a ^ b) = (-a) V (-b) -(a V b) = (-a) ^ (-b)       (de Morgan's laws) a ^ -a = 0  a V -a = 1 a ^ 1 = a  a V 0 = a a ^ 0 = 0  a V 1 = 1 -1 = 0  -0 = 1 There are several common alternative notations for the "-" or {logical complement} operator. If a and b are elements of a Boolean algebra, we define a "= b to mean that a ^ b = a, or equivalently a V b = b. Thus, for example, if ^, V and - denote set intersection, union and complement then "= is the inclusive subset relation. The relation "= is a {partial ordering}, though it is not necessarily a {linear ordering} since some Boolean algebras contain incomparable values. Note that these laws only refer explicitly to the two distinguished constants 1 and 0 (sometimes written as {LaTeX} \top and \bot), and in {two-valued logic} there are no others, but according to the more general mathematical definition, in some systems variables a, b and c may take on other values as well. (1997-02-27)

box ::: n. --> A tree or shrub, flourishing in different parts of the world. The common box (Buxus sempervirens) has two varieties, one of which, the dwarf box (B. suffruticosa), is much used for borders in gardens. The wood of the tree varieties, being very hard and smooth, is extensively used in the arts, as by turners, engravers, mathematical instrument makers, etc.
A receptacle or case of any firm material and of various shapes.


branch 1. "mathematics" An {edge} in a {tree}. 2. "programming" A {jump}.

Brentano, Franz: (1838-1917) Who had originally been a Roman Catholic priest may be described as an unorthodox neo-scholastic. According to him the only three forms of psychic activity, representation, judgment and "phenomena of love and hate", are just three modes of "intentionality", i.e., of referring to an object intended. Judgments may be self-evident and thereby characterized as true and in an analogous way love and hate may be characterized as "right". It is on these characterizations that a dogmatic theory of truth and value may be based. In any mental experience the content is merely a "physical phenomenon" (real or imaginary) intended to be referred to, what is psychic is merely the "act" of representing, judging (viz. affirming or denying) and valuing (i.e. loving or hating). Since such "acts" are evidently immaterial, the soul by which they are performed may be proved to be a purely spiritual and imperishable substance and from these and other considerations the existence, spirituality, as also the infinite wisdom, goodness and justice of God may also be demonstrated. It is most of all by his classification of psychic phenomena, his psychology of "acts" and "intentions" and by his doctrine concerning self-evident truths and values that Brentano, who considered himself an Aristotelian, exercised a profound influence on subsequent German philosophers: not only on those who accepted his entire system (such as A. Marty and C. Stumpf) but also those who were somewhat more independent and original and whom he influenced either directly (as A. Meinong and E. Husserl) or indirectly (as M. Scheler and Nik. Hartmann). Main works: Psychologie des Aristoteles, 1867; Vom Dasein Gottes, 1868; Psychologie vom empirischen Standpunkt, 1874; Vom Ursprung sittliches Erkenntnis, 1884; Ueber die Zukunft der Philosophie, 1893; Die vier Phasen der Philos., 1895. -- H.Go. Broad, C.D.: (1887) As a realistic critical thinker Broad takes over from the sciences the methods that are fruitful there, classifies the various propositions used in all the sciences, and defines basic scientific concepts. In going beyond science, he seeks to reach a total view of the world by bringing in the facts and principles of aesthetic, religious, ethical and political experience. In trying to work out a much more general method which attacks the problem of the connection between mathematical concepts and sense-data better than the method of analysis in situ, he gives a simple exposition of the method of extensive abstraction, which applies the mutual relations of objects, first recognized in pure mathematics, to physics. Moreover, a great deal can be learned from Broad on the relation of the principle of relativity to measurement.

brindavan &

Brouwer, Luitzen Egbertus Jan: (1881-) Dutch mathematician. Professor of mathematics at the University of Amsterdam, 1912-. Besides his work in topology, he is known for important contributions to the philosophy and foundations of mathematics. See Mathematics and Intuitionism (mathematical)). -- A.C.

Bruno, Giordano: (1548-1600) A Dominican monk, eventually burned at the stake because of his opinions, he was converted from Christianity to a naturalistic and mystical pantheism by the Renaissance and particularly by the new Copernican astronomy. For him God and the universe were two names for one and the same Reality considered now as the creative essence of all things, now as the manifold of realized possibilities in which that essence manifests itself. As God, natura naturans, the Real is the whole, the one transcendent and ineffable. As the Real is the infinity of worlds and objects and events into which the whole divides itself and in which the one displays the infinite potentialities latent within it. The world-process is an ever-lasting going forth from itself and return into itself of the divine nature. The culmination of the outgoing creative activity is reached in the human mind, whose rational, philosophic search for the one in the many, simplicity in variety, and the changeless and eternal in the changing and temporal, marks also the reverse movement of the divine nature re-entering itself and regaining its primordial unity, homogeneity, and changelessness. The human soul, being as it were a kind of boomerang partaking of the ingrowing as well as the outgrowing process, may hope at death, not to be dissolved with the body, which is borne wholly upon the outgoing stream, but to return to God whence it came and to be reabsorbed in him. Cf. Rand, Modern Classical Philosophers, selection from Bruno's On Cause, The Principle and the One. G. Bruno: De l'infinito, universo e mundo, 1584; Spaccio della bestia trionfante, 1584; La cena delta ceneri, 1584; Deglieroici furori, 1585; De Monade, 1591. Cf. R. Honigswald, Giordano Bruno; G. Gentile, Bruno nella storia della cultura, 1907. -- B.A.G.F. Brunschvicg, Leon: (1869-) Professor of Philosophy at the Ecole Normale in Paris. Dismissed by the Nazis (1941). His philosophy is an idealistic synthesis of Spinoza, Kant and Schelling with special stress on the creative role of thought in cultural history as well as in sciences. Main works: Les etapes de la philosophie mathematique, 1913; L'experience humaine et la causalite physique, 1921; De la connaissance de soi, 1931. Buddhism: The multifarious forms, philosophic, religious, ethical and sociological, which the teachings of Gautama Buddha (q.v.) have produced. They centre around the main doctrine of the catvari arya-satyani(q.v.), the four noble truths, the last of which enables one in eight stages to reach nirvana (q.v.): Right views, right resolve, right speech, right conduct, right livelihood, right effort, right mindfulness, right concentration. In the absence of contemporary records of Buddha and Buddhistic teachings, much value was formerly attached to the palm leaf manuscripts in Pali, a Sanskrit dialect; but recently a good deal of weight has been given also the Buddhist tradition in Sanskrit, Tibetan, and Chinese. Buddhism split into Mahayanism and Hinayanism (q.v.), each of which, but particularly the former, blossomed into a variety of teachings and practices. The main philosophic schools are the Madhyamaka or Sunyavada, Yogacara, Sautrantika, and Vaibhasika (q.v.). The basic assumptions in philosophy are a causal nexus in nature and man, of which the law of karma (q.v.) is but a specific application; the impermanence of things, and the illusory notion of substance and soul. Man is viewed realistically as a conglomeration of bodily forms (rupa), sensations (vedana), ideas (sanjna), latent karma (sanskaras), and consciousness (vijnana). The basic assumptions in ethics are the universality of suffering and the belief in a remedy. There is no god; each one may become a Buddha, an enlightened one. Also in art and esthetics Buddhism has contributed much throughout the Far East. -- K.F.L.

B. Russell, Mathematical logic as based on the theory of types, American Journal of Mathematics, vol. 30 (1908), pp. 222- 262.

B. Russell, Introduction to Mathematical Philosophy, London, 1919. - --

B. Russell, Introduction to Mathematical Philosophy, London, 1919.

B. Russell, On some difficulties in the theory of transfinite numbers and order types. Proceedings of the London Mathematical Society, ser 2. vol. 4 (1906), pp 29-53.

B. Russell, The Principles of Mathematics, Cambridge, England, 1903; 2nd edn. London, 1937, and New York, 1938.

B. Russell, The Principles of Mathematics, Cambridge, England, 1903; 2nd edn., London, 1937, and New York, 1938.

B. The Probability-Relation. Considering the general grounds of probability, it is pertinent to analyze the proper characteristics of this concept and the valid conditions of its use in inferential processes. Probability presents itself as a special relation between the premisses and the conclusion of an argument, namely when the premisses are true but not completely sufficient to condition the truth of the conclusion. A probable inference must however be logical, even though its result is not certain, for its premisses must be a true sign of its conclusion. The probability-relation may take three aspects: it is inductive, probable or presumptive. In strict induction, there is an essential connection between the facts expressed in the premisses and in the conclusion, which almost forces a factual result from the circumstances of the predication. This type of probability-relation is prominent in induction proper and in statistics. In strict probability, there is a logical connection between the premisses and the conclusion which does not entail a definite factual value for the latter. This type of probability-relation is prominent in mathematical probability and circumstantial evidence. In strict presumption, there is a similarity of characteristics between the fact expressed in the conclusion and the real event if it does or did exist. This type of probability-relation is prominent in analogy and testimony. A presumptive conclusion should be accepted provisionally, and it should have definite consequences capable of being tested. The results of an inductive inference and of a probable inference may often be brought closer together when covering the same field, as the relations involved are fundamental enough for the purpose. This may be done by a qualitative analysis of their implications, or by a quantitative comparison of their elements, as it is done for example in the methods of correlation. But a presumptive inference cannot be reduced to either of the other two forms without losing its identity, because the connection between its elements is of an indefinite character. It may be said that inductive and probable inferences have an intrinsic reasonableness, while presumptive inferences have an extrinsic reasonableness. The former involve determinism within certain limits, while the latter display indeterminacy more prominently. That is why very poor, misleading or wrong conclusions are obtained when mathematical methods are applied to moral acts, judiciary decisions or indirect testimony The activity of the human will has an intricate complexity and variability not easily subjected to calculation. Hence the degree of probability of a presumptive inference can be estimated only by the character and circumstances of its suggested explanation. In moral cases, the discussion and application of the probability-relation leads to the consideration of the doctrines of Probabilism and Probabiliorism which are qualitative. The probability-relation as such has the following general implications which are compatible with its three different aspects, and which may serve as general inferential principle: Any generalization must be probable upon propositions entailing its exemplification in particular cases; Any generalization or system of generalizations forming a theory, must be probable upon propositions following from it by implication; The probability of a given proposition on the basis of other propositions constituting its evidence, is the degree of logical conclusiveness of this evidence with respect to the given proposition; The empirical probability (p = S/E) of a statement S increases as verifications accrue to the evidence E, provided the evidence is taken as a whole; and Numerical probabilities may be assigned to facts or statements only when the evidence includes statistical data or other numerical information which can be treated by the methods of mathematical probability. C. Mathematical Probability. The mathematical theory of probability, which is also called the theory of chances or the theory of relative possibilities, is concerned with the application of mathematical methods to the determination of the likelihood of any event, when there are not sufficient data to determine with certainty its occurrence or failure. As Laplace remarked, it is nothing more than common sense reduced to calculation. But its range goes far beyond that of common sense for it has not only conditioned the growth of various branches of mathematics, such as the theory of errors, the calculus of variations and mathematical statistics, but it has also made possible the establishment of a number of theories in the natural and social sciences, by its actual applications to concrete problems. A distinction is usually made between direct and inverse probability. The determination of a direct or a priori probability involves an inference from given situations or sets of possibilities numerically characterized, to future events related with them. By definition, the direct probability of the occurrence of any particular form of an event, is the ratio of the number of ways in which that form might occur, to the whole number of ways in which the event may occur, all these forms being equiprobable or equally likely. The basic principles referring to a priori probabilities are derived from the analysis of the various logical alternatives involved in any hypothetical questions such as the following: (a) To determine whether a cause, whose exact nature is or is not known, will prove operative or not in certain circumstances; (b) To determine how often an event happens or fails. The comparison of the number of occurrences with that of the failures of an event, considered in simple or complex circumstances, affords a baisis for several cases of probable inference. Thus, theorems may be established to deal with the probability of success and the probability of failure of an event, with the probability of the joint occurrence of several events, with the probability of the alternative occurrence of several events, with the different conditions of frequency of occurrence of an event; with mathematical expectation, and with similar questions. The determination of an a posteriori or inverse probability involves an inference from given situations or events, to past conditions or causes which rnay have contributed to their occurrence. By definition, an inverse probability is the numerical value assigned to each one of a number of possible causes of an actual event that has already occurred; or more generally, it is the numerical value assigned to hypotheses which attempt to explain actual events or circumstances. If an event has occurred as a result of any one of n several causes, the probability that C was the actual cause is Pp/E (Pnpn), when P is the probability that the event could be produced by C if present, and p the probability that C was present before the occurrence of that event. Inverse probability is based on general and special assumptions which cannot always be properly stated, and as there are many different sets of such assumptions, there cannot be a coercive reason for making a definite choice. In particular, the condition of the equiprobability of causes is seldom if ever fulfilled. The distinction between the two kinds of probability, which has led to some confusion in interpreting their grounds and their relations, can be technically ignored now as a result of the adoption of a statistical basis for measuring probabilities. In particular, it is the statistical treatment of correlation which led to the study of probabilities of concurrent phenomena irrespective of their direction in time. This distinction may be retained, howe\er, for the purpose of a general exposition of the subject. Thus, a number of probability theorems are obtained by using various cases of direct and inverse probability involving permutations and combinations, the binomial theorem, the theory of series, and the methods of integration. In turn, these theurems can be applied to concrete cases of the various sciences.

But all this must not be taken in too rigid and mechanical a sense. It is an immense plastic movement full of the play of possibilities and must be seized by a flexible and subtle tact or sense in the seeing conscioosness. It cannot be reduced to a too rigorous logical or mathematical formula. Two or three points must be pressed in order that this plasticity may not be lost to our view.

But while Peirce thought of pragmatism as akin to the mathematical method, James' motivation and interest was largely moral and religious. Thus in his Will to Believe (New World, 1896) he argues, in line with Pascal's wager, that "we have the right to believe at our own risk any hypothesis that is live enough to tempt our will," i.e. if it is not resolvable intellectually. Speaking of religious scepticism, he says. "We cannot escape the issue by remaining sceptical . . . because, although we do avoid error in that way if religion be untrue, we lose the good, if it be true, just as certainly as if we positively choose to disbelieve". The position of the religious skeptic is: ''Better risk loss of truth than chance of error, . . ." Later, in 1907 in the Lowell Lectures he stated that "on pragmatistic principles, if the hypothesis of God works satisfactorily in the widest sense of the word, it is true", and took a position between absolutism and materialism which he called "pragmatistic or melioristic" theism. In the same lectures he announces that " 'the true', to put it briefly, is only the expedient in the way of thinking, . . ." James also identifies truth with verifiability, thus anticipating both the experimentalism of Dewey and the operationalism of Bridgman and the logical positivists.

Calc "tool, mathematics" An extensible, advanced desk calculator and mathematical tool written in {Emacs Lisp} by Dave Gillespie "daveg@synaptics.com". Calc runs as part of {GNU Emacs}. You can use Calc as only a simple four-function calculator, but it also provides additional features including choice of algebraic or {RPN} ({stack}-based) entry, logarithms, trigonometric and financial functions, {arbitrary precision}, complex numbers, vectors, matrices, dates, times, infinities, sets, algebraic simplification, differentiation, and integration. FTP calc-2.02.tar.z from your nearest {GNU archive site}. (2000-10-20)

calculate ::: v. i. --> To ascertain or determine by mathematical processes, usually by the ordinary rules of arithmetic; to reckon up; to estimate; to compute.
To ascertain or predict by mathematical or astrological computations the time, circumstances, or other conditions of; to forecast or compute the character or consequences of; as, to calculate or cast one&


calculating ::: p. pr. & vb. n. --> of Calculate ::: a. --> Of or pertaining to mathematical calculations; performing or able to perform mathematical calculations.
Given to contrivance or forethought; forecasting; scheming; as, a cool calculating disposition.


calculus ::: n. --> Any solid concretion, formed in any part of the body, but most frequent in the organs that act as reservoirs, and in the passages connected with them; as, biliary calculi; urinary calculi, etc.
A method of computation; any process of reasoning by the use of symbols; any branch of mathematics that may involve calculation.


Calculus of Communicating Systems (CCS) A mathematical model (a formal language) for describing processes, mostly used in the study of {parallelism}. A CCS program, written in {behaviour expressions syntax} denotes a process behaviour. Programs can be compared using the notion of {observational equivalence}. ["A Calculus of Communicating Systems", LNCS 92, Springer 1980]. ["Communication and Concurrency", R. Milner, P-H 1989]. (1994-11-29)

CAMAL "tool" CAMbridge ALgebra system. A {symbolic mathematics} system used in Celestial Mechanics and General Relativity. CAMAL was implemented in {BCPL} on {Titan}. ["CAMAL User's Manual", John P. Fitch, Cambridge U, England (1975)]. ["The Design of the Cambridge Algebra System", S.R. Bourne et al, Proc 2nd Symp of Symb & Alg Manip, SIGSAM 1971]. (1995-02-16)

canonical (Historically, "according to religious law") 1. "mathematics" A standard way of writing a formula. Two formulas such as 9 + x and x + 9 are said to be equivalent because they mean the same thing, but the second one is in "canonical form" because it is written in the usual way, with the highest power of x first. Usually there are fixed rules you can use to decide whether something is in canonical form. Things in canonical form are easier to compare. 2. "jargon" The usual or standard state or manner of something. The term acquired this meaning in computer-science culture largely through its prominence in {Alonzo Church}'s work in computation theory and {mathematical logic} (see {Knights of the Lambda-Calculus}). Compare {vanilla}. This word has an interesting history. Non-technical academics do not use the adjective "canonical" in any of the senses defined above with any regularity; they do however use the nouns "canon" and "canonicity" (not "canonicalness"* or "canonicality"*). The "canon" of a given author is the complete body of authentic works by that author (this usage is familiar to Sherlock Holmes fans as well as to literary scholars). "The canon" is the body of works in a given field (e.g. works of literature, or of art, or of music) deemed worthwhile for students to study and for scholars to investigate. The word "canon" derives ultimately from the Greek "kanon" (akin to the English "cane") referring to a reed. Reeds were used for measurement, and in Latin and later Greek the word "canon" meant a rule or a standard. The establishment of a canon of scriptures within Christianity was meant to define a standard or a rule for the religion. The above non-technical academic usages stem from this instance of a defined and accepted body of work. Alongside this usage was the promulgation of "canons" ("rules") for the government of the Catholic Church. The usages relating to religious law derive from this use of the Latin "canon". It may also be related to arabic "qanun" (law). Hackers invest this term with a playfulness that makes an ironic contrast with its historical meaning. A true story: One Bob Sjoberg, new at the {MIT AI Lab}, expressed some annoyance at the incessant use of jargon. Over his loud objections, {GLS} and {RMS} made a point of using as much of it as possible in his presence, and eventually it began to sink in. Finally, in one conversation, he used the word "canonical" in jargon-like fashion without thinking. Steele: "Aha! We've finally got you talking jargon too!" Stallman: "What did he say?" Steele: "Bob just used "canonical" in the canonical way." Of course, canonicality depends on context, but it is implicitly defined as the way *hackers* normally expect things to be. Thus, a hacker may claim with a straight face that "according to religious law" is *not* the canonical meaning of "canonical". (2002-02-06)

Cantor 1. "person, mathematics" A mathematician. Cantor devised the diagonal proof of the uncountability of the {real numbers}: Given a function, f, from the {natural numbers} to the {real numbers}, consider the real number r whose binary expansion is given as follows: for each natural number i, r's i-th digit is the complement of the i-th digit of f(i). Thus, since r and f(i) differ in their i-th digits, r differs from any value taken by f. Therefore, f is not {surjective} (there are values of its result type which it cannot return). Consequently, no function from the natural numbers to the reals is surjective. A further theorem dependent on the {axiom of choice} turns this result into the statement that the reals are uncountable. This is just a special case of a diagonal proof that a function from a set to its {power set} cannot be surjective: Let f be a function from a set S to its power set, P(S) and let U = { x in S: x not in f(x) }. Now, observe that any x in U is not in f(x), so U != f(x); and any x not in U is in f(x), so U != f(x): whence U is not in { f(x) : x in S }. But U is in P(S). Therefore, no function from a set to its power-set can be surjective. 2. "language" An {object-oriented language} with {fine-grained concurrency}. [Athas, Caltech 1987. "Multicomputers: Message Passing Concurrent Computers", W. Athas et al, Computer 21(8):9-24 (Aug 1988)]. (1997-03-14)

Cantor, Contributions to the Founding of the Theory of Trasfinite Numbers, translated and with an introduction bv P.E.B. Jourdain, Chicago and London, 1915. Whitehead and Russell, Principia Mathematica, vol. 2.

Cantor, Georg (Ferdinand Ludwig Philipp), 1845-1918, (Russian born) German mathematician. Professor of mathematics at Halle, 1872-1913. He is known for contributions to the foundations of (mathematical) analysis, and as the founder of the theory of transfinite cardinal numbers (q.v.) and ordinal numbers (q.v.). See Infinite. -- A.C.

cardinality "mathematics" The number of elements in a set. If two sets have the same number of elements (i.e. there is a {bijection} between them) then they have the same cardinality. A cardinality is thus an {isomorphism class} in the {category} of sets. {aleph 0} is defined as the cardinality of the first {infinite} {ordinal}, {omega} (the number of {natural numbers}). (1995-03-29)

Carl Friedrich Gauss "person" A German mathematician (1777 - 1855), one of all time greatest. Gauss discovered the {method of least squares} and {Gaussian elimination}. Gauss was something of a child prodigy; the most commonly told story relates that when he was 10 his teacher, wanting a rest, told his class to add up all the numbers from 1 to 100. Gauss did it in seconds, having noticed that 1+...+100 = 100+...+1 = (101+...+101)/2. He did important work in almost every area of mathematics. Such eclecticism is probably impossible today, since further progress in most areas of mathematics requires much hard background study. Some idea of the range of his work can be obtained by noting the many mathematical terms with "Gauss" in their names. E.g. {Gaussian elimination} ({linear algebra}); {Gaussian primes} (number theory); {Gaussian distribution} (statistics); {Gauss} [unit] (electromagnetism); {Gaussian curvature} (differential geometry); {Gaussian quadrature} (numerical analysis); {Gauss-Bonnet formula} (differential geometry); {Gauss's identity} ({hypergeometric functions}); {Gauss sums} ({number theory}). His favourite area of mathematics was {number theory}. He conjectured the {Prime Number Theorem}, pioneered the {theory of quadratic forms}, proved the {quadratic reciprocity theorem}, and much more. He was "the first mathematician to use {complex numbers} in a really confident and scientific way" (Hardy & Wright, chapter 12). He nearly went into architecture rather than mathematics; what decided him on mathematics was his proof, at age 18, of the startling theorem that a regular N-sided polygon can be constructed with ruler and compasses if and only if N is a power of 2 times a product of distinct {Fermat primes}. (1995-04-10)

Carnap's work has been devoted especially to formal logic and its applications to problems of epistemology and the philosophy of science. His writings in formal logic include a textbook of mathematical logic and a comprehensive monograph devoted to logical syntax, a new branch of logical research to whose development Carnap has greatly contributed.

Cartesian coordinates "mathematics, graphics" (After Renee Descartes, French philosopher and mathematician) A pair of numbers, (x, y), defining the position of a point in a two-dimensional space by its perpendicular projection onto two axes which are at right angles to each other. x and y are also known as the {abscissa} and {ordinate}. The idea can be generalised to any number of independent axes. Compare {polar coordinates}. (1997-07-08)

Cartesianism: The philosophy of the French thinker, Rene Descartes (Cartesius) 1596-1650. After completing his formal education at the Jesuit College at La Fleche, he spent the years 1612-1621 in travel and military service. The reminder of his life was devoted to study and writing. He died in Sweden, where he had gone in 1649 to tutor Queen Christina. His principal works are: Discours de la methode, (preface to his Geometric, Meteores, Dieptrique) Meditationes de prima philosophia, Principia philosophiae, Passions de l'ame, Regulae ad directionem ingenii, Le monde. Descartes is justly regarded as one of the founders of modern epistemology. Dissatisfied with the lack of agreement among philosophers, he decided that philosophy needed a new method, that of mathematics. He began by resolving to doubt everything which could not pass the test of his criterion of truth, viz. the clearness and distinctness of ideas. Anything which could pass this test was to be readmitted as self-evident. From self-evident truths, he deduced other truths which logically follow from them. Three kinds of ideas were distinguished: innate, by which he seems to mean little more than the mental power to think things or thoughts; adventitious, which come to him from without; factitious, produced within his own mind. He found most difficulty with the second type of ideas. The first reality discovered through his method is the thinking self. Though he might doubt nearly all else, Descartes could not reasonably doubt that he, who was thinking, existed as a res cogitans. This is the intuition enunciated in the famous aphorism: I think, therefore I am, Cogito ergo sum. This is not offered by Descartes as a compressed syllogism, but as an immediate intuition of his own thinking mind. Another reality, whose existence was obvious to Descartes, was God, the Supreme Being. Though he offered several proofs of the Divine Existence, he was convinced that he knew this also by an innate idea, and so, clearly and distinctly. But he did not find any clear ideas of an extra-mental, bodily world. He suspected its existence, but logical demonstration was needed to establish this truth. His adventitious ideas carry the vague suggestion that they are caused by bodies in an external world. By arguing that God would be a deceiver, in allowing him to think that bodies exist if they do not, he eventually convinced himself of the reality of bodies, his own and others. There are, then, three kinds of substance according to Descartes: Created spirits, i.e. the finite soul-substance of each man: these are immaterial agencies capable of performing spiritual operations, loosely united with bodies, but not extended since thought is their very essence. Uncreated Spirit, i.e. God, confined neither to space nor time, All-Good and All-Powerful, though his Existence can be known clearly, his Nature cannot be known adequately by men on earth, He is the God of Christianity, Creator, Providence and Final Cause of the universe. Bodies, i.e. created, physical substances existing independently of human thought and having as their chief attribute, extension. Cartesian physics regards bodies as the result of the introduction of "vortices", i.e. whorls of motion, into extension. Divisibility, figurability and mobility, are the notes of extension, which appears to be little more thin what Descartes' Scholastic teachers called geometrical space. God is the First Cause of all motion in the physical universe, which is conceived as a mechanical system operated by its Maker. Even the bodies of animals are automata. Sensation is the critical problem in Cartesian psychology; it is viewed by Descartes as a function of the soul, but he was never able to find a satisfactory explanation of the apparent fact that the soul is moved by the body when sensation occurs. The theory of animal spirits provided Descartes with a sort of bridge between mind and matter, since these spirits are supposed to be very subtle matter, halfway, as it were, between thought and extension in their nature. However, this theory of sensation is the weakest link in the Cartesian explanation of cognition. Intellectual error is accounted for by Descartes in his theory of assent, which makes judgment an act of free will. Where the will over-reaches the intellect, judgment may be false. That the will is absolutely free in man, capable even of choosing what is presented by the intellect as the less desirable of two alternatives, is probably a vestige of Scotism retained from his college course in Scholasticism. Common-sense and moderation are the keynotes of Descartes' famous rules for the regulation of his own conduct during his nine years of methodic doubt, and this ethical attitude continued throughout his life. He believed that man is responsible ultimately to God for the courses of action that he may choose. He admitted that conflicts may occur between human passions and human reason. A virtuous life is made possible by the knowledge of what is right and the consequent control of the lower tendencies of human nature. Six primary passions are described by Descartes wonder, love, hatred, desire, joy and sorrow. These are passive states of consciousness, partly caused by the body, acting through the animal spirits, and partly caused by the soul. Under rational control, they enable the soul to will what is good for the body. Descartes' terminology suggests that there are psychological faculties, but he insists that these powers are not really distinct from the soul itself, which is man's sole psychic agency. Descartes was a practical Catholic all his life and he tried to develop proofs of the existence of God, an explanation of the Eucharist, of the nature of religious faith, and of the operation of Divine Providence, using his philosophy as the basis for a new theology. This attempted theology has not found favor with Catholic theologians in general.

Cartesian product "mathematics" (After Renee Descartes, French philosper and mathematician) The Cartesian product of two sets A and B is the set A x B = {(a, b) | a in A, b in B}. I.e. the product set contains all possible combinations of one element from each set. The idea can be extended to products of any number of sets. If we consider the elements in sets A and B as points along perpendicular axes in a two-dimensional space then the elements of the product are the "{Cartesian coordinates}" of points in that space. See also {tuple}. (1995-03-01)

Cassirer, Ernst: (1874-) Has been chiefly interested in developing the position of the neo-Kantian Philosophy of the Marburg School as it relates to scientific knowledge. Looking at the history of modern philosophy as a progressive formulation of this position, he has sought to extend it by detailed analyses of contemporary scientific developments. Of note are Cassirer's investigations in mathematics, his early consideration of chemical knowledge, and his treatment of Einstein's relativity theory. Main works: Das Erkenntntsprobleme, 3 vols. (1906); Substanz-u-Funktionsbegriff, 1910 (tr. Substance and Function); Philosophie der Symbolischen Forme (1923); Phanom. der Erkenntnis, 1929; Descartes; Leibniz. -- C.K.D.

Category of Unity: Kant: The first of three a priori, quantitative (so-called "mathematical") categories (the others being "plurality" and "totality") from which is derived the synthetic principle, "All intuitions (appearances) are extensive magnitudes." By means of this principle Kant seeks to define the object of experience a priori with reference to its spatial features. See Crit. of pure Reason, B106, B202ff. -- O.F.K Catharsis: (Gr. katharsis) Purification; purgation; specifically the purging of the emotions of pity and fear effected by tragedy (Aristotle). -- G.R.M.

Cauchy sequence "mathematics" A sequence of elements from some {vector space} that converge and stay arbitrarily close to each other (using the {norm} definied for the space). (2000-03-10)

CAYLEY "symbolic mathematics, tool" A {symbolic mathematics} system for {group theory} written by John Cannon of the {University of Sydney}, Australia in 1976. Cayley was used at about 100 sites but has been superseded by a much more general system, {Magma}. ["An Introduction to the Group Theory Language CAYLEY", J. Cannon, Computational Group Theory, M.D. Atkinson ed, Academic Press 1984, pp. 148-183]. (2000-09-03)

CCalc A {symbolic mathematics} system for {MS-DOS}, available from {Simtel}. (1995-04-12)

Centrum voor Wiskunde en Informatica (CWI, Centre for Mathematics and Computer Science) An independent research institute active in the fields of mathematics and computer science. CWI also aims to transfer new knowledge in these fields to society, trade and industry CWI is funded for 70 percent by NWO, the National Organisation for Scientific Research. The remaining 30 percent is obtained through national and international programmes and contract research commissioned by industry. Address: Kruislaan 413, 1098 SJ Amsterdam, The Netherlands; P.O.Box 94079, 1090 GB Amsterdam, The Netherlands. Telephone: +31 (20) 5929 333. {(http://cwi.nl/)}. {(ftp://ftp.cwi.nl/pub/)}.

cepstrum "mathematics" (Coined in a 1963 paper by Bogert, Healey, and Tukey) The {Fourier transform} of the log-magnitude spectrum: fFt(ln( | fFt(window . signal) | )) This function is used in {speech recognition} and possibly elsewhere. Note that the outer transform is NOT an inverse Fourier transform (as reported in many respectable DSP texts). [What's it for?] (1997-01-07)

Certainty: (Lat. Certus, sure) The alleged indubitability of certain truths, especially of logic and mathematics. -- L.W.

Chalmers University of Technology "body, education" A Swedish university founded in 1829 offering master of science and doctoral degrees. Research is carried out in the main engineering sciences as well as in technology related mathematical and natural sciences. Five hundred faculty members work in more than 100 departments organised in nine schools. Chalmers collaborates with the University of Göteborg. Around 8500 people work and study on the Chalmers campus, including around 500 faculty members and some 600 teachers and doctoral students. About 4800 students follow the master degree programs. Every year 700 Masters of Science in Engineering and in Architecture graduate from Chalmers, and about 190 PhDs and licentiates are awarded. Some 40% of Sweden's engineers and architects are Chalmers graduates. About a thousand research projects are in progress and more than 1500 scientific articles and research reports are published every year. Chalmers is a partner in 80 EC research projects. {(http://chalmers.se/Home-E.html)}. Address: S-412 96 Göteborg, Sweden. (1995-02-16)

chaos "mathematics" A property of some {non-linear dynamic systems} which exhibit sensitive dependence on initial conditions. This means that there are initial states which evolve within some finite time to states whose separation in one or more dimensions of {state space} depends, in an average sense, exponentially on their initial separation. Such systems may still be completely {deterministic} in that any future state of the system depends only on the initial conditions and the equations describing the change of the system with time. It may, however, require arbitrarily high precision to actually calculate a future state to within some finite precision. ["On defining chaos", R. Glynn Holt "rgholt@voyager.jpl.nasa.gov" and D. Lynn Holt "lholt@seraph1.sewanee.edu". {(ftp://mrcnext.cso.uiuc.edu/pub/etext/ippe/preprints/Phil_of_Science/Holt_and_Holt.On_Defining_Chaos)}] Fixed precision {floating-point} arithmetic, as used by most computers, may actually introduce chaotic dependence on initial conditions due to the accumulation of rounding errors (which constitutes a non-linear system). (1995-02-07)

Characteristica Universalis: The name given by Leibniz to his projected (but only partially realized) "universal language" for the formulation of knowledge. This language was to be ideographic, with simple characters standing for simple concepts, and combinations of them for compound ideas, so that all knowledge could be expressed in terms which all could easily learn to use and understand. It represents an adumbration of the more recent and more successful logistic treatment of mathematics and science. It is to be distinguished, however, from the "universal calculus," also projected by Leibniz, which was to be the instrument for the development and manipulation of systems in the universal language. -- W.K.F.

characteristic function "mathematics" The characteristic function of set returns True if its argument is an element of the set and False otherwise. (1995-04-13)

Charles Babbage "person" The British inventor known to some as the "Father of Computing" for his contributions to the basic design of the computer through his {Analytical Engine}. His previous {Difference Engine} was a special purpose device intended for the production of mathematical tables. Babbage was born on December 26, 1791 in Teignmouth, Devonshire UK. He entered Trinity College, Cambridge in 1814 and graduated from Peterhouse. In 1817 he received an MA from Cambridge and in 1823 started work on the Difference Engine through funding from the British Government. In 1827 he published a table of {logarithms} from 1 to 108000. In 1828 he was appointed to the Lucasian Chair of Mathematics at Cambridge (though he never presented a lecture). In 1831 he founded the British Association for the Advancement of Science and in 1832 he published "Economy of Manufactures and Machinery". In 1833 he began work on the Analytical Engine. In 1834 he founded the Statistical Society of London. He died in 1871 in London. Babbage also invented the cowcatcher, the dynamometer, standard railroad gauge, uniform postal rates, occulting lights for lighthouses, Greenwich time signals, and the heliograph opthalmoscope. He also had an interest in cyphers and lock-picking. [Adapted from the text by J. A. N. Lee, Copyright September 1994]. Babbage, as (necessarily) the first person to work with machines that can attack problems at arbitrary levels of {abstraction}, fell into a trap familiar to {toolsmiths} since, as described here by the English ethicist, Lord Moulton: "One of the sad memories of my life is a visit to the celebrated mathematician and inventor, Mr Babbage. He was far advanced in age, but his mind was still as vigorous as ever. He took me through his work-rooms. In the first room I saw parts of the original Calculating Machine, which had been shown in an incomplete state many years before and had even been put to some use. I asked him about its present form. 'I have not finished it because in working at it I came on the idea of my {Analytical Machine}, which would do all that it was capable of doing and much more. Indeed, the idea was so much simpler that it would have taken more work to complete the Calculating Machine than to design and construct the other in its entirety, so I turned my attention to the Analytical Machine.'" "After a few minutes' talk, we went into the next work-room, where he showed and explained to me the working of the elements of the Analytical Machine. I asked if I could see it. 'I have never completed it,' he said, 'because I hit upon an idea of doing the same thing by a different and far more effective method, and this rendered it useless to proceed on the old lines.' Then we went into the third room. There lay scattered bits of mechanism, but I saw no trace of any working machine. Very cautiously I approached the subject, and received the dreaded answer, 'It is not constructed yet, but I am working on it, and it will take less time to construct it altogether than it would have token to complete the Analytical Machine from the stage in which I left it.' I took leave of the old man with a heavy heart." "When he died a few years later, not only had he constructed no machine, but the verdict of a jury of kind and sympathetic scientific men who were deputed to pronounce upon what he had left behind him, either in papers or in mechanism, was that everything was too incomplete of be capable of being put to any useful purpose." [Lord Moulton, "The invention of algorithms, its genesis, and growth", in G. C. Knott, ed., "Napier tercentenary memorial volume" (London, 1915), p. 1-24; quoted in Charles Babbage "Passage from the Life of a Philosopher", Martin Campbell-Kelly, ed. (Rutgers U. Press and IEEE Press, 1994), p. 34]. Compare: {uninteresting}, {Ninety-Ninety Rule}. (1996-02-22)

CHARYBDIS "mathematics, tool" A {Lisp} program to display mathematical expressions. It is related to {MATHLAB}. [Sammet 1969, p. 522]. (1994-11-15)

Chitta ::: Chitta is ordinarily used for the mental consciousness in general, thought, feeling, etc. taken together with a stress now on one side or another, sometimes on the feelings as in citta-pramathı, sometimes on the thought-mind—that is why I translated it [on p. 75 (maccittah. )] "heart and mind" in its wider sense.
   Ref: CWSA Vol. 13, Page: 92


Choice, axiom of, or Zermelo's axiom, is the name given to an assumption of logical or logico-mathematical character which may be stated as follows: Given a class K whose members are non-empty classes, there exists a (one-valued) monadic function f whose range is K, such that f(x) &isin: x for all members x of K. This had often been employed unconsciously or tacitly by mathematicians -- and is apparently necessary for the proofs of certain important mathematical theorems -- but was first made explicit by Zermelo in 1904, who used it in a proof that every class can be well-ordered. Once explicitly stated the assumption was attacked by many mathematicians as lacking in validity or as not of legitimately mathematical character, but was defended by others, including Zermelo.

chrestomathic ::: a. --> Teaching what is useful.

chrestomathy ::: n. --> A selection of passages, with notes, etc., to be used in acquiring a language; as, a Hebrew chrestomathy.

chromatic number "mathematics" The smallest number of colours necessary to colour the nodes of a {graph} so that no two adjacent nodes have the same colour. See also: {four colour map theorem}. {Graph Theory Lessons (http://utc.edu/~cpmawata/petersen/lesson8.htm)}. {Eric Weisstein's World Of Mathematics (http://mathworld.wolfram.com/ChromaticNumber.html)}. {The Geometry Center (http://geom.umn.edu/~zarembe/grapht1.html)}. (2000-03-18)

CIMS PL/I "language" A {PL/I} subset from the Courant Institute of Mathematical Sciences. ["CIMS PL/I", P.W. Abrahams, Courant Inst]. (1997-12-15)

cittapramathi ::: [confusing the mind; exciting passion].

CLAM "mathematics, tool" A system for {symbolic mathematics}, especially General Relativity. It was first implemented in {ATLAS} {assembly language} and later {Lisp}. See also {ALAM}. ["CLAM Programmer's Manual", Ray d'Inverno & Russell-Clark, King's College London, 1971]. (1994-11-08)

clique "mathematics" A {maximal} {totally connected} {subgraph}. Given a {graph} with {nodes} N, a clique C is a {subset} of N where every node in C is directly connected to every other node in C (i.e. C is totally connected), and C contains all such nodes (C is maximal). In other words, a clique contains all, and only, those nodes which are directly connected to all other nodes in the clique. [Is this correct?] (1996-09-22)

CLISP "language" 1. A {Common Lisp} implementation by {Bruno Haible (http://haible.de/bruno/)} of {Karlsruhe University} and {Michael Stoll (http://math.uni-duesseldorf.de/~stoll/)}. of {Munich University}, both in Germany. CLISP includes an {interpreter}, {bytecode compiler}, almost all of the {CLOS} {object system}, a {foreign language interface} and a {socket interface}. An {X11} interface is available through {CLX} and {Garnet}. Command line editing is provided by the {GNU} readline library. CLISP requires only 2 MB of {RAM}. The {user interface} comes in German, English, French, Spanish, Dutch, and Russian and can be changed at {run time}. CLISP is {Free Software} and distributed under the {GPL}. It runs on {microcomputers} ({OS/2}, {Microsoft Windows}, {Amiga}, {Acorn}) as well as on {Unix} workstations ({Linux}, {BSD}, {SVR4}, {Sun4}, {Alpha}, {HP-UX}, {NeXTstep}, {SGI}, {AIX}, {Sun3} and others). {Official web page (http://clisp.cons.org)}. {Mailing list (http://lists.sourceforge.net/lists/listinfo/clisp-list)}. (2003-08-04) 2. {Conversational LISP}. (2019-11-21)

closed interval "mathematics" An {interval} that includes both endpoints. (2019-08-31)

closed set "mathematics" A set S is closed under an operator * if x*y is in S for all x, y in S. (1994-12-16)

coded character set "character, standard" A mapping, generally 1:1, from a set of {integers}, known as {character codes} or {code positions}, to a set of {characters} that may include letters, digits, punctuation, {control codes}, mathematical and typographic symbols. There are several {standard} coded character sets, the most widely used is {ASCII}, generally in its {Latin-1} dialect, with {Unicode} becoming slowly more common; while {EBCDIC} and {Baudot} are extinct except in {legacy systems}. (2009-01-06)

COLASL "mathematics, application" An early system for numerical problems on the {IBM 7030}. It used a special {character set} for input of natural mathematical expressions. [Sammet 1969, pp. 265-271]. (1995-01-04)

combination 1. "mathematics" A {set} containing a certain number of objects selected from another set. The number of combinations of r objects chosen from a set of n is n C r = n! / ((n-r)! r!) where "n C r" is normally with n and r as subscripts or as n above r in parentheses. See also {permutation}. 2. "reduction" In the theory of {combinators}, a combination denotes an expression in which {function application} is the only operation. (1995-04-10)

Combinatory Logic: A branch of mathematical logic, which has been extensively investigated by Curry, and which is concerned with analysis of processes of substitution, of the use of variables generally, and of the notion of a function. The program calls, in particular, for a system of logic in which variables are altogether eliminated, their place being taken by the presence in the system of certain kinds of function symbols. For a more detailed and exact account, reference must be made to the papers cited below. -- A.C.

combinatory logic "logic" A system for reducing the operational notation of {logic}, mathematics or a {functional language} to a sequence of modifications to the input data structure. First introduced in the 1920's by {Schoenfinkel}. Re-introduced independently by {Haskell Curry} in the late 1920's (who quickly learned of Schoenfinkel's work after he had the idea). Curry is really responsible for most of the development, at least up until work with Feys in 1958. See {combinator}. (1995-01-05)

Comma "project" COMputable MAthematics. An {ESPRIT} project at KU {Nijmegen}. (1994-11-30)

complexity "algorithm" The level in difficulty in solving mathematically posed problems as measured by the time, number of steps or arithmetic operations, or memory space required (called time complexity, computational complexity, and space complexity, respectively). The interesting aspect is usually how complexity scales with the size of the input (the "{scalability}"), where the size of the input is described by some number N. Thus an {algorithm} may have computational complexity O(N^2) (of the order of the square of the size of the input), in which case if the input doubles in size, the computation will take four times as many steps. The ideal is a constant time algorithm (O(1)) or failing that, O(N). See also {NP-complete}. (1994-10-20)

complex number "mathematics" A number of the form x+iy where i is the square root of -1, and x and y are {real numbers}, known as the "real" and "imaginary" part. Complex numbers can be plotted as points on a two-dimensional plane, known as an {Argand diagram}, where x and y are the {Cartesian coordinates}. An alternative, {polar} notation, expresses a complex number as (r e^it) where e is the base of {natural logarithms}, and r and t are real numbers, known as the magnitude and phase. The two forms are related: r e^it = r cos(t) + i r sin(t)     = x + i y where x = r cos(t) y = r sin(t) All solutions of any {polynomial equation} can be expressed as complex numbers. This is the so-called {Fundamental Theorem of Algebra}, first proved by Cauchy. Complex numbers are useful in many fields of physics, such as electromagnetism because they are a useful way of representing a magnitude and phase as a single quantity. (1995-04-10)

computed ::: determined by mathematics, especially by numerical methods.

Comte, Auguste: (1798-1857) Was born and lived during a period when political and social conditions in France were highly unstable. In reflecting the spirit of his age, he rose against the tendency prevalent among his predecessors to propound philosophic doctrines in disregard of the facts of nature and society. His revolt was directed particularly against traditional metaphysics with its endless speculations, countless assumptions, and futile controversies. To his views he gave the name of positivism. According to him, the history of humanity should be described in terms of three stages. The first of these was the theological stage when people's interpretation of reality was dominated by superstitions and prejudicesj the second stage was metaphysical when people attempted to comprehend, and reason about, reality, but were unable to support their contentions by facts; and the third and final stage was positive, when dogmatic assumptions began to be replaced by factual knowledge. Accordingly, the history of thought was characterized by a certain succession of sciences, expressing the turning of scholarly interest toward the earthly and human affairs, namely; mathematics, astronomy, physics, chemistry, biology, and sociology. These doctrines were discussed in Comte's main work, Cours de philosophic positive. -- R.B.W.

cone ::: n. --> A solid of the form described by the revolution of a right-angled triangle about one of the sides adjacent to the right angle; -- called also a right cone. More generally, any solid having a vertical point and bounded by a surface which is described by a straight line always passing through that vertical point; a solid having a circle for its base and tapering to a point or vertex.
Anything shaped more or less like a mathematical cone; as, a volcanic cone, a collection of scoriae around the crater of a volcano,


Consequence: (Ger. Konsequenz) In Husserl: The relation of formal-analytic inclusion which obtains between certain noematic senses. Consequence: See Valid. Consequence-logic: (Ger. Konsequenzlogik) Consistency-logic (Logik der Widerspruchslosigkeit); pure apophantic analytics (in a strict sense); a level of pure formal logic in which the only thematic concepts of validity are consequence, inconsequence, and compatibility. Consequence-logic includes the essential content of traditional syllogistics and the disciplines making up formal-mathematical analysis. -- D.C.

Contemporary ideas concerning the abstract nature of mathematics (q. v.) and the status of applied geometry have important historical roots in the discovery of non-Euclidean geometries. -- A.C.

Cournot, Antoine Augustin: (1801-1877) French mathematician, economist, and philosopher, is best known for his interest in probability. His philosophical writings, long neglected, reflect disagreement both with the positivism of his own day and with the earlier French rationalism. His place between the two is manifest in his doctrine that order and contingency, continuity and discontinuity, are equally real. This metaphysical position led him to conclude that man, though he cannot attain certain truth of nature, can by increasing the probable truth of his statements approach this truth. Cournot's mathematical investigations into probability and his mathematical treatment of economics thus harmonize with his metaphysics and epistemology. Main works: Exposition de la theorie des chances et des probabdites, 1843; Essai sur les fondements de la connaissance, 2 vols. 1851; Consid. sur les marches des idees, 1872; Materialisme, Vitalisme, Rationalism, 1875; Traite de l'Enchainement des idees fondamentales dans les sciences et dans l'histoire, 1881.

C. S. Peirce, On the algebra of logic, American Journal of Mathematics, vol. 7 (1885), pp. 180-202; reprinted in his Collected Papers, vol. 3.

Cudworth, Ralph: (1617-1688) Was the leading Cambridge Platonist (q.v.). His writings were devoted to a refutation of Hobbesean materialism which he characterized as atheistic. He accepted a rationalism of the kind advanced by Descartes. He found clear and distinct fundamental notions or categories reflecting universal reason, God's mind, the nature and essence of things and the moral laws, which he held to be as binding on God as the axioms of mathematics. His two most important works are The True Intellectual System of the Universe, and A Treatise concerning Eternal and Immutable Morality. -- L.E.D.

Cusa. Nicholas of: (1401-1464) Born in Cusa (family name: Krebs), educated in the mystical school of Deventer, and at the Universities of Heidelberg, Padua and Cologne. He became a Cardinal in 1448, Bishop of Brixen in 1450, and died at Todi. He was interested in mathematics, astronomy, philosophy and ecclesiastical policy. His thought is Neo-Platonic and mystical, he is critical of Aristotelian Scholasticism. His theories of "learned ignorance" and the "concordance of contraries" have been historically influential. Chief works: De concordantia Catholica, De docta ignorantia, De conjecturis (Opera, Paris, 1514). E. Van Steenberghe, Le Card. N. de Cuse,l'action, la pensee (Paris, 1920). -- V.J.B.

C. W. Morris, Foundations of the Theory of Signs, International Encyclopedia of Unified Science, vol. 1, no 2, Chicago, 1938. R. Carnap. Foundations of Logic and Mathematics, International Encyclopedia of Unified Science, vol 1, no 3, Chicago, 1939.

D'Alemhert, Jean Le Rond: (1717-1783) Brilliant French geometer. He was for a time an assistant to Diderot in the preparation of the Encyclopaedia and wrote its "Discours Preliminaire." He advanced a noteworthy empirical theory of mathematics in opposition to the stand of Plato or Descartes. He was greatly influenced by Bacon in his presentation of the order and influence of the sciences. He was greatly opposed to organized religion and sceptical as to the existence and nature of God. His ethical views were based on what he characterized as the evidence of the heart and had sympathy as their mainspring. -- L.E.D.

dasa-gavas (dasha-gavas; dashagava) ::: the ten rays; the ten types or dasa-gavas forms of consciousness in the evolutionary scale: the pasu, vanara, pisaca, pramatha, raks.asa, asura, deva, sadhyadeva (or siddhadeva), siddhadeva (or siddhasura) and satyadeva (or siddha purus.a or siddhadeva).

Declarative Memory ::: The part of long-term memory where factual information is stored, such as mathematical formulas, vocabulary, and life events.

Dedekind, (Julius Wilhelm) Richard: (1831-1916) German mathematician. Professor of mathematics at Brunswick, 1862-1894. His contributions to the foundations of arithmetic and analysis are contained in his Stetigkeit und Irrationale Zahlen (1st edn., 1872, 5th edn., 1927) and Was Sind und Was Sollen die Zahlen? (1st edn., 1888, 6th edn., 1930). -- A.C.

De Morgan, Augustus: (1806-1871) English mathematician and logician. Professor of mathematics at University College, London, 1828-1831, 1836-1866. His Formal Logic of 1847 contains some points of an algebra of logic essentially similar to that of Boole (q. v.), but the notation is less adequate than Boole's and the calculus is less fully worked out and applied. De Morgan, however, had the notion of logical sum for arbitrary classes -- whereas Boole contemplated addition only of classes having no members in common. De Morgan's laws (q. v.) -- as they are now known -- were also enunciated in this work. The treatment of the syllogism is original, but has since been susperseded, and does not constitute the author's real claim to remembrance as a logician. (The famous controversy with Sir William Hamilton over the latter's charge of plagiarism in connection with this treatment of the syllogism may therefore be dismissed as not of present interest.)

D. E. Smith, A Source Book in Mathematics, New York and London, 1929.

D. Hilbert, Die Grundlagen der Mathematik, Abhandlungen aus dem Mathematischen Seminar der Hamburgischen Universität, vol. 6 ( 1928), pp. 65-85 ; reprinted in Hilbert's Grundlagen der Geometrie, 7th edn.

diagram ::: n. --> A figure or drawing made to illustrate a statement, or facilitate a demonstration; a plan.
Any simple drawing made for mathematical or scientific purposes, or to assist a verbal explanation which refers to it; a mechanical drawing, as distinguished from an artistical one. ::: v. t.


diagraphics ::: n. --> The art or science of descriptive drawing; especially, the art or science of drawing by mechanical appliances and mathematical rule.

diesis ::: n. --> A small interval, less than any in actual practice, but used in the mathematical calculation of intervals.
The mark /; -- called also double dagger.


D. In mathematics, (1) it is a numerical or algebraical index showing the number of times the element it affects must be multiplied by itself; concurrently, it denotes the product arising from the continued mutiplication of a quantity by itself. (2) In the theory of aggregates, the power of a class is the number of its elements, its cardinal number (q.v.). -- T.G.

D. Interpretations of Probability. The methods and results of mathematical probability (and of probability in general) are the subject of much controversy as regards their interpretation and value. Among the various theories proposed, we shall consider the following Probability as a measure of belief, probability as the relative frequency of events, probability as the truth-frequency of types of argument, probability as a primitive notion, probability as an operational concept, probability as a limit of frequencies, and probability as a physical magnitude determined by axioms. I. Probability as a Measure of Belief: According to this theory, probability is the measure or relative degree of rational credence to be attached to facts or statements on the strength of valid motives. This type of probability is sometimes difficult to estimate, as it may be qualitative as well as quantitative. When considered in its mathematical aspects, the measure of probable inference depends on the preponderance or failure of operative causes or observed occurrences of the case under investigation. This conception involves axioms leading to the classic rule of Laplace, namely: The measure of probability of any one of mutually exclusive and apriori equiprobable possibilities, is the ratio of the number of favorable possibilities to the total number of possibilities. In probability operations, this rule is taken as the definition of direct probability for those cases where it is applicable. The main objections against this interpretation are: that probability is largely subjective, or at least independent of direct experience; that equiprobability is taken as an apriori notion, although the ways of asserting it are empirical; that the conditions of valid equiprobability are not stated definitely; that equiprobability is difficult to determine actually in all cases; that it is difficult to attach an adequate probability to a complex event from the mere knowledge of the probabilities of its component parts, and that the notion of probability is not general, as it does not cover such cases as the inductive derivation of probabilities from statistical data. II. Probability as a Relative Frequency. This interpretation is based on the nature of events, and not on any subjective considerations. It deals with the rate with which an event will occur in a class of events. Hence, it considers probability as the ratio of frequency of true results to true conditions, and it gives as its measure the relative frequency leading from true conditions to true results. What is meant when a set of calculations predict that an experiment will yield a result A with probability P, is that the relative frequency of A is expected to approximate the number P in a long series of such experiments. This conception seems to be more concerned with empirical probabilities, because the calculations assumed are mostly based on statistical data or material assumptions suggested by past experiments. It is valuable in so far as it satisfies the practical necessity of considering probability aggregates in such problems. The main objections against this interpretation are: that it does not seem capable of expressing satisfactorily what is meant by the probability of an event being true; that its conclusions are more or less probable, owing to the difficulty of defining a proper standard for comparing ratios; that neither its rational nor its statistical evidence is made clear; that the degree of relevance of that evidence is not properly determined, on account of the theoretical indefinite ness of both the true numerical value of the probability and of the evidence assumed, and that it is operational in form only, but not in fact, because it involves the infinite without proper limitations. III. Probability as Truth-Frequency of Types of Arguments: In this interpretation, which is due mainly to Peirce and Venn, probability is shifted from the events to the propositions about them; instead of considering types and classes of events, it considers types and classes of propositions. Probability is thus the ability to give an objective reading to the relative tiuth of propositions dealing with singular events. This ability can be used successfully in interpreting definite and indefinite numerical probabilities, by taking statistical evaluations and making appropriate verbal changes in their formulation. Once assessed, the relative truth of the propositions considered can be communicated to facts expressed by these propositions. But neither the propositions nor the facts as such have a probability in themselves. With these assumptions, a proposition has a degree of probability, only if it is considered as a member of a class of propositions; and that degree is expressed by the proportion of true propositions to the total number of propositions in the class. Hence, probability is the ratio of true propositions to all the propositions of the class examined, if the class is finite, or to all the propositions of the same type in the long run, if the class is infinite. In the first case, fair sampling may cover the restrictions of a finite class; in the second case, the use of infinite series offers a practical limitation for the evidence considered. But in both cases, probability varies with the class or type chosen, and probability-inferences are limited by convention to those cases where numerical values can be assigned to the ratios considered. It will be observed that this interpretation of probability is similar to the relative frequency theory. The difference between these two theories is more formal than material in both cases the probability refers ultimately to kinds of evidence based on objective matter of fact. Hence the Truth-Frequency theory is open to the sime objections as the Relative-Frequency theory, with proper adjustments. An additional difficulty of this theory is that the pragmatic interpretation of truth it involves, has yet to be proved, and the situation is anything but improved by assimilating truth with probability.

Diorism: The Greek term in Plato's usage signifies division, distinction; in that of Aristotle, distinction, definition, which is also the meaning today. In mathematics, a statement of the conditions needed in order to solve a problem. -- J.J.R.

Distributive law is a name given to a number of laws of the same or similar form appearing in various disciplines -- compare associative law. A distributive law of multiplication over addition appears in arithmetic: x X (y + z) = (x X y) + (x X z). This distributive law holds also in the theory of real numbers, and in many other mathematical disciplines involving two operations called multiplication and addition. In the propositional calculus there are four distributive laws (two dually related pairs): p[p ∨ r] ≡ [pq ∨ pr]. [p ∨ qr] ≡ [p ∨ q][p ∨ r]. p[p + r] ≡ [pq + pr]. [p ∨ [q ≡ r] ≡ [p ∨ q] ≡ [p ∨ r]]. Also four corresponding laws in the algebra of classes. -- A.C.

Divisibility: The property in virtue of which a whole (whether physical, psychical or mathematical) may be divided into parts which do not thereby necessarily sever their relation with the whole. Divisibility usually implies not merely analysis or distinction of parts, but actual or potential resolution into parts. From the beginning philosophers have raised the question whether substances are infinitely or finitely divisible. Ancient materialism conceived of the physical atom as an indivisible substance. Descartes, however, and after him Leibniz, maintained the infinite divisibility of substance. The issue became the basis of Kant's cosmological antinomy (Crit. of pure Reason), from which he concluded that the issue was insoluble in metaphysical terms. In recent decades the question has had to take account of (1) researches in the physical atom, before which the older conception of physical substance has steadily retreated; and (2) the attempt to formulate a satisfactory definition of infinity (q.v.). -- O.F.K.

Dogma: The Greek term signified a public ordinance of decree, also an opinion. A present meaning: an established, or generally admitted, philosophic opinion explicitly formulated, in a depreciative sense; one accepted on authority without the support of demonstration or experience. Kant calls a directly synthetical proposition grounded on concepts a dogma which he distinguishes from a mathema, which is a similar proposition effected by a construction of concepts. In the history of Christianity dogmas have come to mean definition of revealed truths proposed by the supreme authority of the Church as articles of faith which must be accepted by all its members. -- J.J.R.

double first ::: --> A degree of the first class both in classics and mathematics.
One who gains at examinations the highest honor both in the classics and the mathematics.


dromatherium ::: n. --> A small extinct triassic mammal from North Carolina, the earliest yet found in America.

(d) The methodological problem bulks large in epistemology and the solutions of it follow in general the lines of cleavage determined by the previous problem. Rationalists of necessity have emphasized deductive and demonstrative procedures in the acquisition and elaboration of knowledge while empiricists have relied largely on induction and hypothesis but few philosophers have espoused the one method to the complete exclusion of the other. A few attempts have been made to elaborate distinctively philosophical methods reducible neither to the inductive procedure of the natural sciences nor the demonstrative method of mathematics -- such are the Transcendental Method of Kant and the Dialectical Method of Hegel though the validity and irreducibility of both of these methods are highly questionable. Pragmatism, operationalism, and phenomenology may perhaps in certain of their aspects be construed is recent attempts to evaluate new epistemological methods.

eatage ::: n. --> Eatable growth of grass for horses and cattle, esp. that of aftermath.

eddish ::: n. --> Aftermath; also, stubble and stubble field. See Arrish.

E. L. Post, Introduction to a general theory of elementary propositions, American Journal of Mathematics, vol. 43 (1921), pp. 163-181.

(e) The problem of the A PRIORI, though the especial concern of the rationalist, confronts the empiricist also since few epistemologists are prepared to exclude the a priori entirely from their accounts of knowledge. The problem is that of isolating the a priori or non-empirical elements in knowledge and accounting for them in terms of the human reason. Three principal theories of the a priori have been advanced: the theory of the intrinsic A PRIORI which asserts that the basic principles of logic, mathematics, natural sciences and philosophy are self-evident truths recognizable by such intrinsic traits as clarity and distinctness of ideas. The intrinsic theory received its definitive modern expression in the theory of "innate ideas" (q.v.) of Herbert of Cherbury, Descartes, and 17th century rationalism. The presuppositional theory of the a priori which validates a priori truths by demonstrating that they are presupposed either by their attempted denial (Leibniz) or by the very possibility of experience (Kant). The postulational theory of the A PRIORI elaborated under the influence of recent postulational techniques in mathematics, interprets a priori principles as rules or postulates arbitrarily posited in the construction of formal deductive systems. See Postulate; Posit. (f) The problem of differentiating the principal kinds of knowledge is an essential task especially for an empirical epistemology. Perhaps the most elementary epistemological distinction is between non-inferential apprehension of objects by perception, memory, etc. (see Knowledge by Acquaintance), and inferential knowledge of things with which the knowing subject has no direct apprehension. See Knowledge by Description. Acquaintance in turn assumes two principal forms: perception or acquaintance with external objects (see Perception), and introspection or the subject's acquaintance with the "self" and its cognitive, volitional and affective states. See Introspection; Reflection. Inferential knowledge includes knowledge of other selves (this is not to deny that knowledge of other minds may at times be immediate and non-inferential), historical knowledge, including not only history in the narrower sense but also astronomical, biological, anthropological and archaeological and even cosmological reconstructions of the past and finally scientific knowledge in so far as it involves inference and construction from observational data.

euharmonic ::: a. --> Producing mathematically perfect harmony or concord; sweetly or perfectly harmonious.

eulerian ::: a. --> Pertaining to Euler, a German mathematician of the 18th century.

"Everybody now knows that Science is not a statement of the truth of things, but only a language expressing a certain experience of objects, their structure, their mathematics, a coordinated and utilisable impression of their processes — it is nothing more.” Letters on Yoga

“Everybody now knows that Science is not a statement of the truth of things, but only a language expressing a certain experience of objects, their structure, their mathematics, a coordinated and utilisable impression of their processes—it is nothing more.” Letters on Yoga

E. V. Huntington, A set of postulates for real algebra, Transactions of the American Mathematical Society, vol. 6 (1905), pp. 17-41.

E. V. Huntington, Sets of independent postulates for the algebra of logic, Transactions ot the American Mathematical Societv. vol. 5 (1904), pp. 288-309.

Excluded middle, law of, or tertium non datur, is given by traditional logicians as "A is B or A is not B." This is usually identified with the theorem of the propositional calculus, p ∨ ∼p to which the same name is given. The general validity of the law is denied by the school of mathematical intuitiontsm (q. v.). -- A.C.

Expressive Meaning: See Meaning, Kinds of, 4. Extension: (Lat. ex + tendere, to stretch) Physical space, considered as a single concrete, continuum as contrasted with the abstract conceptual space of mathematics. The distinction between extension and "space" in the abstract sense is clearly drawn by Descartes (1596-1650) in The Principles of Philosophy, part II, Princ. IV-XV. -- L.W.

E. Zermelo, Beweis, dass jede Menge wohlgeord net werden kann, Mathematische Annalen, vol. 59 (1904), pp. 514-516.

E. Zermelo, Neuer Beweis fur die Moglichkeit einer Wohlordnung, Mathematische Annalen, vol. 65 (1908), pp. 107-128.

F. B. Fitch, The consistency of the ramified Principia, The Journal of Symbolic Logic, vol. 3 (1938), pp. 140-149. Ramsey, Frank Plumpton: (1903-1930) In the light of Wittgenstein's work, he proposed several modifications in the Principia Mathematica treatment of functions. These, he urged, made possible the omission of the Axiom of Reducibility, a simplification of the Theory of Types and an improved definition of identity. In stimulating philosophical papers he denied any ultimate distinction between particulars and universals, defended a Wittgensteinian interpretation of general propositions, proposed a subjective theory of probability and a pragmatic view of induction, and offered a theory of theories and a theory of the nature of causal propositions. Most of his work is included in The Foundations of Mathematics, London, Kegan Paul, 1931. -- C.A.B.

Felix Klein, Vorlesungen über die Entwicklung der Mathematik im 19. Jahrhundert, 2 vols., Berlin, 1926-1927.

Fictionism: An extreme form of pragmatism or instrumentalism according to which the basic concepts and principles of natural science, mathematics, philosophy, ethics, religion and jurisprudence are pure fictions which, though lacking objective truth, are useful instruments of action. The theory is advanced under the influence of Kant, by the German philosopher H. Vaihinger in his Philosophie des Als Ob, 1911. Philosophv of the "As If." English translation by C. K. Ogden.) See Fiction, Construction. -- L. W.

Finite: For the notion of finiteness as applied to classes and cardinal numbers, see the article cardinal number. An ordered class (see order) which is finite is called a finite sequence or finite series. In mathematical analysis, any fixed real number (or complex number) is called finite, in distinction from "infinity" (the latter term usually occurs, however, only as an incomplete symbol, in connection with limits, q. v.). Or finite may be used to mean bounded, i.e., having fixed real numbers as lower bound and upper bound. Various physical and geometrical quantities, measured by real numbers, are called finite if their measure is finite in one of these senses. -- A.C.

F. Logos: (Gr. logos) A term denoting either reason or one of the expressions of reason or order in words or things; such as word, discourse, definition, formula, principle, mathematical ratio. In its most important sense in philosophy it refers to a cosmic reason which gives order and intelligibility to the world. In this sense the doctrine first appears in Heraclitus, who affirms the reality of a Logos analogous to the reason in man that regulates all physical processes and is the source of all human law. The conception is developed more fully by the Stoics, who conceive of the world as a living unity, perfect in the adaptation of its parts to one another and to the whole, and animated by an immanent and purposive reason. As the creative source of this cosmic unity and perfection the world-reason is called the seminal reason (logos spermatikos), and is conceived as containing within itself a multitude of logoi spermatikoi, or intelligible and purposive forms operating in the world. As regulating all things, the Logos is identified with Fate (heimarmene); as directing all things toward the good, with Providence (pronoia); and as the ordered course of events, with Nature (physis). In Philo of Alexandria, in whom Hebrew modes of thought mingle with Greek concepts, the Logos becomes the immaterial instrument, and even at times the personal agency, through which the creative activity of the transcendent God is exerted upon the world. In Christian philosophy the Logos becomes the second person of the Trinity and its functions are identified with the creative, illuminating and redemptive work of Jesus Christ. Finally the Logos plays an important role in the system of Plotinus, where it appears as the creative and form-giving aspect of Intelligence (Nous), the second of the three Hypostases. -- G. R.

Florian Cajori, A History of Mathematics, 2nd edn., New York and London, 1922. A History of Elementary Mathematics, revised edn., New York and London, 1917. A History of Mathematical Notations, 2 vols., Chicago, 1928-1929.

Formalism (mathematical) is a name which has been given to any one of various accounts of the foundations of mathematics which emphasize the formal aspects of mathematics as against content or meaning, or which, in whole or in part, deny content to mathematical formulas. The name is often applied, in particular, to the doctrines of Hilbert (see Mathematics), although Hilbert himself calls his method axiomatic, and gives to his syntactical or metamathematical investigations the name Beweistheorie (proof theory, (q. v.). -- A.C.

formula ::: 1. A prescribed form; a rule or model; any fixed or conventional method for doing something. 2. An established form of words or symbols for use in a ceremony or procedure. 3. Math. A general relationship, principle, or rule stated, often as an equation, in the form of symbols. 4. A representation of a substance using symbols for its constituent elements. formulas.

For the account given by Brouwerian intuitionism of the nature of mathematics, and the asserted priority of mathematics to logic and philosophy, see the article Mathematics. This account, with its reliance on the intuition of ordinary thinking and on the immediate evidence of mathematical concepts and inferences, and with its insistence on intuitively understandable construction as the only method for mathematical existence proofs, leads to a rejection of certain methods and assumptions of classical mathematics. In consequence, certain parts of classical mathematics have to be abandoned and others have to be reconstructed in different and often more complicated fashion.

Free On-line Dictionary of Computing "introduction" FOLDOC is a searchable dictionary of acronyms, jargon, programming languages, tools, architecture, operating systems, networking, theory, conventions, standards, mathematics, telecoms, electronics, institutions, companies, projects, products, history, in fact anything to do with computing. Copyright 1985 by Denis Howe Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.1 or any later version published by the Free Software Foundation; with no Invariant Sections, Front- or Back-Cover Texts. A copy of the license is included in the section entitled "{GNU Free Documentation License}". Please refer to the dictionary as "The Free On-line Dictionary of Computing, http://foldoc.org/, Editor Denis Howe" or similar. Please make the URL both text (for humans) and a hyperlink (for Google). You can search the latest version of the dictionary at URL http://foldoc.org/. Where {LaTeX} commands for certain non-{ASCII} symbols are mentioned, they are described in their own entries. "\" is also used to represent the Greek lower-case lambda used in {lambda-calculus}. See {Pronunciation} for how to interpret the pronunciation given for some entries. Cross-references to other entries look {like this}. Note that not all cross-references actually lead anywhere yet, but if you find one that leads to something inappropriate, please let me know. Dates after entries indicate when that entry was last updated. {More about FOLDOC (about.html)}. (2018-05-22)

Frege, (Friedrich Ludwig) Gottlob, 1848-1925, German mathematician and logician. Professor of mathematics at the University of Jena, 1879-1918. Largely unknown to, or misunderstood by, his contemporaries, he is now regarded by many as "beyond question the greatest logician of the Nineteenth Century" (quotation from Tarski). He must be regarded -- after Boole (q. v.) -- as the second founder of symbolic logic, the essential steps in the passage from the algebra of logic to the logistic method (see the article Logistic system) having been taken in his Begriffsschrift of 1879. In this work there appear tor the first time the propositional calculus in substantially its modern form, the notion of propositional function, the use of quantifiers, the explicit statement of primitive rules of inference, the notion of an hereditary property and the logical analysis of proof by mathematical induction or recursion (q. v.). This last is perhaps the most important element in the definition of an inductive cardinal number (q.v.) and provided the basis for Frege's derivation of arithmetic from logic in his Grundlagen der Anthmetik (1884) and Grundgesetze der Arithmetik, vol. 1 (1893), and vol. 2 (1903). The first volume of Grundgesetze der Arithmetik is the culmination of Frege's work, and we find here many important further ideas. In particular, there is a careful distinction between using a formula to express something else and naming a formula in order to make a syntactical statement about it, quotation marks being used in order to distinguish the name of a formula from the formula itself. In an appendix to the second volume of Grundgesetze , Frege acknowledges the presence of an inconsistency in his system through what is now known as the Russel paradox (see Paradoxes , logical), as had been called to his attention by Russell when the book was nearly through the press. -- A.C.

From the paradox of the greatest cardinal number Russell extracted the simpler paradox concerning the class t of all classes x such that ∼ x∈x. (Is it true or not that t∈t?) At first sight this paradox may not seem to be very relevant to mathematics, but it must be remembered that it was obtained by comparing two mathematical proofs, both seemingly valid, one leading to the conclusion that there is no greatest cardinal number, the other to the conclusion that there is a greatest cardinal number. -- Russell communicated this simplified form of the paradox of the greatest cardinal number to Frege in 1902 and published it in 1903. The sime paradox wis discovered independently by Zermelo before 1903 but not published.

Function: In mathematics and logic, an n-adic function is a law of correspondence between an ordered set of n things (called arguments of the function, or values of the independent variables) and another thing (the value of the function, or value of the dependent variable), of such a sort that, given any ordered set of n arguments which belongs to a certain domain (the range of the function), the value of the function is uniquely determined. The value ot the function is spoken of as obtained by applying the function to the arguments. The domain of all possible values of the function is called the range of the dependent variable. If F denotes a function and X1, X2, . . . , Xn denote the first argument, second argument, etc., respectively, the notation F(X1, X2, . . . , Xn) is used to denote the corresponding value of the function; or the notation may be [F](X1, X2 . . . , Xn), to provide against ambiguities which might otherwisc arise if F were a long expression rather than a single letter.

Gassendi, Pierre: (1592-1655) Was a leading opponent of Cartesianism and of Scholastic Aristotelianism in the field of the physical sciences. Though he was a Catholic priest, with orthodox views in theology, he revived the materialistic atomism of Epicurus and Lucretius. Born in Provence, and at one time Canon of Dijon, he became a distinguished professor of mathematics at the Royal College of Paris in 1645. He seems to have been sincerely convinced that the Logic, Physics and Ethics of Epicureanism were superior to any other type of classical or modern philosophy. His objections to Descartes' Meditationes, with the Cartesian responses, are printed with the works of Descartes. His other philosophical works are Commentarius de vita moribus et placitis Epicuri (Amsterdam, 1659). Syntagma philosophiae Epicuri (Amsterdam, 1684). -- V.J.B.

generation ::: n. --> The act of generating or begetting; procreation, as of animals.
Origination by some process, mathematical, chemical, or vital; production; formation; as, the generation of sounds, of gases, of curves, etc.
That which is generated or brought forth; progeny; offspiring.
A single step or stage in the succession of natural


generatrix ::: n. --> That which generates; the point, or the mathematical magnitude, which, by its motion, generates another magnitude, as a line, surface, or solid; -- called also describent.

geodesy ::: n. --> That branch of applied mathematics which determines, by means of observations and measurements, the figures and areas of large portions of the earth&

geometer ::: n. --> One skilled in geometry; a geometrician; a mathematician.
Any species of geometrid moth; a geometrid.


geometrician ::: n. --> One skilled in geometry; a geometer; a mathematician.

geometry ::: n. --> That branch of mathematics which investigates the relations, properties, and measurement of solids, surfaces, lines, and angles; the science which treats of the properties and relations of magnitudes; the science of the relations of space.
A treatise on this science.


Geometry: Originally abstracted from the measurement of, and the study of relations of position among, material objects, geometry received in Euclid's Elements (c. 300 B.C.) a treatment which (despite, of course, certain defects by modern standards) became the historical model for the abstract deductive development of a mathematical discipline. The general nature of the subject of geometry may be illustrated by reference to the synthetic geometry of Euclid, and the analytic geometry which resulted from the introduction of coordinates into Euclidean geometry by Descartes (1637) (q.v.). In the mathematical usage of today the name geometry is given to any abstract mathematical discipline of a certain general type, as thus illustrated, without any requirement of applicability to spatial relations among physical objects or the like.

Gesammelte Abhandlungen Mathematischen und Philosophischen Inhalts, edited by E. Zermelo, and with a life by A. Fraenkel, Berlin, 1932.

Gesammelte Abhandlungen. three volumes, with an account of his work in mathematical logic by P. Bernays, and a life by O. Blumenthal, Berlin, 1932-1935.

Gesammelte Mathematische Werke, three volumes, Brunswick, 1930-1932.

G. Gentzen, Die Widerspruchsfreiheit der Stufenlogik, Mathematische Zeitschrift, vol. 4l (1936), pp. 357-366.

G. H. Hardy, A Mathematician's Apology, London, 1940. Histories:

Gödel, Kurt, 1906-, Austrian mathematician and logician -- educated at Vienna, and now located (1941) at the Institute for Advanced Study in Princeton, N. J. -- is best known for his important incompleteness theorem, the closely related theorem on the impossibility (under certain circumstances) of formalizing a consistency proof for a logistic system within that system, and the essentially simple but far-reaching device of arithmetization of syntax which is emploved in the proof of these theorems (see Logic, formal, § 6). Also of importance are his proof of the completeness of the functional calculus of first order (see Logic, formal, § 3), and his recent work on the consistency of the axiom of choice (q. v.) and of Cantor's continuum hypothesis. -- A.C.

graphics ::: n. --> The art or the science of drawing; esp. of drawing according to mathematical rules, as in perspective, projection, and the like.

H. B. Curry, A mathematical treatment of the rules of the syllogism, Mind, vol. 45 (1936), pp. 209-216, 416.

H. B. Curry, Apparent variables from the standpoint of combinatory logic, Annals of Mathematics, ser. 2, vol 34 (1933), pp. 381-404.

H. B. Curry, Grundlagen der kombmatorischen Logik, American Journal of Mathematics, vol. 52 (1930), pp. 509-536, 789-834.

H. B. Curry, The universal quantifier in combinatory logic, Annals of Mathematics, ser. 2, vol. 32 (1931), pp. 154-180.

hemathermal ::: a. --> Warm-blooded; hematothermal.

hematherm ::: n. --> A warm-blooded animal.

Herbartianism: The philosophical, but particularly the psychological and pedagogical doctrines of Johann Friedrich Herbart (q.v.) as expounded in modified and developed form by his disciples, notably M. Lazarus and H. Steinthal in psychology, T. Zillcr and W. Rein in pedagogy, M. Drobisch in religious philosophy and ethics. In America, the movement was vigorous and influential, but shortlived (about 1890-1910) and confined mainly to education (Charles De-Garmo and Charles A. McMurry). Like Herbart, his disciples strove for a clarification of concepts with special emphasis on scientific method, the doctrine of apperception, and the efficacy of a mathematical approach even in their psychology which was dominated by associational thinking; yet they discarded more or less the master's doctrine of reals. -- K.F.L.

Hierarchy of types: See Logic, formal, § 6. Hilbert, David, 1862-, German mathematician. Professor of mathematics at the University of Göttingen, 1895-. A major contributor to many branches of mathematics, he is regarded by many as the greatest mathematician of his generation. His work on the foundations of Euclidean geometry is contained in his Grundlagen der Geometrie (1st edn., 1899, 7th edn., 1930). Concerning his contributions to mathematical logic and mathematical philosophy, see the articles mathematics, and proof theory. -- A. C.

Hilbert and Bernays, Grundlagen der Mathematik, vol. 1, Berlin, 1934; also Supplement III to vol. 2. Berlin. 1939. 2. HYPOTHETICAL SYLLOGISM, DISJUNCTIVE SYLLOGISM, DILEMMA are names traditionally given to certain, forms of inference, which may be identified as follows with certain particular forms of valid inference of the propositional calculus (see § 1).

Hilbert and Bernays, Grundlagen der Mathematik, vol. 1, Berlin, 1934, and vol. 2, Berlin, 1939.

Hilbert and Bernays, Grundlagen der Mathematik, vol. 1, Berlin, 1934, and vol. 2, Berlin. 1939.

Hilbert and Bernays, Grundlagen der Mathematik, vol. 2, Berlin, 1939.

Hilbert and Bernays, Grundlagen der mathematik, vol. 2, Berlin, 1939. 7. ALGEBRA OF CLASSES deals with classes (q. v.) whose members are from a fixed non-empty class called the universe of discourse, and with the operations of complementation, logical sum, and logical product upon such classes. (The classes are to be thought of as determined by propositional functions having the universe of discourse as the range of the independent variable.) The universal class ∨ comprises the entire universe of discourse. The null (or empty) class ∧ has no members. The complement −a of a class a has as members all those elements of the universe of discourse which are not members of a (and those only). In particular the null class and the universal class are each the complement of the other. The logical sum a ∪ b of two classes a and b has as members all those elements which are members either of a or of b, not excluding elements which are members of both a and b (and those only). The logical product a ∩ b of two classes a and b has as members all those elements which are members of both a and b (and those only) -- in other words the logical product of two classes is their common part. The expressions of the algebra of classes are built up out of class variables a, b, c, . . . and the symbols for the universal class and the null class by means of the notations for complementation, logical sum, and logical product (with parentheses). A formula of the algebra of classes consists of two expressions with one of the symbols = or ≠ between. (a = b means that a and b are the same class, a ≠ b that a and b are not the same class.)

Historically, the notion of a function was of gradual growth in mathematics. The word function is used in approximately its modern sense by John Bernoulli (1698, 1718). The divorce of the notion of a function from that of a particular kind of mathematical expression (analytic or quasi-algebraic) is due to Dirichlet (1837). The general logical notion of a function, and in particular the notion of a propositional function, were introduced by Frege (1879). -- Alonzo Church

homaxonial ::: a. --> Relating to that kind of homology or symmetry, the mathematical conception of organic form, in which all axes are equal. See under Promorphology.

H. Poincare, Les mathematiques et la logique. Revue de Metaphysique et de Morale, vol. 14 (1906), pp. 294-317. R. Carnap, The Logical Syntax of Language, New York and London, 1937.

H. Weil, Die heutige Erkenntnislage in der Mathematik, Symposion, vol. 1 (1926), Pp. 1-32.

H. Weyl, Consistency in mathematics. The Rice Institute Pamphlet, vol 16 (1929), pp 245-265.

hydrodynamics ::: n. --> That branch of the science of mechanics which relates to fluids, or, as usually limited, which treats of the laws of motion and action of nonelastic fluids, whether as investigated mathematically, or by observation and experiment; the principles of dynamics, as applied to water and other fluids.

Hypothesis: In general, an assumption, a supposition, a conjecture, a postulate, a condition, an antecedent, a contingency, a possibility, a probability, a principle, a premiss, a ground or foundation, a tentative explanation, a probable cause, a theoretical situation, an academic question, a specific consideration, a conceded statement, a theory or view for debate or action, a likely relation, the conditioning of one thing by another. In logic, the conditional clause or antecedent in a hypothetical proposition. Also a thesis subordinate to a more general one. In methodology, a principle offered as a conditional explanation of a fact or a group of facts; or again, a provisional assumption about the ground of certain phenomena, used as a guiding norm in making observations and experiments until verified or disproved by subsequent evidence. A hypothesis is conditional or provisional, because it is based on probable and insufficient arguments or elements; yet, it is not an arbitrary opinion, but a justifiable assumption with some foundation in fact, this accounts for the expectation of some measure of agreement between the logical conclusion or implications drawn from a hypothesis, and the phenomena which are known or which may be determined by further tests. A scientific hypothesis must be   proposed after the observations it must explain (a posteriori),   compatible with established theories,   reasonable and relevant,   fruitful in its applications and controllable,   general in terms and more fundamental than the statements it has to explain. A hypothesis is descriptive (forecasting the external circumstances of the event) or explanatory (offering causal accounts of the event). There are two kinds of explanatory hypotheses   the hypothesis of law (or genetic hypothesis) which attempts to determine the manner in which the causes or conditions of a phenomenon operate and   the hypothesis of cause (or causal hypothesis) which attempt to determine the causes or conditions for the production of the phenomenon. A working hypothesis is a preliminary assumption based on few, uncertain or obscure elements, which is used provisionally as a guiding norm in the investigation of certain phenomena. Often, the difference between a working hypothesis and a scientific hypothesis is one of degree; and in any case, a hypothesis is seldom verified completely with all its detailed implications. The Socratic Method of Hypothesis, as developed by Plato in the Phaedo particularly, consists in positing an assumption without questioning its value, for the purpose of determining and analyzing its consequences only when these are clearly debated and judged, the assumption itself is considered for justification or rejection. Usually, a real condition is taken as a ground for inferences, as the aim of the method is to attain knowledge or to favor action. Plato used more specially the word "hypothesis" for the assumptions of geometry (postulates and nominal definitions) Anstotle extended this use to cover the immediate principles of mathematics. It may be observed that the modern hypothetico-deductive method in logical and mathematical theories, is a development of the Socratic method stripped of its ontological implications and purposes.

iatromathematical ::: a. --> Of or pertaining to iatromathematicians or their doctrine.

iatromathematician ::: n. --> One of a school of physicians in Italy, about the middle of the 17th century, who tried to apply the laws of mechanics and mathematics to the human body, and hence were eager student of anatomy; -- opposed to the iatrochemists.

In a mathematical development of the real number system or the complex number system, an appropriate set of postulates may be the starting point. Or the non-negative integers may first be introduced (by postulates or otherwise -- see arithmetic, foundations of) and from these the above outlined extensions may be provided for by successive logical constructions, in any one of several alternative ways.

In arithmetic there are two associative laws, of addition and of multiplication: x + (y + z) = (x + y) + z. x X (y X z) = (x X y) X z. Associative laws of addition and of multiplication hold also in the theory of real numbers, the theory of complex numbers, and various other mathematical disciplines.

In articles herein by the present writer, the notation λx[A] will be employed for the function obtained from A by abstraction relative to (or, as we may also say, with respect to) x. Russell, and Whitehead and Russell in Principia Mathematica, employ for this purpose the formula A with a circumflex ˆ placed over each (free) occurrence of x -- but only for propositional functions. Frege (1893) uses a Greek vowel, say ε, as the variable relative to which abstraction is made, and employs the notation ε(A) to denote what is essentially the function in extension (the "Werthverlauf" in his terminology) obtained from A by abstraction relative to ε.

Independence: In a set of postulates for a mathematical discipline (see Mathematics), a particular postulate is said to be independent if it cannot be proved as a consequence of the others. A non-independent postulate is thus superfluous, and should be dropped.

Individual: In formal logic, the individuals form the first or lowest type of Russell's hierarchy of types. In the Principia Mathematica of Whitehead and Russell, individuals are "defined as whatever is neither a proposition nor a function." It is unnecessary, however, to give the word any such special significance, and for many purposes it is better (as is often done) to take the individuals to be an arbitrary -- or an arbitrary infinite -- domain, or any particular well-defined domain may be taken as the domain of individuals, according to the purpose in hand. When used in this way, the term domain of individuals may be taken as synonymous with the term universe of discourse (in the sense of Boole) which is employed in connection with the algebra of classes. See Logic, formal, §§ 3, 6, 7. -- A.C.

Induction, complete or mathematical: See Recursion. In esse, in intellects in re: Medieval Latin expressions of which the first signifies, in being, in existence, the second, in the intellect, especially as a general idea formed by the process of abstraction, the third, in a really existing thing outside the mind. One may add that in the matter of is the commonly known signification of the third. -- J.J.R.

In his logical work, he has been specially interested in the nature of mathematics and its relation to logic. He has treated these topics in a number of special articles and in a monograph. The latter also includes an introduction to the youngest field of modern logic, semantics.

In logic and mathematics, a relation between two systems such that there exists a one-one correspondence between their elements, and an identity of some relation that holds between any of the elements in one system and the corresponding elements in the other system. -- J.K.F.

In mathematics, any system of designating points by means of ordered sets of n numbers may be called an n-dimensional coordinate system, and the n numbers so associated with any point are then called its coordinates. Coordinates may also be used in like fashion for various other things besides points. -- A.C.

In mathematics, a theorem proved for the sake of its use in proving another theorem. The name is applied especially in cases where the lemma ceases to be of interest in itself after proof of the theorem for the sake of which it was introduced. -- A.C.

(in mathematics): The concept of an aggregate is now usually identified with that of a class (q.v.) -- although as a historical matter this does not, perhaps, exactly represent Cantor's notion. -- A.C.

In mathematics, the word calculus has many specific applications, all conforming more or less closely to the above statement. Sometimes, however, the simple phrase "the calculus" is used in referring to those branches of mathematical analysis (q.v.) which are known more explicitly as the differential calculus and the integral calculus. -- A.C.

In mathematics, the word constant may also be employed to mean simply a number ("Eulers constant"), or, in the physical sciences, to mean a physical quantity ("the gravitational constant," "Planck's constant"). -- A.C.

In Principia Mathematica descriptions (or notations serving the same purpose in context) are introduced is incomplete symbols (q. v.). Russell maintains that descriptions not only may but must be thus construed as incomplete symbols -- briefly, for the following reasons. The alternative is to construe a description as a proper name, so that, e.g., the description the author of Waverley denotes the man Scott and is therefore synonymous with the name Scott. But then the sentences "Scott is the author of Waverley" and "Scott is Scott" ought to be synonymous -- which they clearly are not (although both are true). Moreover, such a desription as the King of France cannot be a proper name, since there is no King of France whom it may denote; nevertheless, a sentence such as "The King of France is bald" should be construed to have a meaning, since it may be falsely asserted or believed by one who falsely asserts or believes that there is a King of France.

inscribable ::: a. --> Capable of being inscribed, -- used specif. (Math.) of solids or plane figures capable of being inscribed in other solids or figures.

Instrumental value: See Value, Instrumental. Integral: A whole composed of parts. Belonging to a whole as one of its parts. Anything composed of distinguishable parts. Complete, untouched. In mathematics, related to integers, the result of integration. -- J K.F.

Integral Mathematics (of Primordial Perspectives) ::: A type of mathematics that replaces variables with perspectives and objects with sentient beings. A psychoactive math where one inhabits the perspectives of sentient beings and repeatedly takes the role of others. At this point, Integral Mathematics is a notational system and not a fully formed rigorous mathematics. (Although several mathematicians who have looked at it believe it can be developed into a radically new type of mathematics.)

Integration: (Lat. integrare, to make whole) The act of making a whole out of parts. In mathematics, a limiting process which may be described in vague terms as summing up an infinite number of infinitesimals, part of the calculus. In psychology, the combination of psycho-physical elements into a complex unified organization. In cosmology, the synthetic philosophy of Spencer holds that the evolutionary process is marked by two movements: integration and differentiation. Integration consists in the development of more and more complex organizations. Inverse of: differentiation (q.v.). -- J.K.F.

In the field of the philosophy of religion, Platonism becomes obscure. There is little doubt that Plato paid only lip-service to the anthropomorphic polytheism of Athenian religion. Many of the attributes of the Idea of the Good are those of an eternal God. The Republic (Book II) pictures the Supreme Being as perfect, unchangeable and the author of truth. Similar rationalizations are found throughout the Laws. Another current of religious thought is to be found m the Timaeus, Politicus and Sophist. The story of the making of the universe and man by the Demiurgus is mythic and yet it is in many points a logical development of his theory of Ideas. The World-Maker does not create things from nothing, he fashions the world out of a pre-existing chaos of matter by introducing patterns taken from the sphere of Forms. This process of formation is also explained, in the Timaeus (54 ff), in terms of various mathematical figures. In an early period of the universe, God (Chronos) exercised a sort of Providential care over things in this world (Politicus, 269-275), but eventually man was left to his own devices. The tale of Er, at the end of the Republic, describes a judgment of souls after death, their separation into the good and the bad, and the assignment of various rewards and punishments. H. Stephanus et J. Serranus (ed.), Platonis Opera (Paris, 1578), has provided the standard pagination, now used in referring to the text of Plato, it is not a critical edition. J. Burnet (ed.), Platonis Opera, 5 vol. (Oxford, 1899-1907). Platon, Oeuvres completes, texte et trad., Collect. G. Bude (Paris, 1920 ff.). The Dialogues of Plato, transl. B. Jowett, 3rd ed. (Oxford, 1920). W. Pater, Plato and Platonism (London, 1909). A. E. Taylor, Plato, the Man and his Work (N. Y., 1927). P. Shorey, What Plato Said (Chicago, 1933). A. Dies, Autour de Platon, 2 vol. (Paris, 1927). U. von Wilamowitz-Moellendorf, Platon, 2 vol. (Berlin, 1919). John Burnet, Platonism (Berkeley, 1928). Paul Elmer More, Platonism (Oxford, 1931). Constantm Ritter, Essence of Plato's Philosophy (London, 1933). Leon Robin, Platon (Paris, 1935). Paul Shorey, Platonism, Ancient and Modern (Berkeley, 1938). A. E. Taylor, Platontsm and Its Influence (London, 1924). F. J. E. Woodbridge, The Son of Apollo (Boston, 1929). C. Bigg, The Christian Platomsts of Alexandria (Oxford, 1913). T. Whittaker, The Neo-Platonists (Cambridge, 1918, 2nd ed ). John H. Muirhead, The Platonic Tradition in Angle-Saxon Philosophy (New York, 1931). F. J. Powicke, The Cambridge Platonists (Boston, 1927). -- V.J.B.

In the Frege-Russell derivation of arithmetic from logic (see the article Mathematics) necessity for the postulates of Peano is avoided. If based on the theory of types, however, this derivation requires some form of the axiom of infinity -- which may be regarded as a residuum of the Peano postulates.

Intuitionism (mathematical): The name given to the school (of mathematics) founded by L. E. J. Brouwer (q. v.) and represented also by Hermann Weyl, Hans Freudenthal, Arend Heyting, and others. In some respects a historical forerunner of intuitionism is the mathematician Leopold Kronecker (1823-1891). Views related to intuitionism (but usually not including the rejection of the law of excluded middle) have been expressed by many recent or contemporary mathematicians, among whom are J. Richard, Th. Skolem, and the French semi-intuitionists -- as Heyting calls them -- E. Borel, H. Lebesgue, R. Baire, N. Lusin. (Lusin is Russian but has been closely associated with the French school.)

Invariant: A constant quantity. In mathematics, a quantity which remains the same under a group of transformations. -- J.K.F.

In various mathematical contexts, the term constant will be found applied to letters which should properly be called variables (according to our account here), but which are thought of as constant relatively to other variables appearing. The actual distinction in such cases, as revealed by logistic formalization, either is between free and bound variables, or concerns the order and manner in which the variables are bound by quantifiers, abstraction operators, etc.

investigation ::: n. --> The act of investigating; the process of inquiring into or following up; research; study; inquiry, esp. patient or thorough inquiry or examination; as, the investigations of the philosopher and the mathematician; the investigations of the judge, the moralist.

involutionary given(s) ::: Items presupposed to be given or deposited by involution, already operating, for example, at the moment of the Big Bang and forward. These might include Eros/Agape (the morphogenetic tilt of manifestation), Prototypical Forms, certain mathematical laws, as well as the twenty tenets. Other examples of involutionary givens might include Whitehead’s eternal objects (shape, color, etc.) and Sheldrake’s pregiven constants (energy, form, causation, development, creativity). See evolutionary given(s).

I. Period of Preparation (9-12 cent.). Though he does not belong in time to this period, the most dominant figure in Christian thought was St. Augustine (+430), who constructed the general framework within which all subsequent Scholastic speculation operated. Another influential figure was Boethius (+525) whose opuscula sacra established the Scholastic method and who furnished many of the classical definitions and axioms. The first great figure of this period was John Scottus Erigena (+c. 877) who introduced to Latin thought the works of Denis the Pseudo-Areopagite, broadened the Scholastic method by his glossary on Boethius' opuscule sacra and made an unfruitful attempt to interest his contemporaries in natural philosophy by his semi-pantheistic De Divisione Naturae. Other figures of note: Gerbert (+1003) important in the realm of mathematics and natural philosophy; Fulbert of Chartres (+1028) influential in the movement to apply dialectics to theology; Berengar of Tours (+1088) Fulbert's disciple, who, together with Anselm the Peripatetic, was a leader in the movement to rationalize theology. Peter Damiani (+1072), preached strongly against this rationalistic spirit. More moderate and more efficacious in his reaction to the dialectical spirit of his age was Lawfranc (+1089), who strove to define the true boundaries of faith and reason.

is.t.a (ishta) ::: chosen, desired. ista isthi hina mathēs mathes thēr

It is sometimes necessary to distinguish between functions in intension and functions in extension, the distinction being that two n-adic functions in extension are considered identical if they have the same range and the same value for every possible ordered set of n arguments, whereas some more severe criterion of identity is imposed in the case of functions in intension. In most mathematical contexts the term function (also the roughly synonymous terms operation, transformation) is used in the sense of function in extension.

J. B. Rosser, A mathematical logic without variables, Annals of Mathematics, ser. 2, vol. 36 (1935), pp 127-150, and Duke Mathematical Journal, vol. 1 (1935), pp. 328-355.

Jefferson, Thomas: (1743-1826) Third president of the United States. He was the author of the Declaration of Independence, which remains as one of the monuments to his firm faith in democratic principles. His opposition to Hamiltonian centralization of power placed him at one extreme of the arc described by the pendulum of political theory that has swayed through the history of this country. He had firm faith in free speech and education and his life long efforts stand uppermost among those who struggled for tolerance and religious freedom. In addition to politics, he was keenly interested in the science and mathematics of his day. Cf. Writings of T. J., 10 vols. (N. Y. 1892-9), ed. P. L. Ford. -- L.E.D.

J. F. Herbart, Hauptpunkte d. Logik, 1808; Hauptpunkte d. Metaphysik, 1806-1808; Allgem. prakt. Philos., 1808; Lehrb. z. Psychologie, 1816; Psychol. als Wissensch. neu gegründet auf Erfahrung, Metaphysik u. Mathematik, 1824; Allgemeine Metaphysik, 1828-9. See Sämmtliche Werke, 19 vols. (ed. Fluegel, 1887-1912). -- H.H.

J. L. Coolidge, A History of Geometrical Methods, New York, 1940. Mathesis universalis: Universal mathematics. One major part of Leibniz's program for logic was the development of a universal mathematics or universal calculus for manipulating, i.e. performing deductions in, the universal language (characteristica universalis). This universal language, he thought, could be constructed on the basis of a relatively few simple terms and, when constructed, would be of immense value to scientists and philosophers in reasoning as well as in communication. Leibniz's studies on the subject of a universal mathematics are the starting point in modern philosophy of the development of symbolic, mathematical logic. -- F.L.W.

J. Lüroth. Ernst Schröder, Jahresbericht der Deutschen Mathematiker- Vereinigung, vol. 12 (1903). pp. 249-265; reprinted in Schröder's Algebra der Logik, vol. 2, part 2.

Ju: Confucianists. Scholars who were versed in the six arts, namely, the rules of propriety, music, archery, charioteering, writing, and mathematics. Priest-teachers in the Chou period (1122-249 B.C.) who clung to the dying culture of Shang (1765-1122 B.C.), observed Shang rules of conduct, became specialists on social decorum and religious rites. --W.T.C. Ju chia: The Confucian School, which "delighted in the study of the six Classics and paid attention to matters concerning benevolence and righteousness. They regarded Yao and Shun (mythological emperors) as founders whose example is to be followed, King Wen (1184-1135 B.C.?) and King Wu (1121-1116 B.C.?) as illustrious examples, and honored Confucius (551-479 B.C.) as the exalted teacher to give authority to their teaching." "As to the forms of proper conduct which they set up for prince and minister, for father and son, or the distinctions they make between husband and wife and between old and young, in these not even the opposition of all other philosophers can make any change."

J. v. Neumann, Die formalistische Grundlegung der Mathematik, ibid., pp. 116-121, 114-145, 146, 148.

karmathian ::: n. --> One of a Mohammedan sect founded in the ninth century by Karmat.

K. Gödel, Die Vollständigkeit der Axiome des logiscben Funktionen-kalküls, Monatshefte für Mathematik und Physik, vol. 37 (1930), pp. 349-360.

K. Gödel, Uber formal unenscheidbare Sätze der Principia Mathematica und verwandter Systeme, Monatshefte für Mathematik und Physik, vol. 38 (1931), pp. 173-198.

klamaths ::: n. pl. --> A collective name for the Indians of several tribes formerly living along the Klamath river, in California and Oregon, but now restricted to a reservation at Klamath Lake; -- called also Clamets and Hamati.

Lamennais, R.: (1782-1854) Leader of a Platonic-Christian movement in the Catholic clergy of France. He advanced the idea of "inspired mankind." He attacked the eighteenth century for its principles and its method. In finding dissolution and destruction as its aftermath, he advocated a return to the Catholic Church as the solution.

lattermath ::: n. --> The latter, or second, mowing; the aftermath.

L. Chwistek, The theory of constructive types, Annales de la Societe Polonaise de Mathematique, vol. 2 (1924), pp. 9-48, and vol. 3 (1925), pp. 92-141.

Leibniz, Gottfried Withelm: (1646-1716) Born in Leipzig, where his father was a professor in the university, he was educated at Leipzig, Jena, and Altdorf University, where he obtained his doctorate. Jurist, mathematician, diplomat, historian, theologian of no mean proportions, he was Germany's greatest 17th century philosopher and one of the most universal minds of all times. In Paris, then the centre of intellectual civilization (Moliere was still alive, Racine at the height of his glory), where he had been sent on an official mission of state, he met Arnauld, a disciple of Descartes who acquainted him with his master's ideas, and Huygens who taught him as to the higher forms of mathematics and their application to physical phenomena. He visited London, where he met Newton, Boyle, and others. At the Hague he came face to face with the other great philosopher of the time, Spinoza. One of Leibniz's cherished ideas was the creation of a society of scholars for the investigation of all branches of scientific truth to combine them into one great system of truth. His philosophy, the work "of odd moments", bears, in content and form, the impress of its haphazard origin and its author's cosmopolitan mode of large number of letters, essays, memoranda, etc., published in various scientific journals. Universality and individuality characterize him both as a man and philosopher.

L. E. J. Brouwer, Intuitionism and formalism. English translation by A. Dresden. Bulletin of the American Mathematical Society, vol. 20 (1913), pp 81-96.

L. E. J. Brouwer, Intuitionisme en Formalisme, Groningen, 1912 ; reprinted in Wiskunde, Waarheid, Werkelijkheid, Groningen, 1919; English translation by A. Dresden, Bulletin of the American Mathematical Society, vol 20 (1913) pp. 81-96.

lemma ::: n. --> A preliminary or auxiliary proposition demonstrated or accepted for immediate use in the demonstration of some other proposition, as in mathematics or logic.

Limit: We give here only some of the most elementary mathematical senses of this word, in connection with real numbers. (Refer to the articles Number and Continuity.)

lines ::: Relatively independent streams or capacities that proceed through levels of development. Howard Gardner’s theory of Multiple Intelligences is one example of the study of developmental lines. There is evidence for over a dozen developmental lines, including cognitive, moral, self-identity, aesthetic, kinesthetic, linguistic, musical, and mathematical. Integral Theory generally classifies these lines according to one of three types: cognitive lines (as studied by Jean Piaget, Robert Kegan, Kurt Fischer, etc.); selfrelated lines (e.g., morals, self-identity, needs, etc.); and capacities or talents (e.g., musical capacity, kinesthetic capacity, introspective capacity). Cognitive development is necessary but not sufficient for development in the self-related lines and appears to be necessary for most of the capacities.

L. Kalmar, On the possibility of definition by recursion, Acta Scientiarum Mathematicarum (Szeged), vol. 9 (1940), pp. 227-232.

L. L. Post, Introduction to a general theory of elementary propositions, American Journal of Mathematics, vol. 43 (1921), pp. 163-185. Truth-value: On the view that every proposition is either true or false, one may speak of a proposition as having one of two truth-values, viz. truth or falsehood. This is the primary meaning of the term truth-value, but generalizations have been consideied according to which there are more than two truth-values -- see propositional calculus, many-valued. -- A.C.

Lmbert is known also for important contributions to mathematics, and astronomy; also for his work in logic, in particular his (unsuccessful, but historically significant) attempts at construction of a mathematical or symbolic logic. Cf. C. I. Lewis, Survey of Symbolic Logic. -- A.C.

Logical meaning: See meaning, kinds of, 3. Logical Positivism: See Scientific Empiricism. Logical truth: See Meaning, kinds of, 3; and Truth, semantical. Logistic: The old use of the word logistic to mean the art of calculation, or common arithmetic, is now nearly obsolete. In Seventeenth Century English the corresponding adjective was also sometimes used to mean simply logical. Leibniz occasionally employed logistica (as also logica mathematica) as one of various alternative names for his calculus ratiocinator. The modern use of logistic (French logistique) as a synonym for symbolic logic (q. v.) dates from the International Congress of Philosophy of 1904, where it was proposed independently by Itelson, Lalande, and Couturat. The word logistic has been employed by some with special reference to the Frege-Russell doctrine that mathematics is reducible to logic, but it would seem that the better usage makes it simply a synonym of symbolic logic. -- A. C.

L. Wittgenstein, Tractatus Logico-Philosophicus, New York and London, 1922. F. P. Ramsey, The foundations of mathematics, Proceedings of the London Mathematical Society, ser. 2, vol. 25 (1926), pp. 338-384; reprinted in his book of the same title, New York and London, 1931.

Main works: De arte combinatoria, 1666 ; Theoria motus concreti et abstracti, 1671 ; Discours de la metaphysique, 1686; Systeme nouveau de la nature, 1695; Nouveaux Essais sur l'entendement humain, 1701 (publ. 1765, criticism of Locke's Essay); Theodicee, 1710; Monadologie, 1714 (letter to Prince Eugene of Savoy). No complete edition of L. exists, but the Prussian Academy of Sciences began one and issued 4 vols. to date. Cf. Gerhardt's edition of L's philosophical works (7 vols., 1875-90) and mathematical works (1849-63), Foucher de Careil's edition, 7 vols. (1859-75), O. Klopp's edition of L.'s historico-political works, 10 vols. (1864-77), L. Couturat's Opuscules et fragments inedits de L., 1903. -- K.F.L.

matha ::: [monastery, hermitage].

mathematical ::: a. --> Of or pertaining to mathematics; according to mathematics; hence, theoretically precise; accurate; as, mathematical geography; mathematical instruments; mathematical exactness.

mathematic ::: a. --> See Mathematical.

mathematician ::: n. --> One versed in mathematics.

mathematics ::: n. --> That science, or class of sciences, which treats of the exact relations existing between quantities or magnitudes, and of the methods by which, in accordance with these relations, quantities sought are deducible from other quantities known or supposed; the science of spatial and quantitative relations.

mathematises ::: to reduce to or as if to mathematical formulas.

mather ::: n. --> See Madder.

mathesis ::: n. --> Learning; especially, mathematics.

mathes ::: n. --> The mayweed. Cf. Maghet.

math ::: n. --> A mowing, or that which is gathered by mowing; -- chiefly used in composition; as, an aftermath.

math&

mathurin ::: n. --> See Trinitarian.

mathusian ::: n. --> A follower of Malthus.

M. Bocher, The fundamental conceptions and methods of mathematics, Bulletin of the American Mathematical Society, vol. 11 (1904), pp. 115-135.

Mean: In general, that which in some way mediates or occupies a middle position among various things or between two extremes. Hence (especially in the plural) that through which an end is attained; in mathematics the word is used for any one of various notions of average; in ethics it represents moderation, temperance, prudence, the middle way. In mathematics:   The arithmetic mean of two quantities is half their sum; the arithmetic mean of n quantities is the sum of the n quantities, divided by n. In the case of a function f(x) (say from real numbers to real numbers) the mean value of the function for the values x1, x2, . . . , xn of x is the arithmetic mean of f(x1), f(x2), . . . , f(xn). This notion is extended to the case of infinite sets of values of x by means of integration; thus the mean value of f(x) for values of x between a and b is ∫f(x)dx, with a and b as the limits of integration, divided by the difference between a and b.   The geometric mean of or between, or the mean proportional between, two quantities is the (positive) square root of their product. Thus if b is the geometric mean between a and c, c is as many times greater (or less) than b as b is than a. The geometric mean of n quantities is the nth root of their product.   The harmonic mean of two quantities is defined as the reciprocal of the arithmetic mean of their reciprocals. Hence the harmonic mean of a and b is 2ab/(a + b).   The weighted mean or weighted average of a set of n quantities, each of which is associated with a certain number as weight, is obtained by multiplying each quantity by the associated weight, adding these products together, and then dividing by the sum of the weights. As under A, this may be extended to the case of an infinite set of quantities by means of integration. (The weights have the role of estimates of relative importance of the various quantities, and if all the weights are equal the weighted mean reduces to the simple arithmetic mean.)   In statistics, given a population (i.e., an aggregate of observed or observable quantities) and a variable x having the population as its range, we have:     The mean value of x is the weighted mean of the values of x, with the probability (frequency ratio) of each value taken as its weight. In the case of a finite population this is the same as the simple arithmetic mean of the population, provided that, in calculating the arithmetic mean, each value of x is counted as many times over as it occurs in the set of observations constituting the population.     In like manner, the mean value of a function f(x) of x is the weighted mean of the values of f(x), where the probability of each value of x is taken as the weight of the corresponding value of f(x).     The mode of the population is the most probable (most frequent) value of x, provided there is one such.     The median of the population is so chosen that the probability that x be less than the median (or the probability that x be greater than the median) is ½ (or as near ½ as possible). In the case of a finite population, if the values of x are arranged in order of magnitude     --repeating any one value of x as many times over as it occurs in the set of observations constituting the population     --then the middle term of this series, or the arithmetic mean of the two middle terms, is the median.     --A.C. In cosmology, the fundamental means (arithmetic, geometric, and harmonic) were used by the Greeks in describing or actualizing the process of becoming in nature. The Pythagoreans and the Platonists in particular made considerable use of these means (see the Philebus and the Timaeus more especially). These ratios are among the basic elements used by Plato in his doctrine of the mixtures. With the appearance of the qualitative physics of Aristotle, the means lost their cosmological importance and were thereafter used chiefly in mathematics. The modern mathematical theories of the universe make use of the whole range of means analyzed by the calculus of probability, the theory of errors, the calculus of variations, and the statistical methods. In ethics, the 'Doctrine of the Mean' is the moral theory of moderation, the development of the virtues, the determination of the wise course in action, the practice of temperance and prudence, the choice of the middle way between extreme or conflicting decisions. It has been developed principally by the Chinese, the Indians and the Greeks; it was used with caution by the Christian moralists on account of their rigorous application of the moral law.   In Chinese philosophy, the Doctrine of the Mean or of the Middle Way (the Chung Yung, literally 'Equilibrium and Harmony') involves the absence of immoderate pleasure, anger, sorrow or joy, and a conscious state in which those feelings have been stirred and act in their proper degree. This doctrine has been developed by Tzu Shu (V. C. B.C.), a grandson of Confucius who had already described the virtues of the 'superior man' according to his aphorism "Perfect is the virtue which is according to the mean". In matters of action, the superior man stands erect in the middle and strives to follow a course which does not incline on either side.   In Buddhist philosophy, the System of the Middle Way or Madhyamaka is ascribed more particularly to Nagarjuna (II c. A.D.). The Buddha had given his revelation as a mean or middle way, because he repudiated the two extremes of an exaggerated ascetlsm and of an easy secular life. This principle is also applied to knowledge and action in general, with the purpose of striking a happy medium between contradictory judgments and motives. The final objective is the realization of the nirvana or the complete absence of desire by the gradual destruction of feelings and thoughts. But while orthodox Buddhism teaches the unreality of the individual (who is merely a mass of causes and effects following one another in unbroken succession), the Madhyamaka denies also the existence of these causes and effects in themselves. For this system, "Everything is void", with the legitimate conclusion that "Absolute truth is silence". Thus the perfect mean is realized.   In Greek Ethics, the doctrine of the Right (Mean has been developed by Plato (Philebus) and Aristotle (Nic. Ethics II. 6-8) principally, on the Pythagorean analogy between the sound mind, the healthy body and the tuned string, which has inspired most of the Greek Moralists. Though it is known as the "Aristotelian Principle of the Mean", it is essentially a Platonic doctrine which is preformed in the Republic and the Statesman and expounded in the Philebus, where we are told that all good things in life belong to the class of the mixed (26 D). This doctrine states that in the application of intelligence to any kind of activity, the supreme wisdom is to know just where to stop, and to stop just there and nowhere else. Hence, the "right-mean" does not concern the quantitative measurement of magnitudes, but simply the qualitative comparison of values with respect to a standard which is the appropriate (prepon), the seasonable (kairos), the morally necessary (deon), or generally the moderate (metrion). The difference between these two kinds of metretics (metretike) is that the former is extrinsic and relative, while the latter is intrinsic and absolute. This explains the Platonic division of the sciences into two classes: those involving reference to relative quantities (mathematical or natural), and those requiring absolute values (ethics and aesthetics). The Aristotelian analysis of the "right mean" considers moral goodness as a fixed and habitual proportion in our appetitions and tempers, which can be reached by training them until they exhibit just the balance required by the right rule. This process of becoming good develops certain habits of virtues consisting in reasonable moderation where both excess and defect are avoided: the virtue of temperance (sophrosyne) is a typical example. In this sense, virtue occupies a middle position between extremes, and is said to be a mean; but it is not a static notion, as it leads to the development of a stable being, when man learns not to over-reach himself. This qualitative conception of the mean involves an adaptation of the agent, his conduct and his environment, similar to the harmony displayed in a work of art. Hence the aesthetic aspect of virtue, which is often overstressed by ancient and neo-pagan writers, at the expense of morality proper.   The ethical idea of the mean, stripped of the qualifications added to it by its Christian interpreters, has influenced many positivistic systems of ethics, and especially pragmatism and behaviourism (e.g., A. Huxley's rule of Balanced Excesses). It is maintained that it is also involved in the dialectical systems, such as Hegelianism, where it would have an application in the whole dialectical process as such: thus, it would correspond to the synthetic phase which blends together the thesis and the antithesis by the meeting of the opposites. --T.G. Mean, Doctrine of the: In Aristotle's ethics, the doctrine that each of the moral virtues is an intermediate state between extremes of excess and defect. -- O.R.M.

mechanics ::: n. --> That science, or branch of applied mathematics, which treats of the action of forces on bodies.

Meinong, Alexius: (1853-1921) Was originally a disciple of Brentano, who however emphatically rejected many of Meinong's later contentions. He claimed to have discovered a new a priori science, the "theory of objects" (to be distinguished from metaphysics which is an empirical science concerning reality, but was never worked out by Meinong). Anything "intended" by thought is an "object". Objects may either "exist" (such as physical objects) or "subsist" (such as facts which Meinong unfortunately termed "objectives", or mathematical entities), they may either be possible or impossible and they may belong either to a lower or to a higher level (such as "relations" and "complexions", "founded" on their simple terms or elements). In the "theory of objects," the existence of objects is abstracted from (or as Husserl later said it may be "bracketed") and their essence alone has to be considered. Objects are apprehended either by self-evident judgments or by "assumptions", that is, by "imaginary judgments". In the field of emotions there is an analogous division since there are also "imaginary" emotions (such as those of the spectator in a tragedy). Much of Meinong's work was of a psychological rather than of a metaphysical or epistemological character. -- H.G.

Metalanguage: A language used to make assertions about another language; any language whose symbols refer to the properties of the symbols of another language. (Formed by analogy with "metamathematics", the study of formalized mathematical systems.) -- M.B.

Metamathematics: See Proof theory, and Syntax, logical. Metaphor: Rhetorical figure transposing a term from its original concept to another and similar one. In its origin, all language was metaphoric; so was poetry. Metaphor is a short fable (Vico). -- L.V.

Metaphysics and psychology are not distinct in Herbert's view. In his day psychology was also philosophy. It was still a metaphysical science in the sense that it is differentiated from physical science. It was only later that psychology repudiated philosophy. Accepting Kant's challenge to make psychology a mathematical science, he developed an elaborate system of mathematical constructions that proved the least fruitful phase of his system. As a mathematical science psychology can use only calculation, not experiment. As the mind or soul is unitary, indivisible. science, including philosophy, is neither analytical nor experimental. Bv denying analysis to psychology, Herbart combatted the division of mind into separate faculties. Psychology is not the mere description of the mind, but the working out of its mathematical laws.

Methodology: The systematic analysis and organization of the rational and experimental principles and processes which must guide a scientific inquiry, or which constitute the structure of the special sciences more particularly. Methodology, which is also called scientific method, and more seldom methodeutic, refers not only to the whole of a constituted science, but also to individual problems or groups of problems within a science. As such it is usually considered as a branch of logic; in fact, it is the application of the principles and processes of logic to the special objects of the various sciences; while science in general is accounted for by the combination of deduction and induction as such. Thus, methodology is a generic term exemplified in the specific method of each science. Hence its full significance can be understood only by analyzing the structure of the special sciences. In determining that structure, one must consider the proper object of the special science, the manner in which it develops, the type of statements or generalizations it involves, its philosophical foundations or assumptions, and its relation with the other sciences, and eventually its applications. The last two points mentioned are particularly important: methods of education, for example, will vary considerably according to their inspiration and aim. Because of the differences between the objects of the various sciences, they reveal the following principal methodological patterns, which are not necessarily exclusive of one another, and which are used sometimes in partial combination. It may be added that their choice and combination depend also in a large degree on psychological motives. In the last resort, methodology results from the adjustment of our mental powers to the love and pursuit of truth. There are various rational methods used by the speculative sciences, including theology which adds certain qualifications to their use. More especially, philosophy has inspired the following procedures:   The Soctattc method of analysis by questioning and dividing until the essences are reached;   the synthetic method developed by Plato, Aristotle and the Medieval thinkers, which involves a demonstrative exposition of the causal relation between thought and being;   the ascetic method of intellectual and moral purification leading to an illumination of the mind, as proposed by Plotinus, Augustine and the mystics;   the psychological method of inquiry into the origin of ideas, which was used by Descartes and his followers, and also by the British empiricists;   the critical or transcendental method, as used by Kant, and involving an analysis of the conditions and limits of knowledge;   the dialectical method proceeding by thesis, antithesis and synthesis, which is promoted by Hegelianlsm and Dialectical Materialism;   the intuitive method, as used by Bergson, which involves the immediate perception of reality, by a blending of consciousness with the process of change;   the reflexive method of metaphysical introspection aiming at the development of the immanent realities and values leading man to God;   the eclectic method (historical-critical) of purposive and effective selection as proposed by Cicero, Suarez and Cousin; and   the positivistic method of Comte, Spencer and the logical empiricists, which attempts to apply to philosophy the strict procedures of the positive sciences. The axiomatic or hypothetico-deductive method as used by the theoretical and especially the mathematical sciences. It involves such problems as the selection, independence and simplification of primitive terms and axioms, the formalization of definitions and proofs, the consistency and completeness of the constructed theory, and the final interpretation. The nomological or inductive method as used by the experimental sciences, aims at the discovery of regularities between phenomena and their relevant laws. It involves the critical and careful application of the various steps of induction: observation and analytical classification; selection of similarities; hypothesis of cause or law; verification by the experimental canons; deduction, demonstration and explanation; systematic organization of results; statement of laws and construction of the relevant theory. The descriptive method as used by the natural and social sciences, involves observational, classificatory and statistical procedures (see art. on statistics) and their interpretation. The historical method as used by the sciences dealing with the past, involves the collation, selection, classification and interpretation of archeological facts and exhibits, records, documents, archives, reports and testimonies. The psychological method, as used by all the sciences dealing with human behaviour and development. It involves not only introspective analysis, but also experimental procedures, such as those referring to the relations between stimuli and sensations, to the accuracy of perceptions (specific measurements of intensity), to gradation (least noticeable differences), to error methods (average error in right and wrong cases), and to physiological and educational processes.

M. H. Stone, The representation of Boolean algebras, Bulletin of the American Mathematical Society. vol. 44 (1938), pp. 807-816.

Mishnah, extra canonical: R. Juda Hanasi included in his Mishnah (now the Mishnah par excellence) selected materials from the older Mishnah-collections, particularly from that of R. Akiba (d. 135 A.D.) and his disciple, R. Meir. In fact, it is assumed that any anonymous statement in the Mishnah is R. Meir's (setam mathnithin R. Meir).

Missing definition "introduction" First, this is an (English language) __computing__ dictionary. It includes lots of terms from related fields such as mathematics and electronics, but if you're looking for (or want to submit) words from other subjects or general English words or other languages, try {(http://wikipedia.org/)}, {(http://onelook.com/)}, {(http://yourdictionary.com/)}, {(http://www.dictionarist.com/)} or {(http://reference.allrefer.com/)}. If you've already searched the dictionary for a computing term and it's not here then please __don't tell me__. There are, and always will be, a great many missing terms, no dictionary is ever complete. I use my limited time to process the corrections and definitions people have submitted and to add the {most frequently requested missing terms (missing.html)}. Try one of the sources mentioned above or {(http://techweb.com/encyclopedia/)}, {(http://whatis.techtarget.com/)} or {(http://google.com/)}. See {the Help page (help.html)} for more about missing definitions and bad cross-references. (2014-09-20)! {exclamation mark}!!!Batch "language, humour" A daft way of obfuscating text strings by encoding each character as a different number of {exclamation marks} surrounded by {question marks}, e.g. "d" is encoded as "?!!!!?". The language is named after the {MSDOS} {batch file} in which the first converter was written. {esoteric programming languages} {wiki entry (http://esolangs.org/wiki/!!!Batch)}. (2014-10-25)" {double quote}

monochord ::: n. --> An instrument for experimenting upon the mathematical relations of musical sounds. It consists of a single string stretched between two bridges, one or both of which are movable, and which stand upon a graduated rule for the purpose of readily changing and measuring the length of the part of the string between them.

Moritz Cantor, Vorlesungen über Geschichte der Mathematik, 4 vols., Leipzig, 1880-1908; 4th edn., Leipzig, 1921.

M. Schönfinkel, Über die Bausteine der mathematischen Logik, Mathematische Annalen, vol. 92 (1924), pp. 305-316.

Multiple Correlation ::: A correlational technique used when there is one X and two or more Y. (Example: the correlation between age and (math and English ability).

multiple ::: n. **1. Math. A number that contains another number an exact number of times. adj. 2.** Having or involving or consisting of more than one part or entity or individual.

Necessity: A state of affairs is said to be necessary if it cannot be otherwise than it is. Inasmuch as the grounds of an assertion of this kind may in general be one of three very distinct kinds, it is customary and valuable to distinguish the three types of necessity affirmed as logical or mathematical necessity, physical necessity, and moral necessity. The distinction between these three was first worked out with precision by Leibniz in his Theodicee.

nematelmia ::: n. pl. --> Same as Nemathelminthes.

nemathecia ::: pl. --> of Nemathecium

nemathecium ::: n. --> A peculiar kind of fructification on certain red algae, consisting of an external mass of filaments at length separating into tetraspores.

Newton's Method: The method of procedure in natural philosophy as formulated by Sir Isaac Newton, especially in his Rules of Reasoning in Philosophy (Mathematical Principles of Natural Philosophy, Book III). These rules are as follows: We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances. Therefore to the same natural effects we must, as far as possible, assign the same causes. The qualities of bodies, which admit neither intension nor remission of degrees, and which are found to belong to all bodies within the reach of our experiments, are to be esteemed the universal qualities of all bodies whatsoever. In experimental philosophy we are to look upon propositions collected by general induction from phaenomena as accurately or very nearly true, notwithstanding any contrary hypotheses that may be imagined, till such time as other phaenomena occur, by which they may either be made more accurate, or liable to exceptions. To this passage should be appended another statement from the closing pages of the same work. "I do not make hypotheses; for whatever is not deduced from the phaenomena is to be called an hypothesis; and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy." -- A.C.S.

Nolini: “The image is that of the comoposition of an army or that of a mathematical series (e.g., arithmetical or geometrical progression). It is composed of regularised uits of different values (group of sums), but all measured and definite and precise—e.g.., in the case of an army—company, brigade, battalion, army—an ascending scale, the whole also forming one big unit, taken in at a single glance—that is the nature of overmind vision.

Null class: See Logic, formal, §7. Number: The number system of mathematical analysis may be described as follows -- with reference, not to historical, but to one possible logical order.

Numerous solutions of these paradoxes have been proposed. Many, however, have the fault that, while they purport to find a flaw in the arguments leading to the paradoxes, no effective criterion is given by which to discover in the case of other (e.g., mathematical) proofs whether they have the same flaw.

of or pertaining to geometry, the branch of mathematics that deals with the deduction of the properties, measurement, and relationships of points, lines, angles, and figures in space.

operand ::: n. --> The symbol, quantity, or thing upon which a mathematical operation is performed; -- called also faciend.

opsimathy ::: n. --> Education late in life.

Other figures worthy of mention who fit wholly into none of the above currents of thought are Raymond Lull (+1315), an active opponent of Averroism and the inventor of the famous Ars magna which intrigued young Leibnitz; Roger Bacon (+c. 1293) who under the influence of Platonism, furthered the mathematical and experimental methods; William of Moerbeke (+1286), one of the greatest philologists of the M.A., who greatly improved the translations of Aristotelian and Neoplatonic literature by consulting directly Greek sources; the first proponents of the via moderna doctrine in Logic, William Shyreswood (+1249) and Petrus Hispanus (+1277).

Pascal, Blaise: (1623-1662) French philosopher mathematician and scientist. He conducted scientific researches including experiments on atmospheric pressure and invented an ingenious calculating machine. He turned from preoccupation with the scientific to the study of man and his spiritual problems and found faith as a sounder guide than reason. At this stage of his thought, theology becomes central. These thoughts are developed in his Provincial Letters and in his posthumously published masterpieces of style, the Pensees. -- L.E.D.

P. Bernays, Sur le platonisme dans les mathematiques, and Quelques points essentiels de la metamathematique, l'Enseignement Mathematique, vol. 34 (1935), pp. 52-95.

Peano, Giuseppe, 1858-1932, Italian mathematician. Professor of mathematics at the University of Turin, 1890-1932. His work in mathematical logic marks a transition stage between the old algebra of logic and the newer methods. It is inferior to Frege's by present standards of rigor, but nevertheless contains important advances, among which may be mentioned the distinction between class inclusion (⊂) and class membership (∈) -- which had previously been confused -- and the introduction of a notation for formation of a class by abstraction (q. v.). His logical notations are more convenient than Frege's, and many of them are still in common use.

Peano is known also for other contributions to mathematics, including the discoverv of the area filling curve which bears his name, and for his advocacy of Latino sine flexione as an international language. -- A.C.

Peano's first publication on mathematicil logic was the introduction to his Calcolo Geometrico, 1888. His postulates for arithmetic (see arithmetic, foundations of) appeared in his Arith¦metices Principia (1889) and in revised form in Sul concetto di numero (Rivista di Matematica, vol. 1 (1891)), and were repeated in successive volumes (more properly, editions) of his Formulaire de Mathematiques (1894-1908). The last-named work, written with the aid of collaborators, was intended to provide a reduction of all mathematics to symbolic notation, and often the encyclopedic aspect was stressed as much as, or more than, that of logical analysis.

P. E. B. Jourdain, Giuseppe Peano, The Quarterly Journal of Pure and Applied Mathematics, vol. 43 (1912), pp. 270-314.

P.E.B. Jourdain, Gottlob Frege, The Quarterly Journal of Pure and Applied Mathematics, vol. 43 (1912), pp. 237-269.

pharmacognosis ::: n. --> That branch of pharmacology which treats of unprepared medicines or simples; -- called also pharmacography, and pharmacomathy.

pharmacomathy ::: n. --> See Pharmacognosis.

philomathematic ::: n. --> A philomath.

philomathic ::: a. --> Of or pertaining to philomathy.
Having love of learning or letters.


philomath ::: n. --> A lover of learning; a scholar.

philomathy ::: n. --> The love of learning or letters.

Philosophers have in the past been concerned with two questions covered by our definition, though attempts to organize the subject as an autonomous department of philosophy are of recent date. Enquiries into the origin of language (e.g. in Plato's Kratylos) once a favorite subject for speculation, are now out of fashion, both with philosophers and linguists. Enquiries as to the nature of language (as in Descartes, Leibniz, and many others) are, however, still central to all philosophical interest in language. Such questions as "What are the most general characters of symbolism?", "How is 'Language' to be defined?", "What is the essence of language?", "How is communication possible?", "What would be the nature of a perfect language?", are indicative of the varying modulations which this theme receives in the works of contemporaries.   Current studies in the philosophy of language can be classified under five hends:   Questions of method, relation to other disciplines, etc. Much discussion turns here upon the proposal to establish a science and art of symbolism, variously styled semiotic, semantics or logical syntax,   The analysis of meaning. Problems arising here involve attention to those under the next heading.   The formulation of general descriptive schemata. Topics of importance here include the identification and analysis of different ways in which language is used, and the definition of men crucial notions as "symbol'', "grammar", "form", "convention", "metaphor", etc.   The study of fully formalized language systems or "calculi". An increasingly important and highly technical division which seeks to extend and adapt to all languages the methods first developed in "metamathematics" for the study of mathematical symbolism.   Applications to problems in general philosophy. Notably the attempt made to show that necessary propositions are really verbal; or again, the study of the nature of the religious symbol. Advance here awaits more generally acceptable doctrine in the other divisions.   References:

physico-mathematics ::: n. --> Mixed mathematics.

Physics: (Gr. physis, nature) In Greek philosophy, one of the three branches of philosophy, Logic and Ethics being the other two among the Stoics (q.v.). In Descartes, metaphysics is the root and physics the trunk of the "tree of knowledge." Today, it is the science (overlapping chemistry, biology and human physiology) of the calculation and prediction of the phenomena of motion of microscopic or macroscopic bodies, e.g. gravitation, pressure, heat, light, sound, magnetism, electricity, radio-activity, etc. Philosophical problems arise concerning the relation of physics to biological and social phenomena, to pure mathematics, and to metaphysics. See Mechanism, Physicalism.. Physis: See Nature, Physics. Picturesque: A modification of the beautiful in English aesthetics, 18th century. -- L.V.

pisaca-asura (pishacha-asura; pisacha-asura; pisacha asura) ::: the pisaca-asura pisaca stage of the asura, which evolves in the second and third manvantaras of the sixth pratikalpa. pis pisaca-pramatha

Plato: (428-7 - 348-7 B.C.) Was one of the greatest of the Greek philosophers. He was born either in Athens or on the island of Aegina, and was originally known as Aristocles. Ariston, his father, traced his ancestry to the last kings of Athens. His mother, Perictione, was a descendant of the family of Solon. Plato was given the best elementary education possible and he spent eight years, from his own twentieth year to the death of Socrates, as a member of the Socratic circle. Various stories are told about his supposed masters in philosophy, and his travels in Greece, Italy, Sicily and Egypt, but all that we know for certain is that he somehow acquired a knowledge of Pythagoreanisrn, Heracleitanism, Eleaticism and othei Pre-Socratic philosophies. He founded his school of mathematics and philosophy in Athens in 387 B.C. It became known as the Academy. Here he taught with great success until his death at the age of eighty. His career as a teacher was interrupted on two occasions by trips to Sicily, where Plato tried without much success to educate and advise Dionysius the Younger. His works have been very well preserved; we have more than twenty-five authentic dialogues, certain letters, and some definitions which are probably spurious. For a list of works, bibliography and an outline of his thought, see Platonism. -- V.J.B.

Platonic Realism: See Realism. Platonism: The philosophy of Plato marks one of the high points in the development of Greek philosophical genius Platomsm is characterised by a partial contempt for sense knowledge and empirical studies, by a high regard for mathematics and its method, by a longing for another and better world, by a frankly spiritualistic view of life, by its use of a method of discussion involving an accumulation of ever more profound insights rather than the formal logic of Aristotle, and, above all, by an unswerving faith in the capacity of the human mind to attain absolute truth and to use this truth in the rational direction of human life and affairs.

Plato's theory of knowledge can hardly be discussed apart from his theory of reality. Through sense perception man comes to know the changeable world of bodies. This is the realm of opinion (doxa), such cognition may be more or less clear but it never rises to the level of true knowledge, for its objects are impermanent and do not provide a stable foundation for science. It is through intellectual, or rational, cognition that man discovers another world, that of immutable essences, intelligible realities, Forms or Ideas. This is the level of scientific knowledge (episteme); it is reached in mathematics and especially in philosophy (Repub. VI, 510). The world of intelligible Ideas contains the ultimate realities from which the world of sensible things has been patterned. Plato experienced much difficulty in regard to the sort of existence to be attributed to his Ideas. Obviously it is not the crude existence of physical things, nor can it be merely the mental existence of logical constructs. Interpretations have varied from the theory of the Christian Fathers (which was certainly not that of Plato himself) viz , that the Ideas are exemplary Causes in God's Mind, to the suggestion of Aristotle (Metaphysics, I) that they are realized, in a sense, in the world of individual things, but are apprehended only by the intellect The Ideas appear, however, particularly in the dialogues of the middle period, to be objective essences, independent of human minds, providing not only the foundation for the truth of human knowledge but afso the ontological bases for the shadowy things of the sense world. Within the world of Forms, there is a certain hierarchy. At the top, the most noble of all, is the Idea of the Good (Repub. VII), it dominates the other Ideas and they participate in it. Beauty, symmetry and truth are high-ranking Ideas; at times they are placed almost on a par with the Good (Philebus 65; also Sympos. and Phaedrus passim). There are, below, these, other Ideas, such as those of the major virtues (wisdom, temperance, courage, justice and piety) and mathematical terms and relations, such as equality, likeness, unlikeness and proportion. Each type or class of being is represented by its perfect Form in the sphere of Ideas, there is an ideal Form of man, dog, willow tree, of every kind of natural object and even of artificial things like beds (Repub. 596). The relationship of the "many" objects, belonging to a certain class of things in the sense world, to the "One", i.e. the single Idea which is their archetype, is another great source of difficulty to Plato. Three solutions, which are not mutually exclusive, are suggested in the dialogues (1) that the many participate imperfectly in the perfect nature of their Idea, (2) that the many are made in imitation of the One, and (3) that the many are composed of a mixture of the Limit (Idea) with the Unlimited (matter).

Poincare, Henri: (1854-1912) French mathematician and mathematical physicist to whom many important technical contributions are due. His thought was occupied by problems on the borderline of physics and philosophy. His views reflect the influence of positivism and seem to be closely related to pngmatism. Poincare is known also for his opposition to the logistic method in the foundations of mathematics, especially as it was advocated by Bertrand i (q.v.) and Louis Couturat, and for his proposed resolution of the logical paradoxes (q.v.) by the prohibition of impredicattve definition (q.v.). Among his books, the more influential are Science and Hypothesis, Science and Method, and Dernieres Pensees. -- R.B.W.

polymathic ::: a. --> Pertaining to polymathy; acquainted with many branches of learning.

polymathist ::: n. --> One versed in many sciences; a person of various learning.

polymathy ::: n. --> The knowledge of many arts and sciences; variety of learning.

Positivism: First associated with the doctrine of Auguste Comte that the highest form of knowledge is simple description presumably of sensory phenomena. The doctrine was based on an evolutionary "law of three stages", believed by Comte to have been discovered by him in 1822 but anticipated by Turgot in 1750. The three stages were the theological, in which anthropomorphic wills were resorted to to explain natural events, the metaphysical, in which these wills were depersonalized and became forces and essences, and finally the positive. It should be noted that positivistic description was supposed to result in mathematical formulas, not in introspective psychology. See Scientific Empiricism I. -- G.B.

Postulate: See Mathematics. Potency: (Scholastic) Potency is opposed to act as asserted of being. It means the capacity of being or of being thus. Prime matter (q.v.) is pure potency, indetermined in regard to actual corporeal being. Any change or development or, generally, becoming presupposes a corresponding potency. Some potencies belong to the nature of a thing, others are merely passive and consist in non-repugnance. Thus to be thrown is not due to a potency strictly speaking in the stone which has, in regard to this a "merely obediential" potency. The first kind is also called operative potency. -- R.A.

pramatha ::: a kind of being on the lower vital plane, related to the pisaca; the fourth of the ten types of consciousness (dasa-gavas) in the evolutionary scale: mind concentrated on the heart and the emotional and aesthetic part of the citta.

pramatha-asura (pramatha-asura) ::: the pramatha stage of the asura, which evolves in the fourth manvantara of the sixth pratikalpa. pramatha-r pramatha-raksasa

pramathanatha ::: lord of the demoniac, [Siva].

pramatha ::: [one of a class of demons attending on Siva].

pramathesvari (pramatheswari) ::: Kali as ruler of the emotional mind pramathesvari (pramatha).

Probability: In general Chance, possibility, contingency, likelihood, likehness, presumption. conjecture, prediction, forecast, credibility, relevance; the quality or state of being likely true or likely to happen; a fact or a statement which is likely true, real, operative or provable by future events; the conditioning of partial or approximate belief or assent; the motive of a presumption or prediction; the conjunction of reasonable grounds for presuming the truth of a statement or the occurrence of an event; the field of knowledge between complete ignorance and full certitude; an approximation to fact or truth; a qualitative or numerical value attached to a probable inference, and by extension, the systematic study of chances or relative possibilities as forming the subject of the theory of probability. A. The Foundation of Probability. We cannot know everything completely and with certainty. Yet we desire to think and to act as correctly as possible hence the necessity of considering methods leading to reasonable approximations, and of estimating their results in terms of the relative evidence available in each case. In D VI-VII (infra) only, is probability interpreted as a property of events or occurrences as such: whether necessary or contingent, facts are simply conditioned by other facts, and have neither an intelligence nor a will to realize their certainty or their probability. In other views, probability requires ultimately a mind to perceive it as such it arises from the combination of our partial ignorance of the extremely complex nature and conditions of the phenomena, with the inadequacy of our means of observation, experimentation and analysis, however searching and provisionally satisfactory. Thus it may be said that probability exists formally in the mind and materially in the phenomena as related between themselves. In stressing the one or the other of these two aspects, we obtain (1) subjectize probability, when the psychological conditions of the mind cause it to evaluate a fact or statement with fear of possible error; and (2) objective probability, when reference is made to that quality of facts and statements, which causes the mind to estimate them with a conscious possibility of error. Usually, methods can be devised to objectify technically the subjective aspect of probability, such as the rules for the elimination of the personal equation of the inquirer. Hence the methods established for the study and the interpretation of chances can be considered independently of the state of mind as such of the inquirer. These methods make use of rational or empirical elements. In the first case, we are dealing with a priori or theoretical probability, which considers the conditions or occurrences of an event hypothetically and independently of any direct experience. In the second case, we are dealing with inductive or empirical probability. And when these probabilities are represented with numerals or functions to denote measures of likelihood, we are concerned with quantitative or mathematical probability. Methods involving the former cannot be assimilated with methods involving the latter, but both can be logically correlated on the strength of the general principle of explanation, that similar conjunctions of moral or physical facts demand a general law governing and justifying them.

proficient ::: n. --> One who has made considerable advances in any business, art, science, or branch of learning; an expert; an adept; as, proficient in a trade; a proficient in mathematics, music, etc. ::: a. --> Well advanced in any branch of knowledge or skill; possessed of considerable acquirements; well-skilled; versed; adept,

promorphology ::: n. --> Crystallography of organic forms; -- a division of morphology created by Haeckel. It is essentially stereometric, and relates to a mathematical conception of organic forms. See Tectology.

Proof by cases: Represented in its simplest form by the valid inference of the propositional calculus, from A ⊃ C and B ⊃ C and A ∨ B to C. More complex forms involve multiple disjunctions, e.g., the inference from A ⊃ D and B ⊃ D and C⊃ D and [A ∨ B] ∨ C to D. The simplest form of proof by cases is thus the same as the simple constructive dilemma (see Logic, formal, § 2), the former term deriving from mathematical usage and the latter from traditional logic. For the more complex forms of proof by cases, and like generalizations of the other kinds of dilemma to the case of more than two major premisses, logicians have devised the names trilemma, tetralemma, polylemma -- but these are not much found in actual use. -- A.C.

Proof theory: The formalization of mathematical proof by means of a logistic system (q. v.) makes possible an objective theory of proofs and provability, in which proofs are treated as concrete manipulations of formulas (and no use is made of meanings of formulas). This is Hilbert's proof theory, or metamathematics. p A central problem of proof theory, according to Hilbert, is the proof of consistency of logistic systems adequate to mathematics or substantial parts of mathematics. -- A logistic system is said to be consistent, relatively to a particular notation in the system called negation, if there is no formula A such that both A and the negation of A are provable (i.e., are theorems). The systems with which Hilbert deals, and the notations in them which he wishes to call negation, are such that, if a formula A and its negation were once proved, every propositional formula could be proved; hence he is able to formulate the consistency by snying that a particular formula (e.g., ∼[0 = 0]) is not provable.

protractor ::: n. --> One who, or that which, protracts, or causes protraction.
A mathematical instrument for laying down and measuring angles on paper, used in drawing or in plotting. It is of various forms, semicircular, rectangular, or circular.
An instrument formerly used in extracting foreign or offensive matter from a wound.
A muscle which extends an organ or part; -- opposed to


Pythagoreanism: The doctrines (philosophical, mathematical, moral, and religious) of Pythagoras (c. 572-497) and of his school which flourished until about the end of the 4th century B.C. The Pythagorean philosophy was a dualism which sharply distinguished thought and the senses, the soul and the body, the mathematical forms of things and their perceptible appearances. The Pythagoreans supposed that the substances of all things were numbers and that all phenomena were sensuous expressions of mathematical ratios. For them the whole universe was harmony. They made important contributions to mathematics, astronomv, and physics (acoustics) and were the first to formulate the elementary principles and methods of arithmetic and geometry as taught in the first books of Euclid. But the Pythagorean sect was not only a philosophical and mathematical school (cf. K. von Fritz, Pythagorean Politics in Southern Italy, 1941), but also a religious brotherhood and a fellowship for moral reformation. They believed in the immortality and transmigration (see Metempsychosis) of the soul which they defined as the harmony of the body. To restore harmony which was confused by the senses was the goal of their Ethics and Politics. The religious ideas were closely related to those of the Greek mysteries which sought by various rites and abstinences to purify and redeem the soul. The attempt to combine this mysticism with their mathematical philosophy, led the Pythagoreans to the development of an intricate and somewhat fantastic symbolism which collected correspondences between numbers and things and for example identified the antithesis of odd and even with that of form and matter, the number 1 with reason, 2 with the soul, etc. Through their ideas the Pythagoreans had considerable effect on the development of Plato's thought and on the theories of the later Neo-platonists.

Rationalism: A method, or very broadly, a theory of philosophy, in which the criterion of truth is not sensory but intellectual and deductive. Usually associated with an attempt to introduce mathematical methods into philosophy, as in Descartes, Leibniz and Spinoza. -- V.J.B.

R. Carnap, Die logizistische Grundlegung der Mathematik, Erkenntnis, vol. 2 (1931), pp. 91-105, 141-144, 145.

R. Carnap, The Logical Syntax of Language, New York and London, 1937. Review by S. MacLane, Bulletin of the American Mathematical Society, vol. 44 (1938), pp. 171-176. Review by S. C. Kleene, The Journal of Symbolic Logic, vol. 4 (1939), pp. 82-87.

Recursion, proof by, or, as it is more often called, proof by mathematical induction or complete induction, is in its simplest form a proof that every non-negative integer possesses a ceirtain property by showing that 0 possesses this property, and that, on the hypothesis that the non-negative integer x possesses this property, then x+1 possesses this property. (The condition (2) is often expressed, following Frege and Russell, by saying that the property is hereditary in the series of non-negative integers.) The name proof by recursion, or proof by mathematical or complete induction, is also given to various similar but more complex forms.

Reducibility, axiom of: An axiom which (or some substitute) is necessary in connection with the ramified theory of types (q.v.) if that theory is to be adequate for classical mathematics, but the admissibility of which has been much disputed (see Paradoxes, logical). An exact statement of the axiom can be made only in the context of a detailed formulation of the ramified theory of types -- which will not here be undertaken. As an indication or rough description of the axiom of reducibility, it may be said that it cancels a large part of ihe restrictive consequences of the prohibition against impredicative definition (q.v.) and, in approximate effect, reduces the ramified theory of types to the simple theory of types (for the latter see Logic, formal, § 6). -- A.C.

Rejected in particular by intuitionism are the use of impredicative definition (q. v.); the assumption that all things satisfying a given condition can be united into a set and this set then treated as an individual thing --or even the weakened form of this assumption which is found in Zermelo's Aussonderungsaxiom or axiom of subset formation (see logic, formal, § 9); the law of excluded middle as applied to propositions whose expression lequires a quantifier for which the variable involved has an infinite range. As an example of the rejection of the law of excluded middle, consider the proposition, "Either every even number greater than 2 can be expressed as the sum of two prime numbers or else not every even number greater than 2 can be expressed as the sum of two prime numbers." This proposition is intuitionistically unacceptable, because there are infinitely many even numbers greater than 2 and it is impossible to try them all one by one and decide of each whether or not it is the sum of two prime numbers. An intuitionist would accept the disjunction only after a proof had been given of one or other of the two disjoined propositions -- and in the present state of mathematical knowledge it is not certain that this can be done (it is not certain that the mathematical problem involved is solvable). If, however, we replace "greater than 2" by "greater than 2 and less than 1,000,000,000," the resulting disjunction becomes intuitionistically acceptable, since the number of numbers involved is then finite. The intuitionistic rejection of the law of excluded middle is not to be understood as an assertion of the negation of the law of excluded middle; on the contrary, Brouwer asserts the negation of the negation of the law of excluded middle, i.e., ∼∼[p ∨ ∼p]. Still less is the intuitionistic rejection of the law of excluded middle to be understood as the assertion of the existence of a third truth-value intermediate between truth and falsehood.

Relativity, theory of: A mathematical theory of space-time (q.v.), of profound epistemological as well as physical importance, comprising the special theory of relativity (Einstein, 1905) and the general theory of relativity (Einstein, 1914-16). The name arises from the fact that certain things which the classical theory regarded as absolute -- e.g. , the simultaneity of spatially distant events, the time elapsed between two events (unless coincident in space-time), the length of an extended solid body, the separation of four-dimensional space-time into a three-dimensional space and a one-dimensional time -- are regarded by the relativity theory as relative (q.v.) to the choice of a coordinate system in space-time, and thus relative to the observer. But on the other hand the relativity theory represents as absolute certain things which are relative in the classical theory -- e.g., the velocity of light in empty space. See Non-Euclidean geometry. -- A.C.

R. Harlev, George Boole, F.R.S., The British Quarterly Review, vol. 44 (1866). pp 141-181 Anon., George Boole, Proceedings of the Royal Society of London, vol. 15 (1867). Obituary notices of fellows deceased, pp. vi-xi. P.E.B. Jourdain, George Boole, The Quarterly Journal of Pure and Applied Mathematics, vol. 41 (1910), pp. 332-352.

rowen ::: n. --> A stubble field left unplowed till late in the autumn, that it may be cropped by cattle.
The second growth of grass in a season; aftermath.


R. Peter, a series of papers (in German) (in the Mathematische Annale, vol. 110 (1934), pp. 612-632; vol. 111 (1935), pp. 42-60; vol. 113 (1936), pp. 489-527. S. C. Kleene, General recursive functions of natural numbers, Mathematische Annalen, vol. 112 (1936), pp. 727- 742. S. C. Kleene, On notation for ordinal numbers, The Journal of Symbolic Logic, vol. 3 (1938), pp. 150-155.

Rule of inference: See logic, formal, §§ 1, 3, and logistic system. Russell, Bertrand A. W.: (1872-) Fellow Trinity College, Cambridge, 1895; lecturer in philosophy, University of Cambridge, 1910-1916. Author of: The Philosophy of Leibniz, 1900; The Principles of Mathematics, 1903; Principia Mathematica (in collaboration with A. N. Whitehead), 3 vols. 1910-13, (second edition, 1925-27); The Problems of Philosophy, 1912; Our Knowledge of the External World, 1914; Introduction to Mathematical Philosophy, 1918; The Analysis of Mind, 1921; The Analysis of Matter, 1927; An Outline of Philosophy, 1928; An Inquiry into Meaning and Truth, 1940. Also numerous other works on philosophy, politics and education, outrageously attacked by reactionaries.

Russell's solution of the paradoxes is embodied in what is now known as the ramified theory of types, published by him in 1908, and afterwards made the basis of Principia Mathematica. Because of its complication, and because of the necessity for the much-disputed axiom of reducibility, this has now been largely abandoned in favor of other solutions.

scheme ::: n. --> A combination of things connected and adjusted by design; a system.
A plan or theory something to be done; a design; a project; as, to form a scheme.
Any lineal or mathematical diagram; an outline.
A representation of the aspects of the celestial bodies for any moment or at a given event.


Schlick, Moritz: (1882-1936) Taught at Rostock, Kiel, Vienna, also visit, prof.; Stanford, Berkeley. Founder of the Vienna Circle (see Scientific empiricism.) Called his own view "Consistent Empiricism." Main contributions: A logically revised correspondence view of the nature of truth. A systematic epistemology based on the distinction of (immediate) experience and (relational) knowledge. Clarified the analytic -- a priori character of logic and mathematics (by disclosing the "implicit definitions" in postulate systems). Repudiation of Kantian and phenomenological (synthetic) apriorism. Physicalistic, epistemological solution of the psycho-physical problem in terms of a double language theory. Earlier critical-realistic views were later modified and formulated as Empirical Realism. Greatly influenced in this final phase by Carnap and especially Wittgenstein, he considered the logical clarification of meanings the only legitimate task of a philosophy destined to terminate the strife of systems. Important special applications of this general outlook to logic and methodology of science (space, time, substance, causality, probability, organic life) and to problems of ethics (meaning of value judgments, hedonism, free-will, moral motivation). An optimistic, poetic view of the meaning of life is expressed in only partly published writings on a "Philosophy of Youth."

Schröder, (Friedrich Wilhelm Karl) Ernst, 1841-1902. German mathematician. Professor of mathematics at Karlsruhe, 1876-1902. His three-volume Algebra der Logik (1890-1895, with a posthumous second part of vol. 2 published in 1905) is an able compendium and systematization of the work of his predecessors. With contributions of his own, and may be regarded as giving in nearly all essentials the final form of the Nineteenth Century algebra of logic (q.v.), including the algebra of relatives (or relations). -- A.C.

Scotism: from the standpoints of number and influence, this was the next most important school of this period. Among the pupils of Duns Scotus, may be mentioned Anthony Andreas (+1320), Francis of Meyronnes (de Mayronis) (+1325) and John de Bassolis (+1347). Walter Burleigh (+1343) was a vigorous opponent of Nominalism; Thomas Bradwardine (+1349), a mathematician and philosopher whose determinism influenced John Wiclif (+1384), John Hus and the German reformers. In the XV cent., this school is represented by William of Vaurouillon (+1464), Nicholas of Orbelhs (+1455), John Anglicus, Thomas Bricot and the great Peter Tartaret (+1494).

Scotism: The philosophical and theological system named after John Duns Scotus (1266? -1308), Doctor Subtilis, a Franciscan student and later professor at Oxford and Paris and the most gifted of the opponents of the Thomist school. The name is almost synonymous with subtlety and the system generally is characterized by excessive criticism, due to Duns Scotus' predilection for mathematical studies -- the influence, perhaps, of his Franciscan predecessor, Roger Bacon, upon him. This spirit led Scotus to indiscriminate attack upon all his great predecessors in both Franciscan and Dominican Schools, especially St. Thomas, upon the ground of the inconclusiveness of their philosophical arguments. His own system is noted especially for its constant use of the so called Scotist or formal distinction which is considered to be on the one hand less than real, because it is not between thing and thing, and yet more than logical or virtual, because it actually exists between various thought objects or "formalities" in one and the sime individual prior to the action of the mind -- distinctio formalis actualis ex natuta rei. e g., the distinction between the essence and existence, between the animality and rationality in a man, between the principle of individuation in him and his matter and form, and between the divine attributes in God, are all formal distinctions. This undoubtedly leaves the system open to the charge of extreme realism and a tendency generally to consider the report of abstract thought with little regard for sense experience. Further by insisting also upon a formal unity of these formalities which exists apart from conception and is therefore apparently real, the system appears to lead logically to monism, e.g., the really distinct materiality in all material things is formally one apart from the abstracting and universalizing activity of the mind. By insisting that this formal unity is less than real unity, the Scotists claim to escape the charge.

sector ::: n. --> A part of a circle comprehended between two radii and the included arc.
A mathematical instrument, consisting of two rulers connected at one end by a joint, each arm marked with several scales, as of equal parts, chords, sines, tangents, etc., one scale of each kind on each arm, and all on lines radiating from the common center of motion. The sector is used for plotting, etc., to any scale.
An astronomical instrument, the limb of which embraces a


See Mathematics, and Non-Euclidean geometry. For a very brief outline of the foundations of plane Euclidean geometry, both from the synthetic and the analytic viewpoint, see the appendix to Eisenhart's book cited below. A more complete account is given bv Forder. -- A.C.

Sextus Empiricus: A physician who lived about 200 A.D. His writings contain numerous arguments of a sceptical empiricistic variety drawn from Pyrrho (q.v.) and directed against dogmatic claims to absolute truth, especially in the sciences and ethics. His Adversus Mathematicos (Against the Mathematicians) is an important source for the history of the sciences of astronomy, geometry, and grammar as well is of the Stoic theology of the period. -- M.F.

Signate: (In Schol.) Refers to the intention or direction of the agent; as distinguished from exercite, which refers to the effects of the work or the exercise. E.g., one who studies mathematics, signate intends to acquire the knowledge of truths concerning quantity, -- but exercite, or in the exercise itself of studying, renders the mind more able and apt for reasoning rightly. -- H.G.

sign ::: n. 1. An act or gesture used to convey an idea, a desire, information, or a command. 2. Any object, action, event, pattern, etc., that conveys a meaning. 3. A mark used to mean something; a symbol that sets something apart from others of its kind. 4. Something that indicates or acts as a token of a fact, condition, etc., that is not immediately or outwardly observable. 5. A signal. 6. A conventional figure or device that stands for a word, phrase, or operation; a symbol, as in mathematics or in musical notation. 7. A displayed structure such as a banner bearing lettering or symbols. 8. An act or significant event that is experienced as indication of divine intervention. 9. A portent of things to come. Sign, sign"s, signs, signless, sign-burdened, flame-signs. v. 10. To affix one"s signature to. 11. To indicate by or as if by a sign; betoken. signs, signed, signing.

Simple conversion of a proposition, A, E, I, or O, consists in interchanging S and P without other change. Thus the converse of S(x) ⊃x P(x) is P(x) ⊃x S(x), and the converse of S(x) ⊃x ∼P(x) is P(x) ⊃x ∼S(x). In mathematics the term converse is used primarily for the simple converse of a proposition A; loosely also for any one of a number of transformations similar to this (e.g., F(x)G(x) ⊃x H (x) may be said to have the converse F(x)H(x) ⊃x G(x)). Simple conversion of a proposition is a valid inference, in general, only in the case of E and I.

skill ::: n. --> Discrimination; judgment; propriety; reason; cause.
Knowledge; understanding.
The familiar knowledge of any art or science, united with readiness and dexterity in execution or performance, or in the application of the art or science to practical purposes; power to discern and execute; ability to perceive and perform; expertness; aptitude; as, the skill of a mathematician, physician, surgeon, mechanic, etc.


solution ::: n. --> The act of separating the parts of any body, or the condition of undergoing a separation of parts; disruption; breach.
The act of solving, or the state of being solved; the disentanglement of any intricate problem or difficult question; explanation; clearing up; -- used especially in mathematics, either of the process of solving an equation or problem, or the result of the process.
The state of being dissolved or disintegrated;


Space: In Aristotle, the container of all objects. In the Cambridge Platonists, the sensorium of God. In Kant: the a priori form of intuition of external phenomena. In modern math., name for certain abstract invariant gioups or set's. See Space-Time. -- P.P.W.

Space-perception: (Lat. spatium) The apprehension of the spatial properties and relations of the concrete objects of ordinary sense perception in contrast to the conceptual knowledge of the abstract spaces of physics and mathematics. Theories of space-perception are: a) nativistic, when they endow the mind with a primitive intuition of space which becomes qualitatively differentiated through sense experience; b) empirical, when they assume that perceptual space emerges fiom the correlation of the spatial features of the different senses. -- L.W.

Space-Time: The four-dimensional continuum including the three dimensions of space (length, width and height) and one of time; the unity of space and time. The concept was first suggested by H. Minkowski and immediately afterward incorporated by A. Einstein into his (special) theory of relativity. The former contended that nothing can exist or be conceived of as physical apart from space-time; for every object must have not only length, width and height, but also duration in time. As a result, a complete description and location of an object must be given in terms of four coordinates. Space-Time is mathematically grounded in world-points, or durationless geometrical points, as the foundation of all four-dimensional measurement; and in world-lines, or geometrical lines cutting across the four dimensions. An enduring geometrical point thus beconus a geometrical line (or possibly a curve) in space-time. Space-Time is physically conceived of as a general structure determined by the relationship among world-events, or four-dimensional events. The universe of four dimensions (the omniverse, as it may be called) includes space with all of its events and objects as well as time with its changes and motions. As such this four-dimensional universe must be changeless and motionless, insofar as things move and change only when taken in abstraction from time, or rather when space and time are regarded as separate.

spermathecae ::: pl. --> of Spermatheca

spermatheca ::: n. --> A small sac connected with the female reproductive organs of insects and many other invertebrates, serving to receive and retain the spermatozoa.

straight ::: a. --> A variant of Strait, a. ::: superl. --> Right, in a mathematical sense; passing from one point to another by the nearest course; direct; not deviating or crooked; as, a straight line or course; a straight piece of timber.
Approximately straight; not much curved; as,


T'ai yang: The Major Mode of Activity See T'ai Chi. T'ai yin: The Major Mode of Passivity. See T'ai Chi. Tai Tung-yuan: (Tai Chen, Tai Shen-hsiu, 1723-1777) carne from a poor family, self-made to be a leader in outstanding intellectual activities of the time, and became an authority in philology, mathematics, geography as well as philosophy. By reinteipreting the teachings of Mencius, he attempted to rediscover the original meanings of Confucius and Mencius. His Tai-shih I-shu (works) consists of 31 chuans in several volumes. -- W.T.C.

Telesio, Bernardino: (1508-1588) was one of the fathers of the scientific movement of the Renaissance. He was born at Cosenza, near Naples, studied philosophy and mathematics at Padua, and natural science at Rome. The Academia Telesiana, which he founded it Naples, stressed empirical methods and Telesio tried to explain all physical phenomena in terms of heat and cold, as expanding and contracting forces in matter. He wrote De Natuta rerum juxta propria principia (1570), ed. V Spampanato, 2 vol. (Modena-Genoa, 1911-13). -- V.J.B.

term ::: 1. A limited period of time. 2. A member or item of a mathematical expression; each of the things constituting a series; an element of any complex whole. 3. A boundary or extreme limit. 4. A word or expression used for some particular thing; a word or expression used for some particular thing. terms.

Term: In common English usage the word "term"' is syntactical or semantical in character, and means simply a word (or phrase), or a word associated with its meaning. The phrase "undefined term" as used in mathematical postulate theory (see mathematics) is perhips best referred to this common meaning of "term " In traditional logic, a term is a concept appearing as subject or predicate (q.v.). of a categorical proposition; also, a word or phrase denoting such a concept. The word "term" has also been employed in a syntactical sense in various special developments of logistic systems (q.v.), usually in a way suggested by the traditional usage.

Thales: 6th Cent. B.C., of the Milesian School of Greek Philosophy, is said to have predicted the eclipse of 585; had probably been to Egypt and was proficient in mathematics and physics. Thales, along with the other cosmological thinkers of the Ionian school, presupposed a single elementary cosmic matter at the base of the transformations of nature and declared this to be water. -- M.F.

That paradoxes of this kind could be relevant to mathematics first became clear in connection with the paradox of the greatest ordinal number, published by Burali-Forti in 1897, and the paradox of the greatest cardinal number, published by Russell in 1903. The first of these had been discovered by Cantor in 1895, and communicated to Hilbert in 1896, and both are mentioned in Cantor's correspondence with Dedekind of 1899, but were never published by Cantor.

The addition to the functional calculus of first order of individual constants (denoting particular individuals) is not often made -- unless symbols for functions from individuals to individuals (so-called "mathematical" or "descriptive" functions) are to be added at the same time. Such an addition is, however, employed in the two following sections as a means of representing certain forms of inference of traditional logic. The addition is really non-essential, and requires only minor changes in the definition of a formula and the list of primitive formulas (allowing the alternative of individual constants at certain places where the above given formulation calls for free individual variables).

The assertion sign was adopted by Russell, and by Whitehead and Russell in Principia Mathematica, in approximately Frege's sense of 1879, and it is from this source that it has come into general use. Some recent writers omit the assertion sign, either as understood, or on the ground that the Frege-Russell distinction between asserted and unasserted propositions is illusory. Others use the assertion sign in a syntactical sense, to express that a formula is a theorem of a logistic system (q.v.); this usage differs from that of Frege and Russell in that the latter requires the assertion sign to be followed by a formula denoting a proposition, or a truth value, while the former requires it to be followed by the syntactical name of such a formula.

The case of infinitely many truth-values was first considered by Lukasiewicz. -- A.C. J. Lukasiewicz, O logice trojwartosciowej, Ruch Fifozoficzny, vol. 5 (1920), pp. 169-171. E. L. Post, Introduction to a general theory of elementary propositions, American Journal of Mathematics, vol. 43 (1921), pp. 163-185. Lukasiewicz and Tarski, Untersuchungen über den Aussagenkalkül, Comptes Rendus des Seances de la Societe des Sciences et des Lettres de Varsovie, Classe III, vol. 23 (1930), pp. 30-50. J. Lukasiewicz, Philosophische Bemerkungen zu mehrwertigen Systemen des Aussagenkalküls, ibid , pp 51-77. Lewis and Langford, Symbolic Logic, New York and London, 1932. Propositional function is a function (q.v.) for which the range of the dependent variable is composed of propositions (q.v.) A monadic propositional function is thus in substance a property (of things belonging to the range of the independent variable), and a dyadic propositional function a relation. If F denotes a propositional function and X1, X2, . . . , Xn denote arguments, the notation F(X1, X2, . . . , Xn) -- or [F](X1, X2, . . . , Xn) -- is used for the resulting proposition, which is said to be the value of the propositional function for the given arguments, and to be obtained from the propositional function by applying it to, or predicating it of the given arguments.

The doctrine that the concepts of mathematics are empirical and the postulates elementary experimental truths has been held in various forms (either for all mathematics, or specially for geometry) by J. S. Mill, H. Helmholtz, M. Pasch, and others. However, the usual contemporary view, especially among mathematicians, is that the propositions of mathematics say nothing about empirical reality. Even in the case of applied geometry, it is held, the geometry is used to organize physical measurement, but does not receive an interpretation under which its propositions become unqualifiedly experimental or empirical in character; a particular system of geometry, applied in a particular way, may be wrong (and demonstrably wrong by experiment), but there is not, in significant cases, a unique geometry which, when applied in the particular way, is right.

The mathematical use of the word "term" appears in such phrases ts "the terms of a sum" (i.e., the separate numbers which are added to form the sum, or the expressions for them), "the terms of a polynomial," "the terms of a proportion," "the terms of an infinite series," etc. Similarly one may speak of "the terms of a logical sum," and the like. -- A.C.

The Method of Statistics. The basic principle of statistical method is that of simplification, which makes possible a concise and comprehensive knowledge of a mass of isolated facts by correlating them along definite lines. The various stages of this method are:   precise definition of the problem or field of inquiry;   collection of material required by the problem;   tabulation and measurement of material in a manner satisfying the purpose of the problem;   clear presentation of the significant features of tabulated material (by means of charts, diagrams, symbols, graphs, equations and the like),   selection of mathematical methods for application to the material obtained;   necessary conclusion from the facts and figures obtained;   general interpretation within the limits of the problem and the procedure used. The special methods of treating statistical data are: collecting, sampling, selecting, tabulating, classifying, totaling or aggregating, measuring, averaging, relating and correlating, presenting symbolically. Each one of these methods uses specialized experimental or mathematical means in its actual application. The special methods of interpreting statistical data already treated are: analyzing, estimiting, describing, comparing, explaining, applying and predicting. In order to be conclusive, the various stages and types of the statistical method must avoid   loose definitions,   cross divisions resulting ftom conflicting interpretations of the problem,   data which are not simultaneous or subject to similar conditions,   conclusions from poor oi incomplete data,   prejudices in judging, even when there is no conuption of evidence. The philosophy of statistics is concerned in general with the discussion and evaluation of the mathematical principles, methods and results of this science; and in particular with a critical analysis of the fitness of biological, psychological, educational, economic and sociological materials, for various types of statistical treatment. The purpose of such an inquiry is to integrate its results into the general problems and schemes of philosophy proper. Cf.. Richard von Mises, Statistics, Probability, and Truth.

The Platonic theory of education is based on a drawing out (educatio) of what is already dimly known to the learner. (Meno, Repub. II-VII, Theaetetus, Laws.) The training of the philosopher-ruler, outlined in the Republic, requires the selection of the most promising children in their infancy and a rigorous disciplining of them in gymnastic, music (in the Greek sense of literary studies), mathematics and dialectic (the study of the Ideas). This training was to continue until the students were about thirty-five years of age; then fifteen years of practical apprenticeship in the subordinate offices of the state were required; finally, at the age of fifty, the rulers were advised to return to the study of philosophy. It should be noted that this program is intended only for an intellectual elite; the military class was to undergo a shorter period of training suited to its functions, and the masses of people, engaged in production, trading, and like pursuits, were not offered any special educational schedule.

The question of whether the operations must be specified or merely conceivable for the proposition to have meaning (which is analogous to the constructibility problem in mathematical discussions) has occasioned considerable criticism, for there appeared to be a danger that important scientific propositions might be excluded as meaningless. To this and other problems of operationalism the logical positivists (or empiricists) have contributed formulary modifications and refinements. See Logical Empiricism. In spite of their frequent difference with regard to the empirical foundation of logic and mathematics, pragmatism has received some support from the strict logicians and mathematical philosophers. One of the most important instances historically was C. I. Lewis' paper "The Pragmatic Element in Knowledge" (University of California Publications in Philosophy, 1926). Here he stated 'that the truth of experience must always be relative to our chosen conceptual systems", and that our choice between conceptual systems "will be determined consciously or not, on pragmatic grounds".

There is also another sense in which it has been held that mathematics is reducible to logic, namely that in the expressions for the postulates of a mathematical discipline the undefined terms are to be given definitions which involve logical terms only, in such a way that postulates and theorems of the discipline thereby become propositions of pure logic, demonstrable on the basis of logical principles only. This view was first taken, as regards arithmetic and analysis, by Frege, and was afterwards adopted by Russell, who extended it to all mathematics.

The term continuity is also employed in mathematics in connection with functions of various kinds. We shall state the definition for the case of a monadic function f for which the range of the independent variable and the range of the dependent variable both consist of real numbers (see the article Function).

"The universe is not merely a mathematical formula for working out the relation of certain mental abstractions called numbers and principles to arrive in the end at a zero or a void unit, neither is it merely a physical operation embodying a certain equation of forces. It is the delight of a Self-lover, the play of a Child, the endless self-multiplication of a Poet intoxicated with the rapture of His own power of endless creation.” The Supramental Manifestation

“The universe is not merely a mathematical formula for working out the relation of certain mental abstractions called numbers and principles to arrive in the end at a zero or a void unit, neither is it merely a physical operation embodying a certain equation of forces. It is the delight of a Self-lover, the play of a Child, the endless self-multiplication of a Poet intoxicated with the rapture of His own power of endless creation.” The Supramental Manifestation

The universe is not merely a mathematical formula for working out the relation of certain mental abstractions called numbers and principles to arrive in the end at a zero or a void unit, neither is it merely a physical operation embodying certain equations of forces. It is the delight of a Self-lover, the play of a Child, the endless self-multiplication of a Poet intoxicated with the rapture of His own power of endless creation.
   Ref: CWSA Vol. 13, Page: 201


The Zermelo set theory has an adequacy to the logical development of mathematics comparable to that of the functional calculus of order omega (§ 6). Indeed, as here actually formulated, its adequacy for mathematics apparently exceeds that of the functional calculus; however, this should not be taken as an essential difference, since both systems are incomplete, in accordance with Gödel'a theorem (§ 6), but are capable of extension.

This definition would make logical syntax coincide with Hilbertian proof theory (q.v.), and in fact the adjectives syntactical, metalogical, metamathematical are used nearly interchangeably. Carnap, however, introduces many topics not considered by Hilbert, and further treats not only the syntax of particular languages but also general syntax, i.e., syntax relating to all languages in general or to all languages of a given kind.

Three senses of "Ockhamism" may be distinguished: Logical, indicating usage of the terminology and technique of logical analysis developed by Ockham in his Summa totius logicae; in particular, use of the concept of supposition (suppositio) in the significative analysis of terms. Epistemological, indicating the thesis that universality is attributable only to terms and propositions, and not to things as existing apart from discourse. Theological, indicating the thesis that no tneological doctrines, such as those of God's existence or of the immortality of the soul, are evident or demonstrable philosophically, so that religious doctrine rests solely on faith, without metaphysical or scientific support. It is in this sense that Luther is often called an Ockhamist.   Bibliography:   B. Geyer,   Ueberwegs Grundriss d. Gesch. d. Phil., Bd. II (11th ed., Berlin 1928), pp. 571-612 and 781-786; N. Abbagnano,   Guglielmo di Ockham (Lanciano, Italy, 1931); E. A. Moody,   The Logic of William of Ockham (N. Y. & London, 1935); F. Ehrle,   Peter von Candia (Muenster, 1925); G. Ritter,   Studien zur Spaetscholastik, I-II (Heidelberg, 1921-1922).     --E.A.M. Om, aum: (Skr.) Mystic, holy syllable as a symbol for the indefinable Absolute. See Aksara, Vac, Sabda. --K.F.L. Omniscience: In philosophy and theology it means the complete and perfect knowledge of God, of Himself and of all other beings, past, present, and future, or merely possible, as well as all their activities, real or possible, including the future free actions of human beings. --J.J.R. One: Philosophically, not a number but equivalent to unit, unity, individuality, in contradistinction from multiplicity and the mani-foldness of sensory experience. In metaphysics, the Supreme Idea (Plato), the absolute first principle (Neo-platonism), the universe (Parmenides), Being as such and divine in nature (Plotinus), God (Nicolaus Cusanus), the soul (Lotze). Religious philosophy and mysticism, beginning with Indian philosophy (s.v.), has favored the designation of the One for the metaphysical world-ground, the ultimate icility, the world-soul, the principle of the world conceived as reason, nous, or more personally. The One may be conceived as an independent whole or as a sum, as analytic or synthetic, as principle or ontologically. Except by mysticism, it is rarely declared a fact of sensory experience, while its transcendent or transcendental, abstract nature is stressed, e.g., in epistemology where the "I" or self is considered the unitary background of personal experience, the identity of self-consciousness, or the unity of consciousness in the synthesis of the manifoldness of ideas (Kant). --K.F.L. One-one: A relation R is one-many if for every y in the converse domain there is a unique x such that xRy. A relation R is many-one if for every x in the domain there is a unique y such that xRy. (See the article relation.) A relation is one-one, or one-to-one, if it is at the same time one-many and many-one. A one-one relation is said to be, or to determine, a one-to-one correspondence between its domain and its converse domain. --A.C. On-handedness: (Ger. Vorhandenheit) Things exist in the mode of thereness, lying- passively in a neutral space. A "deficient" form of a more basic relationship, termed at-handedness (Zuhandenheit). (Heidegger.) --H.H. Ontological argument: Name by which later authors, especially Kant, designate the alleged proof for God's existence devised by Anselm of Canterbury. Under the name of God, so the argument runs, everyone understands that greater than which nothing can be thought. Since anything being the greatest and lacking existence is less then the greatest having also existence, the former is not really the greater. The greatest, therefore, has to exist. Anselm has been reproached, already by his contemporary Gaunilo, for unduly passing from the field of logical to the field of ontological or existential reasoning. This criticism has been repeated by many authors, among them Aquinas. The argument has, however, been used, if in a somewhat modified form, by Duns Scotus, Descartes, and Leibniz. --R.A. Ontological Object: (Gr. onta, existing things + logos, science) The real or existing object of an act of knowledge as distinguished from the epistemological object. See Epistemological Object. --L.W. Ontologism: (Gr. on, being) In contrast to psychologism, is called any speculative system which starts philosophizing by positing absolute being, or deriving the existence of entities independently of experience merely on the basis of their being thought, or assuming that we have immediate and certain knowledge of the ground of being or God. Generally speaking any rationalistic, a priori metaphysical doctrine, specifically the philosophies of Rosmini-Serbati and Vincenzo Gioberti. As a philosophic method censored by skeptics and criticists alike, as a scholastic doctrine formerly strongly supported, revived in Italy and Belgium in the 19th century, but no longer countenanced. --K.F.L. Ontology: (Gr. on, being + logos, logic) The theory of being qua being. For Aristotle, the First Philosophy, the science of the essence of things. Introduced as a term into philosophy by Wolff. The science of fundamental principles, the doctrine of the categories. Ultimate philosophy; rational cosmology. Syn. with metaphysics. See Cosmology, First Principles, Metaphysics, Theology. --J.K.F. Operation: "(Lit. operari, to work) Any act, mental or physical, constituting a phase of the reflective process, and performed with a view to acquiring1 knowledge or information about a certain subject-nntter. --A.C.B.   In logic, see Operationism.   In philosophy of science, see Pragmatism, Scientific Empiricism. Operationism: The doctrine that the meaning of a concept is given by a set of operations.   1. The operational meaning of a term (word or symbol) is given by a semantical rule relating the term to some concrete process, object or event, or to a class of such processes, objectj or events.   2. Sentences formed by combining operationally defined terms into propositions are operationally meaningful when the assertions are testable by means of performable operations. Thus, under operational rules, terms have semantical significance, propositions have empirical significance.   Operationism makes explicit the distinction between formal (q.v.) and empirical sentences. Formal propositions are signs arranged according to syntactical rules but lacking operational reference. Such propositions, common in mathematics, logic and syntax, derive their sanction from convention, whereas an empirical proposition is acceptable (1) when its structure obeys syntactical rules and (2) when there exists a concrete procedure (a set of operations) for determining its truth or falsity (cf. Verification). Propositions purporting to be empirical are sometimes amenable to no operational test because they contain terms obeying no definite semantical rules. These sentences are sometimes called pseudo-propositions and are said to be operationally meaningless. They may, however, be 'meaningful" in other ways, e.g. emotionally or aesthetically (cf. Meaning).   Unlike a formal statement, the "truth" of an empirical sentence is never absolute and its operational confirmation serves only to increase the degree of its validity. Similarly, the semantical rule comprising the operational definition of a term has never absolute precision. Ordinarily a term denotes a class of operations and the precision of its definition depends upon how definite are the rules governing inclusion in the class.   The difference between Operationism and Logical Positivism (q.v.) is one of emphasis. Operationism's stress of empirical matters derives from the fact that it was first employed to purge physics of such concepts as absolute space and absolute time, when the theory of relativity had forced upon physicists the view that space and time are most profitably defined in terms of the operations by which they are measured. Although different methods of measuring length at first give rise to different concepts of length, wherever the equivalence of certain of these measures can be established by other operations, the concepts may legitimately be combined.   In psychology the operational criterion of meaningfulness is commonly associated with a behavioristic point of view. See Behaviorism. Since only those propositions which are testable by public and repeatable operations are admissible in science, the definition of such concepti as mind and sensation must rest upon observable aspects of the organism or its behavior. Operational psychology deals with experience only as it is indicated by the operation of differential behavior, including verbal report. Discriminations, or the concrete differential reactions of organisms to internal or external environmental states, are by some authors regarded as the most basic of all operations.   For a discussion of the role of operational definition in phvsics. see P. W. Bridgman, The Logic of Modern Physics, (New York, 1928) and The Nature of Physical Theory (Princeton, 1936). "The extension of operationism to psychology is discussed by C. C. Pratt in The Logic of Modem Psychology (New York. 1939.)   For a discussion and annotated bibliography relating to Operationism and Logical Positivism, see S. S. Stevens, Psychology and the Science of Science, Psychol. Bull., 36, 1939, 221-263. --S.S.S. Ophelimity: Noun derived from the Greek, ophelimos useful, employed by Vilfredo Pareto (1848-1923) in economics as the equivalent of utility, or the capacity to provide satisfaction. --J.J.R. Opinion: (Lat. opinio, from opinor, to think) An hypothesis or proposition entertained on rational grounds but concerning which doubt can reasonably exist. A belief. See Hypothesis, Certainty, Knowledge. --J.K.F- Opposition: (Lat. oppositus, pp. of oppono, to oppose) Positive actual contradiction. One of Aristotle's Post-predicaments. In logic any contrariety or contradiction, illustrated by the "Square of Opposition". Syn. with: conflict. See Logic, formal, § 4. --J.K.F. Optimism: (Lat. optimus, the best) The view inspired by wishful thinking, success, faith, or philosophic reflection, that the world as it exists is not so bad or even the best possible, life is good, and man's destiny is bright. Philosophically most persuasively propounded by Leibniz in his Theodicee, according to which God in his wisdom would have created a better world had he known or willed such a one to exist. Not even he could remove moral wrong and evil unless he destroyed the power of self-determination and hence the basis of morality. All systems of ethics that recognize a supreme good (Plato and many idealists), subscribe to the doctrines of progressivism (Turgot, Herder, Comte, and others), regard evil as a fragmentary view (Josiah Royce et al.) or illusory, or believe in indemnification (Henry David Thoreau) or melioration (Emerson), are inclined optimistically. Practically all theologies advocating a plan of creation and salvation, are optimistic though they make the good or the better dependent on moral effort, right thinking, or belief, promising it in a future existence. Metaphysical speculation is optimistic if it provides for perfection, evolution to something higher, more valuable, or makes room for harmonies or a teleology. See Pessimism. --K.F.L. Order: A class is said to be partially ordered by a dyadic relation R if it coincides with the field of R, and R is transitive and reflexive, and xRy and yRx never both hold when x and y are different. If in addition R is connected, the class is said to be ordered (or simply ordered) by R, and R is called an ordering relation.   Whitehcid and Russell apply the term serial relation to relations which are transitive, irreflexive, and connected (and, in consequence, also asymmetric). However, the use of serial relations in this sense, instead ordering relations as just defined, is awkward in connection with the notion of order for unit classes.   Examples: The relation not greater than among leal numbers is an ordering relation. The relation less than among real numbers is a serial relation. The real numbers are simply ordered by the former relation. In the algebra of classes (logic formal, § 7), the classes are partially ordered by the relation of class inclusion.   For explanation of the terminology used in making the above definitions, see the articles connexity, reflexivity, relation, symmetry, transitivity. --A.C. Order type: See relation-number. Ordinal number: A class b is well-ordered by a dyadic relation R if it is ordered by R (see order) and, for every class a such that a ⊂ b, there is a member x of a, such that xRy holds for every member y of a; and R is then called a well-ordering relation. The ordinal number of a class b well-ordered by a relation R, or of a well-ordering relation R, is defined to be the relation-number (q. v.) of R.   The ordinal numbers of finite classes (well-ordered by appropriate relations) are called finite ordinal numbers. These are 0, 1, 2, ... (to be distinguished, of course, from the finite cardinal numbers 0, 1, 2, . . .).   The first non-finite (transfinite or infinite) ordinal number is the ordinal number of the class of finite ordinal numbers, well-ordered in their natural order, 0, 1, 2, . . .; it is usually denoted by the small Greek letter omega. --A.C.   G. Cantor, Contributions to the Founding of the Theory of Transfinite Numbers, translated and with an introduction by P. E. B. Jourdain, Chicago and London, 1915. (new ed. 1941); Whitehead and Russell, Princtpia Mathematica. vol. 3. Orexis: (Gr. orexis) Striving; desire; the conative aspect of mind, as distinguished from the cognitive and emotional (Aristotle). --G.R.M.. Organicism: A theory of biology that life consists in the organization or dynamic system of the organism. Opposed to mechanism and vitalism. --J.K.F. Organism: An individual animal or plant, biologically interpreted. A. N. Whitehead uses the term to include also physical bodies and to signify anything material spreading through space and enduring in time. --R.B.W. Organismic Psychology: (Lat. organum, from Gr. organon, an instrument) A system of theoretical psychology which construes the structure of the mind in organic rather than atomistic terms. See Gestalt Psychology; Psychological Atomism. --L.W. Organization: (Lat. organum, from Gr. organon, work) A structured whole. The systematic unity of parts in a purposive whole. A dynamic system. Order in something actual. --J.K.F. Organon: (Gr. organon) The title traditionally given to the body of Aristotle's logical treatises. The designation appears to have originated among the Peripatetics after Aristotle's time, and expresses their view that logic is not a part of philosophy (as the Stoics maintained) but rather the instrument (organon) of philosophical inquiry. See Aristotelianism. --G.R.M.   In Kant. A system of principles by which pure knowledge may be acquired and established.   Cf. Fr. Bacon's Novum Organum. --O.F.K. Oriental Philosophy: A general designation used loosely to cover philosophic tradition exclusive of that grown on Greek soil and including the beginnings of philosophical speculation in Egypt, Arabia, Iran, India, and China, the elaborate systems of India, Greater India, China, and Japan, and sometimes also the religion-bound thought of all these countries with that of the complex cultures of Asia Minor, extending far into antiquity. Oriental philosophy, though by no means presenting a homogeneous picture, nevertheless shares one characteristic, i.e., the practical outlook on life (ethics linked with metaphysics) and the absence of clear-cut distinctions between pure speculation and religious motivation, and on lower levels between folklore, folk-etymology, practical wisdom, pre-scientiiic speculation, even magic, and flashes of philosophic insight. Bonds with Western, particularly Greek philosophy have no doubt existed even in ancient times. Mutual influences have often been conjectured on the basis of striking similarities, but their scientific establishment is often difficult or even impossible. Comparative philosophy (see especially the work of Masson-Oursel) provides a useful method. Yet a thorough treatment of Oriental Philosophy is possible only when the many languages in which it is deposited have been more thoroughly studied, the psychological and historical elements involved in the various cultures better investigated, and translations of the relevant documents prepared not merely from a philological point of view or out of missionary zeal, but by competent philosophers who also have some linguistic training. Much has been accomplished in this direction in Indian and Chinese Philosophy (q.v.). A great deal remains to be done however before a definitive history of Oriental Philosophy may be written. See also Arabian, and Persian Philosophy. --K.F.L. Origen: (185-254) The principal founder of Christian theology who tried to enrich the ecclesiastic thought of his day by reconciling it with the treasures of Greek philosophy. Cf. Migne PL. --R.B.W. Ormazd: (New Persian) Same as Ahura Mazdah (q.v.), the good principle in Zoroastrianism, and opposed to Ahriman (q.v.). --K.F.L. Orphic Literature: The mystic writings, extant only in fragments, of a Greek religious-philosophical movement of the 6th century B.C., allegedly started by the mythical Orpheus. In their mysteries, in which mythology and rational thinking mingled, the Orphics concerned themselves with cosmogony, theogony, man's original creation and his destiny after death which they sought to influence to the better by pure living and austerity. They taught a symbolism in which, e.g., the relationship of the One to the many was clearly enunciated, and believed in the soul as involved in reincarnation. Pythagoras, Empedocles, and Plato were influenced by them. --K.F.L. Ortega y Gasset, Jose: Born in Madrid, May 9, 1883. At present in Buenos Aires, Argentine. Son of Ortega y Munillo, the famous Spanish journalist. Studied at the College of Jesuits in Miraflores and at the Central University of Madrid. In the latter he presented his Doctor's dissertation, El Milenario, in 1904, thereby obtaining his Ph.D. degree. After studies in Leipzig, Berlin, Marburg, under the special influence of Hermann Cohen, the great exponent of Kant, who taught him the love for the scientific method and awoke in him the interest in educational philosophy, Ortega came to Spain where, after the death of Nicolas Salmeron, he occupied the professorship of metaphysics at the Central University of Madrid. The following may be considered the most important works of Ortega y Gasset:     Meditaciones del Quijote, 1914;   El Espectador, I-VIII, 1916-1935;   El Tema de Nuestro Tiempo, 1921;   España Invertebrada, 1922;   Kant, 1924;   La Deshumanizacion del Arte, 1925;   Espiritu de la Letra, 1927;   La Rebelion de las Masas, 1929;   Goethe desde Adentio, 1934;   Estudios sobre el Amor, 1939;   Ensimismamiento y Alteracion, 1939;   El Libro de las Misiones, 1940;   Ideas y Creencias, 1940;     and others.   Although brought up in the Marburg school of thought, Ortega is not exactly a neo-Kantian. At the basis of his Weltanschauung one finds a denial of the fundamental presuppositions which characterized European Rationalism. It is life and not thought which is primary. Things have a sense and a value which must be affirmed independently. Things, however, are to be conceived as the totality of situations which constitute the circumstances of a man's life. Hence, Ortega's first philosophical principle: "I am myself plus my circumstances". Life as a problem, however, is but one of the poles of his formula. Reason is the other. The two together function, not by dialectical opposition, but by necessary coexistence. Life, according to Ortega, does not consist in being, but rather, in coming to be, and as such it is of the nature of direction, program building, purpose to be achieved, value to be realized. In this sense the future as a time dimension acquires new dignity, and even the present and the past become articulate and meaning-full only in relation to the future. Even History demands a new point of departure and becomes militant with new visions. --J.A.F. Orthodoxy: Beliefs which are declared by a group to be true and normative. Heresy is a departure from and relative to a given orthodoxy. --V.S. Orthos Logos: See Right Reason. Ostensible Object: (Lat. ostendere, to show) The object envisaged by cognitive act irrespective of its actual existence. See Epistemological Object. --L.W. Ostensive: (Lat. ostendere, to show) Property of a concept or predicate by virtue of which it refers to and is clarified by reference to its instances. --A.C.B. Ostwald, Wilhelm: (1853-1932) German chemist. Winner of the Nobel prize for chemistry in 1909. In Die Uberwindung des wissenschaftlichen Materialistmus and in Naturphilosophie, his two best known works in the field of philosophy, he advocates a dynamic theory in opposition to materialism and mechanism. All properties of matter, and the psychic as well, are special forms of energy. --L.E.D. Oupnekhat: Anquetil Duperron's Latin translation of the Persian translation of 50 Upanishads (q.v.), a work praised by Schopenhauer as giving him complete consolation. --K.F.L. Outness: A term employed by Berkeley to express the experience of externality, that is the ideas of space and things placed at a distance. Hume used it in the sense of distance Hamilton understood it as the state of being outside of consciousness in a really existing world of material things. --J.J.R. Overindividual: Term used by H. Münsterberg to translate the German überindividuell. The term is applied to any cognitive or value object which transcends the individual subject. --L.W. P

Th. Skolem, Sur la portee du theoreme de Löwenheim-Skolem, Les Entretiens de Zurich sur les Fondements et la Methode des Sciences Mathematiques, Zurich 1941, pp. 25-52. Lucretius, Carus: (98-54 B.C.) Noted Roman poet, author of the famous didactic poem De Natura Rerum, in six books, which forms an interesting exposition of the philosophy of Epicureanism. -- M..F.

Thus in ordinary numerical algebra and in real number theory, the symbols x, y, z are variables, while 0, 1, 3, -- 1/2, π, e are constants. In such mathematical contexts the term constant is often restricted to unambiguous (non-variable) names of numbeis. But such symbols as +, =, < may also be called constants, as denoting particular functions and relations.

T'ime: The general medium in which all events take place in succession or appear to take place in succession. All specific and finite periods of time, whether past, present or future, constitute merely parts of the entire and single Time. Common-sense interprets Time vaguely as something moving toward the future or as something in which events point in that direction. But the many contradictions contained in this notion have led philosophers to postulate doctrines purporting to eliminate some of the difficulties implied in common-sense ideas. The first famous but unresolved controversy arose in Ancient Greece, between Parmenides, who maintained that change and becoming were irrational illusions, and Heraclitus, who asserted that there was no permanence and that change characterized everything without exception. Another great controversy arose centuries later between disciples of Newton and Leibniz. According to Newton, time was independent of, and prior to, events; in his own words, "absolute time, and mathematical time, of itself, and from its own nature, flows equably without regard to anything external." According to Leibniz, on the other hand, there can be no time independent of events: for time is formed by events and relations among them, and constitutes the universal order of succession. It was this latter doctrine which eventually gave rise to the doctrine of space-time, in which both space and time are regarded as two systems of relations, distinct from a perceptual standpoint, but inseparably bound together in reality. All these controversies led many thinkers to believe that the concept of time cannot be fully accounted for, unless we distinguish between perceptual, or subjective, time, which is confined to the perceptually shifting 'now' of the present, and conceptual, or objective, time, which includes til periods of time and in which the events we call past, present and future can be mutually and fixedly related. See Becoming, Change, Duration, Persistence, Space-Time. -- R.B.W.

T. L. Heath, A History of Greek Mathematics, 2 vols., Oxford, 1921.

T. L Heath, A History of Greek Mathematics, vol. I (1921).

T. L. Heath, The Thirteen Books of Euclid's Elements, translated from the text of Heiberg, with introduction and commentary, 3 vols., Cambridge, England, 1908. Gerbert of Aurillac: (Pope Sylvester II, died 1003) Was one of the greatest scholars of the 10th century. He studied at Aurillac with Odo of Cluny, learned something of Arabian science during three years spent in Spain. He taught at the school of Rheims, became Abbot of Bobbio (982), Archbishop of Rheims (991), Archbishop of Ravenna (998), Pope in 999. A master of the seven liberal aits, he excelled in his knowledge of the quadrivium, i.e. logic, math., astron. and music. His works, the most important of which are on mathematics, are printed in PL 139, 57-338. -- V.J.B.

torricellian ::: a. --> Of or pertaining to Torricelli, an Italian philosopher and mathematician, who, in 1643, discovered that the rise of a liquid in a tube, as in the barometer, is due to atmospheric pressure. See Barometer.

Transfinite induction: A generalization of the method of proof by mathematical induction or recursion (see recursion, proof by), applicable to a well-ordered class of arbitrary ordinal number -- especially one of ordinal number greater than omega (see ordinal number) -- in a way similar to that in which mathematical induction is applicable to a well-ordered class of ordinal number omega. -- A.C.

trigonometry ::: n. --> That branch of mathematics which treats of the relations of the sides and angles of triangles, which the methods of deducing from certain given parts other required parts, and also of the general relations which exist between the trigonometrical functions of arcs or angles.
A treatise in this science.


trinitarian ::: a. --> Of or pertaining to the Trinity, the doctrine of the Trinity, or believers in that doctrine. ::: n. --> One who believes in the doctrine of the Trinity.
One of a monastic order founded in Rome in 1198 by St. John of Matha, and an old French hermit, Felix of Valois, for the


Two aspects of Russell's work are likely to remain of permanent importance, his major part in the twentieth century renaissance of logic, his reiterated attempts to identify the methods of philosophy with those of the sciences. (1) While the primary objective of Principia was to prove that pure mathematics could be derived from logic, the success of this undertaking (as to which hardly any dissenting opinion persists) is overshadowed by the importance of the techniques perfected in the course of its prosecution. Without disrespect to other pioneers in the field, it is sufficient to point out that a knowledge of the symbolic logic of Russell and Whitehead is still a necessary prerequisite for understanding contemporary studies in logic, in the foundations of mathematics, and tht philosophy of science.

vagina ::: n. --> A sheath; a theca; as, the vagina of the portal vein.
Specifically, the canal which leads from the uterus to the external orifice if the genital canal, or to the cloaca.
The terminal part of the oviduct in insects and various other invertebrates. See Illust., of Spermatheca.
The basal expansion of certain leaves, which inwraps the stem; a sheath.
The shaft of a terminus, from which the bust of figure


Variable: A letter occurring in a mathematical or logistic formula and serving, not as a name of a particular, but as an ambiguous name of ¦any one of a class of things -- this class being known as the range of the variable, and the members of the class as values of the variable.

VII. Probability as a Physical Magnitude determined by Axioms.. This theory, which is favoured mainly by the Intuitionist school of mathematics, considers probability as a physical constant of which frequencies are measures. Thus, any frequency is an approximate measure of one physical constant attached to an event and to a set of trials: this constant is the probability of that event over the set of trials. As the observed frequencies differ little for large numbers of trials from their corresponding probabilities, some obvious properties of frequencies may be extended to probabilities. This is done without proceeding to the limit, but through general approximation as in the case of physical magnitudes. These properties are not constructed (as in the axiomatization of Mises), but simply described as such, they form a set of axioms defining probability. The classical postulates involved in the treatises of Laplace, Bertrand or Poincare have been modified in this case, under the joint influence of the discovery of measure by Borei, and of the use of abstract sets. Their new form has been fully stated by Kolmogoroff and interpreted by Frechet who proposes to call this latest theory the 'modernized axiomatic definition' of probability. Its interpretation requires that it should be preceded by an inductive synthesis, and followed by numerical verifications.

Vrndavana (Vrindavan, Brindavan, Brindaban) ::: [the place on earth (near Mathura) where Krsna danced with the gopis]; the vaisnava heaven of eternal Beauty and Bliss.

W. Ackermann, Zur Widerspruchsfreiheitt der Zahlentheorie, Mathematische Annalen, vol. 117 (1940), pp 162-194. Propensity: (Lat. propensio, from propendere, to hang forth) A term used to designate a mental appetite or desire. See Appetition. Hume applied the term to the tendency of the mind to pass from one to the other of two associated ideas. -- L.W.

W. Dubislav, Bolzano als Vorlaufer der mathematischen Logik, Philosophisches Jahrbuch der Gorres-Gesellschaft, vol 44 (1931), pp. 448-456. H. Scholz, Die Wissenschaftslehre Bolzanos, Abhandlungen der Frieds'schen Schule , n. s. vol. 6 (1937), pp 399-472.

"We see that the Absolute, the Self, the Divine, the Spirit, the Being is One; the Transcendental is one, the Cosmic is one: but we see also that beings are many and each has a self, a spirit, a like yet different nature. And since the spirit and essence of things is one, we are obliged to admit that all these many must be that One, and it follows that the One is or has become many; but how can the limited or relative be the Absolute and how can man or beast or bird be the Divine Being? But in erecting this apparent contradiction the mind makes a double error. It is thinking in the terms of the mathematical finite unit which is sole in limitation, the one which is less than two and can become two only by division and fragmentation or by addition and multiplication; but this is an infinite Oneness, it is the essential and infinite Oneness which can contain the hundred and the thousand and the million and billion and trillion. Whatever astronomic or more than astronomic figures you heap and multiply, they cannot overpass or exceed that Oneness; for, in the language of the Upanishad, it moves not, yet is always far in front when you would pursue and seize it. It can be said of it that it would not be the infinite Oneness if it were not capable of an infinite multiplicity; but that does not mean that the One is plural or can be limited or described as the sum of the Many: on the contrary, it can be the infinite Many because it exceeds all limitation or description by multiplicity and exceeds at the same time all limitation by finite conceptual oneness.” The Life Divine

“We see that the Absolute, the Self, the Divine, the Spirit, the Being is One; the Transcendental is one, the Cosmic is one: but we see also that beings are many and each has a self, a spirit, a like yet different nature. And since the spirit and essence of things is one, we are obliged to admit that all these many must be that One, and it follows that the One is or has become many; but how can the limited or relative be the Absolute and how can man or beast or bird be the Divine Being? But in erecting this apparent contradiction the mind makes a double error. It is thinking in the terms of the mathematical finite unit which is sole in limitation, the one which is less than two and can become two only by division and fragmentation or by addition and multiplication; but this is an infinite Oneness, it is the essential and infinite Oneness which can contain the hundred and the thousand and the million and billion and trillion. Whatever astronomic or more than astronomic figures you heap and multiply, they cannot overpass or exceed that Oneness; for, in the language of the Upanishad, it moves not, yet is always far in front when you would pursue and seize it. It can be said of it that it would not be the infinite Oneness if it were not capable of an infinite multiplicity; but that does not mean that the One is plural or can be limited or described as the sum of the Many: on the contrary, it can be the infinite Many because it exceeds all limitation or description by multiplicity and exceeds at the same time all limitation by finite conceptual oneness.” The Life Divine

Whitehead, Alfred North: British philosopher. Born in 1861. Fellow of Trinity College, Cambridge, 1911-14. Lecturer in Applied Mathematics and Mechanics at University College, London, 1914-24. Professor of Applied Mathematics at the Imperial College of Science and Technology, London. From 1924 until retirement in 1938, Professor of Philosophy at Harvard University. Among his most important philosophical works are the Principia Mathematica, 3 vols. (1910-13) (with Bertrand Russell; An Enquiry concerning the Principles of Natural Knowledge (1919); The Concept of Nature (1920); Science and the Modern World (1926); Religion tn the Making (1926); Symbolism (1928); Process and Reality (1929); and Adventures of Ideas (1933). The principle of relativity in physics is the key to the understanding of metaphysics. Whitehead opposes the current philosophy of static substance having qualities which he holds to be based on the simply located material bodies of Newtonian physics and the "pure sensations" of Hume. This 17th century philosophy depends upon a "bifurcation of nature" into two unequal systems of reality on the Cartesian model of mind and matter. The high abstractions of science must not be mistaken for concrete realities. Instead, Whitehead argues that there is only one reality, what appears, whatever is given in perception, is real. There is nothing existing beyond what is present in the experience of subjects, understanding by subject any actual entity. There are neither static concepts nor substances in the world; only a network of events. All such events are actual extensions or spatio-temporal unities. The philosophy of organism, as Whitehead terms his work, is based upon the patterned process of events. All things or events are sensitive to the existence of all others; the relations between them consisting in a kind of feeling. Every actual entity is then a "prehensive occasion", that is, it consists of all those active relations with other things into which it enters. An actual entity is further determined by "negative prehension", the exclusion of all that which it is not. Thus every feeling is a positive prehension, every abstraction a negative one. Every actual entity is lost as an individual when it perishes, but is preserved through its relations with other entities in the framework of the world. Also, whatever has happened must remain an absolute fact. In this sense, past events have achieved "objective immortality". Except for this, the actual entities are involved in flux, into which there is the ingression of eternal objects from the realm of possibilities. The eternal objects are universals whose selection is necessary to the actual entities. Thus the actual world is a certain selection of eternal objects. God is the principles of concretion which determines the selection. "Creativity" is the primal cause whereby possibilities are selected in the advance of actuality toward novelty. This movement is termed the consequent nature of God. The pure possibility of the eternal objects themsehes is termed his primordial nature. -- J.K.F.

Whitehead and Russell, Princibia Mathematica. 2nd edn., vol. 1. Cambridge. England, 1925.

Whitehead and Russell, Principia Mathematica, 2nd edn , vol 1, Cambridge, England, 1925.

Whitehead and Russell, Principia Mathematica, 3 vols., Cambridge England, 1st edn. 1910-13, 2nd edn. 1925-27.

Whitehead and Russell (Principia Mathematica) give the name law of absorption to theorem of the propositional calculus, [p ⊃ q] ≡ [p ≡ pq].

Whitehead and Russell, Principia Mathematica, vol. 1.

Whitehead and Russell, Principia Mathematica, vol. 2.

Whitehead and Russell use the term propositional function in approximately the sense above described, but qualify it by holding, as a corollary of Russell's doctrine of descriptions (q.v.), that propositional functions are the fundamental kind from which other kinds of functions are derived -- in fact that non-propositional ("descriptive") functions do not exist except as incomplete symbols. For details of their view, which underwent some changes between publication of the first and the second edition of Principia Mathematica, the reader is referred to that work.

Wilhelm Ackermann, Mengentheorettsche Begründung der Logik, Mathematische Annalen, vol. 115 (1937), pp. 1 -22.

Wolff. Christian: (1679-1754) A most outstanding philosopher of the German Enlightenment, and exponent of an all pervasive rationalism, who was professor of mathematics at Halle. He was a dry and superficial systematic popularizer of dogmatic philosophy whose laws have for him a purely logical and rational foundation. -- H.H.

W. V. Quine, Mathematical Logic, New York, 1940. In psychology: the mental operation by which we proceed from individuals to concepts of classes, from individual dogs to the notion of "the dog." We abstract features common to several individuals, grouping them thus together under one name.

W. V. Quine, Mathematical Logic, New York, 1940. Logic, symbolic, or mathematical logic, or logistic, is the name given to the treatment of formal logic by means of a formalized logical language or calculus whose purpose is to avoid the ambiguities and logical inadequacy of ordinary language. It is best characterized, not as a separate subject, but as a new and powerful method in formal logic. Foreshadowed by ideas of Leibniz, J. H. Lambert, and others, it had its substantial historical beginning in the Nineteenth Century algebra of logic (q. v.), and received its contemporary form at the hands of Frege, Peano, Russell, Hilbert, and others. Advantages of the symbolic method are greater exactness of formulation, and power to deal with formally more complex material. See also logistic system. -- A. C.

W. V. Quine, Mathematical Logic, New York, 1940.

Zermelo, Ernst (Friedrich Ferdinand), 1871-, German mathematician. Professor of mathematics at Zurich, 1910-1916, and at Freiburg, 1926-. His important contributions to the foundations of mathematics are the Zermelo axiomatic set theory (see logic, formal, § 9), and the explicit enunciation of the axiom of choice (q.v.) and proof of its equivalence to the proposition that every class cm be well-ordered. -- A.C.

Zetetic: (Gr. zeteo, to seek) A procedure by inquiry. A search (in mathematics) after unknown quantities. A seeker. -- V.F.



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NEW FULL DB (2.4M)

   78 Richard Matheson
   74 Mathias Malzieu
   72 Matthew Mather
   58 R L Mathewson
   20 Taran Matharu
   18 Albert Einstein
   15 G H Hardy
   13 Lauren Groff
   12 Cotton Mather
   12 Bertrand Russell
   12 Anonymous
   11 Johnny Mathis
   11 Harry Mathews
   10 Jennifer Mathieu
   9 Tim Matheson
   9 Galileo Galilei
   9 Francine Mathews
   8 Richard P Feynman
   8 Henri Poincare
   7 Paul Halmos

*** WISDOM TROVE ***

1:Lottery: A tax on people who are bad at math. ~ ambrose-bierce, @wisdomtrove
2:I'm an expert in higher level math. You + God = Enough ~ zig-ziglar, @wisdomtrove
3:Spirit Math: The quality of your life equals the ratio of appreciation to complaint. ~ alan-cohen, @wisdomtrove
4:Just because you can read, write and do a little math, doesn't mean that you're entitled to conquer the universe. ~ kurt-vonnegut, @wisdomtrove
5:Just because some of us can read and write and do a little math, that doesn't mean we deserve to conquer the universe. ~ kurt-vonnegut, @wisdomtrove
6:Your faith is very important. I have done the math, and you are going to be dead a whole lot longer that you will be alive. ~ zig-ziglar, @wisdomtrove
7:What do I like about math? , When I've got figures in front of me, it relaxes me. Kind of like, everything fits where it belongs. ~ haruki-murakami, @wisdomtrove
8:See how the Ganga flows by and what a nice building! I like this place. This is the ideal kind of place for a Math. (in Belur, West Bengal). ~ swami-vivekananda, @wisdomtrove
9:Christians remind me of schoolboys who want to look up the answers to their math problems in the back of the book rather than work them through. ~ soren-kierkegaard, @wisdomtrove
10:People love to admit they have bad handwriting or that they can't do math. And they will readily admit to being awkward: &
11:If your parents are billionaires, that might actually be an obstacle to your own happiness and self-development. If you go to Oxford or Harvard, that might actually thwart your desire to graduate with a science or math degree. ~ malcolm-gladwell, @wisdomtrove
12:If you've got a dollar and you spend 29 cents on a loaf of bread, you've got 71 cents left; But if you've got seventeen grand and you spend 29 cents on a loaf of bread, you've still got seventeen grand. There's a math lesson for you. ~ steve-martin, @wisdomtrove
13:I'm always interested in understanding the math of things and understanding as much as I can about all aspects of business. And what I learn today may be useful to me two years from now. That's really the wonderful thing about investments is your knowledge is cumulative. ~ warren-buffet, @wisdomtrove
14:I think there are dozens or hundreds of different forms of creativity. Pondering science and math problems for years is different from improvising jazz. Something which seems to me remarkable is how unconscious the creative process is. You encounter a problem, but can't solve it. ~ oliver-sacks, @wisdomtrove
15:Take a random group of 8-year-old American and Japanese kids, give them all a really, really hard math problem, and start a stopwatch. The American kids will give up after 30, 40 seconds. If you let the test run for 15 minutes, the Japanese kids will not have given up. You have to take it away. ~ malcolm-gladwell, @wisdomtrove
16:With the Holy Mother as the centre of inspiration, a Math is to be established on the eastern bank of the Ganga. . . . On the other side of the Ganga a big plot of land will be acquired, where unmarried girls or Brahmacharini widows will live; devout married women will also be allowed to stay now and then. Men will have no concern with this Math. ~ swami-vivekananda, @wisdomtrove
17:If the Lord wills, we shall make this Math a great centre of harmony. Our Lord is the visible embodiment of the harmony of all ideals. He will be established on earth if we keep alive that spirit of harmony here. We must see to it that people of all creeds and sects, from the Brahmana down to the Chandala, may come here and find their respective ideals manifested. ~ swami-vivekananda, @wisdomtrove
18:Superstar lawyers and math whizzes and software entrepreneurs appear at first blush to lie outside ordinary experience. But they don't. They are products of history and community, of opportunity and legacy. Their success is not exceptional or mysterious. It is grounded in a web of advantages and inheritances, some deserved, some not, some earned, some just plain lucky&
19:Math is like water. It has a lot of difficult theories, of course, but its basic logic is very simple. Just as water flows from high to low over the shortest possible distance, figures can only flow in one direction. You just have to keep your eye on them for the route to reveal itself. That’s all it takes. You don’t have to do a thing. Just concentrate your attention and keep your eyes open, and the figures make everything clear to you. In this whole, wide world, the only thing that treats me so kindly is math. ~ haruki-murakami, @wisdomtrove
20:No matter how clear things might become in the forest of story, there was never a clear-cut solution, as there was in math. The role of a story was, in the broadest terms, to transpose a problem into another form. Depending on the nature and the direction of the problem, a solution might be suggested in the narrative. Tengo would return to the real world with that solution in hand. It was like a piece of paper bearing the indecipherable text of a magic spell. It served no immediate practical purpose, but it contained a possibility. ~ haruki-murakami, @wisdomtrove

*** NEWFULLDB 2.4M ***

1:Fun math is an oxymoron. ~ Kiera Cass,
2:I just am not good at math. ~ Phil McGraw,
3:Baseball is like live math. ~ Alyson Richman,
4:Math is easy; design is hard. ~ Jeffrey Veen,
5:Amazon began with a math error.) ~ Brad Stone,
6:You know math isn’t my thing. ~ Carolyn J Rose,
7:I am better at math than spelling. ~ Spike Jonze,
8:The universe is math on fire. ~ Scott Westerfeld,
9:I can, you know, do math and stuff. ~ J K Rowling,
10:Math doesn't lie. Our emotions do. ~ Claudia Gray,
11:i hate math, but i love counting money ~ Anonymous,
12:The math is stark: cut the ~ Christopher McDougall,
13:Math - it's not my best subject. ~ Heather O Rourke,
14:Poetry isn't math was our battle cry ~ Gayle Forman,
15:I was just kind of doing the math. ~ Clayton Kershaw,
16:This is not class warfare. It’s math. ~ Barack Obama,
17:Math is the language of the universe. ~ Lucas Grabeel,
18:Math has never made any sense to me. ~ Stephen Chbosky,
19:Math is one of my favorite subjects. ~ Macaulay Culkin,
20:Forget math and peotry. Especially poetry. ~ C J Redwine,
21:Also, librarians aren’t that good at math. ~ Annie Spence,
22:I just love math and most people don't. ~ Danica McKellar,
23:On A Beautiful Mind, there was a wall of math. ~ Josh Lucas,
24:My success rate is 100 percent. Do the math. ~ Charlie Sheen,
25:There's math, and everything else is debatable! ~ Chris Rock,
26:If Math was a woman, we'd be married already. ~ Mark Gonzales,
27:In the end, climate change is a math problem. ~ Bill McKibben,
28:Math-i-tude Mom- and Dad-i-tude Mad-i-tude A ~ Megan McDonald,
29:Where there is no math, there is no freedom. ~ Edward Frenkel,
30:In the blue time, math kicked ass.
-Dess ~ Scott Westerfeld,
31:Lottery: A tax on people who are bad at math. ~ Ambrose Bierce,
32:Yes, I was really good in physics and in math. ~ Eva Herzigova,
33:I am an Engineer. I don't do Math, I tweak it. ~ Ibrahim Ibrahim,
34:You know, I loved math. My mom was a math teacher. ~ Joan Cusack,
35:I like Math because there's only one right answer. ~ Brendan Fehr,
36:It is hard for westerners to realize that math ~ Daniel L Everett,
37:Math is sometimes called the science of patterns. ~ Ronald Graham,
38:Murder math?’ Yeah, doing murder math in your head. ~ Elliott Kay,
39:Math, it's a puzzle to me. I love figuring out puzzles. ~ Maya Lin,
40:Mom was a math teacher, but reading was her great love ~ John Green,
41:Building Oracle is like doing math puzzles as a kid. ~ Larry Ellison,
42:In math you always check your work. In medicine, no. ~ Michael Lewis,
43:Too much math and science isn't nourishing to the soul. ~ Brodi Ashton,
44:You can fuck your math teacher but you can't fuck math. ~ Scott Sigler,
45:I was particularly good at math and science. ~ William Standish Knowles,
46:I could never have been an accountant. I got a D in math. ~ Rob Marshall,
47:I'm not a math problem." "But I'll still solve you." Neil ~ Nora Sakavic,
48:Just for a screen. ~ Robert Burns, Epistle to Rev. John M'Math, Stanza 8,
49:100% of the people who give 110% do not understand math. ~ Demetri Martin,
50:It was like trying to solve a math equation with a poem. ~ Mara Purnhagen,
51:lottery was just a tax on people who weren’t good at math. ~ Cindi Madsen,
52:... where there's one there's ten.'
That's crazy math. ~ Emma Donoghue,
53:Behavior is math: Truth is found in the sum of its parts. ~ Steve Maraboli,
54:I can't do that," Harry said. "I don't have the math for it. ~ John Scalzi,
55:Math and science were my favorite subjects besides theater. ~ Jason Earles,
56:One sample is poor statistics, my math prof used to say. ~ Arthur C Clarke,
57:No wonder Sherlock Holmes did all that coke. Math is hard. ~ Richard Kadrey,
58:Math?” “Yeah, math. Aren’t all you Asians really good at math? ~ Rick Yancey,
59:And then Satan said, ‘Put the alphabet in math…’ -Coffee Cup ~ Lani Lynn Vale,
60:Math is a product of human minds but not bendable to human will ~ Ian Stewart,
61:I always like a good math solution to any love problem. ~ Michael Patrick King,
62:And the Satan said, 'Put the alphabet in math...' - coffee cup ~ Lani Lynn Vale,
63:I did math in school, obviously. And I loved all my math teachers. ~ Jayma Mays,
64:I joke around all the time, 'I'm Asian; I'm really good at math.' ~ Brenda Song,
65:Come on, let's go see if Aires taught you pool like he did math. ~ Katie McGarry,
66:I really wanted to be veterinarian, but I got a 410 on my math SATs. ~ Meg Cabot,
67:I've always liked all the sciences like math, physics and biology ~ Sigrid Agren,
68:...the lottery was just a tax on people who weren't good at math. ~ Cindi Madsen,
69:Whatever your problems in math are, I assure mine are greater. ~ Albert Einstein,
70:The math is stark: cut the fat, and cut your cancer risk. ~ Christopher McDougall,
71:It is impossible to do math and be frightened at the same time. ~ Randy Wayne White,
72:The math could multiply the horseshit, but it could not decipher it. ~ Cathy O Neil,
73:Trust me, there is no formula for most things that are not math. ~ Daniel Pinkwater,
74:All the math you need in the stock market you get in the fourth grade. ~ Peter Lynch,
75:Calculus was not math. It was a fucking science experiment gone wrong. ~ Abbi Glines,
76:Math is the only place where truth and beauty mean the same thing. ~ Danica McKellar,
77:The careful untangling of a legal issue. Like math, but with words. ~ Liane Moriarty,
78:We cheated on our math tests, we carved some dirty words on the desk. ~ Alice Cooper,
79:I always thought the lottery was a tax on people with poor math skills, ~ Shay Savage,
80:If I wanted to be a doctor today I'd go to math school not med school. ~ Vinod Khosla,
81:No one should be that good at math, even if they are a fiend from Hell. ~ Vivian Shaw,
82:That's the inescapable math of tragedy and the multiplication of grief ~ Ben Sherwood,
83:If you do the math, films featuring women are a good investment. ~ Geoffrey S Fletcher,
84:Math is like going to the gym for your brain. It sharpens your mind. ~ Danica McKellar,
85:we use math not because we’re smart, but because we aren’t smart enough. ~ Jean Tirole,
86:Are we going to do any thinking today, or is it going to be all math? ~ Philip J Hanlon,
87:If you stop at general math, you're only going to make general math money. ~ Snoop Dogg,
88:I picked the college I attended partly because it had no math requirement. ~ John Green,
89:My freshman year of high school I joined the chess and math clubs. ~ Eric Allin Cornell,
90:Somehow life had become a story problem, and William was horrible at math. ~ Jamie Ford,
91:This is bigger than math! You can’t just swap one of us out for another! ~ Claudia Gray,
92:To not know math is a severe limitation to understanding the world. ~ Richard P Feynman,
93:For future reference: do not underestimate the seductive power of math. ~ Rachel Hartman,
94:He stared back like I was an advanced math problem he couldn't interpret. ~ Mia Sheridan,
95:Do the math: You never settle for less than the whole if you knew the half. ~ Talib Kweli,
96:I see screenwriting as a bit like a math equation which I have to solve. ~ Asghar Farhadi,
97:Do the math. Expect catastrophes. Whatever happens, stay the course. ~ William J Bernstein,
98:I did grow up with a really big interest in math and science; I liked it. ~ Linda M Godwin,
99:I'm no quitter, unless it comes to human relationships or math and science. ~ Dov Davidoff,
100:Math and reading are my only weaknesses - other than that, Im perfect. ~ Judah Friedlander,
101:When every other facet of my life was a mess, music stayed true as math. ~ Jennifer Echols,
102:I don't have the time. It would take me too long to go through all of the math. ~ Paul Ryan,
103:MATH...The only place where people can buy 64 watermelons, and nobody wonders why ~ Unknown,
104:Everyone called it Burger Math because all you learned was how to make change. ~ Kami Garcia,
105:I enjoyed like nothing else working in pure math, discovering new formulas. ~ Jerry McNerney,
106:Only Numbers. Pure math. You have to accustom yourself to thinking that way. ~ Anthony Doerr,
107:I love math. I have little secret number tattoos everywhere. I design them. ~ Pauley Perrette,
108:In this whole, wide world, the only thing that treats me so kindly is math. ~ Haruki Murakami,
109:I was a B student in math, simply because my teachers liked me, as an actor. ~ Morgan Freeman,
110:Look, I'm over 40, I'm single, and I work in musical theater - you do the math! ~ Nathan Lane,
111:Without a plane, what was I supposed to do? Math the problem to death? ~ Mary Robinette Kowal,
112:I study the people in the class, in a somewhat dreamy math-soundtracked daze. ~ David Levithan,
113:I was dyslexic, so math and formulas were not necessarily my strong suit. ~ James Van Der Beek,
114:LOTTERY TICKET: a voluntary tax paid by people who are extremely bad at math. ~ Roy H Williams,
115:I like to crack the jokes now and again, but it's only because I struggle with math. ~ Tina Fey,
116:I'm real good with math, with numbers, like my dad was. I'm pretty much dialed in. ~ Hulk Hogan,
117:Simple math and common sense are all you need to do well financially. There ~ Robert T Kiyosaki,
118:I didn't major in math. I majored in miracles, and I still believe in them, too. ~ Mike Huckabee,
119:In school, my favorite subject was math. That's where I learned to count money. ~ French Montana,
120:I spent 10 years working on a math Ph.D., and I finally got kind of good at it. ~ Jerry McNerney,
121:I was always reading books when I should have been doing math and the rest of it. ~ Markus Zusak,
122:Math test tomorrow.
Check.
Complete lack of preparation for test.
Check. ~ Rick Riordan,
123:The world of math is more weird and wonderful than some people want to tell you. ~ Eugenia Cheng,
124:I BET I CAN guess your favorite math subject in high school. It was geometry. ~ Steven H Strogatz,
125:You can count the dead, but you can't count the cost. We've got no math for Heaven. ~ Colum McCann,
126:At Harvard I majored in chemistry with a strong inclination toward math. ~ William Standish Knowles,
127:Cooking and gardening involve so many disciplines: math, chemistry, reading, history. ~ David Chang,
128:‎"[Those] on fixed incomes are the nation's math elite." from pg.88 of Atomic Lobster. ~ Tim Dorsey,
129:I had higher math SATs than in English - yet I became an English major in college. ~ Christie Hefner,
130:In the financial sector, those whom the gods want to destroy they first teach math. ~ Niall Ferguson,
131:I perform my job ten times a day. Seven days a week. For nine years. You do the math. ~ Anne Tibbets,
132:The math of time is simple: you have less than you think and need more than you know. ~ Kevin Ashton,
133:What was she supposed to do with all the Xes? Whoever put letters in math was crazy. ~ Kimberly Loth,
134:You can count the dead, but you can't count the cost. We've got no math for Heaven... ~ Colum McCann,
135:Al-Qaeda's resurgence brings out the worst in the Bush Administration's math and logic. ~ Jon Stewart,
136:I could have gone to medical school, I said. Except for all the math and stuff. ~ MaryJanice Davidson,
137:I hereby demand that all people who are good at math make the world free of illness. ~ Daniel Handler,
138:It is not a morality, but simple math. Among themselves, doves fight as often as hawks. ~ Delia Owens,
139:It is written nowhere in the math of probability theory that one may have no fun. ~ Eliezer Yudkowsky,
140:THE GODEL SOLUTION TO THE EINSTEIN FIELDEQUATIONS: http://www.math.nyu.edu/ ~ momin/stuff/grpaper.pdf,
141:None of the boys were studying for the math test we had today, because none of them cared. ~ Alan Gratz,
142:There was harmony in proportions, Leonardo learned, and math was nature’s brushstroke. ~ Walter Isaacson,
143:Dear Math, please grow up and solve your own problems. I'm tired of solving them for you. ~ Margaret Mead,
144:I’ve wondered if I could take my computer programming skills and apply them to learning math. ~ Anonymous,
145:My kids used to love math. Now it makes them cry. Thanks standardized testing and common core! ~ Louis C K,
146:We can't just throw something out there and assume it works just because it has math in it. ~ Cathy O Neil,
147:Gods of math and physics," she intoned, "I accept your gift of this clever, fair-haired boy. ~ Laini Taylor,
148:I got into writing and thinking about politics because I was told there would be no math. ~ Jeff Greenfield,
149:I was a normal human being, but I did like that. I read a lot. I also liked math and science. ~ Jamie Dimon,
150:Justice is like math, anyone can think she knows the answer, but not every answer is right. ~ Max Gladstone,
151:Music has more rules than math or magic and it's twice as dangers as both or either. ~ Catherynne M Valente,
152:Once you hit 40, you start reexamining the math of it all. I'll trade wisdom for youth any day. ~ Brad Pitt,
153:He perfectly fits the profile of a Hut 8 man, who need not know anything except pure math. ~ Neal Stephenson,
154:Let's make math fun and sexy and glamorous. Smart is sexy, that's one of my main messages. ~ Danica McKellar,
155:If the math works, why then you should be sure of yourself. That’s the whole point of math. ~ Neal Stephenson,
156:Music has more rules than math or magic and it's twice as dangerous as both or either. ~ Catherynne M Valente,
157:Sex is like math: Add the bed, subtract the clothes, divide the legs, and hope you don’t mult— ~ Alex Sanchez,
158:You didn't miss anything in math," he says, and I recognize a Kent McFuller babble coming on. ~ Lauren Oliver,
159:being a math genius doesn’t necessarily translate to financial gain. Lots of geniuses die poor. ~ Lisa Gardner,
160:I knew comedy was the thing for me when I was the only Asian kid in high school... who failed math. ~ Dat Phan,
161:Only in math can you buy sixty cantaloupes and no one asks what the hell is wrong with you. ~ Charles M Schulz,
162:#2—10% of people will find a way to take anything personally. Expect it and treat it as math. ~ Timothy Ferriss,
163:Brian and I were both science students. You know science sort of math and physics side, you know. ~ John Deacon,
164:He had always considered magic to be like math; it was a skill Alex and only Alex had inherited. ~ Chris Colfer,
165:Here then - the after math of meaning. A liftime finished between the space of two frames. ~ Mark Z Danielewski,
166:… I just figured it would be easier to do the math problem with the numbers in the correct colors. ~ Wendy Mass,
167:Math. Are you able to turn off your mind to the world and fill it with symbols that follow rules? ~ Ned Vizzini,
168:Math has a lot of negative stereotypes, but it can actually be fun and incredibly empowering. ~ Danica McKellar,
169:Republicans and Democrats can barely do what they're supposed to do, and they sure can't do math! ~ Lewis Black,
170:The physics principles behind the three-body problem28 are very simple. It’s mainly a math problem. ~ Liu Cixin,
171:Those who do not know history are probably also not doing well in English or math. P.J. O'Rourke ~ P J O Rourke,
172:I dislike math, yet I respect and appreciate the fact that math is the language of the universe. ~ Lucas Grabeel,
173:Our eyes met in the math class. How were we to know that trigonometry would lead to matrimony? ~ Sophie Kinsella,
174:Teacher: "Why are you on the floor?" Johnny: "Because you said to do this math problem without tables! ~ Various,
175:6 people + 6 months + 3 cameramen + 1 reality show = infinite drama. I've done the math." - Rose ~ Krista Ritchie,
176:During my McGill years, I took a number of math courses, more than other students in chemistry. ~ Rudolph A Marcus,
177:he came into the store to threaten you with math and philosophy. The motherfucker’s going down. ~ Jonathan L Howard,
178:The world was precarious, Lotto had learned. People could be subtracted from it with swift bad math. ~ Lauren Groff,
179:He couldn’t see how you could scare the shit out of somebody with math, but it seemed you could. ~ Jonathan L Howard,
180:In WMDs, many poisonous assumptions are camouflaged by math and go largely untested and unquestioned. ~ Cathy O Neil,
181:*** Teacher: "Why are you on the floor?" Johnny: "Because you said to do this math problem without tables! ~ Various,
182:We teach reading, writing and math by [having students do] them. But we teach democracy by lecture. ~ Shelley Berman,
183:grief does not decline in a straight line or along a slow curve like a graph in a child’s math book. ~ Helen Simonson,
184:Kids praised for effort complete 50 percent more hard math problems than kids praised for intelligence. ~ John Medina,
185:They are four words I want you to keep in mind when critic’s math gets loud. He wrote, “We will miss you. ~ Jon Acuff,
186:Treat sins that your children struggle with like basic math. Practice, Practice, and you'll get it. ~ Rachel Jankovic,
187:English teacher: Sam, form a sentence using the word aftermath. Sam: 'I always feel sleepy after math class. ~ Various,
188:The math was irrefutable: The one winning strategy was concealment. Only fools revealed their birthdays. ~ Peter Watts,
189:Although Math can't teach us how to add love or minus hate, it teaches us that every problem has a solution ~ Anonymous,
190:I loved math. I was such a nerd! I really enjoyed working through problems and finding the solution. ~ AnnaLynne McCord,
191:Who cares for Algebra?Who delights in solving math?I only want to live my lifeAlong the creative path. ~ Jennifer Niven,
192:I don't know how it works, the science and math of it all, but I know that love given is courage gained. ~ Annie F Downs,
193:I send my kids to school not only to learn how to read and write and do math, but also to develop socially. ~ Megyn Kelly,
194:I was always good at math and science, and I never realized that that was unusual or somehow undesirable. ~ Marissa Mayer,
195:The steps to solving a problem, from elementary math to breaking out of a police station, remained the same. ~ V E Schwab,
196:English teacher: Sam, form a sentence using the word aftermath.
Sam: 'I always feel sleepy after math class. ~ Various,
197:I liked math - that was my favorite subject - and I was very interested in astronomy and in physical science. ~ Sally Ride,
198:Later in the fifties I got involved in kinetic studies using my long forgotten math background. ~ William Standish Knowles,
199:The schools I went to as a kid made me wary. It was clear to me that everything was a lie except math. ~ Suzan Shown Harjo,
200:You have this weird look on your face," he said. "Like you're doing really complicated math in your head. ~ Rachel Hawkins,
201:English teacher: Sam, form a sentence using the word aftermath. Sam: 'I always feel sleepy after math class.' *** ~ Various,
202:I never got a pass mark in math ... Just imagine - mathematicians now use my prints to illustrate their books. ~ M C Escher,
203:Numbers never lie, after all: they simply tell different stories depending on the math of the tellers. ~ Luis Alberto Urrea,
204:Math proficiency is the gateway to a number of incredible careers that students may never have considered. ~ Danica McKellar,
205:The last thing they want to hear is that math is really about raw creativity and aesthetic sensitivity. Many ~ Paul Lockhart,
206:Everyone has the brainpower to follow the stock market. If you made it through fifth-grade math, you can do it. ~ Peter Lynch,
207:My older brother was cool, so I was suddenly cool by association. And I totally dusted all my old math friends. ~ David Spade,
208:Numbers, letters, lines ... math. That's worse than fish.
No notes. No explanation, just math scribbles. ~ Nadine Brandes,
209:One of the nice things about math and science is it’s obvious, you get the answer or you don’t get the answer. ~ Lisa Randall,
210:We can either save the planet from catastrophic warming, or protect fossil fuel CEOs. Not both. Do the math(s) ~ Bill McKibben,
211:When I was in school I liked math because all the problems had answers. Everything else seemed very subjective. ~ Lisa Randall,
212:can’t take the test,” I said. “I don’t know any math.” “You’ve got money,” Tyler said. “Buy books and learn it. ~ Tara Westover,
213:Unfortunately I have never been good in math. Numbers simply do not interest me or seem as real to me as words. ~ Peter Cameron,
214:A French portion is half of an American portion, and a French meal takes twice as long to eat. You do the math. ~ Elizabeth Bard,
215:never forget that underneath all the math and the MBA bullshit talk, we are all still emotionally driven human ~ Timothy Ferriss,
216:The Mozart Effect comes to mind: the popular idea that listening to classical music makes students better at math. ~ John Medina,
217:Then I would explain, it was no use trying to learn math unless they could communicate it with other people.”4 ~ Walter Isaacson,
218:When reading math, it is important to know where in math you are—what region of this vast subject you are exploring. ~ Anonymous,
219:Just because you can read, write and do a little math, doesn't mean that you're entitled to conquer the universe. ~ Kurt Vonnegut,
220:I was engaged in all the required courses of math and geometry, but the area that I blossomed in was the art program. ~ Paul Smith,
221:Someone has remarked that 'An ideal math talk should have one proof and one joke and they should not be the same'. ~ Ronald Graham,
222:We have 2,500 students and an 8,000-seat basketball arena. You do the math on how important basketball is in Aberdeen. ~ Don Meyer,
223:Women, girls and young ladies tend to be as good or better at math than boys, but you didn't think that either. ~ Sallie Krawcheck,
224:I never did very well in math-I could never seem to persuade the teacher that I hadn't meant my answers literally. ~ Calvin Trillin,
225:I quickly tried to do the math but my brain was a jumbled mess and I couldn’t remember what number comes after potato! ~ Tara Sivec,
226:Marianne, how’s your statistics?” “Math is my worst subject.” “But you can program?” “Of course. I’m not illiterate. ~ Joe Haldeman,
227:Math can explain the reason there's one out of four chance that I'd have blue eyes. But it doesn't explain why me. ~ Heidi W Durrow,
228:their writing.  Park, D. et al., “The Role of Expressive Writing in Math Anxiety,’’ Journal of Experimental Psychology: ~ Anonymous,
229:Who cares for Algebra?
Who delights in solving math?
I only want to live my life
Along the creative path. ~ Jennifer Niven,
230:Why do you have such a crappy attitude about math?"
"I don't. I have a crappy attitude about everything. ~ Laurie Halse Anderson,
231:Dreams are what guide us, art is what defines us, math is what makes it all possible, and love is what lights our way. ~ Mike Norton,
232:If you’re having trouble with a math problem, plug the equation into WolframAlpha.com and it will solve it for you. ~ Keith Bradford,
233:I'm not lazy. I'm just really gifted, only instead of being good at music or math I'm good at sleeping late. ~ Elizabeth Jane Howard,
234:When I was growing up, I always knew I'd be in the top of my class in math, and that gave me a lot of self-confidence. ~ Sergey Brin,
235:I hate math. It's hard, it's stupid, and it's nature's way of separating spinsters from women who end up breeding. ~ Douglas Coupland,
236:I went off to college planning to major in math or philosophy-- of course, both those ideas are really the same idea. ~ Frank Wilczek,
237:What is debt anyway? A debt is just the perversion of a promise. It is a promise corrupted by both math and violence. ~ David Graeber,
238:By 12th grade, the average black or Hispanic is reading and doing math at the level of the average white 8th-grader. 38 ~ Jared Taylor,
239:Just because some of us can read and write and do a little math, that doesn't mean we deserve to conquer the Universe. ~ Kurt Vonnegut,
240:Math is the language of the universe. So the more equations you know, the more you can converse with the cosmos. ~ Neil deGrasse Tyson,
241:My character, Taylor McKessie, is a little bit brighter in the math and science department than I am... okay, a lot. ~ Monique Coleman,
242:...now Eli was my new neighbor. Which was fine with me because I sucked at Math. Math and I were not on speaking terms. ~ Shelly Crane,
243:Reading parenting books—and all self-help books, as far as I’m concerned—is the equivalent of learning math from a dog. ~ Wendy Walker,
244:Success is math; not magic. It is the sum of a behavioral equation… not the spontaneous fruition of wishful thinking. ~ Steve Maraboli,
245:If a child is poor in math but good at tennis, most people would hire a math tutor. I would rather hire a tennis coach. ~ Deepak Chopra,
246:Students coming from father-present families score higher in math and science even when they come from weaker schools. ~ Warren Farrell,
247:I’d chosen my profession because it meant I could move anywhere; no matter the city, science and math teachers were needed. ~ Penny Reid,
248:In Montana, a math teacher is running for the Senate. Win or lose, she plans on demanding a recount because math is fun. ~ Conan O Brien,
249:Math is really about the human mind, about how people can think effectively, and why curiosity is quite a good guide. ~ William Thurston,
250:My mother was an economics professor. I'm proficient in math, and statistics, game theory, symbolic logic and all of that. ~ Dave Hickey,
251:To the extent math refers to reality, we are not certain to the extent we are certain, math does not refer to reality. ~ Albert Einstein,
252:You can go your whole life and not need math or physics for a minute, but the ability to tell a joke is always handy. ~ Garrison Keillor,
253:But in the new (math) approach, the important thing is to understand what you're doing, rather than to get the right answer. ~ Tom Lehrer,
254:You could do math early, but there are no brilliant 16-year-old novelists. They don't know the human condition yet. ~ Neil deGrasse Tyson,
255:I got good grades in math, but I never really enjoyed it. My favorite part of math was algebra, but geometry was the worst. ~ Nathan Kress,
256:It does not take a math genius to understand that when you subtract a mother from the equation what remains is negative. ~ Kwame Alexander,
257:Music is not math. It's science. You keep mixing the stuff up until it blows up on you, or it becomes this incredible potion. ~ Bruno Mars,
258:I’m afraid of a lot of things, but men with big guns aren’t one of them. My kids’ math homework, well, that’s another story.” He ~ J R Rain,
259:A play that works well and is done quite a lot - I've never done the math - but it's probably more remunerative than a movie. ~ Tom Stoppard,
260:. . . I still wouldn't be able to control myself around him, and I'm math geek enough to know that equation doesn't work out. ~ Robin Brande,
261:I think there's no way they should have to teach [math] now. We have computers. We no longer need to know why 3x = 2y/4. ~ Rosie O Donnell,
262:Why did I have to be a good boy just because I had a bad-boy brother? I hated the way my mom and dad did family math. ~ Benjamin Alire S enz,
263:The math helps you have better understanding and helps you have more creative ideas, but you can't replace the creative ideas ~ Jonah Peretti,
264:Well, it’s all math,” he says. “If the math works, why then you should be sure of yourself. That’s the whole point of math. ~ Neal Stephenson,
265:Focused problem solving in math and science is often more effortful than focused-mode thinking involving language and people. ~ Barbara Oakley,
266:It is a little like developing the habit of stealing the test from your teacher’s desk instead of learning how to do the math. ~ Josh Waitzkin,
267:Growing up, I found I was good at two things: Art and Math. To hear my parents say it, though, it was only, 'John is good at Math. ~ John Maeda,
268:Just a girl in my math class"
"Just a girl, huh?"
Gabriel glared at him. "Just a girl."
Chris smiled. "So was Becca. ~ Brigid Kemmerer,
269:President Obama said he plans on training 10,000 new math and science teachers. How about teaching math to that economic team of his? ~ Jay Leno,
270:Though I believe math is a tool of the Enemy, I learned enough to know that to accurately find the sum, you add up all the parts. ~ Jen Hatmaker,
271:doesn’t require very complicated math. One guy told me that if you just designed a clean data display, people were amazed. ~ Kim Stanley Robinson,
272:Here's the thing. Math and I broke up two years ago, and now whenever we get together it's just weird and awkward for both of us. ~ Sariah Wilson,
273:Music has a lot in com­mon with math­e­mat­ics. But in music, two and two need not make four: they add up to what­ever you wish. ~ Jascha Heifetz,
274:We're more than the sum total of our choices, that all the paths we might have taken factor somehow into the math of our identity. ~ Blake Crouch,
275:Dear Miss Ingray, thank you for saving my life. When I grow up I will work for you. I am good at math and I know how to cook noodles. ~ Ann Leckie,
276:He couldn’t imagine such a moment, believed instead that Serena’s beauty was like certain laws of math and physics, fixed and immutable ~ Ron Rash,
277:This much I'm sure of. Chances for winning = 1 - (# of math students playing)/ (# of math students cheering). That's a fraction. ~ Danica McKellar,
278:Believe it or not, lots of people change their majors and abandon their dreams just to avoid a couple of math classes in college. ~ Danica McKellar,
279:If you enjoy math and you write novels, it's very rare that you'll get a chance to put your math into a novel. I leapt at the chance. ~ Mark Haddon,
280:I got a degree in math, from not a good school in Texas, and then I went to work as a software engineer. Just not glamorous at all. ~ Shane Carruth,
281:On Venus you could cook a 16-inch pepperoni pizza in seven seconds, just by holding it out to the air. (Yes, I did the math.) ~ Neil deGrasse Tyson,
282:What do I like about math? , When I've got figures in front of me, it relaxes me. Kind of like, everything fits where it belongs. ~ Haruki Murakami,
283:I believe if every K-12 kid or college student was taught math with Mathematica far more of them would becomes scientists and engineers. ~ Anonymous,
284:I considered law and math. My Dad was a lawyer. I think though I would have ended up in physics if I didn't end up in computer science. ~ Bill Gates,
285:I love music because it's so fecking brilliant. Music is math, and math is the structure of everything and pretty much perfect. ~ Karen Marie Moning,
286:I was good at math and science, and I got lots of degrees in lots of things, but in a parallel universe, I probably became a chef. ~ Nathan Myhrvold,
287:Just as I had long suspected, a person didn't really need math for anything anyway. Maybe some people did. Some limited people. ~ Augusten Burroughs,
288:Look unto the stars to teach us How the master’s thoughts can reach us Each one follows Newton’s math Silently along its path. ~ Neil deGrasse Tyson,
289:When I was 18, science, physics, and math were my favorite. I was a bit of a nerd - the only girl with a lot of boys at chess championships. ~ Bjork,
290:You can be creative in anything - in math, science, engineering, philosophy - as much as you can in music or in painting or in dance. ~ Ken Robinson,
291:How are you?” she asked. It was a question that would’ve required some college-level math and about an hour of discussion to answer. I ~ Ransom Riggs,
292:Math does come easily to me, but I was always much more interested in what theorems imply about the world than in proving them. ~ Antony Garrett Lisi,
293:The No Child Left Behind Program was an incentive to the schools to get their kids up to snuff on math and science and reading. ~ Sandra Day O Connor,
294:[Harriet] hated math. She hated math with every bone in her body. She spent so much time hating it that she never had time to do it. ~ Louise Fitzhugh,
295:How are you?" she asked.
It was a question that would've required some college-level math and about an hour of discussion to answer. ~ Ransom Riggs,
296:In the early days, I often felt that I was taking a math test when we were playing. It was a profound feeling of having to prove myself. ~ Chris Stein,
297:It's as if there is infinity between our lips and we will never actually touch. Like math, where dividing by half can last for eternity. ~ Carrie Ryan,
298:The best minds of my generation are thinking about how to make people click ads,” a former math whiz at Facebook recently lamented.33 ~ Rutger Bregman,
299:The women with the growth mindset—those who thought math ability could be improved—felt a fairly strong and stable sense of belonging. ~ Carol S Dweck,
300:I take great solace that Einstein failed math. I failed math. I also failed English and home economics. Einstein was an underachiever. ~ Danny Bonaduce,
301:People want sex education out of the schools. They believe sex education causes promiscuity. Hey, I took algebra, but I never do math. ~ Elayne Boosler,
302:Hundreds,' Joe says. 'Hundreds and hundreds. But then again, I'm old.'
So old, Jesus was in your math class,' I say. I crack myself up. ~ Deb Caletti,
303:I didn't really think about becoming a professional artist until high school, when I realized that everything else required too much math. ~ Phil Foglio,
304:Suppose you're teaching math. You assume that parallel lines meet at infinity. You'll admit that adds up to something like transcendence. ~ G nter Grass,
305:To be honest, she may be kind of scared of the register. Or maybe she can’t add. She is a Christian. I don’t think they believe in math. ~ Andrea Portes,
306:Earlier today, President Bush said Kerry will be a tough and hard-charging opponent. That explains why Bush's nickname for Kerry is math. ~ Conan O Brien,
307:Once you understand that there's a spiritual math, add soul to the science and subtract the riff-raff. 24-7-365, cause 9 to 5 ain't alive. ~ Kool Moe Dee,
308:There's no reason to stereotype yourself. Doing math is like going to the gym - it's a workout for your brain and it makes you smarter. ~ Danica McKellar,
309:There are only two kinds of math books: Those you cannot read beyond the first sentence, and those you cannot read beyond the first page. ~ Chen Ning Yang,
310:Each individual has a responsibility to get out of bed, learn their ABCs, learn your math tables, not use race and racism as an excuse. ~ Henry Louis Gates,
311:I laugh and go back to looking at my magazine. Actually, it’s not really a magazine. It’s a math journal, because I’m super cool like that. ~ Tarryn Fisher,
312:I loved logic, math, computer programming. I loved systems and logic approaches. And so I just figured architecture is this perfect combination. ~ Maya Lin,
313:smart-boys fuck like they’re composing a piece of math rock: This hand strums around here, and then this finger offers a nice bass rhythm.… ~ Gillian Flynn,
314:What I am trying to say is that more than your own life has to be at stake, before a person becomes desperate enough to resort to math. ~ Eliezer Yudkowsky,
315:I had accepted a job being a math teacher for Teach For America. So, that's what I would have done at least in the two years after I graduated. ~ Chris Baio,
316:Yeah, Silver and his math are jokes, because math has a liberal bias. After all, math is the reason Mitt Romney's tax plan doesn't add up. ~ Stephen Colbert,
317:By 1940 Grace Hopper was bored. She had no children, her marriage was unexciting, and teaching math was not as fulfilling as she had hoped. ~ Walter Isaacson,
318:Extraordinary emblems of math's ability to illuminate the dark corners of the cosmos, black holes have become the cynosures of modern physics. ~ Brian Greene,
319:I thought I was going to be a math major. My parents were both accountants and wanted me to major in business. Math was our compromise. ~ Michael Silverblatt,
320:She ran her hand over my forehead. “You not sick?”
“No,” I said. “It’s called math.”
Mr. Wellington shook his head. “She has an exam. ~ Vanessa Fewings,
321:Hope is good. Without it, well, you do the math. But hope has to be like a prayer. Putting it out there to something more powerful than yourself. ~ Lisa Unger,
322:Predictive modeling generates the entire model from scratch. All the model’s math or weights or rules are created automatically by the computer. ~ Eric Siegel,
323:The motto I have penned on my knuckles is that this is the best world we have—because it’s the only world we have. It’s the simplest math ever. ~ Caitlin Moran,
324:I certainly was a geeky kid myself, but to me, math and science were always these magical things- powerful tools you could use in incredible ways. ~ Ben Mezrich,
325:See how the Ganga flows by and what a nice building! I like this place. This is the ideal kind of place for a Math. (in Belur, West Bengal). ~ Swami Vivekananda,
326:We expect the states to show us whether or not we're achieving simple objectives-like literacy, literacy in math, the ability to read and write. ~ George W Bush,
327:You’ve helped me see that IT is not merely a department. Instead, it’s pervasive, like electricity. It’s a skill, like being able to read or do math. ~ Gene Kim,
328:In fact, NSF was the leading successful efforts to improve U.S. math and science education long before the Department of Education was even created. ~ Bob Inglis,
329:Math has proven the existence of God, because it is absolute and without contradiction; but the devil must exist as well, because we cannot prove it ~ Y ko Ogawa,
330:We all know that there are these exemplars who can take the toughest students, and they'll teach them two-and-a-half years of math in a single year. ~ Bill Gates,
331:What is the answer, Evan?" Ms Granger asked.
Giraffe, I wanted to answer. It was on the tip of my tongue. Giraffe.
This was in math class, ~ David Levithan,
332:That does not count as math, because one does not have to understand how it works or what it means in order to think that it looks sort of beautiful. ~ John Green,
333:The world was precarious, Lotto had learned. People could be subtracted from it with swift bad math. If one might die at any moment, one must live! ~ Lauren Groff,
334:Studies show American students are becoming less proficient in math. Experts say we should have seen this coming, but nobody could put 2 and 2 together. ~ Jay Leno,
335:Christians remind me of schoolboys who want to look up the answers to their math problems in the back of the book rather than work them through. ~ Soren Kierkegaard,
336:If you love math, have a knack for numbers, study hard and become a successful accountant; who cares if you can't draw a straight line or sing on key? ~ Nick Carter,
337:I look around for someplace to sit, but of course there's nowhere. It's the bathroom in the math wing, not the bathroom in Blair Waldorf's house. ~ Lauren Barnholdt,
338:Too bad relationships weren’t math problems with precise answers. They were essay questions in a philosophy class, and they came down to judgement. ~ Lauren Blakely,
339:All the traditional STEM fields, the science, technology, engineering, and math fields, are stoked when you dream big in an agency such as NASA. ~ Neil deGrasse Tyson,
340:It was just like a digital fixation with cards and math and science and then I started to look at images of great magicians from Houdini down the line. ~ David Blaine,
341:We write in darkness. We love
in alleys. We breathe into beige
paper bags. Anything to mollify
the confusion. Anything to simplify
the math. ~ Bill Yarrow,
342:You do his homework?"
"Just the math. It's a miracle he can count to ten."
"I can count to one." Gabriel gave him the finger.
Chris sighed. ~ Brigid Kemmerer,
343:You only get one sunrise and one sunset a day, and you only get so many days on the planet. A good photographer does the math and doesn't waste either. ~ Galen Rowell,
344:As a child, however, I knew so many African Americans working in science, math, and engineering that I thought that’s just what black folks did. ~ Margot Lee Shetterly,
345:if you give the learner enough of the appropriate data, it can approximate any function arbitrarily closely—which is math-speak for learning anything. ~ Pedro Domingos,
346:If you're a waiter and you're waiting on me, you might get five percent, you might get seventy percent. It depends on how bad my math skills are that day. ~ Kelly Ripa,
347:We need all hands on deck, and that means clearing hurdles for women and girls as they navigate careers in science, technology, engineering, and math. ~ Michelle Obama,
348:A hit show takes Hollywood magic indeed, but it also takes a lot of math and science, plus the study of polls and trends to make and sell a TV show. ~ Kristoffer Polaha,
349:Gematria is simply a man-made game that uses numbers; and NO, this is NOT Math! Projecting a game unto nature does not deem it to be part of, Science! ~ Ibrahim Ibrahim,
350:Markets are fundamentally volatile. No way around it. Your problem is not in the math. There is no math to get you out of having to experience uncertainty. ~ Ed Seykota,
351:The U.S. ranks 25th in math and 21st in science. We are woefully behind. The only way to change this situation is through public-private partnerships. ~ Klaus Kleinfeld,
352:You don't have to like your teacher. [...] But that woman's got the kind of math in her head that you need in yours. Focus on that and ignore the rest. ~ Michelle Obama,
353:I was good at math, math was my thing - but I was not nearly good enough to be an astrophysicist. I was way outta my league. I realized this very quickly. ~ Sam Trammell,
354:Let's face it; by and large math is not easy, but that's what makes it so rewarding when you conquer a problem, and reach new heights of understanding. ~ Danica McKellar,
355:People who like math. So I was trying to imagine—” “When seven billion die, and only some thousands remain, where do the seven billion souls go?” “Yes. ~ Neal Stephenson,
356:The difference between good at math and bad at math is hard work. It's trying. It's trying hard. It's trying harder than you've ever tried before. That's it. ~ Anonymous,
357:As a child, however, I knew so many African Americans working in science, math, and engineering that I thought that’s just what black folks did. My ~ Margot Lee Shetterly,
358:[Math] curriculum is obsessed with jargon and nomenclature seemingly for no other purpose than to provide teachers with something to test the students on. ~ Paul Lockhart,
359:Math is my favorite subject. It's the universal language. I like the fact that wherever you go in the whole world, two plus two will still be four. ~ Dakota Blue Richards,
360:no matter how much tech companies talk about algorithms like they’re nothing but advanced math, they always reflect the values of their creators: ~ Sara Wachter Boettcher,
361:Somehow it's O.K. for people to chuckle about not being good at math. Yet if I said, 'I never learned to read,' they'd say I was an illiterate dolt. ~ Neil deGrasse Tyson,
362:The New York Times - but the whole country gives it that weight. It's like the Asian kid in math class. Everybody in the media cheats off The New York Times. ~ Bill Maher,
363:In American math classes, we teach a lot of concepts poorly over many years. In the Asian systems they teach you very few concepts very well over a few years. ~ Bill Gates,
364:Nothing is something after all. There’s math that proves this, of course, but also observations. I know it seems like math and observations are opposites. ~ Emily Fridlund,
365:This was one of the problems with math department graduates. When it came to areas they weren't interested in, their memory was surprisingly short-lived. ~ Haruki Murakami,
366:Thought
It does not take
a math genius
to understand that
when you subtract
a mother
from the equation
what remains
is negative. ~ Kwame Alexander,
367:Alone, you're vastly outnumbered; but in the company of another, by some weird miracle of human math, the odds seem wonderfully improved in your favor. ~ Charles D Ambrosio,
368:Alone, you’re vastly outnumbered; but in the company of another, by some weird miracle of human math, the odds seem wonderfully improved in your favor. ~ Charles D Ambrosio,
369:I can’t help thinking that we’re more than the sum total of our choices, that all the paths we might have taken factor somehow into the math of our identity. ~ Blake Crouch,
370:In life two negatives don't make a positive. Double negatives turn positive only in math and formal logic. In life things just get worse and worse and worse. ~ Robert McKee,
371:I prefer home-schooling because you can work at your own pace and go towards more what you're interested in, whether it be history or geography or math. ~ Q orianka Kilcher,
372:All human states are organic brain states - happiness, sadness, fear, lust, dreaming, doing math problems and writing novels - and our brains are not static. ~ Siri Hustvedt,
373:I can't stop biting my nails. It's a bad habit of mine. I like anything to do with math and numbers. I know a lot of people don't like geometry, but for me it's fun. ~ Khleo,
374:I want every math teacher to know math. I want every science teacher to have expertise in science. I want them to know how to inspire and engage young people. ~ Barack Obama,
375:When something is beautiful in math, everything is just perfectly lined up, and you see through sheer thought that something really beautiful can take place. ~ Shane Carruth,
376:A well-known mathematician once told me that the great thing about liking both math and sex was that he could do either one while thinking about the other. ~ Steven Landsburg,
377:I didn't know there were this many math guys," Hale said as they stepped onto the crowded concourse. Kat cleared her throat. "And women," he added. "Math women. ~ Ally Carter,
378:I don’t know if math is real in the sense that it’s woven into the fabric of the cosmos, or if it’s something that we invent and impose upon it. I don’t know. ~ Rivka Galchen,
379:I want to reach back into my history with a grade-school pink eraser, scrubbing away my decisions like mistakes on a math test. To bad I drew my mistakes in ink. ~ Emery Lord,
380:Forever, just the word fills Beverly with an unaccountable, schoolmarmish sort of rage. Forever, that's got to be bad math, right? Such terrifying math. ~ Karen Russell,
381:There is an almost complete overlap between men and women’s math scores. The majority of women have a male math twin: a man with the same math score as they do. ~ Hans Rosling,
382:Activism is setting a goal of something you would like to be different, and figuring out what would have to change to achieve that goal. It's sort of like math. ~ Rachel Maddow,
383:Community is essential when it comes to successfully living out the Christian walk in a day-to-day context. So the math is simple: More community = More disciples. ~ Ed Stetzer,
384:Even if you’re bad at math, you’re probably much better at it than the smartest chimpanzee, whose genetic identity varies in only trifling ways from ours. ~ Neil deGrasse Tyson,
385:In some ways, I never outgrew my adolescence. I wake up in the morning and think, 'Oh my God, I'm late for a math test!' But then I say, 'Wait a minute. I'm 40. ~ Daniel Clowes,
386:I've taught statistics, math courses and what I've found is that often if you teach them algebraically the formulas, you'll have one group of kids doing well. ~ Robert Sternberg,
387:Our equation should not be that math is hard, and so programming is hard. Rather, it should be that programming can be fun, and this means that math can be fun, too. ~ Anonymous,
388:stereotyping of Asians as racially gifted in math and science is a consequence not so much of their academic habits as shifting immigration and corporate priorities. ~ Anonymous,
389:There is something very pleasing about the principles of science and the rules of math, because they are so inevitable and so harmonious - in the abstract, anyway. ~ Lydia Davis,
390:Circles, homework coupons, what foolishness would she next hear? And so she began to teach him mathematics—she called it “maths” and he called it “math ~ Chimamanda Ngozi Adichie,
391:I was very good in math and physics. In the Soviet time, we had a lot of Olympic-style competitions for different disciplines: I was always winning in my region. ~ Oleg Deripaska,
392:She’d been in math classes with Quentin since they were ten years old, and anything he could do she could do just as well, backward and in high heels if necessary. ~ Lev Grossman,
393:So, I don’t know if math is real in the sense that it’s woven into the fabric of the cosmos, or if it’s something that we invent and impose upon it. I don’t know. ~ Rivka Galchen,
394:The fixed mindset, plus stereotyping, plus women's trust in people's assessments: I think we can begin to understand why there's a gender gap in math and science. ~ Carol S Dweck,
395:There's fancy math to explain all this, of course. (...) But when you saw the Aurora, saw her floating and rising, you forget all about the match and just stared. ~ Kenneth Oppel,
396:A new study found that students who are taught abstinence end up with better math scores. Of course, if you join the math team, the abstinence takes care of itself. ~ Jimmy Fallon,
397:I am your Ted's song-legend, Crow of the death-chill, please. The God-eating, trash-licking, word-murdering, carcass-desecrating math-bomb motherfucker, and all that. ~ Max Porter,
398:If anyone tells you it's impossible to be fabulous and smart and make a ton of money using math, well, they can just get in line behind you - and kiss your math. ~ Danica McKellar,
399:...the thing about dieting is that it's really horrible and boring for a longer period of time than feeling pretty in small jeans feels. That's just basic math. ~ Brittany Gibbons,
400:I continued to study Math and Physics on my own, but one and a half years later I realized that I did want to be a composer, and after that I never changed my mind. ~ Gyorgy Ligeti,
401:Math and science need to be made more hospitable places for women. And women need all the growth mindset they can get to take their rightful places in these fields. ~ Carol S Dweck,
402:Not only can I teach you math, I can teach you math in bed, Jordan. You know, I'll add the bed, you subtract the clothes, you divide the legs, and I'll multiply ~ Miranda Kenneally,
403:Sense and logic clearly weren’t one of Errik’s strengths. A monkey with a math problem, all dragging knuckles and grunts, he clenched his fists and dug his heels in. ~ Tim Marquitz,
404:After the war, I went to the University of Chicago, where I was pleased to study anthropology, a science that was mostly poetry, that involved almost no math at all. ~ Kurt Vonnegut,
405:Here’s how the math works. You need to meet two criteria: First, you have to create enough each year that you can earn, on average, $100 profit from each true fan. ~ Timothy Ferriss,
406:I didn't know there were this many math guys," Hale said as they stepped onto the crowded concourse.
Kat cleared her throat.
"And women," he added. "Math women. ~ Ally Carter,
407:I don't want just a night or a week or a month with you. I want you all the time. I like you better than calculus, and math is the only thing that unites the universe. ~ Helen Hoang,
408:If you’re not interested in them, they will become obsessed with you. If you are interested in them, they will disappear. It’s like … it’s like math. It’s an equation. ~ Aziz Ansari,
409:Once you found the math in a thing, you knew everything about it, and you could manipulate it to your heart’s content with nothing more than a pencil and a napkin. ~ Neal Stephenson,
410:Science Technology Engineering and Math is still necessary to know if you dream of being a filmmaker. Filmmaking is an art form, but with the use of STEM. - Kailin Gow. ~ Kailin Gow,
411:When I originally entered UCLA, I had planned to go for a film major, but I kept finding myself taking math classes for fun, 'cause I missed them from high school! ~ Danica McKellar,
412:When it turned out that he could, Karou dropped to her knees to genuflect. "Gods of math and physics," she intoned, "I accept your gift of this clever fair-haired boy ~ Laini Taylor,
413:Learning through the arts reinforces critical academic skills in reading, language arts and math, and provides students with the skills to creatively solve problems. ~ Michelle Obama,
414:Quinn until he messaged me his nightly text, which had turned somewhat math-mushy recently: If I were a function, you would be my asymptote. I always tend toward you. He ~ Penny Reid,
415:I have been involved with science and math education my whole life. My hope is to continue to promote the love of these beautiful disciplines to the next generation. ~ Tohoru Masamune,
416:I'm thinking of switching banks, and my friend said, 'Well, what's wrong with Citibank?' Well, they can't spell 'city.' I hope their math is better than their English is. ~ Arj Barker,
417:Tengo has an innate knack for precision in all realms, including correct punctuation and discovering the simplest possible formula necessary to solve a math problem. ~ Haruki Murakami,
418:You know when you're a kid and you think, 'Oh no, I've got double math, this is never gonna end,' but then it ends, and it's like it never happened? That's like life. ~ Craig Ferguson,
419:I'd never had a mind for math. ... It was a logic that made little sense to me. In my perception, the world wasn't a graph or a formula or an equation. It was a story. ~ Cheryl Strayed,
420:In math, you could get 100 percent. It was very fair. That's what I liked about math. You could figure it out, and the teacher couldn't have a stupid opinion about it. ~ Norm MacDonald,
421:When general relativity was first put forward in 1915, the math was very unfamiliar to most physicists. Now we teach general relativity to advanced high school students. ~ Brian Greene,
422:When you take a look at the problems our country is facing, debt is No. 1. The math is downright scary and the credit markets aren't going to keep on giving us cheap rates. ~ Paul Ryan,
423:I liked English and art and did a lot of painting. And for some reason I was good at math, but I wasn't an A student. I really had to work hard to get good grades. ~ Natasha Bedingfield,
424:It's such a diversion to be constantly thinking of better ways I can teach people math that my hunger is for that really, for new ways of translating the beauty of it. ~ Danica McKellar,
425:Mathematicians grow very old; it is a healthy profession. The reason you live long is that you have pleasant thoughts. Math and physics are very pleasant things to do. ~ Dirk Jan Struik,
426:Mr. Merrick, I'd like to speak with you."
Mr. Merrick. He hated when teachers called him that, like he was an old man stopping by to learn a few math tricks. ~ Brigid Kemmerer,
427:People can talk tough without having to do the primitive math of violence, because they believe that law enforcement will either intervene and stop or punish an attacker. ~ Jack Donovan,
428:Some kids are good at math, some kids can run, and acting was an interest of mine. Because I knew you could do it for a living I decided, that's what I'm going to do. ~ Jonny Lee Miller,
429:Test scores aren't perfect, but having a test score for math or reading or other things that we can objectively measure is a meaningful component that makes a lot of sense. ~ Bill Gates,
430:That was the great thing about numbers: it required no faith to believe that two plus two equaled four. And math never, ever condemned you for your thoughts and desires. ~ Michael Grant,
431:The commercial break before Final Jeopardy is usually the only time that the show stops tape. You’re given as long as you want to do the math required to make your wager. ~ Ken Jennings,
432:Although I was first drawn to math and science by the certainty they promised, today I find the unanswered questions and the unexpected connections at least as attractive. ~ Lisa Randall,
433:Being an electronic genius was a reputation I had, maybe being even into math and science almost exclusively and not wanting to be in the other normal parts of the world. ~ Steve Wozniak,
434:If she thought I’d be much help with math problems, then we already had trouble. Most of what I’d learned in high school and college had long ago departed from my brain. ~ Carolyn J Rose,
435:In school math and science were my favorite subjects, but I probably in my true self I'm more of a people person. At the same time, I don't think that's how I recharge. ~ Emily Deschanel,
436:Mace had to be six foot three, had the prerequisite Nightingale Investigation Team killer bod; black hair, jade eyes and a jaw so square, it could be used in math class. ~ Kristen Ashley,
437:playing with numbers was still considered taboo, a subject best left to the later years, despite America’s obvious and enduring math handicap. For too long, what American ~ Amanda Ripley,
438:Real frontier-busting math explores new worlds . . . . If you can communicate that experience, somewhere between math and uncertainty, life experience provides the balance. ~ John Madden,
439:There is an idea that a mind is wasted on the arts unless it makes you good in math or science. There is some evidence that the arts might help you in math and science. ~ Wynton Marsalis,
440:data science requires more than math skills: it also takes people who have a wide-ranging curiosity, and whose innovation is guided by their own experience—not just data. ~ Daniel Goleman,
441:I couldn't picture myself with a boyfriend, but if I had to, I envisioned a nice normal guy who turned in his math homework on time and maybe even played rec baseball. ~ Becca Fitzpatrick,
442:Spending time with math people is a lot of fun. As a result of the play, I've had semi-drunken dinners with mathematicians all over the country. I recommend the experience. ~ David Auburn,
443:Why don't we teach sex the way we teach math or history? It is such a deeply crucial and healing part of life and we offer no road map. I think it is core to ending violence. ~ Eve Ensler,
444:I'm not good at math. Numbers are a terrifying thing to me. My father is a whiz with money and the stock market, and he tries to explain it to me, and I find it terrifying. ~ Chris Gethard,
445:In baseball, we count everything,” Babe said. “Baseball’s a math teacher’s dream for teaching kids arithmetic. It’s numbers and statistics. It’s long division and decimals. I ~ Tony Castro,
446:It is like breathing to us, and to ignore math in this story would be akin to listening to Frank Zappa without ever having taken hallucinogens, an incomplete experience. ~ Stuart Rojstaczer,
447:What's great is that because math is such a universal language, really, our fans come in all shapes and sizes, all ages and genders and races and backgrounds and cultures. ~ David Krumholtz,
448:Common Core, the initiative that claims to more accurately measure K-12 student knowledge in English and math, also encourages children to step up their "critical thinking." ~ David Harsanyi,
449:When girls are asking themselves 'Who am I?' for the first time and they hear all this bad PR about math, they think, 'Well, whoever I am, I'm not somebody who likes math.' ~ Danica McKellar,
450:You can't plan the kind of deep love that results in children. Fatherhood was not a conscious decision. It was part of the wonderful ride I was on. All the math finally worked. ~ Johnny Depp,
451:And by the same token, I appreciate math, because I can't do math. If I have to read a map or figure out the tip on a restaurant bill, I might start to tear up a little bit. ~ Thomas F Wilson,
452:People assume because I'm a coffee expert I drink lots of coffee. I can't. It takes me half an hour to brew my perfect cup. Do the math. I simply don't have time to drink more. ~ Kevin Sinnott,
453:The average actor might only be able to book six to eight guest star jobs a year - that would be high. So when you start doing the math, you can't live on that in Los Angeles. ~ Beth Broderick,
454:If you're not a flaming Filipino dancing queen, they never, ever expect the Asian guy to be asking about gay sex. They always figure you want to talk about math. Or the violin. ~ David Levithan,
455:No one really buys records anymore. You can look at sales and do that math real quick. Unfortunately, it's fast food in the music industry. People don't ingest full records anymore. ~ Tommy Lee,
456:Skibbereen have a hard time at [math]; the best that the smartest of them can do with adding two plus two is guessing: three plus one. Correct, sort of, but not always useful. ~ Gregory Maguire,
457:Yeah, Silver and his math are jokes, because math has a liberal bias. After all, math is the reason Mitt Romney's tax plan doesn't add up. ~ Stephen Colbert, The Colbert Report (2012-11-05)[3].,
458:Bashful=Spanish, Miss Gardenia
Doc=Psychology, Mr. Wang
Happy=Chemistry 2, Mr. Durbin
Dopey=English Lit., Mr. Purcell
Dippy=Math, Mrs. Craig
Dumbass=PE, Coach Crater ~ Lisa McMann,
459:You know a lot about math," I said. You know a lot about math? What type of statement was that? Right along the lines of "Hey, you have hair and it's red and curly." Real smooth. ~ Katie McGarry,
460:My knowledge of science came from being with Carl, not from formal academic training. Carl gave me a thrilling tutorial in science and math that lasted the 20 years we were together. ~ Ann Druyan,
461:We need more math classes, we need more science. It's the art of math and the art of science that creates all the innovation, and we have a tradition of great arts, great music. ~ Wynton Marsalis,
462:Everybody has fucked-up families, even normal kids, even the ones who aren’t in here. There’s no magic math equation that makes us addicts, nothing that separates us from everyone else. ~ Amy Reed,
463:I want my girls to love math. I want them to think that being a scientist is the coolest possible job on the planet. I want them to not be afraid to lean toward their femininity. ~ Jennifer Garner,
464:Math is hard work and it occupies your mind—and it doesn’t hurt to learn all you can of it, no matter what rank you are; everything of any importance is founded on mathematics. ~ Robert A Heinlein,
465:I like doing math that involves measuring the lengths of numbers written out on the page (which is really just a way of loosely estimating log10x). It works, but it feels so wrong. ~ Randall Munroe,
466:See, it’s just a matter of looking at the lines and doing the math.” “Ugh, more math. I do enough of that as it is.” He laughed. “But this is fun math.” “Fun math is an oxymoron.” Kile ~ Kiera Cass,
467:There's a branch of math called the foundations of math. It's kind of like quantum mechanics. It's about how this very complex theory of math can be built up from very basic parts. ~ Tristan Perich,
468:Teaching kids how to nourish their creativity and curiosity, while still providing a sound foundation in critical thinking, literacy and math, is the best way to prepare them for ~ Peter H Diamandis,
469:Desar's chosen field in mathematics was so esoteric that nobody in the Institute or the Math Federation could really check on his progress. That was precisely why he had chosen it. ~ Ursula K Le Guin,
470:I reviewed some of his articles and knew Albert couldn’t manage all those mathematical calculations on his own. You were always better at math than him. Than most of us, actually.” I ~ Marie Benedict,
471:He went back to the TV, and after I finished washing the dishes by hand—no dishwasher—I went upstairs unwillingly to work on my math homework. I could feel a tradition in the making. ~ Stephenie Meyer,
472:There is number of different efforts around the country are to try to redesign the math pathway and the courses that students have to take to make it more applicable to the real world. ~ Anya Kamenetz,
473:The steps to solving a problem, from elementary math to breaking out of a police station, remained the same. A simple matter of understanding the problem, and selecting the best solution. ~ V E Schwab,
474:I love teaching online at my website and soon I'll be writing a math book. I love to teach math. I just don't have time for a full-time teaching gig. Acting is way too time-consuming. ~ Danica McKellar,
475:Math tip: Beans tend to triple in size when you cook them, so if you want to end up with 1½ cups of cooked beans (the standard can measurement), you want to start with ½ cup dried beans. ~ Thug Kitchen,
476:I’m told finance doesn’t require very complicated math. One guy told me that if you just designed a clean data display, people were amazed. So it’s more just advanced programming, ~ Kim Stanley Robinson,
477:I thought, well, you might see curves there, but that's just a bone - so even if I lose weight that's not going to change anything. That's how I look. That's my shape. Do the math. ~ Christina Hendricks,
478:It is a mistake to suppose that requiring the nonmathematical to take more advanced math courses will enhance their understanding and not merely exacerbate their sense of inadequacy. ~ William Raspberry,
479:let me let you in on a little secret as to why the new American gulag is going to be so popular. MSNBC has already done the math on this one: Prison = Entertainment! Now and forever! You ~ Cintra Wilson,
480:I'm a mathematician, basically. What I do is look around for problems where I can find useful applications for mathematics. All I do, really, is the math, and other people have the ideas. ~ Freeman Dyson,
481:Science, math and engineering can give you the exhilarating power to become not mere spectators or consumers, but the active explorers, makers and doers who will help invent the future. ~ Susan Hockfield,
482:My previous outlook could be summed up as follows: Life is shit. Math makes sense. Fictional characters are superior to real people because real people are equal parts pitiful and predictable. ~ Penny Reid,
483:The most important thing we can do is inspire young minds and to advance the kind of science, math and technology education that will help youngsters take us to the next phase of space travel. ~ John Glenn,
484:They look at what's more important, like subjects to help with the SAT's, etc. They miss that music is vital. It offers a break from a stressful day of science and math and it's different. ~ Justin Guarini,
485:When I was in school, my favorite subject was math. I took algebra and calculus. At an early age I grasped it and understood it quickly. I just enjoyed breaking the codes and solving problems. ~ Chris Bosh,
486:I started in a business background, but then it was like, 'you know, I can't do math,' so I changed it to a liberal arts degree and got my Bachelor of Arts in Communications and it made sense. ~ Jeff Dunham,
487:Ask your brain to do math every day, and it gets better at math. Ask your brain to worry, and it gets better at worrying. Ask your brain to concentrate, and it gets better at concentrating. ~ Kelly McGonigal,
488:Kids at the school, which launched a year and a half ago, aren't called students but "innovators." They receive a hardcore focus on STEM skills (that's science, technology, engineering and math). ~ Anonymous,
489:Marijuana-steeped conversations concerning questions of wave formation often take on mystical dimensions. Oceanographers and meteorologists can get even farther out there. They smoke math. ~ Patrick E McLean,
490:These are the dilemmas for cancer patients. Who and what to believe? A particular treatment is not foolproof, or as many medical experts remind us, is not math, with a fixed and certain outcome. ~ Tom Brokaw,
491:At the fourth grade level, girls at the same percentages of boys say they're interested in careers in engineering or math or astrophysics, but by eighth grade that has dropped precipitously. ~ Chelsea Clinton,
492:We must be willing to pay inspiring math and science teachers, who have high paying alternatives in industry, more to teach and reward students who take more challenging courses in high school. ~ Mark Kennedy,
493:When I was young I liked taking tests. I happened to be good at it. Certain subjects came easily, like math. All the science stuff. I would just read the textbooks in the first few days of class. ~ Bill Gates,
494:But I looked over at him, with his substitute math teacher glasses and hopeful expression, and my smile faded. He hadn't learned yet that things didn't work out just because you wanted then to. ~ Morgan Matson,
495:Damn it, Asher. Half of me is pissed as hell at how you treated
Danny, half of me feels sorry for you, and half of me—”
“Is horrifyingly bad at math?” Asher asked. Oliver glared at
him. ~ Cardeno C,
496:I am intentionally avoiding the standard term which, by the way, did not exist in Euler's time. One of the ugliest outgrowths of the "new math" was the premature introduction of technical terms. ~ George Polya,
497:Most people who open restaurants will fail, because they lack the fundamental understanding of restaurant math. Either they think they're superstar cooks or they think they're superstar hosts. ~ Joe Bastianich,
498:Then the voices started to argue and I threw my math book across the room in frustration.  It was a pretty bad sign when the voices inside your head started fighting with one another. ~ Jenna Elizabeth Johnson,
499:I think scientists have a valid point when they bemoan the fact that it's socially acceptable in our culture to be utterly ignorant of math, whereas it is a shameful thing to be illiterate. ~ Jennifer Ouellette,
500:Oh, he was a decent-enough high school student, good grades and well-liked, but his test scores were nothing to write home about. He might as well have Christmas-treed the math test. ~ Thomas Christopher Greene,
501:She had the stabbing, prickly feeling she had gotten in the third grade when she'd cheated on a math test. It was throbbing, gut-pounding feeling that she was a big fake about to be caught. ~ Jodi Lynn Anderson,
502:What makes you think they’re spying on you?” “Voco. An aut where a fraa or suur is called out from the math—Evoked—and goes to do something praxic for the Panjandrums. We never see them again. ~ Neal Stephenson,
503:Ask your brain to do math every day, and it gets better at math. Ask your brain to worry, and it gets better at worrying. Ask your brain to concentrate, and it gets better at concentrating. Not ~ Kelly McGonigal,
504:Was everything going to continue to come toward these kids earlier and earlier so that they emerged from the womb with their teeth wired, wearing glasses and helmets, scheduling math tutors? ~ Meg Mitchell Moore,
505:A surprising proportion of mathematicians are accomplished musicians. Is it because music and mathematics share patterns that are beautiful? ~ Martin Gardner in The Dover Math and Science Newsletter May 16, 2011.,
506:If you’re the very luckiest kind of astronaut ever, your big payoff is that you get to visit a barren airless wasteland for five minutes, do some more math, and then go home—ice cream not guaranteed. ~ Lindy West,
507:The fact that the same symbolic programming primitives work for those as work for math kinds of things, I think, really validates the idea of symbolic programming being something pretty general. ~ Stephen Wolfram,
508:"The Mother's child shall be a hero, a Mahâvira. In unhappiness, sorrow, death, and desolation, the Mother's child shall always remain fearless." ~ Swami Vivekananda (Belur Math, 1901)#SwamiVivekananda #BelurMath,
509:In high school, we studied a lot of poetical forms. I was really interested in the math that was involved and the strange live break ups. That gave me a great amount of respect for a rhymed stanza. ~ Joanna Newsom,
510:Mom was never much of a math person, but she took me to the public library before I could read, got me a library card, showed me how to use it, and always made sure I had access to kids’ books at home. ~ J D Vance,
511:My brother and I were born in an Irish county called Tipperary. We were both very math- and science-inclined in high school. My dad trained as an electrical engineer, and my mom is in microbiology. ~ John Collison,
512:It's estimated that across Africa 100 elephants are killed for their tusks every day. It takes nothing more than simple math to get to what that adds up to in a year, and it's a distressing figure. ~ Graydon Carter,
513:Since I was born I wanted to entertain and communicate. I wanted to communicate so badly ... My sixth-grade math teacher taped my mouth. I'm still out to get her [for that]. It was very traumatizing! ~ Jenna Elfman,
514:Tom was not good at math. He’d started to lose his way in middle school, as so many American kids did. It had happened gradually; first he hadn’t understood one lesson, and then another and another. ~ Amanda Ripley,
515:Within the United States, there is a real division between the PhDs given in science and math to the Asian community, to the traditional white community, and then to African-Americans and Hispanics. ~ Juan Enriquez,
516:I do the math. On one side: Anderson, the entire police force, the media, and most likely the pope himself. On the other side, my innocence. This does not add up to a terribly encouraging bottom line. ~ Jeff Lindsay,
517:Sometimes I wondered exactly what it might take to break Andy out of his math-nerd turret: a tidal wave? Decepticon invasion? Godzilla tromping down Fifth Avenue? He was a planet without an atmosphere. ~ Donna Tartt,
518:While President Obama shirks his responsibility to advance solutions to our fiscal challenges, he can no longer hide from the merciless math of the balance sheet. Conservatives have made certain of that. ~ Paul Ryan,
519:you are a mirror if you continue to starve yourself of love you’ll only meet people who’ll starve you too if you soak yourself in love the universe will hand you those who’ll love you too - a simple math ~ Rupi Kaur,
520:We have completely neutered grace (my good works save me, but we still call it grace), made God a math equation (God will like me if I’m good), and turned Jesus into Mr. Rogers (“Howdy, neighbor”). ~ Jefferson Bethke,
521:Space is for everybody. It's not just for a few people in science or math, or for a select group of astronauts. That's our new frontier out there, and it's everybody's business to know about space. ~ Christa McAuliffe,
522:Economics anxiety may be even more common than the often identified 'math anxiety,' for unlike math, which has its personal uses, economics is seen as a mysterious set of forces manipulated from above. ~ Gloria Steinem,
523:My background is basically scientific math. My Dad was a physicist, so I have it in my blood somewhere. Scientific method is very important to me. I think anything that contradicts it is probably not true. ~ John Astin,
524:A math teacher’s least favorite thing to hear from a student is “I get the concept, but I couldn’t do the problems.” Though the student doesn’t know it, this is shorthand for “I don’t get the concept. ~ Jordan Ellenberg,
525:For those of you who are about to embark on reading The Math Book from cover to cover, look for the connections, gaze in awe at the evolution of ideas, and sail on the shoreless sea of imagination. ~ Clifford A Pickover,
526:I didn't get a Bachelor's degree - I got a Bachelor's of Fine Arts, which means I didn't have to take humanities, math, and stuff like that. I think I had to take Art History, which I failed a few times. ~ Stephen Furst,
527:If you want to understand science, you have to understand math. In business, if you're enumerate, you're going to be a klutz. The good thing about business is that you don't have to know any higher math. ~ Charlie Munger,
528:I saw the head of NOW - National Organization of Women - saying that women still only make 70 cents on the dollar to every man. I'm not sure I'm going to believe that. Women are notoriously bad at math. ~ Bonnie McFarlane,
529:Numbers still gave Astrid pleasure. That was the great thing about numbers: it required no faith to believe that two plus two equaled four. And math never, ever condemned you for your thoughts and desires. ~ Michael Grant,
530:People are more easily manipulated when they don't have information. If you ensure that kids grow up without basic reading skills, math skills, and so forth, then you ensure that they can't act effectively. ~ Tony Kushner,
531:Sometimes the current even starts to flow in the other direction: sometimes, particularly in university math and science departments, nerds deliberately exaggerate their awkwardness in order to seem smarter. ~ Paul Graham,
532:I hated science in high school. Technology? Engineering? Math? Why would I ever need this? Little did I realize that music was also about science, technology, engineering and mathematics, all rolled into one. ~ Mickey Hart,
533:Their Internet usage is growing very rapidly, and even they can do the math: If everyone in China needed an IPv4 address - just one - this country would use up one third of the entire public IP address space. ~ Vinton Cerf,
534:The Polytechnic was a new sort of college dedicated to producing teachers and professors for various math or scientific disciplines, and it was one of the few universities in Europe to grant women degrees. ~ Marie Benedict,
535:There is certainly the intention of efforts like the Common Core to raise education standards and make sure that every student masters advanced math concepts - algebra, geometry, statistics and probability. ~ Anya Kamenetz,
536:Yeah, but I’m the second most fucked up person I know, and when you put two negatives together, you get a positive. That’s math, Caleb. Math is the language of the universe. You can’t argue with the universe. ~ C J Roberts,
537:Her touch is like doing simple math
When she sleeps in the bed, subtracting clothes
There is a red ink, like a sparkling red wine, adding colors
Dividing body, remembering gods, without multiplying ~ Santosh Kalwar,
538:I don't know all the answers in life, but the beauty in math is that the answer is always there."
He scoffed. "Yet I never seem to be able to find it."
"Maybe you've been looking in the wrong place. ~ Rachel Hawthorne,
539:Listening to the data is important... but so is experience and intuition. After all, what is intuition at its best but large amounts of data of all kinds filtered through a human brain rather than a math model? ~ Steve Lohr,
540:My first feeling was that there was no way to continue. Writing isn't like math;in math, two plus two always equals four no matter what your mood is like. With writing, the way you feel changes everything. ~ Stephenie Meyer,
541:We don’t learn about taking care of ourselves the way we learn math. Although information is useful and sometimes critical, self-care isn’t only an intellectual process. It’s our experiences that change us. ~ Melody Beattie,
542:I think it's not particularly necessary to lead a religious life. People progress just as well in music, or art, or math or science or gardening or whatever. It all seems to work as well and the process is good. ~ Jim Henson,
543:I was an undergraduate at Princeton, and I was pressed by the math department to go on to graduate school. Actually they gave me fellowships that paid my way, otherwise I would not have been able to continue. ~ Alonzo Church,
544:It'll turn out you mean love,' Sholto said. 'At the moment math is the only thing that excites you so you're nosing around numbers as if numbers are life. But in two years you'll be telling me about some boy. ~ Elizabeth Knox,
545:Logan’s overall score was a six-point-seven. Jimmy only has a score of six-point-four. Even with today’s new math, six-point-seven is greater than six-point-four. I can show you with a graph if that would help. ~ Harlan Coben,
546:Italian cuisine, at its very best, is a math problem that doesn't add up. A tangle of noodles, a few scraps of pork, a grating of cheese are transformed into something magical. 1+1=3: more alchemy than cooking. ~ Matt Goulding,
547:It baffled me how people could resist math's gorgeousness, but people did, and people do. The fine of its purity drives them away, the purity of the fine, unmixed with the heaviness of unnecessitated being. ~ Rebecca Goldstein,
548:My friends scoffed at my anxiety and said dumb things like, 'Fifty is the new forty!' Which just made me realize that there are a whole lot of other people who suck at math as bad as I do. No. Fifty is fifty. ~ Celia Rivenbark,
549:Being forced to sit between my mortal enemy and my ex-girlfriend every afternoon made seventh-period math feel like my own private Kobayashi Maru, a brutal no-win scenario designed to test my emotional fortitude. ~ Ernest Cline,
550:He rolled his eyes. "First, my Dad's Korean and my mom was Swedish. Second, I totally suck at math. I don't like cuckoo clocks or skiing or fancy chocolate either." I sputtered a laugh. "I think that's Swiss. ~ Kelley Armstrong,
551:In addition to giving our children the science and math skills they need to compete in the new global context, we should also encourage the ability to think creatively that comes from a meaningful arts education. ~ Barack Obama,
552:I'd always been the confident guy in school. I was good in math and English, but I was still shy. I couldn't get up and speak in front of people. I was asked to do it when I was 10 years old and I burst out crying. ~ Chris Vance,
553:The best way to be appreciative for your life is to live it; don't die for any other reason but love. Dreams are what guide us, art is what defines us, math is makes it all possible, and love is what lights our way. ~ Mike Norton,
554:Writing is so wrapped up in ego, but with math one is just trying to get it right, although you're often wrong. I think math helped me become a good critic of myself, come at writing a little less personally. ~ Bonnie Jo Campbell,
555:a 1997 Boston Globe article notes that “several new studies highlight the problems boys have in reading and writing, showing that they are far worse than the well-advertised problems for girls in math and science ~ Geoffrey Canada,
556:He rolled his eyes. "First, my Dad's Korean and my mom was Swedish. Second, I totally suck at math. I don't like cuckoo clocks or skiing or fancy chocolate either."
I sputtered a laugh. "I think that's Swiss. ~ Kelley Armstrong,
557:I am insubstantial. A tangled, vaporous creature that lives in my brain, almost wholly imaginary. I can be here with him as easily as I can inhabit a sonnet or an organic molecule, or crawl inside a math problem. ~ Brenna Yovanoff,
558:And you’re overthinking things, Charming.  Do the math.  Naked, interested man, check.  Wet, willing woman, double check.  Now insert part A into slot B and we can move on to the engineering portion of our quiz today. ~ Jane Cousins,
559:Math was a two-part exam and I once didn't go for the second part. I knew I'd done so badly on the first it was hopeless. I re-took it about four or five times. I think I eventually got it by getting the top GCSE grade. ~ Rob Brydon,
560:The degree to which the arts are included in our educational curriculum is totally inadequate. The arts are just as important as math and science in an education and just as important as any other endeavour in our lives. ~ Ken Danby,
561:When I got to college, I was intending to study film. But I found that my brain was feeling mushy, so I took a few math classes. I started doing really well at them, and solving equations was this, like, drug rush. ~ Danica McKellar,
562:I never had a mind for math. I simply couldn't hold the formulas and numbers in my head. It was logic that made little sense to me. In my perception, the world wasn't a graph or formula or an equation. It was a story ~ Cheryl Strayed,
563:program and not. “It’s just like sports,” Dhuey said. “We do ability grouping early on in childhood. We have advanced reading groups and advanced math groups. So, early on, if we look at young kids, in kindergarten ~ Malcolm Gladwell,
564:The vast majority of us imagine ourselves as like literature people or math people. But the truth is that the massive processor known as the human brain is neither a literature organ or a math organ. It is both and more. ~ John Green,
565:you are a mirror
if you continue to starve yourself of love
you'll only meet people who'll starve you too
if you soak yourself in love
the universe will hand you those
who'll love you too
- a simple math ~ Rupi Kaur,
566:I didn't think that college math was for me. I didn't think I'd be able to hack it. And that perception of math not being for girls, not being for girls who see themselves as socially well adjusted has got to change. ~ Danica McKellar,
567:Learning is about much more than science and math. Doing theater, music, and art in school really helps children's minds grow because they're using different parts of their brains. Parents who care should insist on that. ~ Julie Taymor,
568:First of all, relationships might be built on trust, but they are also built on attraction. It's critical, it's chemical, it's animal. And it's one hundred percent required to make the rest of the math work out right. ~ Delancey Stewart,
569:That is the inescapable math of tragedy and the multiplication of grief. Too many good people die a little when they lose someone they love. One death begets two or twenty or one hundred. It's the same all over the world. ~ Ben Sherwood,
570:We've lost something that's been with us for so long, and something that drew a lot of us into mathematics. But perhaps that's always the way with math problems, and we just have to find new ones to capture our attention. ~ Andrew Wiles,
571:All over China, parents tell their children to stop complaining and to finish their quadratic equations and trigonometric functions because there are sixty-five million American kids going to bed with no math at all. ~ Michael Cunningham,
572:Anything we were studying in school, like math, or understanding somebody's behavior outside of school, kind of worked its way into something I could understand by way of a musical experience I'd had or something I'd heard. ~ Blake Mills,
573:i can't wrap my head around the fact
that i have to convince half the world's population
my body is not their bed
i am busy learning the consequences of womanhood
when i should be learning science and math instead ~ Rupi Kaur,
574:I do not intend to give you any homework - no difficult math questions, or anything like that, and conjugating English verbs is outside my sphere of interest. However, from time to time I'll give you a short assignment. ~ Jostein Gaarder,
575:Oh, and in case you don’t recognize me, since apparently waitressing here requires such a transformation, I’ll be the hot one doing math in her head.” I lean toward Ryder, my lips close to his ear. “No push-up bra necessary. ~ Eve Jagger,
576:People love to admit they have bad handwriting or that they can't do math. And they will readily admit to being awkward: 'I'm such a klutz!' But they will never admit to having a poor sense of humor or being a bad driver. ~ George Carlin,
577:but you know the minute I graduated high school I never looked at a single math problem again, right? I send everything with numbers on it to my accountant, or I make Michael deal with it.” “Great. Spoken like a true feminist, ~ Meg Cabot,
578:I’d never had a mind for math. I simply couldn’t hold the formulas and numbers in my head. It was a logic that made little sense to me. In my perception, the world wasn’t a graph or formula or an equation. It was a story. ~ Cheryl Strayed,
579:I'm a scientist. I find beauty in absolutes. I love the clarity of math, its unwavering dependability. Math will never say one thing and do another one. It will never harm you on purpose because its only purpose is truth. ~ Sylvain Neuvel,
580:What math concept do people find most counterintuitive? The idea that there is more than one kind of infinity. Or that, in a room with 23 randomly chosen people, the chance that two share a birthday is greater than 50 percent. ~ Anonymous,
581:What's all this whining about the environment? They're always talking about 'stop the clearcuts.' I mean do the math people. If we were out of trees then we wouldn't have any clearcuts to be complaining about now would we? ~ George W Bush,
582:Education happens to be something that all people, all cultures, need to embrace. Math, science, the words of the world. To be able to speak and be able to have clarity and to be able to think. Those are the greatest of gifts. ~ Bill Cosby,
583:Javel saw evil in those bright blue eyes, not malevolence but something much worse: an evil born of lack of self-awareness, an evil that didn’t know it was evil and therefore could justify anything. Evil that did the math. ~ Erika Johansen,
584:People will tell you that you have to know math to be a scientist, or physics or chemistry. They're wrong. ... What comes first is a question, and you're already there. It's not nearly as involved as people make it out to be. ~ Hope Jahren,
585:Pick up a fifth-grade math or rhetoric textbook from 1850 and you’ll see that the texts were pitched then on what would today be considered college level. The continuing cry for “basic skills” practice is a smoke screen ~ John Taylor Gatto,
586:whose students are willing to concentrate and sit still long enough and focus on answering every single question in an endless questionnaire are the same countries whose students do the best job of solving math problems. ~ Malcolm Gladwell,
587:And you're a bad boy?" I asked.
Ollie's grin was contagious. "Oh, I'm a bad, bad boy."
Cam shot his friend a look. "Yeah, as in bad at spelling, math, english, cleaning up after yourself, talking to people, and I could go on. ~ J Lynn,
588:The governors of Oklahoma and South Carolina signed bills within the past week repealing the Common Core state standards, guidelines for children’s achievement in reading and math between kindergarten and high school graduation. ~ Anonymous,
589:From inside the elephant, the bird had sounded like it could convince a mountain to turn into a volcano. Now it sounded like her math teacher that one time he had tried to perform a cappella but had stepped on a Lego piece. ~ Roshani Chokshi,
590:I love acting. Acting is a true love of mine, acting and math. Although they are both creative, they use very different sides of your brain. And I love both. Acting is my first love, and that's my main career, it really is. ~ Danica McKellar,
591:I managed to mostly keep everything up to date between missions. Before I'd come on it had been a real mess. Apparently killing and math were mutually exclusive skill sets for most people, but I'd gotten the books cleaned up. ~ Larry Correia,
592:I suppose I felt doomed to be an artist early on because of the way I drew all over the books that I needed for school, from ancient history to math. I was more interested in drawing in the margins than actually doing the work. ~ Nancy Spero,
593:Then again, Einstein (pretty good at math) was also quite clear when he concluded, There are only two ways to live your life. One is as though nothing is a miracle. The other is as though everything is a miracle. ~ Amy Krouse Rosenthal,
594:Things happen. Things that physics and math and crap that gets measured in a lab can't explain. People aren't just laws and rules, Claire. They're... sparks. Sparks of something beautiful and huge. And some sparks glow brighter ~ Rachel Caine,
595:Before the math and the momentum overwhelm us all, we are going to solve this nation's economic problems. And I'm going to level with you: We don't have that much time. But if we are serious, and smart, and we lead, we can do this. ~ Paul Ryan,
596:But what is hard to understand is why the math and science gap launched a massive movement on behalf of girls, and yet a much larger gap in reading, writing, and school engagement created no comparable effort for boys. ~ Christina Hoff Sommers,
597:We actually have a candidate for the mind of God. The mind of God we believe is cosmic music, the music of strings resonating through 11 dimensional hyperspace. That is the mind of God. ~ Michio Kaku, Math is the Mind of God (29 December 2012),
598:Winning meant saving lives. Winning meant we survived. Winning meant the monsters died. It was simple math and anyone who didn’t understand that vampire hunting was just that simple wasn’t going to be very good at the job. ~ Laurell K Hamilton,
599:I feel like math and writing are the same thing. You're putting together a lot of complex things to satisfy different requirements. It's got to be aesthetically pleasing; it's got to have subtext; it's got to convey information. ~ Shane Carruth,
600:Math can explain the reason there’s a one out of four chance that I’d have blue eyes. But it doesn’t explain why me. And science or math can’t explain what makes one person lucky, or what makes a person lucky enough to survive. ~ Heidi W Durrow,
601:If your parents are billionaires, that might actually be an obstacle to your own happiness and self-development. If you go to Oxford or Harvard, that might actually thwart your desire to graduate with a science or math degree. ~ Malcolm Gladwell,
602:You have six math Ph.D. Caucasian gentlemen from the Northeast of the country, great. You put one more in the mix, you haven't added much. It's only when you add something different that you really are able to accomplish more. ~ Sallie Krawcheck,
603:It’s unbelievable today, but there was a time when the government classed crypto as a munition and made it illegal for anyone to export or use it on national security grounds. Get that? We used to have illegal math in this country. ~ Cory Doctorow,
604:Those of us who teach math should try to turn this bug into a feature. We should be up front about the fact that word problems force us to make simplifying assumptions. That’s a valuable skill—it’s called mathematical modeling. ~ Steven H Strogatz,
605:If you've got a dollar and you spend 29 cents on a loaf of bread, you've got 71 cents left; But if you've got seventeen grand and you spend 29 cents on a loaf of bread, you've still got seventeen grand. There's a math lesson for you. ~ Steve Martin,
606:I was talking to a homeless man at the laundry mat recently, and he said that when we reduce Christian spirituality to math we defile the Holy. I thought that was very beautiful and comforting because I have never been good at math. ~ Donald Miller,
607:Math is supremely important. Do you know how important it is…” and then proceeds to lecture on about the importance of math in life until her children beg her to stop because they would rather just do the math than listen to her. ~ Maya Thiagarajan,
608:My message is: You don't have to give up being popular, fun, or fashionable in order to be smart; they can go hand and hand. Doing math is a great way to exercise your brain; being smart is going to make you more powerful in life. ~ Danica McKellar,
609:Interestingly, the only class that Eric actually enjoyed in Korea was math. He noticed it on his first day of school. Something was very different about how math was taught in Korea. Something that not even Minnesota had figured out. ~ Amanda Ripley,
610:I've actually become much, much dumber through being married and having these children. I find that I'm not half as sharp that I once was. I can't even help them with their 4th and 5th grade vocabulary and math work at this point. ~ Patrick Warburton,
611:Scientific research and other studies have demonstrated that arts education can enhance American students' math and language skills and improve test scores which in turn increase chances of higher education and good jobs in the future. ~ Thad Cochran,
612:The real work of us mathematicians, from now until, roughly, fifty years from now, when computers won't need us anymore, is to make the transition from human-centric math to machine-centric math as smooth and efficient as possible. ~ Doron Zeilberger,
613:To say that math is important because it is useful is like saying that children are important because we can train them to do spiritually meaningless labor in order to increase corporate profits. Or is that in fact what we are saying? ~ Paul Lockhart,
614:Teaching kids how to nourish their creativity and curiosity, while still providing a sound foundation in critical thinking, literacy and math, is the best way to prepare them for a future of increasingly rapid technological change. ~ Peter H Diamandis,
615:What are the chances you’d ever meet someone like that? he wondered. Someone you could love forever, someone who would forever love you back? And what did you do when that person was born half a world away? The math seemed impossible. ~ Rainbow Rowell,
616:Half the time he felt entirely out of control. Half the time he threw up walls out of fear. And half the time he opted out of life before anyone had the chance to discard him. No matter that the math didn’t add up, it was just how he felt. ~ Laura Kaye,
617:In physics, your solution should convince a reasonable person. In math, you have to convince a person who's trying to make trouble. Ultimately, in physics, you're hoping to convince Nature. And I've found Nature to be pretty reasonable. ~ Frank Wilczek,
618:Why don’t high school math teachers ever come up with cool problems like this? If a 150-pound Irish wolfhound launches himself at seventeen miles per hour at a 250-pound draugr, will that dead motherfucker go down? The answer is Hel yes. ~ Kevin Hearne,
619:I actually don't believe that everybody should necessarily try to learn to code. I think it's reasonably specialized, and nobody really expects most people to have to do it. It's not like knowing how to read and write and do basic math. ~ Linus Torvalds,
620:I hadn’t spoken to Rick in nine years.” “Nine years,” I repeated. “That would be right around the time we met.” She looked at me. “Don’t be dazzled by my mathematical prowess,” I said. “Math is one of my hidden talents. I try not to brag. ~ Harlan Coben,
621:This phrase did not have the ring of verisimilitude because I am famously bad at math. If I'm in charge of tipping at a restaurant, the waiter will either fall to his knees in gratitude or slash my tires. There ain't no Mr. In Between. ~ Celia Rivenbark,
622:Bast had insisted we keep everyone up-to-speed on the regular subjects like math and reading, although she did sometimes add her own elective courses, such as Advanced Cat Grooming, or Napping. There was a waiting list to get into Napping. ~ Rick Riordan,
623:But I've been in so much trouble. I threw an apple at Lea's face. I fought guards. I cheated on my trig exam."
Aiden looked at me, frowning. "You cheated on your math exam?"
"Uh, forget that. Anyway, wow, I'm just surprised. ~ Jennifer L Armentrout,
624:Every three days, I’d wake up, look at calendar, eat, drink, bathe, et cetera. I would only spend one hour awake each time. I did the math: for the next four months, 120 days total. I would spend only fourth hours in a conscious state. ~ Ottessa Moshfegh,
625:The President's call for more math and science students is not being heeded by his party's leaders in Congress. They are cutting over $10 billion from student aide while refusing to fully fund No Child Left Behind. Something doesn't add up. ~ Jim Clyburn,
626:The South Carolina Education Oversight Committee found that the new South Carolina math standards were 92 percent in alignment with the content of the Common Core. In other words, the math they’re asking students to learn is largely the same. ~ Anonymous,
627:Success comes from hard work and the accumulation of small numbers. Unlike yesterday, today’s prosperity can bloom from continuous intelligent production. For the first time in history, life as a full-time writer has become about simple math. ~ Sean Platt,
628:The green fractals of the forest and the eons of faint star clusters above—my math’s teacher’s order in the universe—were nothing like the thoughts that jumped at me like thieves. When your friend has a boyfriend, you are supposed to back off. ~ Anya Allyn,
629:They found Mr. Jesse in a boat?" I asked. "I'm wondering if maybe he just up and died. Maybe there ain't no murder. Like the fish weren't biting and he died of boredom. It happens. Boredom kills. I've had close brushes myself, during math. ~ Sheila Turnage,
630:And all things, whatsoever ye shall ask in prayer, believing, ye shall receive” (Math. 21:22). “Therefore I say unto you, what things soever ye desire, when ye pray, believe that ye receive them, and ye shall have them” (Mark 11:24). ~ Florence Scovel Shinn,
631:Comedy is like math - you can check your answer because you know you've gotten it right if you get a laugh. It just makes sense to me. I feel like because I've had to keep that tool in my box for so long, I'm ready to show it off a bit. ~ Jennifer Carpenter,
632:I think that great programming is not all that dissimilar to great art. Once you start thinking in concepts of programming it makes you a better person...as does learning a foreign language, as does learning math, as does learning how to read. ~ Jack Dorsey,
633:Music rhythms are mathematical patterns. When you hear a song and your body starts moving with it, your body is doing math. The kids in their parents' garage practicing to be a band may not realize it, but they're also practicing math. ~ Kareem Abdul Jabbar,
634:Children need far more than basic skills in reading, writing, and math, as important as those might be. Children also need to learn how to think for themselves, how to find meaning in what they learn, and how to work and live together. ~ Marshall B Rosenberg,
635:Environment-based education produces student gains in social studies, science, language arts, and math; improves standardized test scores and grade-point averages; and develops skills in problem-solving, critical thinking, and decision-making. ~ Richard Louv,
636:Is it not enough that species after species on this earth fades into extinction at a rate of one per minute?" I did some math. "That means every species on your planet would be extinct in ninety-six years. When did you start counting? ~ Karina Lumbert Fabian,
637:I don't believe that math and nature respond to democracy. Just because very clever people have rejected the role of the infinite, their collective opinions, however weighty, won't persuade mother nature to alter her ways. Nature is never wrong. ~ Janna Levin,
638:Or an amicable pair,” said Sam. “Sorry?” “In math, that’s what we call two numbers each of which is equal to the sum of the divisors of the other. The smallest ones, 220 and 284, were regarded by the Pythagoreans as symbols of true friendship. ~ Reginald Hill,
639:We spend more per pupil than any other country, but among industrialized nations, American students rank near the bottom in science and math. Only 13 percent of high school seniors know what high school seniors should know about American history. ~ Glenn Beck,
640:Art saved my life in two ways. It made me feel special, because I could do things my friends couldn't, but it also gave me a way to demonstrate to my teacher that, despite the fact that I couldn't write a paper or do math, I was paying attention. ~ Chuck Close,
641:I always loved science and math growing up. I was born in Iran; I grew up there and then came to the United States when I was about 16 years old. And I thought that this was my opportunity to get involved with something really cool and great. ~ Anousheh Ansari,
642:The idea here, of course, is, you know, mathematics is the language of science, it's the way that we understand the natural world. And there's definitely been a push to sort of study advanced math and kind of reawaken the love of advanced math. ~ Anya Kamenetz,
643:You’re probably better at math than I am, because pretty much everyone’s better at math than I am, but it’s okay, I’m fine with it. See, I excel at other, more important things—guitar, sex, and consistently disappointing my dad, to name a few. ~ Jennifer Niven,
644:I use minimal software to make my music - a wav editor and a calculator for my beats to make sure everything falls on mathematical precision. If you were just mapping this out visually, it works by math. I guess it's slightly engineering influenced. ~ Girl Talk,
645:Speaking of human computers, there is a guy named Art Benjamin, he's a human calculator. He says it's a skill he learned as a kid. Now he's a math professor at Harvey Mudd. He can find the square root of a six digit number in a few seconds. Practice. ~ Bill Nye,
646:As processor speeds and shared processors create cheap unlimited processing power we will be able to turn our bodies into a math equation that can be crossed against the properties of medicine and nature to create medicine unique to each individual. ~ Mark Cuban,
647:It was gonna be a race [2016] that set a foundation for the Left in the future. But given the math, I didn't think he was gonna make it. And so I started to shift to Hillary [Clinton] and to discussions of the platform and discussions of what to do. ~ Tom Hayden,
648:So many people think that social studies and weird lessons in social studies, teaching kids in America are bad, is it the result of Common Core? And it's not. It's not. Common Core does not deal with social studies. It's basically writing and math. ~ Megyn Kelly,
649:... suddenly I was a kid in the hall standing outside my locker about to head to Math. But that was how it went sometimes, the English language, when you really needed it, crumbled to clay in your mouth. That's when all the real things were said. ~ Marisha Pessl,
650:Dum walks backwards, talking to us. “We’re going back to high school where our survival instincts are at their finest.”

“If you get the urge to graffiti the walls or beat up your old math teacher,” says Dee, “do it where the birds can’t see you. ~ Susan Ee,
651:... You get surreal numbers by playing games. I used to feel guilty in Cambridge that I spent all day playing games, while I was supposed to be doing mathematics. Then, when I discovered surreal numbers, I realized that playing games IS math. ~ John Horton Conway,
652:I want to help middle-school girls stay interested in math and be good at it, and see it as friendly and accessible and not this scary thing. Everyone else in society tells them it's not for them. It's for nerdy white guys with pocket protectors. ~ Danica McKellar,
653:I was never as focused in math, science, computer science, etcetera, as the people who were best at it. I wanted to create amazing screensavers that did beautiful visualizations of music. It's like, "Oh, I have to learn computer science to do that." ~ Kevin Systrom,
654:Get your math book out. We're gonna cure this case of the stupids', he said as he sat down next to me on my bed, pointing at a stack of books underneath a pile of my dirty clothes. 'Jesus, open a window, it smells like death shit in here', he added. ~ Justin Halpern,
655:Pierce bites his knuckle and leans forward, forcing me out of my head. “Do you have any idea how sexy that is?” “You think it’s sexy that I can do math in my head?” “Yes. You’re gorgeous, outspoken, and intelligent. It’s a hard-on-inducing trifecta. ~ Helena Hunting,
656:Research and development needs permanent tax credits to build the technology that spurs our growth. But no government programs alone can get America's students to study more science and math parents must push and help their children to meet this goal. ~ Ernest Istook,
657:the Asian mothers I spoke with all reiterated the importance of “study routines” or “study schedules.” If children assume that they will have to do supplementary math every Saturday morning, then they will accept it as part of their weekly routine. ~ Maya Thiagarajan,
658:A strip club is one of the few places where two groups voluntarily come together who have such precipitous contrasts in net worth and familiarity with violence, each group with a head-and-shoulders edge in one category. The basic math of a tropical storm. ~ Tim Dorsey,
659:by the boats in the harbor. What else would you like to know?” “You plan to keep him tomorrow night?” “I get thirty-six hours, once a month. That’s 9:00 a.m. tomorrow until 9:00 p.m. Sunday. Do the math. It’s not that complicated.” The waiter pops in to ~ John Grisham,
660:In high school, a teacher once suggested that I be a math major in college. I thought, 'Me? You've got to be joking!' I mean, in junior high, I used to come home and cry because I was so afraid of my math homework. Seriously, I was terrified of math. ~ Danica McKellar,
661:My main concern with the condition of mathematics in high school is that there's a lot of fear involved! Math is not, generally speaking, presented in a fun way. The concepts, as I see them, are fun, and that's the way I'd like to convey them myself. ~ Danica McKellar,
662:I've been staying after school getting help in trig from Laura Johnson. Shit, it's just school work. And it's fucking Laura, granny panties, Johnson! It's not like I've been secretly banging her as she whispers math problems in my ear or something. ~ A Meredith Walters,
663:Learning improves in school environments where there are comprehensive music and arts programs. They increase the ability of young people to do math. They increase the ability of young people to read. And most important of all, they're a lot of fun. ~ William J Clinton,
664:Mathematically, maybe,” I said. “But trust isn’t one of those things that lends itself well to math.” “Sure it does,” Bob said. “You trust somebody, they betray you, you get a negative value. You never trust, they can never disappoint you, you break even. ~ Jim Butcher,
665:Forcing your spouse to stop doing that bad habit that drives you crazy, or making your kid be better at math or at art or at swimming, or making your parents or your in-laws not be annoying in the way that they're annoying, these are sometimes doomed goals. ~ Ian Bogost,
666:In fact, people who are extremely adept at mental tasks that demand cognitive control and a roaring working memory—like solving complex math problems—can struggle with creative insights if they have trouble switching off their fully concentrated focus.5 ~ Daniel Goleman,
667:I tend to jot down moments, lines, interactions that don't really make any sense. I try and explain these scattered notes to my close friends, and they become more and more logical. I see screenwriting as a bit like a math equation which I have to solve. ~ Asghar Farhadi,
668:It is this breathtaking image [of] success that motivates us and motivates kids to follow and understand rocket science: to understand the importance of physics and math and, in many ways, to have that awe at exploration of the frontiers of the unknown. ~ Steve Jurvetson,
669:As Einstein once wrote (more ringingly in German than in this English translation by one of us [DG]) to honor Isaac Newton: Look unto the stars to teach us How the master’s thoughts can reach us Each one follows Newton’s math Silently along its path. ~ Neil deGrasse Tyson,
670:In Korea, math moved fluidly. When the teacher asked questions, the kids answered as if math were a language that they knew by heart. As in Tom’s class in Poland, calculators weren’t allowed, so kids had learned mental tricks to manipulate numbers quickly. ~ Amanda Ripley,
671:Memorizing multiplication tables may be a seminal school experience, among the few that kids today share with their grandparents. But a Stanford University professor says rapid-fire math drills are also the reason so many children fear and despise the subject. ~ Anonymous,
672:Well, I had a lot of help from my father with the soldering and so on, and he was very good at math and was fascinated with computers, and so I was fortunate enough to have a bunch of exposure going all the way back to high school - this was in the 1960s. ~ Mitchell Kapor,
673:Albert Einstein had Max Talmud, his first mentor. It was Max who introduced a ten-year-old Einstein to key texts in math, science, and philosophy. Max took one meal a week with the Einstein family for six years while guiding young Albert. No one is self-made. ~ Gary Keller,
674:First of all, as you know, there are two kinds of people in the world: those who divide everyone into two kinds of people and those who don’t. But actually, there are three kinds of people in the world: those who are good at math and those who aren’t. ~ Neil deGrasse Tyson,
675:I enjoyed mathematics from a very young age. At the beginning of college, I had this illusion, which was kind of silly in retrospect, that if I just understood math and physics and philosophy, I could figure out everything else from first principles. ~ Erez Lieberman Aiden,
676:Saying no”, argues the author Kevin Ashton, “has more creative power than ideas, insights and talent combined. No guards time, the thread from which we weave our creations. The math of time is simple: you have less than you think and need more than you know. ~ Kevin Ashton,
677:Statistical malfeasance has very little to do with bad math. Judgement an integrity turn out to be surprisingly important. A detailed knowledge of statistics does not deter wrongdoing any more than a detailed knowledge of the law averts criminal behavior. ~ Charles Wheelan,
678:With political messaging, as with most WMDs [Weapons for Math Destruction], the heart of the problem is almost always the objective. Change that objective from leeching off people to helping them, and a WMD is disarmed -- and can even become a force for good. ~ Cathy O Neil,
679:Andrew’s kissing Amanda again, her back pinned against the door frame, his hands working through a geometry problem where the goal is to find the point of intersection where two legs bisect. People would like math so much more if it involved real life like that. ~ Julia Kent,
680:I stopped in my tracks. Looking bemused, Alaric did the same. “What year did we go to block-by-block private cell towers? Anybody know?” “Uh… two thousand twenty,” said Alaric, after a long pause to do the math inside his head. “I remember when they put ours in. ~ Mira Grant,
681:Testing may convincingly demonstrate the presence of bugs, but can never demonstrate their absence."- Edsger W. Dijkstra, Computing Pioneer (1930–2002), "Programming as a discipline of mathematical nature," Am. Math. Monthly, 81 (1974), No. 6, pp. 608–12. ~ Gerald M Weinberg,
682:At one point I wanted to work for NASA and be an astrophysicist, so I did physics, math, and chemistry before realizing I probably wasn't quite smart enough to do that. But I am still hugely interested in cosmology and astrophysics. That is my geeky subject area. ~ Gemma Chan,
683:People expect the math to be simplified, but I want to surprise them right from the start. When the brain gets lost, it doesn't stop working. It tries to makes sense of things. It begins to speculate and guess, and that's when things open up. That's exciting. ~ Simon McBurney,
684:When I was growing up, no one ever said to me, "You cannot do math because you're a girl." But, there was an understanding growing up that math and science were for boys. Somebody lied to me because Katherine Johnson woman exists, all of these women existed. ~ Taraji P Henson,
685:Because the math is, if you - 5 percent of a million is a lot more than 5 percent of a thousand. So yeah, someone who makes more money, numerically, it's gonna be higher. But the greatest gains, percentage-wise, for people, are gonna be at the lower end of our plan. ~ Ted Cruz,
686:I'm skipping, but Cam doesn't have a class until this afternoon, so he's a good boy."
"And your a bad boy?"
"Oh, I'm a bad, bad boy."
"Yeah, as in bad at spelling, math, english, cleaning up after yourself, talking to people, and I could go on. ~ Jennifer L Armentrout,
687:I recognize that I have a unique position to be a role model to young girls because I am doing something that they consider glamorous, which is acting, and yet I took a time to really get my education and study mathematics, and I think math is the cat's meow. ~ Danica McKellar,
688:I tell students that even if they don't like math right now, they can use math as a brain-sharpening tool - a tool that not only builds the foundation for a great career, but that also builds self-confidence, no matter what they choose to do with their lives. ~ Danica McKellar,
689:Like I realize that this is irrational,but when they tell you that you have,say,a 20 percent chance of living five years, the math kicks in and you figure that's one in five...so you look around and think,as any person would:I gotta outlast four of these bastards. ~ John Green,
690:One of the most amazing things about mathematics is the people who do math aren't usually interested in application, because mathematics itself is truly a beautiful art form. It's structures and patterns, and that's what we love, and that's what we get off on. ~ Danica McKellar,
691:tutor in the computer lab. Claire was an art history major. She had never been good at math. Or at least she’d never tried to be, which was the same thing. She could vividly remember the first time she’d sat down with Paul and gone over one of her assignments. ~ Karin Slaughter,
692:When you do the math and examine how much energy is produced per atomic union, you find that fusing anything to iron’s twenty-six protons costs energy. That means post-ferric fusion* does an energy-hungry star no good. Iron is the final peal of a star’s natural life. ~ Sam Kean,
693:Why haven't we fixed sick yet? You scientists there-- put down those starfish and HELP us. I hereby demand that all the people who are good at math make the world free of illness. The rest of us will write you epic poems and staple them together into a booklet. ~ Daniel Handler,
694:I mean can you walk to school on your own? Can you study science? Can you study math? Can you go to a normal school? Do you need to go to a special school? What is going to become of you when you grow up? Are you going to have to live on social security and SSI? ~ Sheena Iyengar,
695:What destroys more self-confidence than any other educational thing in America is being assigned to some remedial math when you get into some college, and then it's not taught very well and you end up with this sense of, 'Hey, I can't really figure those things out.' ~ Bill Gates,
696:Math-thinking, I would say, encourages flipping and substituting letters in words (in the novel, one of the boys double-majors in math and myth, for example, and his twin cracks a joke about the father's handwriting that morphs "cacography" into "dadography"). ~ Mary Kay Zuravleff,
697:My father was really good with math. It's a funny thing, I don't remember my father or my mother being so mechanical-minded. My father always wanted to be a doctor, but he came from a really poor family in Georgia, and there was no way he was going to be a doctor. ~ Herbie Hancock,
698:Rachel bit her lip. "I hope you're right. I'm a little worried. What if someone asks what's on the next math test and I start spouting a prophecy in the middle of geometry class? The Pythagorean theorem shall be problem two...Gods, that would be embarrassing. ~ Rick Riordan,
699:Some advice: keep the flame of curiosity and wonderment alive, even when studying for boring exams. That is the well from which we scientists draw our nourishment and energy. And also, learn the math. Math is the language of nature, so we have to learn this language. ~ Michio Kaku,
700:True,” Adam said. “But I can read numbers, Bob. Logan’s overall score was a six-point-seven. Jimmy only has a score of six-point-four. Even with today’s new math, six-point-seven is greater than six-point-four. I can show you with a graph if that would help.” Gaston ~ Harlan Coben,
701:They come in here every once in a while, and she goes to one corner and he goes to the other, and then they move around the store creating parabolas as they come together and bounce apart. They're the weirdest couple on Earth. I want to write math equations about them. ~ Sandy Hall,
702:Here's an uplifting story. Congratulations to the Little League team from Huntington Beach, California. Yeah, they beat Japan to win the Little League World Series. That's pretty good. See, that proves that when math and science aren't involved, our kids can beat anybody. ~ Jay Leno,
703:We believed we could prepare our kids for a more competitive world. And today, our younger students have earned the highest math and reading scores on record. Our high school graduation rate has hit an all-time high. And more Americans finish college than ever before. ~ Barack Obama,
704:This is the way it was in Yates County. Bald Girls. Wild boys formed from math. Geniuses all around, just waiting to be discovered, or waiting to rot in trailers behind their parents' barns, die penniless, mourned only by the Amish from whom they bought all those eggs. ~ Lydia Netzer,
705:Ada’s ability to appreciate the beauty of mathematics is a gift that eludes many people, including some who think of themselves as intellectual. She realized that math was a lovely language, one that describes the harmonies of the universe and can be poetic at times. ~ Walter Isaacson,
706:I don't know anything about making movies. I'd never been on a film set. I'm really kind of an idiot when it comes to figuring out where objects are in space. If they're both moving, I can't do the math. If you ever see me driving down a road, go somewhere else quickly. ~ Tony Kushner,
707:Indeed, there is something to be said for the old math when taught by a poorly trained teacher. He can, at least, get across the fundamental rules of calculation without too much confusion. The same teacher trying to teach new math is apt to get across nothing at all. ~ Martin Gardner,
708:Studies show that even a brief connection with a role model can vastly increase unconscious motivation. For example, being told that you share a birthday with a mathematician can improve the amount of effort you’re willing to put into difficult math tasks by 62 percent. ~ Daniel Coyle,
709:Dad claims that library science is the foundation of all sciences just as math is the key -- and we will survive or founder, depending on how well the librarians do their jobs. Librarians didn't look glamorous to me but maybe Dad had hit on a not very obvious truth. ~ Robert A Heinlein,
710:Is it any wonder that the cultural archetype of my generation is the Nerd, whose apps and gadgets symbolize the hope of economic growth? “The best minds of my generation are thinking about how to make people click ads,” a former math whiz at Facebook recently lamented. ~ Rutger Bregman,
711:Math held out a hand for James to grasp, and James jumped down onto the roof of the bus, landing with a thunk. Math caught his arm to steady him, not wanting him to slip on the wet surface. “James!” Callum poked his head through the trap door. “What are you doing here? ~ Sarah Woodbury,
712:In most countries, attending some kind of early childhood program (i.e., preschool or prekindergarten) led to real and lasting benefits. On average, kids who did so for more than a year scored much higher in math by age fifteen (more than a year ahead of other students). ~ Amanda Ripley,
713:twenty-five poorest countries already spend twenty percent of their GDP on water. This twenty percent, about thirty cents, ain’t much, but do the math again: four billion people spending thirty cents a day is a $1.2 billion market every day. It’s $400 billion a year. ~ Peter H Diamandis,
714:I had become a bridge between the natural world and the human one. I fit into both places and belonged to neither. Half of my heart lived with the wild wolves, the other half lived with my family.

In case you cannot do the math: no one can survive with half a heart. ~ Jodi Picoult,
715:I'm always interested in understanding the math of things and understanding as much as I can about all aspects of business. And what I learn today may be useful to me two years from now. That's really the wonderful thing about investments is your knowledge is cumulative. ~ Warren Buffett,
716:I smiled. Mom laughed, shaking her head. “That’s the punchline? Why is that even funny?” “It’s the Pythagorean theorem,” said Lauren. “It’s a math formula for . . . something.” “Right triangles,” I said, and looked pointedly at Margaret. “I told you I’d already done geometry. ~ Dan Wells,
717:I went home every night to New Jersey - or most nights - and to help with the six-grade math homework or to make breakfast in the morning, just to make sure that that was there. When I was single and didn't have children, I used to laugh at this notion of quality time. ~ Kellyanne Conway,
718:But in psychology our goal is descriptive. We want to discover how the moral mind actually works, not how it ought to work, and that can’t be done by reasoning, math, or logic. It can be done only by observation, and observation is usually keener when informed by empathy. ~ Jonathan Haidt,
719:Love. You can learn all the math in the ’verse, but you take a boat in the air you don’t love, she’ll shake you off just as sure as the turning of worlds. Love keeps her in the air when she oughtta fall down, tells you she’s hurting ’fore she keens. Makes her a home. ~ Keith R A DeCandido,
720:When I was younger, I loved math. Everything about math. But in school, math now has letters. Like what does x equal? There are also long stories with characters, and although the story is supposed to end with some number, all the words block my path to getting there. ~ Lynda Mullaly Hunt,
721:I failed math twice, never fully grasping probability theory. I mean, first off, who cares if you pick a black ball or a white ball out of the bag? And second, if you’re bent over about the color, don’t leave it to chance. Look in the damn bag and pick the color you want. ~ Janet Evanovich,
722:It doesn’t include math or logic, nor does it address issues of judgment, such as aesthetics or morality. Science has a simple goal: to figure out what the world actually is. Not all the possible ways it could be, nor the particular way it should be. Just what it is. There’s ~ Sean Carroll,
723:Logic leaves us no choice. In that sense, math always involves both invention and discovery: we invent the concepts but discover their consequences. … in mathematics our freedom lies in the questions we ask – and in how we pursue them – but not in the answers awaiting us. ~ Steven Strogatz,
724:The folks who invented Lent—no, it wasn’t Jesus’s idea—decided that just like Christ’s time in the desert, it should last forty days. Actually, from Ash Wednesday to Holy Saturday it’s forty-six days, so it looks like the first thing someone ever gave up for Lent was math. ~ Jenny McCarthy,
725:I'm not a plumber who accidentally blew up or a math professor who accidentally backed into notoriety. I have a master's from Yale drama, and I auditioned for this. So obviously I want to be in the limelight in some capacity, or I want to be in entertainment in some capacity. ~ Adam Richman,
726:I had done quite a bit of research about math education when I spoke before Congress in 2000 about the importance of women in mathematics. The session of Congress was all about raising more scholarships for girls in college. I told them I felt that it's too late by college. ~ Danica McKellar,
727:Several do math on their fingers. Then they raise their hands as one. “Can we see it?” “No.” “Not even open the first door?” “No.” “Have you seen it?” “I have not.” “So how do you know it’s really there?” “You have to believe the story.” “How much is it worth, Monsieur? Could ~ Anthony Doerr,
728:And what is a marriage except adding A to B and hoping it equals an amount greater than the sum of its parts? Briefly, the promise of a new life almost made the math work. Except A was still A, and B was still B. We could create a new life, but we couldn’t stop being ourselves. ~ Lisa Gardner,
729:I am not concerned about proving anything to any other discipline outside the scope of math itself where my function lies nowadays; and when it comes to my own statements that I have built on top of numbers, they are restricted to my own context, hence, the quoting cladding. ~ Ibrahim Ibrahim,
730:I never got a pass mark in math... Just imagine - mathematicians now use my prints to illustrate their books. Funny me consorting with all these learned folks, as though I were their long lost brother. I guess they are unaware of the fact that I am ignorant about the whole thing. ~ M C Escher,
731:When I cook with my son, I might chop vegetables and have fun with different shapes. Cooking is a way to teach kids about other things, like reading or math with all of the weights and measures. There are so many things that are part of cooking that are also very educational. ~ Emeril Lagasse,
732:I think math is a hugely creative field, because there are some very well-defined operations that you have to work within. You are, in a sense, straightjacketed by the rules of the mathematics. But within that constrained environment, it's up to you what you do with the symbols. ~ Brian Greene,
733:Play with your dolls for not more than half an hour, no more than fifteen minutes, no more than a second, a millisecond. If you learned math as fast as you ran outside to play, then you might be a genius. But you do not and you are not. You're a hole where knowledge goes to sleep. ~ Weike Wang,
734:I think there are dozens or hundreds of different forms of creativity. Pondering science and math problems for years is different from improvising jazz. Something which seems to me remarkable is how unconscious the creative process is. You encounter a problem, but can't solve it. ~ Oliver Sacks,
735:I think we need more math majors who don't become mathematicians. More math major doctors, more math major high school teachers, more math major CEOs, more math major senators. But we won't get there unless we dump the stereotype that math is only worthwhile for kid geniuses. ~ Jordan Ellenberg,
736:Casey, I want to be polite and present myself as decent. I know the math of regret and nostalgia. The potency of your touch times the distance between that touch and today determines the intensity of my desperation. I regret leaving you, and I’m disappointed you let me go. ~ Terese Marie Mailhot,
737:Sure, go ahead.” Calvin fished in his pocket and pulled out a wad of folded paper. “As a matter of fact, I have some junk of mine to finish up. Math. That’s one thing I have a hard time keeping up in. I’m okay on anything to do with words, but I don’t do as well with numbers. ~ Madeleine L Engle,
738:Do you mean ter tell me," he growled at the Dursleys, "that this boy—this boy!—knows nothin' abou'—about ANYTHING?" Harry thought this was going a bit far. He had been to school, after all, and his marks weren't bad. I know some things," he said. "I can, you know, do math and stuff. ~ J K Rowling,
739:I’ve got space to brake on the inside,” Dana said. “And about thirty seconds to make it through the gap. Which is a kilometer and a half long. You do the math. I’m doing this by the seat of my pants.” “My math brain just went to bed and pulled the cover over his head,” Hartwell said. ~ John Ringo,
740:So you're not going to die, are you?" she [Astor] asked politely.

"Not yet," I said. "Not until after you do your homework."

She nodded, glanced toward the kitchen, and said, "I hate math." Then she wandered away down the hall, presumably to hate math at closer range. ~ Jeff Lindsay,
741:Dad claims that library science is the foundation of all sciences just
as math is the key -- and we will survive or founder, depending on how
well the librarians do their jobs. Librarians didn't look glamorous to
me but maybe Dad had hit on a not very obvious truth. ~ Robert A Heinlein,
742:I hate the idea that, when it comes to books and learning, hard is often seen as the opposite of fun. It's strange to me that we should be so quick to give up on a book or a math problem when we are so willing to grapple, for centuries if necessary, with a single level of Angry Birds. ~ John Green,
743:By now, at age thirty-three, comparing myself to my mother had become an increasingly unnerving habit. Every year I’d do the math, calculating where I was in relation to where she’d been, and then, on the prediction that I’d also die when she had, figure out how many years I had left. ~ Kate Bolick,
744:I was working at Kentucky Fried Chicken when my math teacher said, "You're failing in school, you're messing up, why don't you just try this?" I said, "Alright, let me try it," and I started going to acting classes and I loved it. I thought, "I may not make it but I love doing it." ~ John Leguizamo,
745:If you want me to fix your homework, you need to leave me alone.” Then he spotted her. “You’re back.”
“Yeah.” She glanced between him and Gabriel. “You do his homework?”
“Just the math. It’s a miracle he can count to ten.”
“I can count to one.” Gabriel gave him the finger. ~ Brigid Kemmerer,
746:Math is “maths,” an elevator is a “lift,” a truck is a “lorry,” a flashlight is a “torch,” and “crisps” are what they call potato chips, while “chips” over here means French fries. Just as riding the double-decker buses thrills me, I get a thrill out of hearing people talk. ~ Heather Vogel Frederick,
747:The Tour (de France) is essentially a math problem, a 2,000-mile race over three weeks that's sometimes won by a margin of a minute or less. How do you propel yourself through space on a bicycle, sometimes steeply uphill, at a speed sustainable for three weeks? Every second counts. ~ Lance Armstrong,
748:I'm a good example of wanting to apologize only for my precise share of a problem--as I calculate it, of course--and I expect my husband Steve to apologize for his share, also as I calculate it. Since we're not always of one mind on the math, it can lead to the theater of the absurd. ~ Harriet Lerner,
749:The Dean’s complaining to his Faculty. “Why do you scientists need such expensive equipment? Why can’t you be like the Math Department, which only needs a blackboard and a wastepaper basket? Better still, like the Department of Philosophy. That doesn’t even need a wastepaper basket… ~ Arthur C Clarke,
750:In ninth grade, I came up with a new form of rebellion. I hadn't been getting good grades, but I decided to get all A's without taking a book home. I didn't go to math class, because I knew enough and had read ahead, and I placed within the top 10 people in the nation on an aptitude exam. ~ Bill Gates,
751:Math is discovered. To be invented requires an inventor, but math exists outside of humanity. But ultimately, the laws of the universe will be reduced down to a single equation, perhaps no more than one inch long. But leaves the final question, where did that one inch equation come from? ~ Michio Kaku,
752:Why is it that there was always a unit on history, math, science and god knows what other useless, totally forgettable information you taught those seventh graders year after year, but never any unit on death? No exercises, no workbooks, no final exams on the only subject that matters? ~ Nicole Krauss,
753:A lot of young girls don't realise how diverse the career opportunities are in games development. Many think that you need elite math skills and a vast knowledge of all things tech to work in games, and haven't thought about avenues like design, producing, art, writing or composing. ~ Rhianna Pratchett,
754:At this point, scientists have identified over 300 specific genes that play a direct role in mental retardation. That link between genes and intelligence is pretty clear. However, scientists have not found a gene for A-level math ability or a gene for having a “natural ear for languages. ~ Hunter Maats,
755:Drest had made a careful study of the Discordian philosophy and realized it was the kind of outlandish nonsense that would appeal to the kind of people who made all the trouble in history-brilliant, intellectual, slightly deranged dope fiends and oddball math-and-technology buffs. ~ Robert Anton Wilson,
756:Math is perfect (in principle), but mathematicians are not (because they are humans), hence the mathematics that (human) mathematicians do is influenced by the weltanschauung of the people around them. ~ Doron Zeilberger "Computerized Deconstruction". Appeared in Adv. Appl. Math. v. 31 (2003), 532-543.,
757:Do you mean ter tell me," he growled at the Dursleys, "that this boy—this boy!—knows nothin' abou'—about ANYTHING?"
Harry thought this was going a bit far. He had been to school, after all, and his marks weren't bad.
"I know some things," he said. "I can, you know, do math and stuff. ~ J K Rowling,
758:Michael Harris opens the doors and gently guides you into a magic world. Once inside, you can't help but feel mesmerized, eager to see how deep the rabbit hole goes. And no wonder: a major thinker of our time is talking to you about math and so much more, like you've never heard before. ~ Edward Frenkel,
759:There is such a thing as nonnerdy applied mathematics: find a problem first, and figure out the math that works for it (just as one acquires language), rather than study in a vacuum through theorems and artificial examples, then change reality to make it look like these examples. ~ Nassim Nicholas Taleb,
760:We will always have STEM with us. Some things will drop out of the public eye and will go away, but there will always be science, engineering and technology. And there will always, always be mathematics. Everything is physics and math. ~ Katherine Johnson, "Katherine Johnson: A Lifetime of STEM" (2013).,
761:In my own research when I'm working with equations, I never feel like I really understand what I'm doing if I'm solely relying on the mathematics for my understanding. I need to have a visual picture in my mind. I'm constantly translating from the math to some intuitive mind's-eye picture. ~ Brian Greene,
762:In second grade we were taught simple math, but not the way it is taught in other countries. In North Korea, even arithmetic is a propaganda tool. A typical problem would go like this: “If you kill one American bastard and your comrade kills two, how many dead American bastards do you have? ~ Yeonmi Park,
763:Many a graduate student has come to grief when they discover, after a decade of being told they were “good at math,” that in fact they have no real mathematical talent and are just very good at following directions. Math is not about following directions, it’s about making new directions. ~ Paul Lockhart,
764:My love for math eventually became a passion. I went to math camp when I was fourteen and came home clutching a Rubik’s Cube to my chest. Math provided a neat refuge from the messiness of the real world. It marched forward, its field of knowledge expanding relentlessly, proof by proof. And ~ Cathy O Neil,
765:What the mortgage bubble was all about was big banks like Goldman Sachs taking big bundles of subprime mortgages that were lent out largely to low-income, highly risky borrowers, and applying this kind of magic-pixie-dust math to these bundles of securities and slapping AAA ratings on them. ~ Matt Taibbi,
766:So what should we say when children complete a task—say, math problems—quickly and perfectly? Should we deny them the praise they have earned? Yes. When this happens, I say, “Whoops. I guess that was too easy. I apologize for wasting your time. Let’s do something you can really learn from! ~ Carol S Dweck,
767:By the end of an intense four years at UCLA, I had co-authored a new math proof, which the media, in fact, loved. As it turned out, math itself blazed my entry back into the spotlight and consequently into wonderful acting jobs like 'The West Wing' and others. You just never know, do you? ~ Danica McKellar,
768:I think that we should give visas to people - green cards, rather, to people who graduate with skills that we need. People around the world with accredited degrees in science and math get a green card stapled to their diploma, come to the U.S. of A. We should make sure our legal system works. ~ Mitt Romney,
769:Mathematics is a versatile art; it can be applied to widely different purposes. Math has no morality; it does not care what it counts or what it proves. ~ Brian Stableford, Ashes and Tombstones, in Peter Crowther (ed.) Moon Shots (1999), reprinted in David G. Hartwell (ed.) Year's Best SF 5 (2000), p. 412.,
770:The most recent edition of the test—called the Programme for International Student Assessment (PISA)—was conducted in 2012, and it found that among the OECD’s thirty-four members, the United States ranked twenty-seventh, twentieth, and seventeenth in math, science, and reading, respectively. ~ Fareed Zakaria,
771:The world is colors and motion, feelings and thoughts and what does math have to do with it? Not much, if 'math' means being bored in high school, but in truth mathematics is the one universal science. Mathematics is the study of pure pattern and everything in the cosmos is a kind of pattern. ~ Rudy Rucker,
772:We take over six hundred pages of math and force-feed it to the universe through an electromagnetic funnel. We tell the universe ‘I don’t care what you think. I’m lifting my foot here and putting it down there.’ ” “And the universe doesn’t object?” Arthur finished off his whiskey. “Not so far. ~ Peter Clines,
773:Cooking was not a chore for Tengo. He always used it as a time to think - about everyday problems, about math problems, about his writing, or about metaphysical propositions. He could think in a more orderly fashion while standing in the kitchen and moving his hands than while doing nothing. ~ Haruki Murakami,
774:Somethings you know right away to be final- when you lose your last baby tooth...Other times, you have to work out the milestone via subtraction, a math you do to assign significance, like when I figured out that I'd just blown through my last-ever wednesday with Mom on the day after she died. ~ Karen Russell,
775:Four out of the five Nobel Prize laureates in Physics and Chemistry that year were from countries other than the United States. Americans were terrified that the country was falling behind in math and science, so nationwide there was a renewed commitment to education, especially in those fields. ~ Susan Orlean,
776:Katherine Johnson passion for math, the way I light up when I get asked questions about acting is the way her eyes danced when she talked about math and how she wanted people to fall in love with numbers the way that she did. If I had a teacher like that, I could have been a rocket scientist. ~ Taraji P Henson,
777:In a way, math isn't the art of answering mathematical questions, it is the art of asking the right questions, the questions that give you insight, the ones that lead you in interesting directions, the ones that connect with lots of other interesting questions -the ones with beautiful answers. ~ Gregory Chaitin,
778:My dad, a mathematician, raised me to believe that mathematics is beautiful, so math is a part of my imaginative terrain. In my late 20s I wrote several 11-line poems because I wanted to create poems that couldn't be uniformly divided into couplets, tercets, or quatrains, 11 being a prime number. ~ James Arthur,
779:When I was in high school, my math teacher Mr. Packwood used to say, "If you're stuck on a problem, don't sit there and think about it; just start working on it. Even if you don't know what you're doing, the simple act of working on it will eventually cause the right ideas to show up in your head". ~ Mark Manson,
780:Yes. It was Tatiana, not specter but matter. She was measurable. His little Newton had mass and occupied space. A small finite matter in infinite space. That is what math gave him—principles of design that tied together the boundless universe. That is why he measured her. Because she was order. ~ Paullina Simons,
781:But people are so determined to fit everyone into a box with a nice, easily grasped, perfectly defined label. It helps them sleep at night, to know their world as certainly as they know math, or numbers, or the spelling of their own name. Black. White. Right. Wrong. Gay. Straight. Female. Male. But ~ Daryl Banner,
782:Holy shit, twenty thousand people died during the institutions operation? He opened his calculator on the phone and did quick math. The place opened in 1893, closed in 1994… oh holy shit… an average of fifteen patients died a month? He repeated the calculations and came up with the same thing again. ~ Lucian Bane,
783:Take a random group of 8-year-old American and Japanese kids, give them all a really, really hard math problem, and start a stopwatch. The American kids will give up after 30, 40 seconds. If you let the test run for 15 minutes, the Japanese kids will not have given up. You have to take it away. ~ Malcolm Gladwell,
784:We may discover resources on the moon or Mars that will boggle the imagination, that will test our limits to dream. And the fascination generated by further exploration will inspire our young people to study math, and science, and engineering and create a new generation of innovators and pioneers. ~ George W Bush,
785:You're still riding home with me right?" He asks Courtney watching me at the corner of his eye. What's with this guy? he looks like he's about one second from taking a baseballbat to my knees. Or wanting to. I wonder if this is how serial killers start out. Wasn't Unabomber really goos at math? ~ Lauren Barnholdt,
786:Ask a kid who's struggling in math if he likes being in a mixed-level class, and he'll tell you he feels like a moron. Ask the math genius if he likes being in a mixed-level class, and he'll tell you he's sick of doing all the work during group projects. Sometimes, it's better to sort like with like. ~ Jodi Picoult,
787:There was an older guy in the photos on the bookshelf who was probably Isaiah’s brother, who was most likely dead and that was no doubt the reason Isaiah was so messed up. His face was either blank as Dodson’s math assignment or his eyes were tight and his jaw hard-set like he was about to smack somebody. ~ Joe Ide,
788:You’re still concentrating, right?” BT asked to my retreating back. “Yes I’m still concentrating, Mrs. Weinstedder.” “What?” “Nothing, just my old algebra teacher.” “So somehow this whole scene reminded you of an old math teacher? Who did the wiring in your head? Because you should get your deposit back. ~ Mark Tufo,
789:I thought about the hours we spent practicing increasingly complex math problems. He taught me that lack of knowledge and lack of intelligence were not the same. The former could be remedied with a little patience and a lot of hard work. And the latter? “Well, I guess you’re up shit creek without a paddle. ~ J D Vance,
790:You know there's always that kid in your class — and every class has one — the kid who draws all the time and is really good? That was not me. I was a lousy draftsman. But as soon as I figured out that I could make things come alive, like using the corners of my math book to make flipbooks, I was hooked. ~ Pete Docter,
791:the kid can learn, but he only wants to do one thing at a time. He could spend days on end hunched over just one page of a botany book and then wouldn’t talk about anything else. Then the next week it would be astronomy. He’s become reasonably literate, though, and he’s not bad at math either. ~ Viktor Arnar Ing lfsson,
792:There's a fundamental disconnection in society in the way we live, this way we live that we take so for granted, and we've become very separate from one another and we don't really take lot of time to realize that. And the math is overwhelming to the point of despair, but the answers could be so simple. ~ Amanda Palmer,
793:Fashion is not just about what we wear, but...fashion is also a business. It is an art, it's a career that involves science, engineering, accounting and so much more. People can learn about the math behind Charles James' designs, and think, 'Maybe I should pay closer attention to geometry this semester' ~ Michelle Obama,
794:Find your self-respect now. Don't dumb yourselves down. Think of yourself as capable and worthy of finding a guy who is going to respect you, too. It's so important, I mean, and the confidence you get from feeling smart and tackling something like mathematics, which is a challenge, right? Math is hard. ~ Danica McKellar,
795:He had forgotten that grief does not decline in a straight line or along a slow curve like a graph in a child's math book. Instead, it was almost as if his body contained a big like of garden rubbish full both of heavy lumps of dirt and of harp thorny brush that would stab him when he least expected it. ~ Helen Simonson,
796:Plato was synthesis of Europe and Asia, and a decidedly Oriental element pervades his philosophy, giving it a sunrise color. ~ Ralph Waldo Emerson, Abhedananda, Swami India and her people, a study in the social. political, educational and religious conditians of India. [6th ed.] Calcutta, Ramakrishna Vedanta Math [1945],
797:What if everything about me is totally made up? What if I’m actually…I don’t know. A wanted fugitive in the States.”
“Julia.” He reached across the table and grabbed her hand. “Nobody makes up being a high school math teacher.”
“That’s why it’s the perfect disguise!”
He shook his head. “Nobody. ~ Rebecca Brooks,
798:Infants and young children are not just sitting twiddling their thumbs, waiting for their parents to teach them to read and do math. They are expending a vast amount of time and effort in exploring and understanding their immediate world. Healthy education supports and encourages this spontaneous learning. ~ David Elkind,
799:In our travels, we have come across many equations--math for understanding the universe, for making music, for mapping stars, and also for tipping, which is important. Here is our favorite equation: Us plus Them equals All of Us. It is very simple math. Try it sometime. You probably won’t even need a pencil. ~ Libba Bray,
800:boy is getting all Ds and Fs in math so his parents send him to Catholic school. On his first report card, his parents are shocked to see their son getting straight As. When his parents ask him why, he says, “Well, when I went into the chapel and saw that guy nailed to a plus sign, I knew they were serious. ~ Harlan Coben,
801:Hey, Ma! Dad just figured out how to do the math to calculate my age and date of conception. He's having some kind of apoplexy over it. I think you need to come in here before he pisses on your floor. And if he does, I did not do it, so don't yell at me for it. And I will not clean it up." - Talyn Batur ~ Sherrilyn Kenyon,
802:America's demographic shift was obvious to everyone in the 2010 Census - but Republicans stubbornly rejected math, facts, and polls to their electoral peril. While Republicans tailored their platform by and for the pale stale and male, among us, Obama and Democrats are embracing America's diverse mosaic. ~ Christine Pelosi,
803:I don't think they understand it's as important as math and science. It rounds you out as a person. I think it gives you a love of certain things. You don't have to become the next great composer. It's just nice to have heard certain things or to have seen certain things. It's part of being a human being. ~ Marvin Hamlisch,
804:Our schools display an enormous bias in educating the mind rather than the whole person. We place major emphasis on reasoning, logic and math, with almost no concern for emotions, intuition and creativity. Our students become memorizing mimics and dull conformists, rather than exciting and feeling creators. ~ John Bradshaw,
805:students who were told to think about the happiest day of their lives right before taking a standardized math test outperformed their peers.19 And people who expressed more positive emotions while negotiating business deals did so more efficiently and successfully than those who were more neutral or negative. ~ Shawn Achor,
806:The problem with cinema nowadays is that it's a math problem. People can read a film mathematically; they know when this comes or that comes; in about 30 minutes, it's going to be over and have an ending. So film has become a mathematical solution. And that is boring, because art is not mathematical. ~ Nicolas Winding Refn,
807:Will Bates was drummed out of Carter and reassigned to teach industrial arts in a middle school. He was given an unsatisfactory evaluation rating, placed on probation for a year, and had his salary frozen. And, of course, he was forbidden to teach math to prevent further threats to the sanctity of football. ~ H G Bissinger,
808:The ultimate act of cowardice is the fat-headed wrestling guy sitting behind the frail kid in math class, clipping him on the ear, saying: 'What are you going to do about that, faggot?' That is cowardice. When the bullets start flying past that jock's saucer-shaped ears, that's not cowardice. That's payback. ~ Doug Stanhope,
809:Her team had become NASA’s first computer programmers. The women still worked closely with the engineers, almost all of whom were men, but it was no longer enough for them just to be good at math. They needed to know how to build, fix, and run programs on the IBM computers, something the engineers rarely did. ~ Nathalia Holt,
810:Most children, even very bright ones, need constant review and practice to truly own a concept in grammar, math or science. In schools today, on paper it may appear that kids are learning skills, but in reality they are only renting them, soon to forget what they've learned over the weekend or summer vacation. ~ Rafe Esquith,
811:Most of the time I liked school and got good grades. In junior high, though, I hit a stumbling block with math - I used to come home and cry because of how frustrated I was! But after a few good teachers and a lot of perseverance, I ended up loving math and even choosing it as a major when I got to college. ~ Danica McKellar,
812:The old, been-around-forever, profitless formula is: Sales – Expenses = Profit The new, Profit First Formula is: Sales – Profit = Expenses The math in both formulas is the same. Logically, nothing has changed. But Profit First speaks to human behavior—it accounts for the regular Joes of the world, like me, ~ Mike Michalowicz,
813:My go-to gifts are scarves from my friend Matin Maulawizada's nonprofit organization, Afghan Hands, which supports disenfranchised women in Afghanistan. In exchange for their beautiful embroidery, the women are given financial aid and classes in math and literacy. The scarves are all stunning and one of a kind. ~ Claire Danes,
814:Students never think it can be the teacher's fault and so I thought I was stupid. I was frustrated and would come home and cry because I couldn't do it. Then we got a new teacher who made math accessible. That made all the difference and I learned that it's how you present it that makes it scary or friendly. ~ Danica McKellar,
815:Nothing. Because wasn't that how I felt that day? If you zoom close- if you really get close to someone, if you really get close to yourself- then you lose the other person, you lose yourself entirely. You get so close you can't see anymore. Your mind becomes all these abstract fragments. English becomes math. ~ David Levithan,
816:On the evening of the third day, I can feel him looking at me. He has a funny expression on his face, like he’s doing math in his head. Finally he says, “So what’s that thing you got around your neck?” and it’s clear what he’s up to. “There’s no value in it,” I say. “Looks like silver,” he says, peering ~ Christina Baker Kline,
817:We tend to see math and science as a steady state of facts rather than as the accumulated knowledge of linear traditions. As Korzybski put it, we see further because we “stand on the shoulders”5 of the previous generation. The danger of such a position is that we can forget to put our own feet on the ground. ~ Douglas Rushkoff,
818:The more complex a behavior is, the more rigorous and complicated the science behind it. Math, chemistry, that’s the easy stuff—closed models with discrete answers. To understand behavior—human or elephant—the systems are far more complex, which is why the science behind them must be that much more intricate. But ~ Jodi Picoult,
819:It only takes about 50 contact hours to transmit basic literacy and math skills well enough that kids can be self-teachers from then on. The cry for 'basic skills' practice is a smokescreen behind which schools pre-empt the time of children for twelve years and teach them the six lessons I've just taught you. ~ John Taylor Gatto,
820:The much-storied disenchantment with mathematics among Western children starts in the third and fourth grades, and Fuson argues that perhaps a part of that disenchantment is due to the fact that math doesn’t seem to make sense; its linguistic structure is clumsy; its basic rules seem arbitrary and complicated. ~ Malcolm Gladwell,
821:You're not born knowing how to do math. You're taught that. You're not born knowing how to hate someone. You're taught that. And so I feel I want to use my platform to raise awareness about it. To help raise something positive. In America, you look around and a lot of things that happen - it all stems from that. ~ Draymond Green,
822:I found myself often asking the question, "Who deserves to be made fun of?" Depending on your mood, the answer can be no one or everyone. It took me a while to understand the math of how those field pieces came together. I don't think that ridicule is ever funny, but there are times when that gets the biggest response. ~ Ed Helms,
823:Dylan Bennet Klebold was born brilliant. He started school a year early, and by third grade was enrolled in the CHIPS program: Challenging High Intellectual Potential Students. Even among the brains, Dylan stood out as a math prodigy. The early start didn’t impede him intellectually, but strained his shyness further. ~ Dave Cullen,
824:If market pricing is the only legitimate test of quality, why are we still bothering with proven theorems? Why don't we just have a vote on whether a theorem is true? To make it better we'll have everyone vote on it, especially the hundreds of millions of people who don't understand the math. Would that satisfy you? ~ Jaron Lanier,
825:Characteristically, Samuelson intimidated those who questioned his techniques with the statement “Those who can, do science, others do methodology.” If you knew math, you could “do science.” This is reminiscent of psychoanalysts who silence their critics by accusing them of having trouble with their fathers. ~ Nassim Nicholas Taleb,
826:Her baby boy would play little league baseball, star in the school play and be good at math. She didn't know then that she should have had much simpler dreams for her beautiful son, that she should have looked upon her newborn baby boy and thought 'I hope you learn to talk and use the bathroom by the time you're seven. ~ Lisa Genova,
827:I'm not much of a math and science guy. I spent most of my time in school daydreaming and managed to turn it into a living. When I was making "Star Wars," I wasn't restrained by any kind of science. I simply said, "I'm going to create a world that's fun and interesting, makes sense, and seems to have a reality to it." ~ George Lucas,
828:So somebody told me that if I wasn't a coffee drinker yet, by the end of college I'd have to be, because a math major is so tough I would have to stay up very late. I was going to need coffee to do that. Well, merely because they said that, I never drank coffee in college, never got addicted to it, never needed it. ~ Danica McKellar,
829:And here’s a fact that should get you thinking: when Social Security set the retirement age at sixty-five, the average life expectancy for a male was sixty-one. It makes us realize how little Social Security was designed to pay out. The subsequent surge in life expectancy has changed the math of retirement entirely. ~ George Friedman,
830:Animation wasn't my love, but drawing was. I loved drawing, and when it came time to graduate from high school, I looked around and it was like, "Wow, I don't really want to study math. I don't really want to study science. I don't really want to study literature. Is there a place where I can go and draw cartoons?" ~ Harland Williams,
831:There was no protection, no quota system when it came to luck. It was like that moment in math when a child learns that the odds of heads or tails is always one-in-two, no matter how many times one has flipped the coin and gotten heads. Every flip, the odds are the same. Every day, you could be unlucky all over again. ~ Laura Lippman,
832:This was only the second time Carswell Thorne had stopped to ponder one Kate Fallow. The first time, he had wondered why she liked books so much, and if it had anything to do with why he liked spaceships. Because they could take you somewhere far, far way from here. This time, he was wondering what her math score was. ~ Marissa Meyer,
833:Before the work of Georg Cantor in the nineteenth century, the study of the infinite was as much theology as science; now, we understand Cantor’s theory of multiple infinities, each one infinitely larger than the last, well enough to teach it to first-year math majors. (To be fair, it does kind of blow their minds.) ~ Jordan Ellenberg,
834:By the time I slip back to my room, it's almost six. Jasmine is in bed, awake and waiting for me..."Where were you?"
Where was I? Chased by a fat guard, hit by a laugh attack and nearly thrown out of Stanford University Math Camp, never to see the light of the campus ever again, and certainly not as a future student. ~ Justina Chen,
835:College was an experience I'll always cherish. Now I fund a scholarship at my alma mater in my late father's name—he'd laugh to know that it's a science scholarship, when I can barely do math! I also fund a nursing scholarship at the Oglala Lakota College in Kyle, South Dakota, in the name of my mother, who was a nurse. ~ Diana Palmer,
836:Math just wasn't my favorite. I didn't get how important math is and how it relates to real life. That's why I think I was turned off to it. Once I got down arithmetic and a little bit of algebra, I think I checked out. As I've gotten older, I think there's a lot more relation to math. English was my favorite subject. ~ Adam Rodriguez,
837:In physics, theories are made of math. We don’t use math because we want to scare away those not familiar with differential geometry and graded Lie algebras; we use it because we are fools. Math keeps us honest—it prevents us from lying to ourselves and to each other. You can be wrong with math, but you can’t lie. ~ Sabine Hossenfelder,
838:This was only the second time Carswell Thorne had stopped to ponder one Kate Fallow. The first time, he had wondered why she liked books so much, and if it had anything to do with why he liked spaceships. Because they could take you somewhere far, far away from here. This time , he was wondering what her math score was. ~ Marissa Meyer,
839:If somebody is working on a new medicine, computer science helps us model those things. We have a whole group here in Seattle called the Institute for Disease Modelling that is a mix of computer science and math-type people, and the progress we're making in polio or plans for malaria or really driven by their deep insights. ~ Bill Gates,
840:Yes, I took a remedial algebra course in college. I struggled in math in high school and didn’t have confidence to plunge in with a for-credit algebra course. The remedial course gave me a lot of confidence so that when I took the for-credit algebra course it was fairly easy and I got a ‘B,’ of which I remain proud today! ~ Jim Stafford,
841:You can be obsessed with makeup and hair products and, you know, your appearance and still be absolutely making smart life decisions and work on your smarts, develop your smarts by studying something like math. Then you'll make much better decisions on the brands of clothing that you buy or whatever it is that you want. ~ Danica McKellar,
842:I noticed there were so many people, especially women, who would come up to me having recognized me from TV and say, 'I heard you were a math person, why math? Oh my gosh, I could never do math!' I could just see their self-esteem crumbling; I thought that was silly, so I wanted to make math more friendly and accessible. ~ Danica McKellar,
843:We think there's a reason for everything, as if life was supposed to make sense. It's not exactly math. People aren't numbers. Everybody knows life doesn't make any sense at all, so we just better deal with the whole mess. Have a beer. Have a cup of coffee. Have a piece of cake. Go out to a movie. Enjoy the Popcorn. ~ Benjamin Alire S enz,
844:In colleges, there are no gender separations in courses of study, and students can freely choose their majors. There are no male and female math classes. But women generally choose college courses that pay less in the labor market. Those are the choices that women themselves make. Those choices contribute to the pay gap. ~ Phyllis Schlafly,
845:Most people that derail as leaders in the corporate world, it's not because they couldn't do the math and calculate return on investment properly. The issues are communication and understanding. All of what typically would've been called the 'soft stuff.' You have to be authentic. You have to be dialed into the soft stuff. ~ Douglas Conant,
846:Welcome to the world of grown-ups. You might be good at math, and somebody pays for tht, but what you really love to do is sing. Do you think Oscar prizes above all else his ability to book guests into a hotel?.. The sad fact of the world... is almost nobody exactly chooses what they get paid to do."
Peggy to James ~ Elizabeth McCracken,
847:I'm a visual thinker, really bad at algebra. There's others that are a pattern thinker. These are the music and math minds. They think in patterns instead of pictures. Then there's another type that's not a visual thinker at all, and they're the ones that memorize all of the sports statistics, all of the weather statistics. ~ Temple Grandin,
848:No party has a monopoly on wisdom. No democracy works without compromise. But when Governor Romney and his allies in Congress tell us we can somehow lower our deficit by spending trillions more on new tax breaks for the wealthy - well, you do the math. I refuse to go along with that. And as long as I'm President, I never will. ~ Barack Obama,
849:Late twenties, single, female. Do the math.
Flirty flings were fabulous until you hit the big three-O, all downhill
from there. Biological clocks started ticking like time bombs waiting to
detonate, gravity exerted more force on your life than your mom, and
suddenly, the dog-ugliest creep looked like Jake Gyllenhaal. ~ Nicola Marsh,
850:My grandmother taught me to read before I went to school. I was reading the newspaper when I was five. And Grandpa taught me to do math and figure. They believed in living simply. Grandpa grew a garden, and Grandma canned food for the winter. They taught me to work and to love to learn new things. I wasn't really afraid or shy. ~ Carolyn Brown,
851:Our children learn reading, writing, math, science, and other subjects in school that can help them earn a living. But ver few school programs teach young people how to live - how to deal with anger, how reconcile conflicts, how to breathe, smile, and transform internal formations. There needs to be a revolution in education, ~ Thich Nhat Hanh,
852:People will tell you that you have to know math to be a scientist, or physics or chemistry. They’re wrong. That’s like saying you have to know how to knit to be a housewife, or that you have to know Latin to study the Bible. Sure, it helps, but there will be time for that. What comes first is a question, and you’re already there. ~ Hope Jahren,
853:rigor mattered. Koreans understood that mastering difficult academic content was important. They didn’t take shortcuts, especially in math. They assumed that performance was mostly a product of hard work—not God-given talent. This attitude meant that all kids tried harder, and it was more valuable to a country than gold or oil. ~ Amanda Ripley,
854:The thing I want you especially to understand is this feeling of divine revelation. I feel that this structure was "out there" all along I just couldn't see it. And now I can! This is really what keeps me in the math game-- the chance that I might glimpse some kind of secret underlying truth, some sort of message from the gods. ~ Paul Lockhart,
855:Great literature remains great when it says new things to new generations, and the loops of a knot quite nicely parallel the contours and convolutions of Carroll’s plot anyway.What’s more, he probably would have been delighted at how this whimsical branch of math invaded the real world and became crucial to understanding our biology. ~ Sam Kean,
856:Predictive modeling generates the entire model from scratch. All the model’s math or weights or rules are created automatically by the computer. The machine learning process is designed to accomplish this task, to mechanically develop new capabilities from data. This automation is the means by which PA builds its predictive power. ~ Eric Siegel,
857:From somewhere, back in my youth, heard Prof say, 'Manuel, when faced with a problem you do not understand, do any part of it you do understand, then look at it again.' He had been teaching me something he himself did not understand very well—something in math—but had taught me something far more important, a basic principle. ~ Robert A Heinlein,
858:I had no problem with math. I liked it, actually. It was straightforward in a way nothing else seemed to be in life. There was only one right answer, and usually only one right way to reach it. It had none of those uncertainties of writing and reading, where a single word could change the meaning of a sentence. Math was fine. ~ Alexandra Bracken,
859:I think talent has a huge amount to do with concentration, concentration rather than the athletic ability of your neurons. If you can concentrate on an esoteric piece of math, how can you think about the rest of your life? That's why people can leave their car keys in the gutter; they're in the midst of obsession and concentration. ~ Ethan Canin,
860:had a girl in this class,” Corcoran said. “She was a horrible math student in fifth grade. She cried every Saturday when we did remedial stuff. Huge tears and tears.” At the memory, Corcoran got a little emotional himself. He looked down. “She just e-mailed us a couple weeks ago. She’s in college now. She’s an accounting major. ~ Malcolm Gladwell,
861:Other than a little training in commercial math at what was known as an “abacus school,” Leonardo was mainly self-taught. He often seemed defensive about being an “unlettered man,” as he dubbed himself with some irony. But he also took pride that his lack of formal schooling led him to be a disciple of experience and experiment. ~ Walter Isaacson,
862:Some people focus more on sonics. Some people focus more on story. I focus on both sonics and story, but music sometimes, just music itself, can turn into more of a maths problem. I guess everything in life is a math problem, but it can be more about an empirical route to getting the symmetry that you want, and this vibe, sonically. ~ Frank Ocean,
863:Tools of the Mind, by contrast, doesn’t focus much on reading and math abilities. Instead, all of its interventions are intended to help children learn a different kind of skill: controlling their impulses, staying focused on the task at hand, avoiding distractions and mental traps, managing their emotions, organizing their thoughts. ~ Paul Tough,
864:To the fixed-mindset person, intelligence and skill are seen as a sum game. Either you can do math or you can’t. You’re artistic or you’re not. You have what it takes to sell or to be a great speaker or you don’t. Not surprisingly, Dweck found that people who have a fixed mindset are more likely to rate high on the impostor scale. ~ Valerie Young,
865:I’ve sometimes joked and said God doesn’t know very much math, because when you give to others, it should be that you are subtracting from yourself. But in this incredible kind of way—I’ve certainly found that to be the case so many times—you gave and it then seems like in fact you are making space for more to be given to you. “And ~ Dalai Lama XIV,
866:mathematics professor in Russia slugging it out with another mathematics professor in India, kilobyte for kilobyte, over some stupefyingly arcane detail in prime number theory, while an eighteen-year-old, tube-fed math prodigy in Cambridge jumps in every few days with an even more stupefying explanation of why they are both wrong. ~ Neal Stephenson,
867:Math . . . music .. . starry nights . . . These are secular ways of achieving transcendence, of feeling lifted into a grand perspective. It's a sense of being awed by existence that almost obliterates the self. Religious people think of it as an essentially religious experience but it's not. It's an essentially human experience. ~ Rebecca Goldstein,
868:They said I had to get fatter.
I told them my goal was 080.00 and if they wanted my respect, they'd better stop lying to me.
When my brain started working again, I checked their math. Someone had made a mistake because they didn't figure in the snakes in my head and the thick shadows hiding inside the cage of my ribs. ~ Laurie Halse Anderson,
869:What makes it possible to learn advanced math fairly quickly is that the human brain is capable of learning to follow a given set of rules without understanding them, and apply them in an intelligent and useful fashion. Given sufficient practice, the brain eventually discovers (or creates) meaning in what began as a meaningless game. ~ Keith Devlin,
870:felicity. It’s simple math, though. Add up the pleasurable aspects of your life, then subtract the unpleasant ones. The result is your overall happiness. The same calculations, Bentham believed, could apply to an entire nation. Every action a government took, every law it passed, should be viewed through the “greatest happiness” prism. ~ Eric Weiner,
871:If I'm teaching girls that do love to make cookies and do love fashion - that they can use math as a part of that - you think that's me saying, come on girls you belong in the kitchen, you belong shopping? Or, do you think it's me showing them how math is part of all their life, even the part they thought it had nothing to do with? ~ Danica McKellar,
872:
   Extraordinary, some people have said when he speaks now of how he got here.



   Through hard work, he says, and the learning of advanced math.



   Amazing, others have said.



   But such progress he's made in one generation that to progress beyond him, I feel as if I must leave America and colonize the moon.

~ Weike Wang,
873:You’re probably better at math than I am, because pretty much everyone’s better at math than I am, but it’s okay, I’m fine with it. See, I excel at other, more important things—guitar, sex, and consistently disappointing my dad, to name a few. By the way, it's apparently true that you'll never use it in the real world. Math, I mean. ~ Jennifer Niven,
874:You’re probably better at math than I am, because pretty much everyone’s better at math than I am, but it’s okay, I’m fine with it. See, I excel at other, more important things—guitar, sex, and consistently disappointing my dad, to name a few. By the way, it’s apparently true that you’ll never use it in the real world. Math, I mean. ~ Jennifer Niven,
875:He tells me that high school is no utopia, but I'm not convinced. What else would you call a place that exists solely to teach you about the world? What do you call a place with friends and teachers and libraries and book club and math club and debate club and any other kind of club and after-school activities and endless possibilities? ~ Nicola Yoon,
876:I'm sick of you all acting like I'm this English freak raining on your little math-science parade. Sung seems to think my contribution to this team is a little less than everyone else's."
"Anyone can memorize book titles!" Sung shouted. "Oh, please.Like I care what you think? You don't even know the difference between Keats and Byron. ~ Holly Black,
877:When cornered, desperate, or isolated, man reverts to those instincts that aim straight at survival. Quick and just. They will always be the trump cards because they are passed on more frequently from one generation to the next than the gentler genes. It is not a morality, but simple math. Among themselves, doves fight as often as hawks. ~ Delia Owens,
878:Me: u + me = wild animal sex 2nite?

She responds right away. Good, she’s still up.

Her: u = tempting – me = already in bed ÷ sleep.

Me: Why the division sign??

Her: I don’t know. I was trying to answer in math. Bottom line: I’m in bed.

Me: Perfect. That’s right where I want u to be. I’ll be there in 45. ~ Elle Kennedy,
879:Phyllis explained to him, trying to give of her deeper self, 'Don't you find it so beautiful, math? Like an endless sheet of gold chains, each link locked into the one before it, the theorems and functions, one thing making the next inevitable. It's music, hanging there in the middle of space, meaning nothing but itself, and so moving...' ~ John Updike,
880:If present trends continue, our country may soon find itself far behind many other nations in both science and technology nations where, if you inform strangers that you are a mathematician, they respond with admiration and not by telling you how much they hated math in school, and how they sure could use you to balance their checkbooks. ~ Martin Gardner,
881:I was never a class clown or anything like that, but I do remember being in the first grade and my teacher, Mr. Chad, told the class one day that we were going to do some exercises. He meant math exercises, but I stood up and started doing jumping jacks. To this day, I don't know what possessed me to do that, but all my friends cracked up. ~ Will Ferrell,
882:The interaction between math and physics is a two-way process, with each of the two subjects drawing from and inspiring the other. At different times, one of them may take the lead in developing a particular idea, only to yield to the other subject as focus shifts. But altogether, the two interact in a virtuous circle of mutual influence. ~ Edward Frenkel,
883:Mindset changes are not happening from change in legislation. Like desegregation. We legally got rid of legal segregation, but schools are still segregated. You can demand people have better math understanding, but it depends how you interpret math understanding, and what you want it for, and if you think everybody can and should have that. ~ Deborah Meier,
884:There was a survey done a few years ago that affected me greatly. it was discovered that intelligent people either estimate their intelligence accurately or slightly underestimate themselves, but stupid people overestimate their intelligence and by huge margins. (And these were things like straight up math tests, not controversial IQ tests.) ~ Harvey Pekar,
885:is, it seems to be the same folks who are inclined to sue builders who did not perfectly protect them from the depredations of an earthquake who will be the first to claim that their son failed his math test because of attention deficit disorder, and not because he spent the night before at a video arcade instead of studying complex fractions. ~ Lionel Shriver,
886:So, at a minimum, our educational systems must be retooled to maximize these needed skills and attributes: strong fundamentals in writing, reading, coding, and math; creativity, critical thinking, communication, and collaboration; grit, self-motivation, and lifelong learning habits; and entrepreneurship and improvisation—at every level. The ~ Thomas L Friedman,
887:The real irony is that the view of infinity as some forbidden zone or road to insanity - which view was very old and powerful and haunted math for 2000+ years - is precisely what Cantor's own work overturned. Saying that infinity drove Cantor mad is sort of like mourning St. George's loss to the dragon: it's not only wrong but insulting. ~ David Foster Wallace,
888:I'll be taking a two-hour after-school class twice a week for seven and a half weeks.
After those thirty hours of classroom time, which will bring me to the end of March, I'll need six hours behind the wheel.
And then and only then will I be able to drive.
I do the math in my mind as I speed home on my motorcycle from the firdt class. ~ Travis Thrasher,
889:I smiled despite myself.

"We're pretty far from perfect, Kitten.'m the most fucked up person you know."

"Yeah but I'm the most fucked up person I know, and when you put two negatives together, you get a positive. That's Math Caleb. Math is the language of universe. You can't argue with the universe." Her grin was patently ridiculous. ~ C J Roberts,
890:john stuart mill knew several languages, advanced math and read many great books' before he was ten years old. his father taught him. in his early twenties he had a nervous breakdown and didn't leave his bed for three years. he read poetry and at started to feel better. he was a feminist and cared about human rights. five people went to his funeral ~ Megan Boyle,
891:Looking at numbers as groups of rocks may seem unusual, but actually it's as old as math itself. The word "calculate" reflects that legacy - it comes from the Latin word calculus, meaning a pebble used for counting. To enjoy working with numbers you don't have to be Einstein (German for "one stone"), but it might help to have rocks in your head. ~ Steven Strogatz,
892:Sorry, the points are already deducted. And taking into account his schedule, and then the standard deviation from the average man’s schedule, I figure ninety percent of his time would go elsewhere. I’d never get uninterrupted coitus.” “Penis math,” Amy said. “Impressive.” She looked at Mallory. “See, this is why a guy shouldn’t date an accountant. ~ Jill Shalvis,
893:We’re pretty far from perfect, Kitten. I’m the most fucked up person you know.” “Yeah, but I’m the second most fucked up person I know, and when you put two negatives together, you get a positive. That’s math, Caleb. Math is the language of the universe. You can’t argue with the universe.” Her grin was patently ridiculous. I love you so goddamn much. ~ C J Roberts,
894:I have this math teacher, Mr. Allen. He said that when you're a point, all you see is the point. When you're a line, all you see is the line and the point. When you're in three dimensions, you see three dimensions and lines and points. Just because we can't see a fourth dimension doesn't mean it doesn't exist. It just means we haven't reached it yet. ~ Jodi Picoult,
895:I have this math teacher, Mr. Allen. He said that when you’re a point, all you see is the point. When you’re a line, all you see is the line and the point. When you’re in three dimensions, you see three dimensions and lines and points. Just because we can’t see a fourth dimension doesn’t mean it doesn’t exist. It just means we haven’t reached it yet. ~ Jodi Picoult,
896:Brüks digested that. “Well, if it was supposed to be some kind of compliment, her delivery needs work. You’d think someone with all that brainpower would be able to cobble together a few social skills.” “Funny thing”—Moore’s voice was expressionless—“Sengupta couldn’t figure out how someone with all your interpersonal skills could be so shitty at math. ~ Peter Watts,
897:Looking at numbers as groups of rocks may seem unusual, but actually it's as old as math itself. The word "calculate" reflects that legacy -- it comes from the Latin word calculus, meaning a pebble used for counting. To enjoy working with numbers you don't have to be Einstein (German for "one stone"), but it might help to have rocks in your head. ~ Steven H Strogatz,
898:People think they don’t understand math, but it’s all about how you explain it to them. If you ask a drunkard what number is larger, 2/3 or 3/5, he won’t be able to tell you. But if you rephrase the question: what is better, 2 bottles of vodka for 3 people or 3 bottles of vodka for 5 people, he will tell you right away: 2 bottles for 3 people, of course. ~ Anonymous,
899:With the Holy Mother as the centre of inspiration, a Math is to be established on the eastern bank of the Ganga. . . . On the other side of the Ganga a big plot of land will be acquired, where unmarried girls or Brahmacharini widows will live; devout married women will also be allowed to stay now and then. Men will have no concern with this Math. ~ Swami Vivekananda,
900:Get a grip, dude, you’re losing bad.” “Depends how you look at it.” “Only so many ways to look at a fourteen-seven score.” Wyatt shrugged, palming the ball in both hands. “Way I figure, I have a beautiful wife inside, and you’re playing footsie with your engaged, possibly mentally ill adversary.” He chucked the ball at Jake, grinning. “You do the math. ~ Denise Hunter,
901:If you've never programmed a computer, you should. There's nothing like it in the whole world. When you program a computer, it does exactly what you tell it to do. It's like designing a machine — any machine, like a car, like a faucet, like a gas-hinge for a door — using math and instructions. It's awesome in the truest sense: it can fill you with awe. ~ Cory Doctorow,
902:What makes screenplays difficult are the things that require the most discipline and care and are just not seen by most people. I'm talking about movement - screenwriting is related to math and music, and if you zig here, you know you have to zag there. It's like the descriptions for a piece of music - you go fast or slow or with feeling. It's the same. ~ Robert Towne,
903:You know, students who major in elementary education - they're going to be grade school teachers - they have the highest rates of math anxiety of any college major. And they bring that into the classroom. So you find students being introduced to math concepts by teachers who may have not only a lack of training but also a lack of enthusiasm about math. ~ Anya Kamenetz,
904:If time was infinite, then three seconds and three years represented the same infinitely small fraction of it. And so, if inflicting three years of fear and suffering was wrong, as everyone would agree, then inflicting three seconds of it was no less wrong. He caught a fleeting glimpse of God in the math here, in the infinitesimal duration of a life. ~ Jonathan Franzen,
905:People can believe whatever they want – Heaven, Hell, angels, gods – if it gives you a reason to get up in the morning or helps you sleep at night, then it’s energy well spent. But if someone wants to wax intellectual about a divine creator who is by all accounts infallible, I always had the same response: the universe’s one and only absolute is math. ~ Blake Northcott,
906:A creative person may write, paint, sculpt, or think up math formulae; he or she might dance or sing or play a musical instrument. Those are the fingers, but creativity is the hand that gives them life. And just as all hands are basically the same—form follows function—all creative people are the same once you get down to the place where the fingers join. ~ Stephen King,
907:Grace doesn’t add up. This probably explains why most couples shy away from making grace the default mode of their relationships. It’s counterintuitive. Intimidating too. Grace is so … selfless. We prefer the simple math behind the cause-effect dynamic within relationships. You scratch my back: I’ll scratch yours. You nick my car; I’ll burn down your garage. ~ Tim Kimmel,
908:I shouldn't be jealous because it's not real--she's like a math problem, the kind where you got the right answer but didn't show any of your work. She is the right answer, but she didn't get there by going through anything difficult, by questioning, by doubting. She landed there by playing a part, but she's never done the work.

I'm still jealous. ~ Jackson Pearce,
909:It has been proven time and time again in countless studies that students who actively participate in arts education are twice as likely to read for pleasure, have strengthened problem-solving and critical thinking skills, are four times more likely to be recognized for academic achievement, four times more likely to participate in a math and science fair. ~ Quincy Jones,
910:People think they don’t understand math, but it’s all about how you explain it to them. If you ask a drunkard what number is larger, 2/3 or 3/5, he won’t be able to tell you. But if you rephrase the question: what is better, 2 bottles of vodka for 3 people or 3 bottles of vodka for 5 people, he will tell you right away: 2 bottles for 3 people, of course. ~ Israel Gelfand,
911:I have always had an uncomfortable relationship with math. I don’t like numbers for the sake of numbers. I am not impressed by fancy formulas that have no real-world application. I particularly disliked high school calculus for the simple reason that no one ever bothered to tell me why I needed to learn it. What is the area beneath a parabola? Who cares? ~ Charles Wheelan,
912:It was while I was studying philosophy that I came to understand. . . that it is no sign of moral or spiritual strength to believe that for which one has no evidence, neither a priori evidence as in math, nor a posteriori evidence as in science. . . . It's a violation almost immoral in its transgressiveness to shirk the responsibilities of rationality. ~ Rebecca Goldstein,
913:Since when do you wear cologne to learn math? Oh, my son is growing up right in front of my very eyes. Maybe I should get out the video camera.

Maybe you should tie me to a stake, douse me in kerosene, and torch me right on our front lawn.

I won't need any kerosene, Steven - I'm sure the cologne will go up pretty fast!

Ha-ha, Mom. ~ Jordan Sonnenblick,
914:Analysis of President Bush's tax plan has revealed that several elaborate tricks and gimmicks were used to make it look like a $1.35 trillion cut, but in reality it's going to be closer to costing $1.8 trillion. Critics claim it's math so fuzzy, you have to squint to see our nation's future of subsistence farming and post-apocalyptic roving motorcycle gangs. ~ Jon Stewart,
915:Math is a way to describe reality and figure out how the world works, a universal language that has become the gold standard of truth. In our world, increasingly driven by science and technology, mathematics is becoming, ever more, the source of power, wealth, and progress. Hence those who are fluent in this new language will be on the cutting edge of progress. ~ Anonymous,
916:I can’t talk about our love story, so I will talk about math. I am not a mathematician, but I know this: There are infinite numbers between 0 and 1. There’s .1 and .12 and .112 and an infinite collection of others. Of course, there is a bigger infinite set of numbers between 0 and 2, or between 0 and a million. Some infinities are bigger than other infinities. A ~ John Green,
917:The most important steps that I followed were studying math and science in school. I was always interested in physics and astronomy and chemistry and I continued to study those subjects through high school and college on into graduate school. That's what prepared me for being an astronaut; it actually gave me the qualifications to be selected to be an astronaut. ~ Sally Ride,
918:You're sure your new roommate won't be like the last one who wore tinfoil socks and had a tendency to occasionally urinate in the refrigerator. You're sure you'll pass Math 106 this time around. You're determined to actually join some clubs this year and not just sit around in your dorm eating spray cheese from a can and watching youtube videos about cats. ~ Patrick Rothfuss,
919:...who'd walk to school on Monday and who'd have to pass the smoking heap of what used to be their neighborhoods because when adults are haunted, it's the kids who get the worst frights...The word "aftermath" came to mind. I guess it means the time after something terrible happens when you do the math to figure out what has been added and what's been subtracted. ~ Emil Ferris,
920:Byron; and, realistically, quite a number of those infants will die without my care, and Josephine is hardly a creature with potential, hardly anybody’s idea of a tabula rasa, a blank slate—hell, she’s a slate that’s had bad math scrawled on it and then been waxed so that nothing can ever be written on it again. I’ve treated sheep that had more of a right to live. ~ Tim Powers,
921:Hmm. Real life is different from math. Things in life don’t necessarily flow over the shortest possible route. For me, math is—how should I put it?—math is all too natural. It’s like beautiful scenery. It’s just there. There’s no need to exchange it with anything else. That’s why, when I’m doing math, I sometimes feel I’m turning transparent. And that can be scary. ~ Anonymous,
922:What was your job back on Earth? I’ve always been curious. I taught eighth-grade math in Tallahassee. Huh, I said. That’s not what I expected. Are you kidding? Powell said back. You try teaching algebra to a bunch of little shitheads for thirty-eight years straight. The way I figure it I’ve got about another decade before my rage from that gets entirely burned up. ~ John Scalzi,
923:I've always felt that a teacher can introduce recreational math; and I'm defining it in the very broad sense to include anything that has a spirit of play about it. I don't know of any better way to hook the interests of the students. ~ Martin Gardner, quoted by Anthony Barcellos in "A Conversation With Martin Gardner", The Two-Year College Math Journal 10(4), 1979, pp. 223-244.,
924:math performance in Asian American women, built around the stereotypes of Asians being good at math, and women not. Half the subjects were primed to think of themselves as Asian before a math test; their scores improved. Half were primed about gender; scores declined. Moreover, levels of activity in cortical regions involved in math skills changed in parallel. ~ Robert M Sapolsky,
925:When Republicans recently charged the President with promoting 'class warfare,' he answered it was 'just math.' But it's more than math. It's a matter of morality.

Republicans have posed the deepest moral question of any society: whether we're all in it together. Their answer is we're not.

President Obama should proclaim, loudly and clearly, we are. ~ Robert B Reich,
926:Next Generation was immensely popular at the time, and I was still riding high on the success of Stand by Me. They couldn’t understand why I was so intimidated by these actors – my face was splashed across the cover of every teen magazine in print. Why was I so intimidated? I was a 16 year-old geek, with a chance to meet The Big Three from Star Trek. You do the math. ~ Wil Wheaton,
927:You can't. Do you hear me? You think you've figured something out? You run over here so pleased with yourself because you changed your mind. Now you're certain. You're so... sloppy. You don't know anything. The book, the math, the dates, the writing, all that stuff you decided with your buddies, it's just evidence. It doesn't finish the job. It doesn't prove anything. ~ David Auburn,
928:America ranks 21st when it comes to math education. We rank 25th when it comes to science. We used to be number one in the proportion of college graduates. We now rank ninth. And at an age where knowledge, skills, are the determinant of how successful we're going to be, unless we reverse that we're going to keep slipping behind economically to a lot of other countries. ~ Barack Obama,
929:At first, when California started winning its water lawsuits and shutting off cities, the displaced people just followed the water-right to California. It took a little while before the bureaucrats realized what was going on, but finally someone with a sharp pencil did the math and realized that taking in people along with their water didn't solve a water shortage. ~ Paolo Bacigalupi,
930:If the Lord wills, we shall make this Math a great centre of harmony. Our Lord is the visible embodiment of the harmony of all ideals. He will be established on earth if we keep alive that spirit of harmony here. We must see to it that people of all creeds and sects, from the Brahmana down to the Chandala, may come here and find their respective ideals manifested. ~ Swami Vivekananda,
931:There are two versions of math in the lives of many Americans: the strange and boring subject that they encountered in classrooms and an interesting set of ideas that is the math of the world, and is curiously different and surprisingly engaging. Our task is to introduce this second version to today's students, get them excited about math, and prepare them for the future. ~ Jo Boaler,
932:Let’s be honest. You’re not Einstein, but don’t let assholes like that teacher make you feel stupid. You’re plenty smart, and good at other stuff. You know that, right?” “Yeah.” “Don’t just say yeah like a fucking mope. Let me hear you say it. Say you know you’re good at stuff.” “I’m good at stuff.” “That’s right. You’re good at stuff. Fuck that math teacher,” he said. ~ Justin Halpern,
933:To many, mathematics is a collection of theorems. For me, mathematics is a collection of examples; a theorem is a statement about a collection of examples and the purpose of proving theorems is to classify and explain the examples... ~ John B. Conway, Subnormal Operators (1981) Research Notes in Math., 51, Pitman Advanced Publishing Program, Boston-London-Melbourne, ISBN 0-8218-2184-9.,
934:Simulation is no substitute for math—it could never provide a proof—but if Peskin’s conjecture was false, this approach would save me a lot of time by revealing a counterexample. This sort of evidence is extremely valuable in math. When you’re trying to prove something, it helps to know it’s true. That gives you the confidence you need to keep searching for a rigorous ~ Steven H Strogatz,
935:The teacher might be talking about history or math, but what the students in a traditional classroom are learning is how to be students in a classroom. And they are learning it very well. They are learning how to take notes. They are learning how to surreptitiously communicate with peers. They are learning how to ask questions to endear themselves to authority figures. It ~ Clark Aldrich,
936:I’m smart in some ways- pretty good vocabulary, solid at math – but I am definitely the stupidest smart person there is… I was going to be the worst friend in the history of dying girls… Because I don’t really have a moral compass and I need to rely on (Earl) for guidance, or else I might accidentally become like a hermit or a terrorist or something. How fucked up is that. ~ Jesse Andrews,
937:When I was in high school, I was in a special math class. I was infatuated with physics, particularly nuclear physics, Einstein, and the Big Bang. I read a lot about black holes. And partly because I'm so lazy I thought you could do all this just by looking at the sky and thinking up universes. It didn't seem like hard work when I was a kid, so I enrolled in this class. ~ Aleksandar Hemon,
938:I thought you had the best grades, Charlotte,” Lina said to me. “No, Ximena does,” Maya interjected. She started counting off on her fingers. “Ximena. Charlotte. Simon. Me. And then either Auggie or Remo. Auggie’s actually got better grades than Remo in math, but he didn’t do that well in Spanish on his last few quizzes, and that’s bringing his whole grade point average down. ~ R J Palacio,
939:Even when I was failing math and everything else and I was feeling so bad about myself, you sat down with me and said, “Honey, there are those who do well at math, and then there are those, like yourself, who have been blessed with a creative mind and a wonderful imagination. I just know you are going on to do great things.” You’ll never know how you changed my life that day. ~ Fannie Flagg,
940:It surprised him that his grief was sharper than in the past few days. He had forgotten that grief does not decline in a straight line or along a slow curve like a graph in a child's math book. Instead, it was almost as if his body contained a big pile of garden rubbish full both of heavy lumps of dirt and of sharp thorny brush that would stab him when he least expected it. ~ Helen Simonson,
941:Stay alert! Don’t let someone’s words blind you from their behavior...

They can say all the right things, they can make you feel things you've never felt before, but don't be fooled; their actions will reveal their true character, desires, and priorities.

Behavior speaks; pay attention to what it tells you. Behavior is math; pay attention to what it reveals. ~ Steve Maraboli,
942:The thing about Markham that keeps it off my radar is that it pretty much doesn’t have a single team that I can bet on, or against. I’m not saying that reflects negatively on Markham as an institution; it is known for turning out leaders in fields as diverse as the sciences, math, engineering, and the arts. That’s all well and good, but it doesn’t get you into a bowl game. ~ David Rosenfelt,
943:I smiled despite myself.

Caleb: "We're pretty far from perfect, Kitten. I'm the most fucked up person you know."

Livvie: "Yeah but I'm the second most fucked up person I know, and when you put two negatives together, you get a positive. That's Math Caleb. Math is the language of universe. You can't argue with the universe."

Her grin was patently ridiculous. ~ C J Roberts,
944:BERTRAND RUSSELL, The Philosophy of Logical Atomism We've associated that word philosophy with academic study that in its own way has gotten so far beyond the layman that if you read contemporary philosophy you've no clue, because it's almost become math. And it's odd that if you don't do that and you call yourself a philosopher that you always get 'homespun' attached to it. ~ Bertrand Russell,
945:GOOD DESIGN IS SIMPLE. You hear this from math to painting. In math it means that a shorter proof tends to be a better one. Where axioms are concerned, especially, less is more. It means much the same thing in programming. For architects and designers, it means that beauty should depend on a few carefully chosen structural elements rather than a profusion of superficial ornament. ~ Paul Graham,
946:Personally, I think sex should be like math. At school. No one really cares if they’re crap at math. They even proclaim it. They’ll say to anyone, “Yeah, I don’t mind science and English, but I’m absolutely shithouse at math.” And other people will laugh and say, “Yeah, me, too. I wouldn’t have a clue about all that logarithm shit.” You should be able to say that about sex, too. ~ Markus Zusak,
947:Look, this is a man, he's got great numbers. He talks about numbers. I'm beginning to think not only did he invent the Internet, but he invented the calculator. It's fuzzy math. It's a scaring - trying to scare people in the voting booth. Under my tax plan, that he continues to criticize, I set a third - the federal government should take no more than a third of anybody's check. ~ George W Bush,
948:concerted cultivation. He gets taken to museums and gets enrolled in special programs and goes to summer camp, where he takes classes. When he’s bored at home, there are plenty of books to read, and his parents see it as their responsibility to keep him actively engaged in the world around him. It’s not hard to see how Alex would get better at reading and math over the summer. ~ Malcolm Gladwell,
949:Hey, what are you doing with your hand?”   Eli’s voice came out high pitched in surprise, as she clutched at Rafe’s shoulders.
“It’s the best place for leverage if you’re going to make that ladder.”
“My ass?  Really?”
“What can I say, I’ve done the math, factored in the weight and height ratios and your ass is definitely where I will gain the most leverage in lifting you. ~ Jane Cousins,
950:It's a mistake to get too narrow too fast. Kids today, many of them will live past 100, and you cant predict what you might work on. The things you're passionate about and interested in, get experience with them by going deep on projects. I would encourage science projects, plays. Pursue science, math, writing, history - the 21st century demands a lot of cross-disciplinary thinking. ~ Megan Smith,
951:Quiet: The Power of Introverts in a World That Can’t Stop Talking, Frank Partnoy’s Wait: The Art and Science of Delay, Linda Kaplan-Thaler’s The Power of Nice: How to Conquer the Business World with Kindness and The Power of Small: Why Little Things Make All the Difference, and Cathy O’Neil’s Weapons of Math Destruction: How Big Data Increases Inequality and Threatens Democracy. ~ Timothy Ferriss,
952:Win sidled up next to him. “Did you give them the full-wattage smile?” “I’d say a good eighty, ninety watts.” Win studied the young women before making a declaration: “Lesbians,” he said. “Must be.” “A lot of that going around, isn’t there?” Myron did the math in his head. He probably had fifteen to twenty years on them. When it comes to young girls, you just never want to feel it. ~ Harlan Coben,
953:We live today in a world where most of the really important developments in everything from math and physics and astronomy to public policy and psychology and classical music are so extremely abstract and technically complex and context-dependent that it's next to impossible for the ordinary citizen to feel that they (the developments) have much relevance to her actual life. ~ David Foster Wallace,
954:Continuation of the outbreak depended on the likelihood of encounters between people who were infectious and people who could be infected. This idea became known as the “mass action principle.” It was all about math. The same year, 1906, a Scottish physician named John Brownlee proposed an alternate view, contrary to Hamer’s. Brownlee worked as a clinician and hospital administrator ~ David Quammen,
955:How are you?” she asked.

It was a question that would’ve required some college-level math and about an hour of discussion to answer. I felt a hundred conflicting things, the great bulk of which canceled out to equal cold and tired and not particularly interested in talking. So I said, “I’m fine, just trying to dry off,” and flapped the front of my soggy sweater to demonstrate. ~ Ransom Riggs,
956:It is true that Samudramanthan can be interpreted to mean “churning the ocean”. But the root of manthan is manth or math. Which can have multiple meanings in English. Churn is just one of those meanings. Math can also mean stir, agitate or mix. So, if we were to disregard the traditional interpretation of the title itself, it could mean either “stirring the ocean” or “mixing the ocean”. ~ Anonymous,
957:People will tell you that you have to know math to be a scientist, or physics or chemistry. They’re wrong. That’s like saying you have to know how to knit to be a housewife, or that you have to know Latin to study the Bible. Sure, it helps, but there will be time for that. What comes first is a question, and you’re already there. It’s not nearly as involved as people make it out to be. ~ Hope Jahren,
958:We had the schools we wanted, in a way. Parents did not tend to show up at schools demanding that their kids be assigned more challenging reading or that their kindergarteners learn math while they still loved numbers. They did show up to complain about bad grades, however. And they came in droves, with video cameras and lawn chairs and full hearts, to watch their children play sports. ~ Amanda Ripley,
959:A few years after Shawn took the job with the cabinet company, he decided to go back to school to get his teaching degree. He wanted to do more good in the world. Sitting behind an accounting desk wouldn’t accomplish that. Now, he teaches high school math, a subject most teachers shrink from. He wanted to influence the lives of children, and he is. His students respect him and so do I. ~ M Weidenbenner,
960:There's a kind of a line between music and math, so I guess I got the music gene, thank goodness. But my mother wasn't too thrilled. She wanted me to go to university and get a degree or do something, and my father, he liked opera so he wasn't too thrilled either, because he wanted me to be an opera singer and I didn't have - as he said, I don't really have the strength to do that. ~ Olivia Newton John,
961:What Chinese parents understand is that nothing is fun until you're good at it[...] Tenacious practice, practice, practice is crucial for excellence; rote repetition is underrated in America. Once a child starts to excel at something—whether it's math, piano, pitching or ballet—he or she gets praise, admiration and satisfaction. This builds confidence and makes the once not-fun activity fun. ~ Amy Chua,
962:For as long as we can remember,” [Griff] said, “I mean literally our whole conscious lives, time has been neatly divided into semesters and years. Each year completely distinguishable and unique. First grade, third grade. We didn’t measure by age, we measured by grade. Like I know I broke my arm in sixth grade but I’d have to do the math to figure out what year that was, or how old I was. ~ Ben Monopoli,
963:I had authority issues. In my defense, my math teacher had it coming. She’d made me write one hundred on the black board, so I wrote one, zero, zero in words since one hundred consisted of those numbers. Because she hadn't been specific in her instructions,she’d berated me for being a smart aleck. The whole class had laughed at me. The next morning, they had to cut her out of her chair. ~ Kate Evangelista,
964:NAEP is central to any discussion of whether American students and the public schools they attend are doing well or badly. It has measured reading and math and other subjects over time. It is administered to samples of students; no one knows who will take it, no one can prepare to take it, no one takes the whole test. There are no stakes attached to NAEP; no student ever gets a test score. ~ Diane Ravitch,
965:A majority of students who come into community colleges are still stuck at high school level or remedial math. And when they take it in college, they still don't pass it. So the Carnegie Foundation got together and created two accelerated courses that focus on real-world applications of numbers like for health, for civics, for personal finance - concepts that you and I use every single day. ~ Anya Kamenetz,
966:In short, Mr. Ryan’s plan is devoid of credible math or hard policy choices. And it couldn’t pass even if Republicans were to take the presidency and both houses of Congress. Mr. Romney and Mr. Ryan have no plan to take on Wall Street, the Fed, the military-industrial complex, social insurance or the nation’s fiscal calamity and no plan to revive capitalist prosperity - just empty sermons. ~ David Stockman,
967:Simulation is no substitute for math—it could never provide a proof—but if Peskin’s conjecture was false, this approach would save me a lot of time by revealing a counterexample. This sort of evidence is extremely valuable in math. When you’re trying to prove something, it helps to know it’s true. That gives you the confidence you need to keep searching for a rigorous proof. Programming ~ Steven H Strogatz,
968:I don't think that everyone should become a mathematician, but I do believe that many students don't give mathematics a real chance. I did poorly in math for a couple of years in middle school; I was just not interested in thinking about it. I can see that without being excited mathematics can look pointless and cold. The beauty of mathematics only shows itself to more patient followers. ~ Maryam Mirzakhani,
969:No one had ever told her this basic fact: not everyone got to be loved. It was like those stupid bell curves they'd had to study in math class. There was the big, swollen, happy middle, a whale lump full of blissful couples and families eating around a big dining room table and laughing. And then, at the tapered ends, there were the abnormal people, the weirdos and freaks, and zeros like her. ~ Lauren Oliver,
970:When I was a child I could do math and art, so I had left- and right-brain capabilities. But I've seen my children, who are more right-brained, struggling. My son was told he wouldn't make it to college, but he dogged it through and ended up being accepted by 10 major art schools after the high school advisor said, "Please don't apply. You're going to be disappointed." That kid's an artist now. ~ Frank Gehry,
971:Life is not a math problem, Charlotte.” If it was, I’d have been a lot better at it. I’d often wished I could work out people as easily as I did arithmetic: simply break them down to their common denominators and solve. Numbers didn’t lie; there was always an answer, and the answer was either right or it was wrong. Simple. But nothing in life was simple, and there was no answer here to solve for. ~ Kate Quinn,
972:Music is math, and one you understand that…How can anyone not be in awe? It’s the audible expression behind the laws of the universe. It feels like the only thing, apart from God, that lives outside time. Once released, it lives on and it can make you laugh and cry, rip you apart and heal you, all withing a few discrete notes strung together. And while it follows rules, expression is limitless. ~ Katherine Reay,
973:No one had ever told her this basic fact: Not everyone gets to be loved. It was like those stupid bell curves they'd had to study in math class. There was the big, swollen, happy middle, a whale hump full of blissful couples and families eating around a big dining room table and laughing. And then, at the tapered ends, there where the abnormal people, the weirdo's and freaks and zero's like her. ~ Lauren Oliver,
974:I worry about Lily, sluggish as she is. Will she see Carter's truths? Will he tell her? God knows she won't hear them. She's moving too fast to hear anyone's music but her own. She's so set, but I know he could make her settled. I tried to sync their noise into music, but they both pushed back. Too obdurate to be oblong.
Silly Lily. How can she resist someone who brings gum and sounds like math? ~ Emily McKay,
975:New Rule: Food companies must face the facts: One container equals one serving. Look, we’re Americans, and that means once we open the bag, there’s no stopping us until we’re licking stray bits of powdered cheese off the carpet. So stop trying to give us nutritional information based on a fraction of the package. It assumes a talent for two things that we’re really not capable of: restraint and math. ~ Bill Maher,
976:What’s infinity plus one?” I interrupted Katy, asking Finn my own question. “It’s still infinity,” Finn said, sighing.
“Wrong. It’s two.”
“Oh yeah? How do you figure?”
I pointed at Finn and said, “Infinity.” Then I pointed at myself and said, “Plus one. That’s two, genius.”
“I really wish I hadn’t told you my name.”
“Ha. Gotcha! You think you’re so good at math, but I just stumped you. ~ Amy Harmon,
977:I feel like I'm playing some giant video game, or trying to solve a really complicated math equation. 'One girl is trying to avoid forty raiding parties of between fifteen to twenty people each, spread out across a radius of seven miles. If she has to make it 2.7 miles through the center, what is the probablitiy she will wake up tomorrow morning in a jail cell? Please feel free to round pi to 3.14'. ~ Lauren Oliver,
978:Math ain't about numbers! If you think math is about numbers, you probably think that Shakespeare is all about words. You probably think that dancing is all about shoes. You probably think that music is all about notes. Math ain't about numbers! Math is about logic, it's about beauty, it's about connections, it's about how you get from one place to another. ~ Cliff Stoll, Klein Bottles - Numberphile (June 22, 2015),
979:One day he finally got a math concept (converting between hours and fractions of hours, as I remember) he'd been struggling and struggling with, so I praised him up and down, and told him it was a good day, a day to remember.   "It was just one minute," he said. "What's the rest of the day gonna do for me?"   "Sometimes you only get one good minute a day," I said. "You just have to make the most of it. ~ Claire Cook,
980:Music is math, and once you understand that . . . How can anyone not be in awe? It’s the audible expression behind the laws of the universe. It feels like the only thing, apart from God, that lives outside time. Once released, it lives on and it can make you laugh and cry, rip you apart and heal you, all within a few discrete notes strung together. And while it follows rules, expression is limitless. ~ Katherine Reay,
981:But had it been the wine? Maybe it was something else. I was no math expert, but this was an intoxicating equation: Hot Guy with Mysterious Past + Way With Pretty Words x Chivalry at Beach / His Aloofness at Coffee Shop (Immunity to My Face & Flirty Efforts) + Innuendo at Hardware Store x Honest Confession about OCD Struggles —> Curiosity + Arousal (Belly Flutters + Pulse Quickening)=ATTACKISS. ~ Melanie Harlow,
982:There's no such thing as "The One", she once said. They were at dinner in Taipei, with a supplier and his wife. The couple had been married forty years. The idea that there's just one person in the world you're meant to be with, it's illogical, she said. She'd had a few drinks and was enjoying her own loud thoughts. The math just doesn't work! Who you end up with, it's really just an accident of proximity. ~ Dave Eggers,
983:Think of those fingers as abilities. A creative person may write, paint, sculpt, or think up math formulae;
he or she might dance or sing or play a musical instrument. Those are the fingers, but creativity is the hand that gives them life.
& just as all hands are basically the same - form follows function - all creative people are the same once you get down to the place where the fingers join. ~ Stephen King,
984:There are many different experiences that cause girls to relinquish their true selves. In early adolescence girls learn how important appearance is in defining social acceptability. Attractiveness is both a necessary and a sufficient condition for girls' success. This is an old, old problem. Helen of Troy didn't launch a thousand ships because she was a hard worker. Juliet wasn't loved for her math ability. ~ Mary Pipher,
985:I know why you didn’t get the money. I was wondering how much sixteen million dollars weighs.” “I can tell you exactly. Bank gets hit, they tell us how many of each denomination was lost. Tally that up, you know how many bills; you have four hundred fifty-four bills in a pound, doesn’t matter what denominations—just do the math. This particular sixteen million weighs eleven hundred forty-two pounds.” Holman ~ Robert Crais,
986:You went to school," Lee said. "I mean, at some point. And it didn't suit you very well. They wanted to teach you things you didn't care about. Dates and math and trivia about dead presidents. They didn't teach persuasion. Your ability to persuade is the single most important determinant of your quality of life, and they didn't cover that at all. Well, we do. And we're looking for students with natural aptitude. ~ Max Barry,
987:At the end of the day, when I am lying in bed and I know the chances of any of our theology being exactly right are a million to one, I need to know that God has things figured out, that if my math is wrong we are still going to be okay. And wonder is that feeling we get when we let go of our silly answers, our mapped out rules that we want God to follow. I don't think there is any better worship than wonder. ~ Donald Miller,
988:At the end of the day, when I am lying in bed and I know the chances of any of our theology being exactly right are a million to one, I need to know that God has things figured out, that if my math is wrong we are still going to be okay. And wonder is that feeling we get when we let go of our silly answers, our mapped out rules that we want God to follow. I don’t think there is any better worship than wonder. ~ Donald Miller,
989:If you want me to fix your homework, you need to leave me alone.” Then he spotted her. “You’re back.” “Yeah.” She glanced between him and Gabriel. “You do his homework?” “Just the math. It’s a miracle he can count to ten.” “I can count to one.” Gabriel gave him the finger.

Kemmerer, Brigid (2012-04-24). Storm (Elemental Book 1) (Kindle Locations 1073-1076). Kensington Publishing Corp. Kindle Edition. ~ Brigid Kemmerer,
990:Holmes, too, continued to embrace an exalted image of herself. In her acceptance speech at Glamour magazine’s Women of the Year Awards at Carnegie Hall, she held herself up as a role model for young women. “Do everything you can to be the best in science and math and engineering,” she urged them. “It’s that that our little girls will see when they start to think about who do they want to be when they grow up. ~ John Carreyrou,
991:I'd say it's that most people think that very wealthy people take huge risks and that's why they have huge rewards. But the very best on earth are completely obsessed with not losing money. That sounds overly simplistic, but they know that if you lost 50 percent, it takes 100 percent to get even. Most people don't make that math in their head, so it takes years and years. They are obsessed with not losing money. ~ Tony Robbins,
992:Men with more “masculine” 2D:4D ratios tend toward higher levels of aggression and math scores; more assertive personalities; higher rates of ADHD and autism (diseases with strong male biases); and decreased risk of depression and anxiety (disorders with a female skew). The faces and handwriting of such men are judged to be more “masculine.” Furthermore, some reports show a decreased likelihood of being gay. ~ Robert M Sapolsky,
993:The historical resonances are sharp. [Louis] Brandeis is nominated on Jan. 28, 1916. Confirmed on June 1. Waits 125 days between nomination and confirmation, which remains an unbroken record, although Merrick Garland will surpass it in July, if my math is right. Anti-Semitism was definitely not the central reason for the opposition, which tended to focus more on his anti-corporate radicalism, but it was a theme. ~ Jeffrey Rosen,
994:There are other reasons we use math in physics. Besides keeping us honest, math is also the most economical and unambiguous terminology that we know of. Language is malleable; it depends on context and interpretation. But math doesn’t care about culture or history. If a thousand people read a book, they read a thousand different books. But if a thousand people read an equation, they read the same equation. ~ Sabine Hossenfelder,
995:One day, you look in the mirror, and see gray hair. One day, you realize there is less of your life left than what you’ve already lived. And you think, How did this happen so fast? It was only yesterday when I was having my first legal drink, when I was diapering him, when I was young. When this realization hits, you start doing the math. How much time do I have left? How much can I fit into that small space? Some ~ Jodi Picoult,
996:I don't want to exaggerate; having as many African American men as we've had in the criminal-justice system, and the amount of time it takes for the damage done by that to wash through our society and our communities, the disadvantages born out of kids being undiagnosed with mental-health problems early, or not getting the kind of exposure to reading and math when they're 4 or 5 or 6 years old, that carries a cost. ~ Barack Obama,
997:Every branch of science likes to think it’s important, and of course, they all are. But they’re specializations. Much of biology, for example, is biochemistry, which is a specialization of organic chemistry, which is a specialization of chemistry, which is a specialization of physics, and physics is practical mathematics. No matter which set of matryoshka dolls you open in science, the innermost is always math. ~ Jonathan L Howard,
998:Okay. Morality in a nutshell. Don't hurt people if you can avoid it. Don't steal stuff unless you're starving or it's really, really important. Work hard. Pay your bills. Try to help others. Always double-check your math if there are explosives involved. If you screwed it up, you need to see it gets fixed. And don't eat anything that talks. If it doesn't fall under one of those categories, just do the best you can. ~ Ursula Vernon,
999:Programming was very different from mathematics, as it was far more creative. In math, there was one right answer, and you worked at a problem until you got to that answer. In programming, there were an infinite number of answers that could be considered correct, just as there might be when writing a book. But the results of programming, unlike a written story, were tangible. Your program had to actually do something. ~ B V Larson,
1000:The effort to solve the three-body problem was a thread that ran through several hundreds of cycles of Trisolaran civilization. Most Redemptionists with some in-depth math and physics knowledge had attempted the three-body problem, and even after knowing that the problem was mathematically unsolvable as posed, the effort did not cease, because solving the three-body problem had become a religious ritual of their faith. ~ Liu Cixin,
1001:Ask an English-speaking seven-year-old to add thirty-seven plus twenty-two in her head, and she has to convert the words to numbers (37 + 22). Only then can she do the math: 2 plus 7 is 9 and 30 and 20 is 50, which makes 59. Ask an Asian child to add three-tens-seven and two-tens-two, and then the necessary equation is right there, embedded in the sentence. No number translation is necessary: It’s five-tens-nine. ~ Malcolm Gladwell,
1002:what is JUST in a world
you’ve ripped in two
as if there could be
a half for me
a half for you
what is FAIR when
there is nothing
left to share
what is YOURS when
your pain is mine to bear
this sad math is mine
this mad path is mine
subtract they say
don’t cry
back to the desk
try
forget addition
multiply
and i reply
this is why
remainders
hate
division ~ Kami Garcia,
1003:...I think there's only one [thing] that anybody teaches, and this is character. And I think that whether you are teaching history, math, or biology, or music, what you are really doing is, you are helping to shape the character of that person who is your student... Music is such a wonderful teaching tool, because while you are developing musical skills, that student can learn a lot about discipline [and] cooperation. ~ Rich Mullins,
1004:Q: What’s hard for you? A: Mostly I straddle reality and the imagination. My reality needs imagination like a bulb needs a socket. My imagination needs reality like a blind man needs a cane. Math is hard. Reading a map. Following orders. Carpentry. Electronics. Plumbing. Remembering things correctly. Straight lines. Sheet rock. Finding a safety pin. Patience with others. Ordering in Chinese. Stereo instructions in German. ~ Tom Waits,
1005:According to the United States Department of Education (DOE), the 2013 National Assessment of Educational Progress (NAEP)11 reports that only 26 percent of the nation’s twelfth graders are proficient in math and only 38 percent are proficient in reading. There is also a twenty-nine percentage point gap between the reading proficiency of white and black twelfth-grade students. And these numbers are unchanged since 2009.12 ~ Mark R Levin,
1006:Maybe Lindsay and I are best friends and we hate each other, both. Maybe I’m only one math class away from being a slut like Anna Cartullo. Maybe I am like her, deep down. Maybe we all are: just one lunch period away from eating alone in the bathroom. I wonder if it’s ever really possible to know the truth about someone else, or if the best we can do is just stumble into each other, heads down, hoping to avoid collision. ~ Lauren Oliver,
1007:There was quite a lot of competitiveness about it, with everybody wanting to beat not only cancer itself, but also the other people in the room. Like, I realize that this is irrational, but when they tell you that you have, say, a 20 percent chance of living five years, the math kicks in and you figure that’s one in five . . . so you look around and think, as any healthy person would: I gotta outlast four of these bastards. ~ John Green,
1008:though, will improve her math and reading skills, and every carefree summer day she spends puts her further and further behind Alex. Alex isn’t necessarily smarter than Katie. He’s just out-learning her: he’s putting in a few solid months of learning during the summer while she watches television and plays outside. What Alexander’s work suggests is that the way in which education has been discussed in the United States ~ Malcolm Gladwell,
1009:You’re smart then . . . aren’t you, Finn?” I heard the awe in my own voice. It wasn’t a question. I had never been school smart, and marveled at those who were. “I thought you were. I was never any good with numbers. Math has always been like a murky pond, and me, a hillbilly stabbing at the fish with a pokey stick, trying to get lucky.”
“That doesn’t make any sense, Bonnie.” Finn laughed softly.
“That’s my point, Clyde ~ Amy Harmon,
1010:Q: What’s hard for you?

A: Mostly I straddle reality and the imagination. My reality needs imagination like a bulb needs a socket. My imagination needs reality like a blind man needs a cane. Math is hard. Reading a map. Following orders. Carpentry. Electronics. Plumbing. Remembering things correctly. Straight lines. Sheet rock. Finding a safety pin. Patience with others. Ordering in Chinese. Stereo instructions in German. ~ Tom Waits,
1011:The key to good worldbuilding is leaving out most of what you create. You, as the author, had damn well better know the where all that dragon food comes from, but that doesn't mean that I, as a reader, want to read a five thousand word essay about you explaining it to me. I don't need to see the math, but I can tell by the details you provide whether or not you've thought these things through to their logical conclusions. ~ Patrick Rothfuss,
1012:My family tried to educate me in the way they thought a young woman should be. But I wanted to learn about mathmatics. I must have gotten that from my father, he was a master of math and science, and I always liked that sort of thing, too. Of course my mother and father did not agree with me on becoming more educated in mathmatics, but I was persistent and eventualy they gave in and I was taught by a wonderful teacher. ~ Florence Nightingale,
1013:Your first kiss isn’t as important as your last.
The math test really didn’t matter.
The pie really did.
The stuff you’re good at and the stuff you’re bad at are just different parts of the same thing.
Same goes for the people you love and the people you don’t–and the people who love you and the people who don’t.
The only thing that mattered was that you cared about a few people.
Life is really, really short. ~ Kami Garcia,
1014:When I was a child, all problems had ended with a single word from my father. A smile from him was sunshine, his scowl a bolt of thunder. He was smart, and generous, and honorable without fail. He could exile a trespasser, check my math homework, and fix the leaky bathroom sink, all before dinner. For the longest time, I thought he was invincible. Above the petty problems that plagued normal people.

And now he was gone. ~ Rachel Vincent,
1015:George Dantzig was a graduate student in math at Berkeley. One day, as usual, he rushed in late to his math class and quickly copied the two homework problems from the blackboard. When he later went to do them, he found them very difficult, and it took him several days of hard work to crack them open and solve them. They turned out not to be homework problems at all. They were two famous math problems that had never been solved. ~ Carol S Dweck,
1016:Despite the lack of money, the instability, and the politics I'd yet to really understand, I found myself having fun. Which was surprising since I'd found myself on a path defined by uncertainty: the very thing I'd been trying to outmaneuver by throwing myself into college, banking, and that godforsaken math class. I wasn't sure where writing would take me, but I was sure that doing it made me feel alive in a way I hadn't before. ~ Anne T Donahue,
1017:In most countries, attending some kind of early childhood program (i.e., preschool or prekindergarten) led to real and lasting benefits. On average, kids who did so for more than a year scored much higher in math by age fifteen (more than a year ahead of other students). But in the United States, kids’ economic backgrounds overwhelmed this advantage. The quality of the early childhood program seemed to matter more than the quantity. ~ Amanda Ripley,
1018:It's amazing to me that not only can we put a probe around Saturn and get images of its moons, but our math and physics are so freaking accurate we can say, "Hey, you know what? On this date at this time if we turn Cassini that way we'll see a moon over 2 million kilometers away pass in front of another one nearly 3 million kilometers away." Every morning, I have a 50/50 chance of finding my keys. That kinda puts things in perspective. ~ Phil Plait,
1019:I've written about 2,000 short stories; I've only published 300 and I feel I'm still learning. Any man who keeps working is not a failure. He may not be a great writer, but if he applies the old fashioned virtues of hard, constant labor, he'll eventually make some kind of career for himself as a writer. Ray Bradbury, 1967 interview (Doing the Math - that means for every story he sold, he wrote six "un-publishable" ones. Keep typing!) ~ Ray Bradbury,
1020:Which meant there was quite a lot of competitiveness about it, with everybody wanting to beat not only cancer itself, but also the other people in the room. Like, I realize that this is irrational, but when they tell you that you have, say, a 20 percent chance of living five years, the math kicks in and you figure that’s one in five . . . so you look around and think, as any healthy person would: I gotta outlast four of these bastards. ~ John Green,
1021:The New START accord cuts the strategic nuclear arsenals on each side to 1,550 warheads. Can any of its critics make a case that our security would be imperiled if, the very next day, Obama and Medvedev made moves to take the levels down to 1,000—then to 500?

If so, come show us the math. If not, it may be time to stop making arms control so politically complicated—time to stop letting arms control get in the way of disarmament. ~ Fred Kaplan,
1022:We are Alaskan Native Indians, Native Hawaiians, and European expatriate Indians, Indians from eight different tribes with quarter-blood quantum requirements and so not federally recognized Indian kinds of Indians. We are enrolled members of tribes and disenrolled members, ineligible members and tribal council members. We are full-blood, half-breed, quadroon, eighths, sixteenths, thirty-seconds. Undoable math. Insignificant remainders. ~ Tommy Orange,
1023:We, however, have all kinds of different ideas about what happiness is. Some must go bungee jumping to experience a rush of joy, while others find bliss staying home. Some are happy in a concert hall, listening to classical music, while children on a playground could be music to the ears of others. Some people experience elation when they solve a complicated equation, while for others a cancelled math class is a happy childhood memory. ~ Haim Shapira,
1024:In whatever you choose to do, do it because it's hard, not because it's easy. Math and physics and astrophysics are hard. For every hard thing you accomplish, fewer other people are out there doing the same thing as you. That's what doing something hard means. And in the limit of this, everyone beats a path to your door because you're the only one around who understands the impossible concept or who solves the unsolvable problem. ~ Neil deGrasse Tyson,
1025:Probably nothing,” Tom ventured, wanting it to be true.
Prophet didn’t argue, but they both decided that school was off-limits for a bit. Remy, of course, didn’t mind a damned bit. Mal offered to tutor him in the interim and that actually worked out quite well. Then again, for all Tom knew, math was a code for bomb building.
When he mentioned that to Prophet, all he got in response was, “They’re both useful life skills. ~ S E Jakes,
1026:When will it begin, anyway?" Sirus held his gaze for a moment, his eyes full of concern- a concern that Joss didn't understand. "Probably sooner than you're ready for." "When's that?" "Well." Sirus sighed, as if doing the math in his head."It'll take us about three minutes to gather this stuff and get to the cabin, and another two or three for Abraham to realize you're here. So I'd say you have about seven more minutes of freedom left. ~ Heather Brewer,
1027:Owing to the math, many of us would never get the chance to marry. But neither would we be welcome to stay on. Five years from now, quite a few of my bunkhouse roommates would be gone from Paradise. Some would run away, but many would be kicked out. Nobody spoke of this practice, of course. There were many, many idiosyncrasies at Paradise that were not to be mentioned aloud, but the throwing away of half our young men was the ugliest one. ~ Sarina Bowen,
1028:I've written about 2,000 short stories; I've only published 300 and I feel I'm still learning. Any man who keeps working is not a failure. He may not be a great writer, but if he applies the old fashioned virtues of hard, constant labor, he'll eventually make some kind of career for himself as a writer.
Ray Bradbury, 1967 interview
(Doing the Math - that means for every story he sold, he wrote six "un-publishable" ones. Keep typing!) ~ Ray Bradbury,
1029:But over the last decade, neuroscientists have discovered that, like an eager student, the brain is remarkably responsive to experience. Ask your brain to do math every day, and it gets better at math. Ask your brain to worry, and it gets better at worrying. Ask your brain to concentrate, and it gets better at concentrating. Not only does your brain find these things easier, but it actually remodels itself based on what you ask it to do. ~ Kelly McGonigal,
1030:As I said in my last book, birds are mean. They're the only pet that, when they escape, the owners are relieved. You can tell a species is evil by doing this simple math. If my blond lab Molly was the size of T-Rex, that would just mean more kibble, more work for the gardener in the backyard, and a harder time moving her to my wife's side of the bed at night. If birds were the size of a T-Rex, the streets would be littered with human remains. ~ Adam Carolla,
1031:He spotted Linda Coldren in a private grandstand tent overlooking the eighteenth hole. She wore sunglasses and a baseball cap pulled low. Myron looked up at her. She did not look back. Her expression was one of mild confusion, like she was working on a math word problem or trying to recall the name behind a familiar face. For some reason, the expression troubled Myron. He stayed in her line of vision, hoping she’d signal to him. She didn’t. Tad ~ Harlan Coben,
1032:When you're the guy behind the camera, you're aware of the reasons for the compromises or the changes that get made. As an actor, you go and do your thing, and someone else down the line then does all the math and goes, "We can't include that thing where he's pretending to be dumb and needling those people, because it takes a minute and a half, and it ruins the next scene. It doesn't make sense." If you're directing, you're the one doing that. ~ Casey Affleck,
1033:For all the time schools devote to the teaching of mathematics, very little (if any) is spent trying to convey just what the subject is about. Instead, the focus is on learning and applying various procedures to solve math problems. That's a bit like explaining soccer by saying it is executing a series of maneuvers to get the ball into the goal. Both accurately describe various key features, but they miss the what and the why of the big picture. ~ Keith Devlin,
1034:I did become homesick, and whenever that happened, I'd hide away in the school library, where the books filled rows and rows of shelves. I'd find a chair and study my lesson books in geography, social studies, biology, and math. I'd lose myself in American and African history, and within the colorful maps of the world. No matter how foreign and lonely the world was outside, the books always reminded me of home, sitting under the mango tree. ~ William Kamkwamba,
1035:In third period Math, we were forced to sit in alphabetical order. Which put me right behind Logan, who was throwing all those passes to Aiden in the scrimmage. He took off his navy blazer and when he leaned forward to write, I could see muscles bulging across his back and shoulders. I can already tell Math is going to suck, but at least I’ll have a nice view.
It’s like what Grandpa always says about real estate. Location, location, location. ~ Jillian Dodd,
1036:The community certainly included black English professors, like my mother, as well as black doctors and dentists, black mechanics, janitors, and contractors, black cobblers, wedding planners, real estate agents, and undertakers, several black lawyers, and a handful of black Mary Kay salespeople. As a child, however, I knew so many African Americans working in science, math, and engineering that I thought that’s just what black folks did. ~ Margot Lee Shetterly,
1037:When you could discern a real threat from everything else, it was called caution. When you couldn't, it was called paranoia.

...

You cannot separate paranoia from knowledge. The more you know, the more possibilities you see. The more possibilities you see, the more possibilities someone else sees. The more "someones" there are, the more "they" there are. It's a matter of simple math before you realize that They might not like you. ~ Craig Clevenger,
1038:As independent as the kid appeared, a twelve-year-old had no business living on her own in an abandoned house. “What are your favorite subjects?” “Math.” “Really? Good for you. I’m terrible at math, though I can do percentages very well.” “Why?” “I’m a bartender. I can calculate tips off the top of my head. I suppose you do much higher math than that.” “Trigonometry and geometry are pretty fun.” Lucy sipped her soda. “Fun? I’m impressed. So do ~ Mary Ellen Taylor,
1039:Q&As covered my fave color (purple), my fave shows (Family Ties and Cosby), my height (5′ 7″), weight (130 pounds) and eye color (hazel). They also printed false information. One said my parents were a psychologist and a newspaper reporter. Sure, my television parents held those careers—my real parents were a math/P.E. teacher and a housewife/manager (of me). I was supposed to be the coolest kid on the planet, but no one knew what a dork I was. ~ Kirk Cameron,
1040:When I heard they would be in Birmingham in two days, I had one request. “Bring my school bag,” I pleaded to my father. “If you can’t go to Swat to fetch it, no matter—buy new books for me, because in March it’s my board examination.” Of course I wanted to come first in class. I especially wanted my physics book because physics is difficult for me, and I needed to practice numericals, as my math is not so good and they are hard for me to solve. ~ Malala Yousafzai,
1041:The product of mathematics is clarity and understanding. Not theorems, by themselves. Is there, for example any real reason that even such famous results as Fermat's Last Theorem, or the Poincaré conjecture, really matter? Their real importance is not in their specific statements, but their role in challenging our understanding, presenting challenges that led to mathematical developments that increased our understanding. ~ Bill Thurston, Math Overflow, Oct 30 2010.,
1042:The real truth - like anything, you have an idea about something you might write and it changes. People reflect on it or you get other ideas and maybe your original idea is radically different than how it ends up being. It's not a theorem. You don't sit down and prove something. You start with an initial idea and it grows and grows. The math of the narrative changes. In some ways your original document and what the film ends up being are quite different. ~ Matt Ross,
1043:Amusingly, Christopher Columbus totally bungled this by relying on subsequent less-accurate calculations and confusing Arabic miles with Italian miles, concluding that he needed to sail only 3,700 km to reach the Orient when the true value was 19,600 km. He clearly wouldn’t have gotten his trip funded if he’d done his math right, and he clearly wouldn’t have survived if America hadn’t existed, so sometimes being lucky is more important than being right. ~ Max Tegmark,
1044:DEMON MATH
What is JUST in a world
you've ripped in two
as if there could be
a half for me
a half for you
what is FAIR when
there is nothing
left to share
what is YOURS when
your pain is mine to bear
this sad math is mine
this mad path is mine
subtract they say
don't cry
back to the desk
try
forget addition
multiply
and i reply
this is why
remainders
hate
division. ~ Kami Garcia,
1045:Loren looked at Christ on the cross behind the Mother Superior’s head. She remembered an old joke, one she heard when she first got here. A boy is getting all Ds and Fs in math so his parents send him to Catholic school. On his first report card, his parents are shocked to see their son getting straight As. When his parents ask him why, he says, “Well, when I went into the chapel and saw that guy nailed to a plus sign, I knew they were serious.” Mother ~ Harlan Coben,
1046:Of course, being a mathematician, I'm always looking for ways to avoid tedious mundane labor. Especially if it means I get to do a bunch of interesting abstract thinking. That's kind of the whole math thing: working hard to find ways to get out of working hard. If you are really, really lazy, and also happen to be really, really clever, then math just might be the life for you (assuming you also have no interest in wealth, fame, or popularity). ~ Paul Lockhart,
1047:Nonmathematical people sometimes ask me, “You know math, huh? Tell me something I’ve always wondered, What is infinity divided by infinity?” I can only reply, “The words you just uttered do not make sense. That was not a mathematical sentence. You spoke of ‘infinity’ as if it were a number. It’s not. You may as well ask, ‘What is truth divided by beauty?’ I have no clue. I only know how to divide numbers.‘Infinity,’ ‘truth,’ ‘beauty’—those are not numbers. ~ Anonymous,
1048:So what were your favorite subjects in school?"

"School?" He leaned back in his chair as though he needed the extra space to think about it. "Probably math. It always made sense. Unlike English, economics, and girls."

"And exactly how do you plan on taking over the free world if you don't understand economics?"

"I'll hire advisers. I'll hire you, in fact."

"Okay. Let me know when your army of junior high zombies is ready. ~ Janette Rallison,
1049:When will it begin, anyway?"
Sirus held his gaze for a moment, his eyes full of concern- a concern that Joss didn't understand.
"Probably sooner than you're ready for."
"When's that?"
"Well." Sirus sighed, as if doing the math in his head."It'll take us about three minutes to gather this stuff and get to the cabin, and another two or three for Abraham to realize you're here. So I'd say you have about seven more minutes of freedom left. ~ Heather Brewer,
1050:Yes, in Math City: 2 + 2 + him (her) = 5 not 4.
And again yes: A stupid man + 5 stupid women + him (her) = 7 stupid or A stupid woman + 5 stupid men + him (her) = 7 stupid.
Professor Six discovered this formula when he was studying about businessman. He saw that a businessman buys 3 apple, but the businessman sales 3 apple + his own benefit which is = 4 apple. Yes, Professor Six announced: "Businessman means "Business" + "Man" = Business + Him = 2 ~ Ahmad Amani,
1051:My parents were so generally unimpressed with their own children that I really believed I could, I don’t know, win something like a Nobel Peace Prize, and they’d only reluctantly attend the ceremony, all the while pointing out that lots of people won Nobel Prizes, that, in fact, they gave out Nobel Prizes every year, and anyway the peace prize was clearly the prize for slackers, so maybe next time I should focus my energy on physics or math or something. ~ Tahereh Mafi,
1052:As far as I know, Clifford Pickover is the first mathematician to write a book about areas where math and theology overlap. Are there mathematical proofs of God? Who are the great mathematicians who believed in a deity? Does numerology lead anywhere when applied to sacred literature? Pickover covers these and many other off-trail topics with his usual verve, humor, and clarity. And along the way the reader will learn a great deal of serious mathematics. ~ Martin Gardner,
1053:Today so many creative and devoted teachers not only have to struggle against unimaginative administrations, fearful parents, and wearied colleagues, they have also to battle entire legislative bodies that have never taught a child yet dare to equate educational success or failure with the ability of fourth graders to choose one out of four given answers to mind-numbing questions that have nothing to do with the joy of literature or the elegance of math. ~ Esm Raji Codell,
1054:Working an integral or performing a linear regression is something a computer can do quite effectively. Understanding whether the result makes sense—or deciding whether the method is the right one to use in the first place—requires a guiding human hand. When we teach mathematics we are supposed to be explaining how to be that guide. A math course that fails to do so is essentially training the student to be a very slow, buggy version of Microsoft Excel. ~ Jordan Ellenberg,
1055:I’ve had several seriously sexual daydreams about the new guy. Have you seen him?” “Cin, I didn’t need to know that.” I jammed my math book into my backpack and slammed the locker door. Cindy rested her petite frame against the locker next to mine. Her radiant baby blues twinkled. “No, I haven’t seen him. Apparently he’s . . . cute?” I asked. She snorted. “Cute? No! He isn’t a kitten. He’s hot, sexier than hell, and has a voice that could melt chocolate. ~ RaShelle Workman,
1056:That first winter, when it was time for her friends to leave, the girl ventured out into the show to say goodbye, and the stunning raven-haired Squaller handed her another gift.

"A blue kefta," said the math teacher, shaking her head. "What would she do with that?"

"Maybe she knew a Grisha who died," replied the cook, taking note of the tears that filled the girl's eyes. They did not see the note that read, You will always be one of us. ~ Leigh Bardugo,
1057:There are people at the extremes who aren't able to do anything musically, and then others sort of fall in the middle. And the same thing with math, and the same thing with art. You'll find people who are geniuses, or prodigies at the far end of the bell shaped curve, and I think you will find some of the acquired savants in that category who happened to have been endowed with that kind of talent, which explains why not everyone becomes an acquired savant. ~ Darold Treffert,
1058:Nonmathematical people sometimes ask me, “You know math, huh? Tell me something I’ve always wondered, What is infinity divided by infinity?” I can only reply, “The words you just uttered do not make sense. That was not a mathematical sentence. You spoke of ‘infinity’ as if it were a number. It’s not. You may as well ask, 'What is truth divided by beauty?’ I have no clue. I only know how to divide numbers. ‘Infinity,’ ‘truth,’ ‘beauty’—those are not numbers. ~ John Derbyshire,
1059:And again. I kept clicking until the photograph was demolished, until it was no more than a mosaic of gray tiles, adding up to nothing.
Nothing. Because wasn’t that how I felt that day? If you zoom close—if you really get close to someone, if you really get close to yourself—then you
lose the other person, you lose yourself entirely. You get so close you can’t see anything anymore. Your mind becomes all these abstract fragments.
English becomes math. ~ David Levithan,
1060:Ain't all buttons and charts, little albatross. Know what the first rule of flying is? Well I s'pose you do, since you already know what I'm 'bout to say.

I do. But I like to hear you say it.

Love. Can know all the math in the 'verse but take a boat in the air that you don't love? She'll shake you off just as sure as a turn in the worlds. Love keeps her in the air when she oughta fall down...tell you she's hurtin' 'fore she keens...makes her a home. ~ Joss Whedon,
1061:I studied physics at Princeton when I was a college student, and my initial intention was to major in it but to also be a writer. What I discovered, because it was a very high-powered physics program with its own fusion reactor, was that to keep up with my fellow students in that program I would need to dedicate myself to math and physics all the time and let writing go. And I couldn't let writing go, so I let physics go and became a science fan and a storyteller. ~ Jon Spaihts,
1062:I didn't think I was good at anything, didn't do well in school. And then in the third grade, I was going to a public school. And the teacher was putting math problems on the board. And I said to myself - it's amazing how you can remember certain incidents at any age that made an impression - I asked myself why is she putting those up when the answers are obvious. And then I saw it wasn't obvious to anybody else in the class. So I said, "Hey, I'm good at something." ~ Charles Koch,
1063:Weight Watchers points is a beautiful system for someone who is absentminded about food. They aren’t the greatest for someone who has had eating disorders all her life. The world became numbers to me and I was doing more math than I ever had before. I got off Weight Watchers and went back to just counting calories. The world became different kinds of numbers, the old, familiar kind. This is how I eat now. The world is still numbers, but it is algebra, not calculus. ~ Melissa Broder,
1064:Superstar lawyers and math whizzes and software entrepreneurs appear at first blush to lie outside ordinary experience. But they don't. They are products of history and community, of opportunity and legacy. Their success is not exceptional or mysterious. It is grounded in a web of advantages and inheritances, some deserved, some not, some earned, some just plain lucky--but all critical to making them who they are. The outlier, in the end, is not an outlier at all. ~ Malcolm Gladwell,
1065:I've seen pretty clear, ever since I was a young un, as religion's something else besides notions. It isn't notions sets people doing the right things--it's feelings. It's the same with the notions in religion as it is with math'matics--a man may be able to work problems straight off in's head as he sits by the fire and smokes his pipe; but if he has to make a machine or a building, he must have a will and a resolution, and love something else better than his own ease. ~ George Eliot,
1066:public class MergeBU
{
private static Comparable[] aux; // auxiliary array for merges
// See page 271 for merge() code.
public static void sort(Comparable[] a)
{ // Do lg N passes of pairwise merges.
int N = a.length;
aux = new Comparable[N];
for (int sz = 1; sz < N; sz = sz+sz) // sz: subarray size
for (int lo = 0; lo < N-sz; lo += sz+sz) // lo: subarray index
merge(a, lo, lo+sz-1, Math.min(lo+sz+sz-1, N-1));
}
} ~ Robert Sedgewick,
1067:Superstar lawyers and math whizzes and software entrepreneurs appear at first blush to lie outside ordinary experience. But they don't. They are products of history and community, of opportunity and legacy. Their success is not exceptional or mysterious. It is grounded in a web of advantages and inheritances, some deserved, some not, some earned, some just plain lucky - but all critical to making them who they are. The outlier, in the end, is not an outlier at all. ~ Malcolm Gladwell,
1068:And for the record, Mama has lovingly prepared that food for him for almost sixty years. The math involved in that level of cooking dedication blows my mind, because three hot meals a day times 350 days a year (I’m allowing for some days off for travel and such) times sixty years equals roughly 63,000 meals, at which point you have to conclude that it might be appropriate at this stage in Mama’s life for somebody to give her a bottomless gift card to the Cracker Barrel. ~ Sophie Hudson,
1069:For me, promotional thing about some new album coming out destroys a lot of the excitement of making records. Records, movies, books - they're not supposed to be like math books. The purpose of them is to kind of take us out of ourselves and give us some sort of alternate experience or respite. To try to maximize the relationship of listening to a record through promotion is like experiencing driving a car by reading about stimulus programs. It kind of defeats the purpose. ~ Will Oldham,
1070:That day.
Even though my back is turned,
I can see what's going on.
The sound of their taunting-
I know what that looks like.
Words like freak and loser-
I know what kind of face says them.
Our teacher is ignoring it;
he does not have the strength to deal with it.
Or maybe he agrees with what's being said.
He agrees by talking math as the notebook
is pulled out of Anton's hand.
Even though he sees what's going on,
his back is turned. ~ David Levithan,
1071:The entropy of a system is related to the number of indistinguishable rearrangements of its constituents, but properly speaking is not equal to the number itself. The relationship is expressed by a mathematical operation called a logarithm; don't be put off if this brings back bad memories of high school math class. In our coin example, it simply means that you pick out the exponent in the number of rearrangements-that is, the entropy is defined as 1,000 rather than 2^1000. ~ Brian Greene,
1072:Hubble’s work confirmed his math—and refuted Einstein’s general theory of relativity. Furthermore, he deduced, if the universe was expanding equally in all directions, it must have initiated in a massive explosion from a single point. This meant that the universe is not infinitely old; it has a certain age, and that the moment of creation—which British astronomer Fred Hoyle later mockingly called the “big bang”—was analogous to God’s first command: Let there be light. ~ Shawn Lawrence Otto,
1073:As Denise Pope outlined in “Doing School,” kids today have tremendous pressure to simply get the work done—to “do school”—rather than to learn. They learn to do tasks, to produce every element the teacher wants to see in a five-paragraph essay, or to memorize every term in bio and every formula in math. They think their next task is to get into certain schools in order to be a success in life, and this mind-set often then extends to career and professional pursuits. I ~ Julie Lythcott Haims,
1074:Ask your child for information in a gentle, nonjudgmental way, with specific, clear questions. Instead of “How was your day?” try “What did you do in math class today?” Instead of “Do you like your teacher?” ask “What do you like about your teacher?” Or “What do you not like so much?” Let her take her time to answer. Try to avoid asking, in the overly bright voice of parents everywhere, “Did you have fun in school today?!” She’ll sense how important it is that the answer be yes. ~ Susan Cain,
1075:On the SB5 Stanford-Binet intelligence test Isaiah’s reasoning scores were near genius levels. His abilities came naturally but were honed in his math classes. He was formally introduced to inductive reasoning in geometry, a tenth-grade subject he took in the eighth. His teacher, Mrs. Washington, was a severe woman who looked to be all gristle underneath her brightly colored pantsuits. Lavender, Kelly green, peach. She talked to the class like somebody had tricked her into it. “All ~ Joe Ide,
1076:Ogling Douglas' wife, who looked trampily deep into bipolar meds & high-end anti-aging crêmes, Jerzy thought: Now that is a hot fuck. He wondered if Douglas got his C by being wayback viral throatstroked by papilloma.....seems like a person would have to go down on a boatload of broads to get HPV in the gullet (well, do the math), if the actor scarfed half as much pussy as dimpled dad kirk-King Leer, Kirk the lyin' King-then he just might have qualified. ~ Bruce Wagner,
1077:Let me say something at the outset. The questions that have been asked so far in this debate illustrate why the American people don't trust the media. This is not a cage match. And, you look at the questions - "Donald Trump, are you a comic-book villain?" "Ben Carson, can you do math?" "John Kasich, will you insult two people over here?" "Marco Rubio, why don't you resign?" "Jeb Bush, why have your numbers fallen?" How about talking about the substantive issues the people care about? ~ Ted Cruz,
1078:Most would live into adulthood, as Patrick had.
(Which meant there was quite a lot of competitiveness about it, with everybody wanting to beat not only cancer itself, but also the other people in the room. Like, I realize that this is irrational, but when they tell you that you have, say, a 20 percent chance of living five years, the math kicks in and you figure that’s one in five…so you look around and think, as any healthy person would: I gotta outlast four of these bastards.) ~ John Green,
1079:Good people care more about people than food. They try to help people and don’t give up even when they get hungry. Only bad people give up. But good people fix things. Good people stay good even when it’s hard to. Even if they’re sick or sad or they have to lose their favorite stuff. Even if they have to die. Good people see past their own fucking lives. They aren’t just hunger and math. They aren’t just animals. Good people are part of the Higher, good people are fuel for the sun. ~ Isaac Marion,
1080:Numbers written on restaurant checks within the confines of restaurants do not follow the same mathematical laws as numbers written on any other pieces of paper in any other parts of the Universe. This single statement took the scientific world by storm. It completely revolutionized it. So many mathematical conferences got held in such good restaurants that many of the finest minds of a generation died of obesity and heart failure and the science of math was put back by years. Slowly, ~ Douglas Adams,
1081:Even the most complex math can be broken into a sequence of trivial steps. Each of these slaves has been trained to complete specific equations in an assembly-line fashion. When taken together, this collective human mind is capable of remarkable feats." Holtzman surveyed the room as if he expected his solvers to give him a resounding cheer. Instead, they studied their work with heavy-lidded eyes, moving through equation after equation with no comprehension of reasons or larger pictures. ~ Brian Herbert,
1082:Do you miss her?
I blinked. Did I what? This was my best friend since preschool we were talking about, the girl whose snack and math homework I’d shared since before I had memorized my own phone number, who’d buried her cold, annoying little feet underneath me during a thousand different movie nights and showed me how to use a tampon. She’d grown up in my kitchen, she was my shadow- self—or I was hers— and Sawyer wanted to know if I missed her? What the hell kind of question was that? ~ Katie Cotugno,
1083:What if at school you had to take an 'art class' in which you were only taught how to paint a fence? What if you were never shown the paintings of Leonardo da Vinci and Picasso? Would that make you appreciate art? Would you want to learn more about it? I doubt it..........but this is how math is taught and so in the eyes of most of us it becomes the equivalent of watching paint dry. While the paintings of the great masters are readily available, the math of the great masters is locked away. ~ Edward Frenkel,
1084:Having neurons wire together can be a good thing. A positive experience with a math teacher can lead to neural connections that link math with pleasure, accomplishment, and feeling good about yourself as a student. But the opposite is equally true. Negative experiences with a harsh instructor or a timed test and the anxiety that accompanies it can form connections in the brain that create a serious obstacle to the enjoyment not only of math and numbers, but exams and even school in general. ~ Daniel J Siegel,
1085:Asian children can perform basic functions, such as addition, far more easily. Ask an English-speaking seven-year-old to add thirty-seven plus twenty-two in her head, and she has to convert the words to numbers (37 + 22). Only then can she do the math: 2 plus 7 is 9 and 30 and 20 is 50, which makes 59. Ask an Asian child to add three-tens-seven and two-tens-two, and then the necessary equation is right there, embedded in the sentence. No number translation is necessary: It’s five-tens-nine. ~ Malcolm Gladwell,
1086:I’m simply trying to do the math,” Gail explained. “This is a societal double standard I have never been able to understand. Men have been kissing since they were quite young, and have kissed many times, and this is considered normal. Yet, women are expected to keep their lips to themselves until they are ready to be married. But if this is always so, who are all these men kissing? Either the world is blindingly unrealistic in its expectations of women, or young boys are practicing on each other. ~ Kate Noble,
1087:Julia, the man collects food in his mustache. He wears pocket protectors, which I’m pretty certain have been out of production since the eighties, right around the time his kind-of-sometimes mullet-hairdo thing went out of style. He makes jokes about irrational numbers. He’s a total cliché of a math teacher. I’m almost certain that he’s not a real person; he’s Frankenstein’s monster but made up of math-teacher clichés. I heard a rumor that he’s got all the known numbers of pi tattooed on his ass. ~ Adi Alsaid,
1088:American parents, teachers, and children were far more likely than their Japanese and Chinese counterparts to believe that mathematical ability is innate; if you have it, you don’t have to work hard, and if you don’t have it, there’s no point in trying. In contrast, most Asians regard math success, like achievement in any other domain, as a matter of persistence and plain hard work. Of course you will make mistakes as you go along; that’s how you learn and improve. It doesn’t mean you are stupid. ~ Carol Tavris,
1089:The point is that there’s something very mathematical about our Universe, and that the more carefully we look, the more math we seem to find. Apropos constants of nature, there are hundreds of thousands of pure numbers that have been measured across all areas of physics, ranging from ratios of masses of elementary particles to ratios of characteristic wavelengths of light emitted by different molecules, and using sufficiently powerful computers to solve the equations describing the laws of nature, ~ Max Tegmark,
1090:Deep practice, however, doesn't obey the same math. Spending more time is effective—but only if you're still in the sweet spot at the edge of your capabilities, attentively building and honing circuits. What's more, there seems to be a universal limit for how much deep practice human beings can do in a day. Ericsson's research shows that most world-class experts—including pianists, chess players, novelists, and athletes—practice between three and five hours a day, no matter what skill they pursue. ~ Daniel Coyle,
1091:Psychologist Robert Zajonc takes this claim one step further: “For most decisions, it is extremely difficult to demonstrate that there has actually been any prior cognitive process whatsoever.”28 It isn’t that the decisions people make are irrational; it’s that the process by which decisions are made are utterly unlike the step-by-step rational process that might be used to solve, say, a math problem. Decisions are typically made in the unconscious mind, by means of some unknown process. Indeed, ~ William B Irvine,
1092:Do you miss her?
I blinked. Did I what? This was my best friend since preschool we were talking about, the girl whose snack and math homework I’d shared since before I had memorized my own phone number, who’d buried her cold, annoying little feet underneath me during a thousand different movie nights and showed me how to use a tampon. She’d grown up in my kitchen, she was my shadow- self—or I was hers— and Sawyer wanted to know if I missed her? What the hell kind of question was that? ~ Katie Cotugno,
1093:On the SAT exam, boys who took the test during 1988–89 at Permian had a combined average score of 915 (433 verbal, 482 mathematical), 19 points below the national average for boys. Girls had a combined score of 840 (404 verbal, 436 mathematical), 75 points below their male counterparts at Permian and 35 points below the national average for girls. Of the 132 girls who took the test during the 1988–89 school year, there wasn’t one who got above a 650 in either the math or verbal portions of the exam. ~ H G Bissinger,
1094:Why were American kids consistently underestimated in math? In middle school, Kim and Tom had both decided that math was something you were either good at, or you weren’t, and they weren’t. Interestingly, that was not the kind of thing that most Americans said about reading. If you weren’t good at reading, you could, most people assumed, get better through hard work and good teaching. But in the United States, math was, for some reason, considered more of an innate ability, like being double-jointed. ~ Amanda Ripley,
1095:One whose testimony made a major impact more than a decade ago is Ben Barres, formerly Barbara Barres, a biologist at Stanford University. In 2006, he wrote in the journal Nature about the bias he had experienced as a woman in the sciences, from losing fellowships to less qualified male candidates to being told a boyfriend must have helped her with her math. He was told that he was smarter than his sister by a man who confused his former, female self for that sister.
(“A Short History of Silence”) ~ Rebecca Solnit,
1096:I used to be jealous; I'm not jealous anymore. And a miracle happened to me, because if you're jealous, it's a cancer, it's a plague on your spirit, it really is. And I actually cured jealousy in a very weird way - I cured it with mathematics. And I'm not a math person at all, but I've been with my wife for about seven years, so we have had sex probably, I'd like to think, like, 9 million times or, at least, 1,500. So, the way I figured it, if she goes out and screws some other guy once - I'm still winning. ~ Marc Maron,
1097:I have some advice for the young generation who are wanting to become successful in life: become more grateful. Once you do that, Allah says, "If you are grateful, I will surely increase you (in everything)." If you're having a hard time in math, science, language and whatever else, become grateful to Allah and He will open doors for you. You'll even get better at basketball and become more athletic. I pray that Allah makes you grateful young people who are examples for others all over the world, ameen. ~ Nouman Ali Khan,
1098:It was on the table when I got here," Matt said in his defense.

Josh eyed the open magazine. "You don't already know how to satisfy your boyfriends in bed?"

Matt ignored this. "Did either of you know there's ninety-nine ways to give a blow job? That's ninety-nine nights of blow jobs."

"Look at you with the math skills," Josh said.

Matt flipped him off while Ty flipped the page. "'How to Give Your Hoo-Ha a Spa Day.' Huh," he said. "I didn't know a woman's hoo-ha needed a spa day. ~ Jill Shalvis,
1099:When I became the NASA administrator — or before I became the NASA administrator — Barack Obama charged me with three things. One was he wanted me to help re-inspire children to want to get into science and math, he wanted me to expand our international relationships, and third, and perhaps foremost, he wanted me to find a way to reach out to the Muslim world and engage much more with dominantly Muslim nations to help them feel good about their historic contribution to science … and math and engineering. ~ Charles Bolden,
1100:What she did NOT appreciate was the homework. Captain Wilkes had scrounged textbooks for her to study. Not just Marine manuals, either. Math, science, English. Chemistry. Yuck! With weekly tests. And he was making her do all her platoon reports, then “annotating” them. He had given her a dictionary and thesaurus, among other things, and after the first report after giving them to her told her she was “not allowed words of more than two syllables.” It was worse than fucking school. “Recess” was killing zombies. ~ John Ringo,
1101:The day passed.
People had butchered my name, teachers hadn’t known what the hell to do with me, my math teacher looked at my face and gave a five-minute speech to the class about how people who don’t love this country should just go back to where they came from and I stared at my textbook so hard it was days before I could get the quadratic equation out of my head.
Not one of my classmates spoke to me, no one but the kid who accidentally assaulted my shoulder with his bio book.
I wished I didn’t care. ~ Tahereh Mafi,
1102:Educators, long disturbed by schoolchildren's lagging scores in math and reading, are realizing there is a different and more alarming deficiency: emotional literacy. And while laudable efforts are being made to raise academic standards, this new and troubling deficiency is not being addressed in the standard school curriculum. As one Brooklyn teacher put it, the present emphasis in schools suggests that "we care more about how well schoolchildren can read and write than whether they'll be alive next week." ~ Daniel Goleman,
1103:It’s easy to forget that teaching is holy work. We forget that building up the intellect- teaching our children to really think- does not happen by the might of human reason, but rather by the grace of God. On an ordinary day, you and I likely have a set of tasks we've scheduled for our kids. But it's more than math. It's more than history. It's the building up of our children's minds and hearts, and we can only do that if we realize that this is how we thank Him for the graces He so lavishly pours out on us. ~ Sarah Mackenzie,
1104:women live the lie from birth on, and then one day they realize that it's too late for them, they're too old to write a book or solve a difficult problem in math, they'll never learn to sing or play the piano, they showed such promise early on. so they run to the priest, their voices take on a hysterical edge, like the one mine has right now, and the priest tells them they have lived righteously and their reward will be in heaven, and he could certainly use someone in the kitchen for the potluck on Sunday night. ~ Haven Kimmel,
1105:I think we can do it."

"But you don't know for sure," he said.

"No."

"Geez, Anita."

"Don't get rattled on me. We can do this."

"But you aren't sure."

"I'm not sure we'll survive the plane ride home, but I'm still getting on the plane."

"Was that supposed to be comforting?" he asked.

"Yeah."

"It wasn't," he said.

"Sorry, but this is as good as it gets. You want certainty, be an accountant."

"I'm not good at math."

"Me either. ~ Laurell K Hamilton,
1106:Where numbers only represent real things, you don’t need a number to express the absence of something. It is an abstract concept and only shows up when the math gets equally abstract. “The point about zero is that we do not need to use it in the operations of daily life,” wrote Alfred North Whitehead, the British mathematician, in 1911. “No one goes out to buy zero fish. It is in a way the most civilized of all the cardinal [numbers], and its use is only forced on us by the needs of cultivated modes of thought. ~ Chris Anderson,
1107:women live the lie from birth on, and then one day they realize that it's too late for them, they're too old to write a book or solve a difficult problem in math, they'll never learn to sing or play the piano, they showed such promise early on. so they run to the priest, their voices take on a hysterical edge, like the one mine has right now, and the priest tells them they have lived righteously and their reward will be in heaven, and he could certainly use someone in the kitchen for the potluck on Sunday night. ~ Haven Kimmel,
1108:IT WAS EASIER FOR PEOPLE to be good at something when more of us lived in small, rural communities. Someone could be homecoming queen. Someone else could be spelling-bee champ, math whiz or basketball star. There were only one or two mechanics and a couple of teachers. In each of their domains, these local heroes had the opportunity to enjoy the serotonin-fuelled confidence of the victor. It may be for that reason that people who were born in small towns are statistically overrepresented among the eminent.68 If ~ Jordan Peterson,
1109:It was on the table when I got here," Matt said in his defense.

Josh eyed the open [Cosmo] magazine. "You don't already know how to satisfy your boyfriends in bed?"

Matt ignored this. "Did either of you know there's ninety-nine ways to give a blow job? That's ninety-nine nights of blow jobs."

"Look at you with the math skills," Josh said.

Matt flipped him off while Ty flipped the page. "'How to Give Your Hoo-Ha a Spa Day.' Huh," he said. "I didn't know a woman's hoo-ha needed a spa day. ~ Jill Shalvis,
1110:Math is like water. It has a lot of difficult theories, of course, but its basic logic is very simple. Just as water flows from high to low over the shortest possible distance, figures can only flow in one direction. You just have to keep your eye on them for the route to reveal itself. That’s all it takes. You don’t have to do a thing. Just concentrate your attention and keep your eyes open, and the figures make everything clear to you. In this whole, wide world, the only thing that treats me so kindly is math. ~ Haruki Murakami,
1111:IT WAS EASIER FOR PEOPLE to be good at something when more of us lived in small, rural communities. Someone could be homecoming queen. Someone else could be spelling-bee champ, math whiz or basketball star. There were only one or two mechanics and a couple of teachers. In each of their domains, these local heroes had the opportunity to enjoy the serotonin-fuelled confidence of the victor. It may be for that reason that people who were born in small towns are statistically overrepresented among the eminent.68 If ~ Jordan B Peterson,
1112:It was great not having a roommate. I didn’t have to turn the lights off and go to bed, like, ever. I took my new medicine and stayed up doing homework late in the night, hyperfocused and erasing and reprinting my math homework. Branches would bang on the glass and scare the shit out of me; there was also a stupid owl out there that was ridiculously loud and hooty. So I was always practically falling out of my desk chair. (Stimulants make the nerves a bit . . . jangly, you know. Especially at three in the morning.) I ~ Cat Marnell,
1113:There is a time for everything, and a season for every activity under the heavens” (Ecclesiastes 3:1). The key to balance is seeking God’s will for me in this season, and not spending time on assignments meant for other people. Overcommitting myself is always a temptation. But with God’s wisdom and an updated list of all my commitments, I get ongoing reality checks that help me make wise decisions. And although I’m not really good at math, I know that a cup and a half of something will never fit in a one-cup container. ~ Renee Swope,
1114:...a large contingent of people majoring in English by default. Because they weren't left-brained enough for science, because history was too dry, philosophy too difficult, geology too petroleum-oriented, and math too mathematical--because they weren't musical, artistic, financially motivated, or really all that smart, these people were pursuing university degrees doing something no different from what they'd done in first grade: reading stories. English was what people who didn't know what to major in majored in. ~ Jeffrey Eugenides,
1115:The lottery is a tax on poor people and on people who can’t do math. Rich people and smart people would be in the line if the lottery were a real wealth-building tool, but the truth is that the lottery is a rip-off instituted by our government. This is not a moral position; it is a mathematical, statistical fact. Studies show that the zip codes that spend four times what anyone else does on lottery tickets are those in lower-income parts of town. The lottery, or gambling of any kind, offers false hope, not a ticket out. ~ Dave Ramsey,
1116:The motto I have penned on my knuckles is that this is the best world we have--because it's the only world we have. It's the simplest math ever. However many terrible, rankling, peeve-inducing things may occur, there are always libraries. And rain-falling-on-sea. And the moon. And love. There is always something to look back on, with satisfaction, or forward to, with joy. There is always a moment where you boggle at the world--at yourself--at the whole, unlikely, precarious business of being alive--and then start laughing ~ Caitlin Moran,
1117:And don’t get me started on your manwhoring,” Tucker grumbles. “You’ve always been a player, but dude, you’ve hooked up with five chicks this week.”

“So?”

“So it’s Thursday. Five girls in four days. Do the fucking math, John.”

Oh shit. He first-named me. Tucker only calls me John when I’ve really pissed him off.

Except now he’s pissed me off, so I first-name him right back. “What’s wrong with that, John?”

Yup, we’re both John. I guess we should take a blood oath and form a club or something. ~ Elle Kennedy,
1118:In October 1957, the first Russian Sputnik orbited the earth. In November, the second Sputnik, carrying the space dog Laika, was sent into space. That same year, a German astronomer published a definitive catalog of planets and stars. Four out of the five Nobel Prize laureates in Physics and Chemistry that year were from countries other than the United States. Americans were terrified that the country was falling behind in math and science, so nationwide there was a renewed commitment to education, especially in those fields. ~ Susan Orlean,
1119:I was born into a working class Irish Catholic family at the brutal bottom of the Great Depression. I suppose this early imprinting and conditioning made me a life-long radical. My education was mostly scientific, majoring in electrical engineering and applied math. Those imprints made me a life-long rationalist. I have become increasingly skeptical about, or detached from, the assumption that radicalism and rationalism are the only correct perspectives with which to view life, but they remain my favorite perspectives. ~ Robert Anton Wilson,
1120:One ounce sliced off a pair of shoes, he said, is equivalent to 55 pounds over one mile. He wasn’t kidding. His math was solid. You take the average man’s stride of six feet, spread it out over a mile (5,280 feet), you get 880 steps. Remove one ounce from each step—that’s 55 pounds on the button. Lightness, Bowerman believed, directly translated to less burden, which meant more energy, which meant more speed. And speed equaled winning. Bowerman didn’t like to lose. (I got it from him.) Thus lightness was his constant goal. Goal ~ Phil Knight,
1121:The Way of Bayes is also an imprecise art, at least the way I'm holding forth upon it. These blog posts are still fumbling attempts to put into words lessons that would be better taught by experience. But at least there's underlying math, plus experimental evidence from cognitive psychology on how humans actually think. Maybe that will be enough to cross the stratospherically high threshold required for a discipline that lets you actually get it right, instead of just constraining you into interesting new mistakes. ~ Eliezer Yudkowsky,
1122:You are growing into consciousness, and my wish for you is that you feel no need to constrict yourself to make other people comfortable. None of that can change the math anyway. I never wanted you to be twice as good as them, so much as I have always wanted you to attack every day of your brief bright life in struggle. The people who must believe they are white can never be your measuring stick. I would not have you descend into your own dream. I would have you be a conscious citizen of this terrible and beautiful world. — ~ Ta Nehisi Coates,
1123:I try to teach Magda some things. Since we’re not men and can’t afford. I take my books to her and sit her in a corner in a nice room that smells of rice with milk and cinnamon and teach her things. She does okay in math. She knows multiplication. At first it was, like, 1 × 1, 1 × 2, and it was never past the two, everything equaled two. 5 × 7, 9 × 8, everything was 2. But now she gets it. She gets history. She likes simpler things, made up stories, poems, but she is awful with language. And she can’t spell to save her life. ~ Miroslav Penkov,
1124:There's spatial intelligence. they're, which end up being, people going into math or music. there's mechanical where you work well with your hands. There's an intelligence with language that would lead someone into writing. So it's not necessarily that you're six years old and you know you're going to be a lawyer Or you're going into tech startups or computers. It's something more elemental than that. It's that this is a skill, a way of thinking that comes naturally to me that I was drawn to and it was very clear in childhood. ~ Robert Greene,
1125:You Bastard was thinking: there seems to be some growing dimensional instability here, swinging from zero to nearly forty-five degrees by the look of it. How interesting. I wonder what’s causing it? Let V equal 3. Let Tau equal Chi/4. cudcudcud Let Kappa/y be an Evil-Smelling-Bugger* (* Renowned as the greatest camel mathematician of all time, who invented a math of eight-dimensional space while lying down with his nostrils closed in a violent sandstorm.) differential tensor domain with four imaginary spin co-efficients. . . ~ Terry Pratchett,
1126:The ways in which acquired savants show up are usually the same ways that congenital, or non-acquired, savant syndrome shows up. They tend to show up in the same areas: music, art, math, visual, spatial skills, and calendar calculating, although calendar calculating probably isn't quite as prominent in that group. They tend to show up quite quickly, or sort of explode on the scene and they then tend to have an obsessive sort of forceful quality about them in the same way as savant skills. So they tend to show up in the same ways. ~ Darold Treffert,
1127:NAEP data show beyond question that test scores in reading and math have improved for almost every group of students over the past two decades; slowly and steadily in the case of reading, dramatically in the case of mathematics. Students know more and can do more in these two basic skills subjects now than they could twenty or forty years ago... So the next time you hear someone say that the system is "broken," that American students aren't as well educated as they used to be, that our schools are failing, tell that person the facts. ~ Diane Ravitch,
1128:No matter how clear things might become in the forest of story, there was never a clear-cut solution, as there was in math. The role of a story was, in the broadest terms, to transpose a problem into another form. Depending on the nature and the direction of the problem, a solution might be suggested in the narrative. Tengo would return to the real world with that solution in hand. It was like a piece of paper bearing the indecipherable text of a magic spell. It served no immediate practical purpose, but it contained a possibility. ~ Haruki Murakami,
1129:People are always saying these things about how there's no need to read literature anymore-that it won't help the world. Everyone should apparently learn to speak Mandarin, and learn how to write code for computers. More young people should go into STEM fields: science, technology, engineering, and math. And that all sounds to be true and reasonable. But you can't say that what you learn in English class doesn't matter. That great writing doesn't make a difference. I'm different. It's hard to put into words, but it's true. Words matter. ~ Meg Wolitzer,
1130:I just want to understand what this is about,” Patricia’s father said. “What did we do that made you want to act out in this way?” Roderick Delfine was a real-estate genius who often worked from home and looked after the girls when they were between nannies, sitting in a high chair at the breakfast bar with his wide face buried in equations. Patricia herself was pretty good at math, except when she thought too much about the wrong things, like the fact that the number 3 looked like an 8 cut in half, so two 3s really ought to be 8. ~ Charlie Jane Anders,
1131:Whether you are raising money, pitching your product to customers, selling the company, or recruiting employees, never forget that underneath all the math and the MBA bullshit talk, we are all still emotionally driven human beings. We want to attach ourselves to narratives. We don’t act because of equations. We follow our beliefs. We get behind leaders who stir our feelings. In the early days of your venture, if you find someone diving too deep into the numbers, that means they are struggling to find a reason to deeply care about you. ~ Timothy Ferriss,
1132:Come back down here, heat supply,” I commanded. “I’m going to close my eyes and you are
going to tell me about math so I can fall asleep. Tell me some theorems. Is that what you called them?
Tell me how Einstein knew e equals mc squared. And start with once upon a time . . . okay?”
“You’re a little bossy, you know that?”
“I know. I have to be. It’s to make up for not being born with a calculator. Now share your wisdom,
Infinity.”
“Once upon a time—”
I giggled and Finn immediately shushed me, continuing on with his “story. ~ Amy Harmon,
1133:What's clarity like? Try to remember that funny feeling inside your head when you had math problems too difficult to solve: the faint buzzing noise in your ears, a heaviness on both sides of your skull, and the sensation that your brain is twitching inside your cranium like a fish on the beach. This is the opposite sensation of clarity. Yet for many people of my era, as they aged, this sensation became the dominant sensation of their lives. It was as though day-to-day twentieth century living had become an unsolvable algebraic equation. ~ Douglas Coupland,
1134:Many young women are less whole and androgynous than they were at age ten. They are more appearance-conscious and sex-conscious. They are quieter, more fearful of holding strong opinions, more careful what they say and less honest. They are more likely to second-guess themselves and to be self-critical. They are bigger worriers and more effective people pleasers. They are less likely to play sports, love math and science and plan on being president. They hide their intelligence. Many must fight for years to regain all the territory they lost. ~ Mary Pipher,
1135:This is it,” said Dad. “Grace Brewster Murray Hopper Hall.” They wound their way upstairs and down long hallways to a door that said MATH LAB. “Here we are!” said Dad. A girl with green eyes and a messy ponytail greeted them. “You must be the Moodys.” “I’m Richard Moody, and this is my daughter, Judy,” said Dad. “Hi, I’m Chloe. Chloe Canfield. My friends call me C-squared, since my name has two Cs and I go to CC. You know, C to the second power, ’cause I’m into math?” “That’s funny,” said Dad, shaking her hand. “I don’t get it,” said Judy. ~ Megan McDonald,
1136:You know; when I look at the night sky and I see this enormous splendor of stars and galaxies, I sometimes ask the question, well how many worlds are we talking about? Well do the math, there are about 100 billion galaxies that are in the visible universe and each galaxy in turn contains about 100 billion stars, you multiply and you get about ten billion trillion stars. Well I think it is the height of arrogance to believe that we are alone in the universe, my attitude is that the universe is teaming, teaming with different kinds of life forms ~ Michio Kaku,
1137:During the 1919 solar eclipse, people go out to measure the positions of the stars and they find exactly what Einstein predicted. Einstein gets a telegram saying this, and somebody asked him, Professor Einstein, what would you have said if the observations didn’t agree with what your prediction of general relativity said should be happening? And Einstein said, “I’d be sorry for the dear lord; the theory is correct.” What he meant by that is the math is just so elegant, so beautiful, so powerful, that almost seemingly it can’t possibly be wrong. ~ Rivka Galchen,
1138:What is especially striking and remarkable is that in fundamental physics, a beautiful or elegant theory is more likely to be right than a theory that is inelegant. A theory appears to be beautiful or elegant (or simple, if you prefer) when it can be expressed concisely in terms of mathematics we already have. Symmetry exhibits the simplicity. The Foundamental Law is such that the different skins of the onion resemble one another and therefore the math for one skin allows you to express beautifully and simply the phenomenon of the next skin. ~ Murray Gell Mann,
1139:Who's counting? It was, of course, the minority who were counting. It always is. Most of the women I know today would dearly like to use their fingers and toes for some activity more enthralling than counting. They have been counting for so long. But the peculiar problem of the new math is that every time we stop adding, somebody starts subtracting. At the very least (the advanced students will understand this) the rate of increase slows. ... The minority members of any group or profession have two answers: They can keep score or they can lose. ~ Ellen Goodman,
1140:Fiqh is man-made!"

By that reasoning and applying your standards, so are logic, math, natural sciences, and virtually every single body of knowledge and its fruits. If being man made is sufficient reason to reject fiqh, it's more than sufficient reason to reject those, too. And before arguing that science is special, know that the epistemology and philosophy of science are also man-made.

UPDATE. Pay particular attention to where it says the "body of knowledge." And if you want to eliminate that qualifier, read up a bit on antirealism. ~ Musa Furber,
1141:I am encouraged as I look at some of those who have listened to their "different drum": Einstein was hopeless at school math and commented wryly on his inadequacy in human relations. Winston Churchill was an abysmal failure in his early school years. Byron, that revolutionary student, had to compensate for a club foot; Demosthenes for a stutter; and Homer was blind. Socrates couldn't manage his wife, and infuriated his countrymen. And what about Jesus, if we need an ultimate example of failure with one's peers? Or an ultimate example of love? ~ Madeleine L Engle,
1142:Forget it once. *** Knock, knock! Who's there? Accordion! Accordion who? Accordion to the TV, it's going to rain tomorrow. *** Yo momma so stupid she tried to commit suicide by jumping off a building but got lost on the way down. *** Teacher: Why is the Mississippi such an unusual river? Student: Because it has four eyes and can't see! *** Teacher: "Why are you on the floor?" Johnny: "Because you said to do this math problem without tables!" *** How do you make an elephant float? Take one elephant, two tons of ice cream, and one ton of soda. Blend. *** In ~ Various,
1143:Meanwhile, improving by 1 percent isn’t particularly notable—sometimes it isn’t even noticeable—but it can be far more meaningful, especially in the long run. The difference a tiny improvement can make over time is astounding. Here’s how the math works out: if you can get 1 percent better each day for one year, you’ll end up thirty-seven times better by the time you’re done. Conversely, if you get 1 percent worse each day for one year, you’ll decline nearly down to zero. What starts as a small win or a minor setback accumulates into something much more. ~ James Clear,
1144:In practice, Bacon’s method doesn’t bother scientists, or most reasonable people, because the chances of being wrong, while present, are usually in a practical sense very small. It is, for example, theoretically possible that chemical processes taking place in your body could cause you to spontaneously combust, but we don’t live our lives worrying about it because the probability is extremely small. That is why math and statistics have become such important parts of science: they quantify the relative probability that a conclusion is true or false. ~ Shawn Lawrence Otto,
1145:I've always been good at math. It's straightforward, black-and-white, right and wrong. Equations. Da thought of people as books to be read, but I've always thought of them more as formulas—full of variables, but always the sum of their parts. That's what their noise is, really: all of a person's components layered messily over one another. Thought and feeling and memory and all of it unorganized, until a person dies. Then it all gets compiled, straightened out into this linear thing, and you see exactly what the various parts add up to. What they equal. ~ Victoria Schwab,
1146:Personally, I think sex should be like math.
At school.
No one really cares if they're crap at math. They even proclaim it. They'll say to anyone, "Yeah, I don't mind science and English, but I'm absolutely shithouse at math." And other people will laugh and say,"Yeah, me too. I would have a clue about all that logarithm shit. You should be able to say that about sex too.
You should be proudly able to say, "Yeah I wouldn't have a clue about all that orgasm shit, ay. I'm okay at everything else but when it comes to that part I wouldn't have a clue. ~ Markus Zusak,
1147:Twice a day the small white compact moved, for meals, she guessed, or bathroom breaks, and about four times a day the Hummer and the Charger swapped positions, but there was apparently no coordination between the agencies, because once a day in the early morning everyone was missing at the same time, for about twenty minutes. Zero agents, zero hour. The street went back to its normal self. Some kind of logic issue, she supposed, or simple math, like in class, with x number of cars, and y number of locations, and z number of hours to cover. Something had to give. ~ Lee Child,
1148:... I succeeded at math, at least by the usual evaluation criteria: grades. Yet while I might have earned top marks in geometry and algebra, I was merely following memorized rules, plugging in numbers and dutifully crunching out answers by rote, with no real grasp of the significance of what I was doing or its usefulness in solving real-world problems. Worse, I knew the depth of my own ignorance, and I lived in fear that my lack of comprehension would be discovered and I would be exposed as an academic fraud -- psychologists call this "imposter syndrome". ~ Jennifer Ouellette,
1149:When I went to Afghanistan in 2003, I walked into a war zone. Entire neighborhoods had been demolished. There were an overwhelming number of widows and orphans and people who had been physically and emotionally damaged; every 10-year-old kid on the street knew how to dismantle a Kalashnikov in under a minute. I would flip through math textbooks intended for third grade, fourth grade, and they would include word problems such as, "If you have 100 grenades and 20 mujahideen, how many grenades per mujahideen do you get?" War has infiltrated every facet of life. ~ Khaled Hosseini,
1150:"It's better to give than to receive." Let me put this as elegantly as possible: "What a crock!" That statement is total hogwash, and in case you haven't noticed, it's usually propagated by people and groups who want you to give and them to receive. The whole idea is ludicrous. What's better, hot or cold, big or small, left or right, in or out? Giving and receiving are two sides of the same coin. Whoever decided that it is better to give than to receive was simply bad at math. For every giver their must be a receiver, and for every receiver there must be a giver. ~ T Harv Eker,
1151:Just like whiskey, the marsh dwellers bootlegged their own laws-not like those burned onto stone tablets or inscribed on documents, but deeper ones, stamped in their genes. Ancient and natural, like those hatched from hawks and doves. When cornered, desperate or isolated, man reverts to those instinct that aim straight at survival. Quick and just. They will always be the trump card because they are passed on more frequently from one generation to the next than the gentler genes It is not a morality, but simple math. Among themselves doves fight as often as hawks. ~ Delia Owens,
1152:T'he dca& id, a bunch of ruunbeha,that mean nothing and everything. That pesky, dangerous box is a booby trap full of good and bad news math. I hate math, I hate the scale. Back in the bun-head ballerina days I would measure myself constantly and then punish or praise accordingly. On punishment days I'd yack. Tis true, tis pathetic, tis my history; a golden nugget that makes me wise and human. However, that box is just that, a small container to cage ourselves. Prison is not sexy. No matter how it looks in the movies, prison is not a place to voluntarily visit. ~ Kris Carr,
1153:People fluent in two languages can lose either one after trauma, since first and second languages* draw on distinct neural circuits. Language deficits can even interfere with math. We seem to have a natural “number circuit” in the parietal lobe that handles comparisons and magnitudes—the basis of most arithmetic. But we learn some things (like the times tables) linguistically, by rote memorization. So if language goes kaput, so too will those linguistically based skills. More strikingly, some people who struggle to string even three words together can sing just fine. ~ Sam Kean,
1154:The money was such an obvious problem that I didn't even get to thinking about any of the others most of the time. It seemed wrong to me, that money should be the difference between a baby and not-a-baby. I had a thing inside of me that I could not afford, and Laura had things inside of her that she couldn't afford not to sell, and on the other end of it there were women spending tens of thousands of dollars to buy them because they felt their own bodies had betrayed them. Any way you looked at it, where there should have been a child, there was a math problem. ~ Danielle Evans,
1155:Funny. The blazer, skirt and tie become automatically sexy the minute you leave school when you're eighteen or nineteen and pull it out for fancy-dress parties. But whilst you're still there, stewing through Math, unable to find anyone who'll let you sit next to them in the cafeteria, crying in the toilet stalls, you know what it represents and you can't bring yourself to make it look alluring. That would be traitorous and phoney. I knew I looked like shit and I was glad I did because that's how the twenty pounds of gray polyester and itchy navy wool made me feel. ~ Emma Forrest,
1156:An eternal question about children is, how should we educate them? Politicians and educators consider more school days in a year, more science and math, the use of computers and other technology in the classroom, more exams and tests, more certification for teachers, and less money for art. All of these responses come from the place where we want to make the child into the best adult possible, not in the ancient Greek sense of virtuous and wise, but in the sense of one who is an efficient part of the machinery of society. But on all these counts, soul is neglected. ~ Thomas Moore,
1157:the shadows caressed the folds. I tried to see how light that was reflected from one object subtly colored the shadows of another object. I noticed how the glint of a lustrous spot on a shiny surface moved when I tilted my head. When I looked at a distant tree and a near one, I tried to visualize the lines of perspective. When I saw an eddy of water, I compared it to a ringlet of hair. When I couldn’t understand a math concept, I did the best I was able to visualize it. When I saw people at a supper, I studied the relationship of their motions to their emotions. ~ Walter Isaacson,
1158:Andromeda said, “I see that you understand the paradox involved. These are axiomatic beliefs. If life is finite, there can be no math, no logic, nothing which says using the Eschaton Engine to obliterate the majority of the universe in self-preservation is wrong. No game theory applies, because there is no retaliation, no tit for tat. No punishment. But if life is infinite, then an infinite game theory applies, and no act where the ends justifies the means is allowed, because there is no Concubine Vector, no eternal imbalance, no chance of any act escaping unpunished. ~ John C Wright,
1159:Kern was the classic oldest son of a strong, iron-willed father, secretly afraid that he couldn’t live up to the model, and thus quite skittish and sensitive to criticism. Even his appearance suggested vulnerability. He had feathery auburn hair with red highlights, broad cheeks and trusting brown eyes that opened wide with disappointment when he was hurt. He mostly excelled at things that required a lot of solitude and a minimum of social contact, math and science, and his best friend was a science nerd and ham-radio freak who lived in the village nearby, Louie DeChiaro. ~ Rinker Buck,
1160:I can always tell which ones are serious and which aren’t. There’s something in their voices that communicates passion and conviction when they’re really excited about getting out of debt. But if they’re just playing around with the idea, if they’re simply curious about it, then their voices are flat. If I don’t hear any passion behind what they’re saying, I know they aren’t ready to cut up the credit cards and dump their debt for good. That’s because getting out of debt isn’t about solving a math problem; it’s about changing your life—and that requires a change of heart. ~ Dave Ramsey,
1161:On January 18, 1897, Indiana state representative Taylor I. Record argued in favor of changing the value of pi. Pi, which can be rounded to 3.14159, is the ratio of a circle’s circumference to its diameter. Tyler believed that the number was inconveniently long; in House Bill 246, he asked that it be rounded up to 3.2. The bill passed the House but was defeated in the Senate when the chairman of Purdue University’s math department successfully pleaded that it would make Indiana a national laughingstock. The value of pi in Indiana remains the same as in every other state. ~ Paul A Offit,
1162:Studying music encourages self-discipline and diligence, traits that carry over into intellectual pursuits and that lead to effective study and work habits. An association of music and math has, in fact, long been noted. Creating and performing music promotes self-expression and provides self-gratification while giving pleasure to others. In medicine, increasing published reports demonstrate that music has a healing effect on patients. For all these reasons, it deserves strong support in our educational system, along with the other arts, the sciences, and athletics. ~ Michael E DeBakey,
1163:thought: maybe this is what a mother feels like at times. When she can’t help one of her children. When she has to just stand by and watch her daughter strike out on the softball field, watch her son fail at math despite whatever effort he may put in. This ache. This defining double bind of roaring, passionate protectiveness and its equal, weighty, leaden uselessness. And even the impatience with it all; and then the guilt about feeling impatient, about finding it a bit oppressive despite the immeasurable love. Maybe this is what mothering sometimes feels like, I thought. ~ Robin Black,
1164:In an era of weaponized sensitivity, participation in public discourse is growing so perilous, so fraught with the danger of being caught out for using the wrong word or failing to uphold the latest orthodoxy in relation to disability, sexual orientation, economic class, race or ethnicity, that many are apt to bow out. Perhaps intimidating their elders into silence is the intention of the identity-politics cabal — and maybe my generation should retreat to our living rooms and let the young people tear one another apart over who seemed to imply that Asians are good at math. ~ Lionel Shriver,
1165:Just like their whiskey, the marsh dwellers bootlegged their own laws – not like those burned onto stone tablets or inscribed on documents, but deeper ones, stamped in their genes. Ancient and natural, like those hatched from hawks and doves. When cornered, desperate, or isolated, man reverts to those instincts that aim straight at survival. Quick and just. They will always be the trump cards because they are passed on more frequently from one generation to the next than the gentler genes. It is not a morality, but simple math. Among themselves, doves fight as often as hawks. ~ Delia Owens,
1166:This thing we have, it hurts, he continued. But the pain is almost sweet because it means YOU happened. We happened. And I can't regret that, no matter how little or how long I get to tag along with you and pretend that I don't hate having people recognize me or take pictures or having people whisper about my record--
" Your record?"
" My criminal record, Bonnie, Nothing platinum there. I'm an ex-con, and starting over and building a new life where I can put it behind me, I'm building a new life where it will never be behind me, and for you, its worth it. It's easy math. ~ Amy Harmon,
1167:The majority of the people of the world today are unsane, not insane, unsane meaning having been exposed to methods of evaluation that have long rendered obsolete, our language in the future will change to a saner language where we have no argument in it, 'can there be such a language?' there is, when engineers talk to each other, it's not subject to interpretation, they use math, they use descriptive systems, if I interpreted what another engineer said in the way I think he meant it: you couldn't build bridges, dams, power transmission lines. The language has to have meaning ~ Jacque Fresco,
1168:Most of today’s educational systems are built upon the same learning hierarchy: math and science at the top, humanities in the middle, art on the bottom. The reason for this is because these systems were developed in the nineteenth century, in the midst of the industrial revolution, when this hierarchy provided the best foundation for success. This is no longer the case. In a rapidly changing technological culture and an ever-growing information-based economy, creative ideas are the ultimate resource. Yet our current educational system does little to nourish this resource. ~ Peter H Diamandis,
1169:Mathematical thinking is not the same as doing mathematics - at least not as mathematics is typically presented in our school system. School math typically focuses on learning procedures to solve highly stereotyped problems. Professional mathematicians think a certain way to solve real problems, problems that can arise from the everyday world, or from science, or from within mathematics itself. The key to success in school math is to learn to think inside-the-box. In contrast, a key feature of mathematical thinking is thinking outside-the-box - a valuable ability in today's world. ~ Keith Devlin,
1170:So, if I'm no cheerleader of sports, why write a chapter about it? Sports do have some positive impact on society. They solve problems, such as how to get inner-city kids to spend $175 on shoes. They serve as a backdrop for some of our most memorable commercials. And they remain the one and only relevant application of math. Not only that, but we have sports to thank for most of the last century's advances in manliness. The system starts in school, where gym class separates the men from the boys. Then those men are taught to be winners, or at least, losers that hate themselves. ~ Stephen Colbert,
1171:Good Stories Always Beat Good Spreadsheets” “Whether you are raising money, pitching your product to customers, selling the company, or recruiting employees, never forget that underneath all the math and the MBA bullshit talk, we are all still emotionally driven human beings. We want to attach ourselves to narratives. We don’t act because of equations. We follow our beliefs. We get behind leaders who stir our feelings. In the early days of your venture, if you find someone diving too deep into the numbers, that means they are struggling to find a reason to deeply care about you. ~ Timothy Ferriss,
1172:Mostly, though, students get what economist Bryan Caplan called narrow vocational training for jobs few of them will ever have. Three-quarters of American college graduates go on to a career unrelated to their major—a trend that includes math and science majors—after having become competent only with the tools of a single discipline. One good tool is rarely enough in a complex, interconnected, rapidly changing world. As the historian and philosopher Arnold Toynbee said when he described analyzing the world in an age of technological and social change, “No tool is omnicompetent.” • ~ David Epstein,
1173:Many people keep deploring the low level of formal education in the United states (as defined by, say, math grades). Yet these fail to realize that the new comes from here and gets imitated elsewhere. And it is not thanks to universities, which obviously claim a lot more credit than their accomplishments warrant. Like Britain in the Industrial Revolution, America's asset is, simply, risk taking and the use of optionality, this remarkable ability to engage in rational forms fo trial and error, with no comparative shame in failing again, starting again, and repeating failure. ~ Nassim Nicholas Taleb,
1174:There is no more important homework than reading. Research shows that the highest achieving students are those who devote leisure time to reading, even when the school day and year are only mid-length and homework isn’t excessive. Recently, the largest-ever international study of reading found that the single most important predictor of academic success is the amount of time children spend reading books, more important even than economic or social status. And one of the few predictors of high achievement in math and science is the amount of time children devote to pleasure reading. ~ Nancie Atwell,
1175:I like the fact that they still run substantive pieces. I'm not sure I like the pieces, but it's nice that they do that. Anyway, it was always sort of ridiculous, me having anything to do with the youth culture, but now that I'm in my 50s, it's extra-double-ridiculous. They were losing interest in me, and I was losing interest in them. When I went to renegotiate my contract at Rolling Stone, I kind of halfheartedly asked if I could do half the work for half the money, and they asked if I could do two-thirds of the work for half the money. I ran that by my agent, since he can do math. ~ P J O Rourke,
1176:Extramuros: (1) In Old Orth, literally “outside the walls.” Often used in reference to the walled city-states of that age. (2) In Middle Orth, the non-mathic world; the turbulent and violent state of affairs that prevailed after the Fall of Baz. (3) In Praxic Orth, geographical regions or social classes not yet enlightened by the resurgent wisdom of the mathic world. (4) In New Orth, similar to sense 2 above, but often used to denote those settlements immediately surrounding the walls of a math, implying comparative prosperity, stability, etc. —THE DICTIONARY, 4th edition, A.R. 3000 ~ Neal Stephenson,
1177:Knowing you don’t have much time left changes things. You get kind of philosophical. And you figure things out—more like, they figure themselves out—and everything gets real clear. Your first kiss isn’t as important as your last. The math test really didn’t matter. The pie really did. The stuff you’re good at and the stuff you’re bad at are just different parts of the same thing. Same goes for the people you love and the people you don’t—and the people who love you and the people who don’t. The only thing that mattered was that you cared about a few people. Life is really, really short. ~ Kami Garcia,
1178:Tools of the Mind, by contrast, doesn’t focus much on reading and math abilities. Instead, all of its interventions are intended to help children learn a different kind of skill: controlling their impulses, staying focused on the task at hand, avoiding distractions and mental traps, managing their emotions, organizing their thoughts. The founders of Tools of the Mind believe that these skills, which they group together under the rubric self-regulation, will do more to lead to positive outcomes for their students, in first grade and beyond, than the traditional menu of pre-academic skills. ~ Paul Tough,
1179:All parents want to send their children to the best possible schools. But because a good school is a relative concept, a family cannot achieve its goal unless it outbids similar families for a house in a neighborhood served by such a school. Failure to do so often means having to send your kids to a school with metal detectors at the front entrance and students who score in the 20th percentile in reading and math. Most families will do everything possible to avoid having to send their kids to a school like that. But because of the logic of musical chairs, they're inevitably frustrated. ~ Robert H Frank,
1180:Furthermore, academic fads have been forced upon successive generations of elementary and secondary school students, including the “New Math,” the “Open Classroom,” “Values Clarification,” “Cooperative Learning,” “Outcome-Based Education,” “No Child Left Behind,” and more recently “Common Core” and “Race to the Top,” for which trillions of dollars have been and are being wasted on inferior educational outcomes. Even the once-heralded school lunch program is not safe from statist overreach, where billions of dollars are spent on federally mandated lunches that many students refuse to eat.23 ~ Mark R Levin,
1181:This is how it differed from math. The role of a story was, in the broadest terms, to transpose a single problem into another form. Depending on the nature and direction of the problem, a solution could be suggested in the narrative. Tengo would return to the real world with that suggestion in hand. It was like a piece of paper bearing the indecipherable text of a magic spell. At times it lacked coherence and served no immediate practical purpose. But it would contain a possibility. Someday he might be able to decipher the spell. That possibility would gently warm his heart from within. ~ Haruki Murakami,
1182:Why did math matter so much? Some reasons were practical: More and more jobs required familiarity with probability, statistics, and geometry. The other reason was that math was not just math. Math is a language of logic. It is a disciplined, organized way of thinking. There is a right answer; there are rules that must be followed. More than any other subject, math is rigor distilled. Mastering the language of logic helps to embed higher-order habits in kids’ minds: the ability to reason, for example, to detect patterns and to make informed guesses. Those kinds of skills had rising value in a ~ Amanda Ripley,
1183:You know what happens when you give a kid a calculator instead of teaching him math?"
"I think you need my help." I cross my arms. "You know what happens when you give a kid a calculator instead of teaching him math?"
He tilts his head, his eyes fetchingly bright.
"Sure he can do math that way," I continue, "but then if you take the calculator from him, suddenly he can't do any math at all, because he's
learned to rely on the calculator. Your power lets you look at people and see exactly what it takes to make them tick. Or crumble. But without
your power, you don't get people. ~ Carolyn Crane,
1184:This is an encouraging finding on two fronts. It means that young black children have continued to make gains relative to their white counterparts. It also means that whatever gap remains can be linked to a handful of readily identifiable factors. The data reveal that black children who perform poorly in school do so not because they are black but because a black child is more likely to come from a low-income, low-education household. A typical black child and white child from the same socioeconomic background, however, have the same abilities in math and reading upon entering kindergarten. ~ Steven D Levitt,
1185:Who thinks they’re not open-minded? Our hypothetical prim miss from the suburbs thinks she’s open-minded. Hasn’t she been taught to be? Ask anyone, and they’ll say the same thing: they’re pretty open-minded, though they draw the line at things that are really wrong. (Some tribes may avoid “wrong” as judgemental, and may instead use a more neutral sounding euphemism like “negative” or “destructive”.)

When people are bad at math, they know it, because they get the wrong answers on tests. But when people are bad at open-mindedness they don’t know it. In fact they tend to think the opposite. ~ Paul Graham,
1186:Jeremy comes home from school, feeling as if he has passed the math test after all. Jeremy is an optimist. Maybe there’s something good on TV. He settles down with the remote control on one of his father’s pet couches: oversized and reupholstered in an orange-juice-colored corduroy that makes it appear as if the couch has just escaped from a maximum security prison for criminally insane furniture. This couch looks as if its hobby is devouring interior decorators. Jeremy’s father is a horror writer, so no one should be surprised if some of the couches he reupholsters are hideous and eldritch. ~ John Joseph Adams,
1187:Now let’s see. The class reps on the council this year are therefore Eivind and Marianne!”

I looked down at the desk in front of me.

One vote.

How was that possible?

And, to cap it off, the one vote was my own.

But I was the best student in the class! At least in Norwegian! And natural and social sciences! And in math I was the second best, or perhaps the third. But, altogether, who could be better than me?

OK, Eivind won. But one vote? How was that possible?

Hadn’t anyone voted for me?

There had to be a mistake somewhere.

No one? ~ Karl Ove Knausg rd,
1188:We have to HIDE from each other because we think that we are the only ones BROKEN. We think we're the only ones whose original selves we ground up and smashed under the jack-booted heel of cultural lies and superstition, patriotism, war lust, war hunger, and a denial of AGGRESSION AGAINST CHILDREN THAT IS THE FOUNDATION OF CULTURE. Culture is everything that is NOT TRUE. If it's true, it's called 'math' or 'science' or 'facts'. Culture is the Stockholm syndrome we have with the historical lies that are convenient to the rules. We love the lies, because we don't think we can be loved if we don't. ~ Stefan Molyneux,
1189:Now, as traditional computing programs are displaced by the operation of AI algorithms, requirements are once again shifting. Machine learning demands the rapid-fire execution of complex mathematical formulas, something for which neither Intel’s nor Qualcomm’s chips are built. Into the void stepped Nvidia, a chipmaker that had previously excelled at graphics processing for video games. The math behind graphics processing aligned well with the requirements for AI, and Nvidia became the go-to player in the chip market. Between 2016 and early 2018, the company’s stock price multiplied by a factor of ten. ~ Kai Fu Lee,
1190:A = A is a simplification, one so radical that it sometimes utterly distorts reality. It skins reality alive. Is A = A useful? Does logic come in handy? Is math a magnificent symbolic system with which to comprehend what's around us? And is math based on A = A? Yes. Absolutely. But math and logic are just that - very, very simplified representations. Symbolic systems with massive powers. But symbolic systems that sometimes do enormous injustice to the richness of that which they attempt to represent. Symbol systems that sometimes do enormous injustice to science's greatest mystery, cosmic creativity. ~ Howard Bloom,
1191:teaching math was convoluted and confusing, his grammar lessons could bore a statue to tears, and when it came to Ethoen history and mythology, Jahrra often found herself tempted to launch her pen at him.  He never got anything right, often obscuring facts or making heroes out to be twisted or idiotic.  Jahrra usually went into daydream mode during his lectures, but one day his lesson was so outrageous she couldn’t even lose herself in her own thoughts. “I wish we didn’t have such an awful teacher,” Gieaun groaned as they streamed out of the stuffy classroom on their final day of school. “I ~ Jenna Elizabeth Johnson,
1192:Thanks for helping me get the bookcase home,” I offer as we walk. I’m not sure why we’re still together. Why he wanted to have lunch, offered to let me do his laundry at his place.

“No problem. Gotta work off those favors I owe you, right?”

Favors? “How many favors do you owe me?”

“Two.”

“Two?”

“Yeah. It was three, but I paid one off with the bookcase. So two.”

“When did we decide you owed me three favors?” This guy totally does math like a government employee.

“Didn’t we?” He looks totally nonplussed with his bad accounting of favors. “We’re here. ~ Jana Aston,
1193:When we got to the Lock-Horne Building on Park Avenue—again Win’s full name is Windsor Horne Lockwood III, so you do the math—Dad said, “You want me to just drop you off?” Sometimes my father leaves me awestruck. Fatherhood is about balance, but how can one man do it so well, so effortlessly? Throughout my life he pushed me to excel without ever crossing the line. He reveled in my accomplishments yet never made them seem to be all that important. He loved without condition, yet he still made me want to please him. He knew, like now, when to be there, and when it was time to back off. “I’ll be okay.” He ~ Harlan Coben,
1194:Politics has a math of its own. Whereas a scientifically minded person might see things this way: One person who says 2+2=5 is an idiot; two people who think 2+2=5 are two idiots; and a million people who think 2+2=5 are a whole lot of idiots — political math works differently. Let’s work backwards: if a million people think 2+2=5, then they are not a million idiots, but a “constituency.” If they are growing in number, they are also a “movement.” And, if you were not only the first person to proclaim 2+2=5, but you were the first to persuade others, then you, my friend, are not an idiot, but a visionary. ~ Jonah Goldberg,
1195:You know what I believe? I remember in college I was taking this math class, this really great math class taught by this tiny old woman. She was talking about fast Fourier transforms and she stopped midsentence and said, ‘Sometimes it seems the universe wants to be noticed.’ “That’s what I believe. I believe the universe wants to be noticed. I think the universe is improbably biased toward consciousness, that it rewards intelligence in part because the universe enjoys its elegance being observed. And who am I, living in the middle of history, to tell the universe that it—or my observation of it—is temporary? ~ John Green,
1196:If other people thought art was important, then it would be required to graduate. But no, I don’t have to take art. I do have to take math, which is just a waste of time because the numbers get all switched up in my brain, plus, calculators exist for a reason. I do have to take history, which is basically memorizing tariff acts till your brain bleeds. I do have to take four years of gym class with a bunch of jerks who punch me if they don’t like what I say. But art? Optional. Even though art and music and literature and all that are what make us human. Algebra doesn’t make us human. Games don’t make us human. ~ Laura Ruby,
1197:For each stop—each timbre, or type of sound, that the organ could make (viz. blockflöte, trumpet, piccolo)—there was a separate row of pipes, arranged in a line from long to short. Long pipes made low notes, short high. The tops of the pipes defined a graph: not a straight line but an upward-tending curve. The organist/math teacher sat down with a few loose pipes, a pencil, and paper, and helped Lawrence figure out why. When Lawrence understood, it was as if the math teacher had suddenly played the good part of Bach’s Fantasia and Fugue in G Minor on a pipe organ the size of the Spiral Nebula in Andromeda— ~ Neal Stephenson,
1198:When I was in high school, my math teacher Mr. Packwood used to say, “If you’re stuck on a problem, don’t sit there and think about it; just start working on it. Even if you don’t know what you’re doing, the simple act of working on it will eventually cause the right ideas to show up in your head.” During that early self-employment period, when I struggled every day, completely clueless about what to do and terrified of the results (or lack thereof), Mr. Packwood’s advice started beckoning me from the recesses of my mind. I heard it like a mantra: Don’t just sit there. Do something. The answers will follow. In ~ Mark Manson,
1199:My basic philosophy of teaching was straightforward and deeply personal. I wanted to teach the way I wished that I myself had been taught. Which is to say, I hoped to convey the sheer joy of learning, the thrill of understanding things about the universe. I wanted to pass along to students not only the logic but the beauty of math and science. Furthermore, I wanted to do this in a way that would be equally helpful to kids studying a subject for the first time and for adults who wanted to refresh their knowledge; for students grappling with homework and for older people hoping to keep their minds active and supple. ~ Salman Khan,
1200:My secret love, Billy Colbert, had to make up the same test.
Afterward, we left the chemistry lab together. 'Well, it was long,' Billy said, 'but it wasn't hard.'
'I thought it was long *and* hard,' I replied.
'Oh, cut it out, Rachel,' Billy remonstrated. 'If there's one thing I can't stand, it's brains who pretend they suffer just as much as the rest of us.'
'I'm not a brain in chemistry,' I protested. 'If I get good grades in science or math, it's because I work. You're the brain in chemistry. I hate that word, brain, anyway. Everyone has a brain, and they're all about the same size, even a moron's. ~ Barbara Cohen,
1201:Are all the scientists here men, then?” “Scientists?” Oiie asked, incredulous. Pae coughed. “Scientists. Oh, yes, certainly, they’re all men. There are some female teachers in the girls’ schools, of course. But they never get past Certificate level.” “Why not?” “Can’t do the math; no head for abstract thought; don’t belong. You know how it is, what women call thinking is done with the uterus! Of course, there’s always a few exceptions, God-awful brainy women with vaginal atrophy.” “You Odonians let women study science?” Oiie inquired. “Well, they are in the sciences, yes.” “Not many, I hope.” “Well, about half. ~ Ursula K Le Guin,
1202:who decided that “astronaut” would be a great dream job for a kid? It’s like 97 percent math, 1 percent breathing some Russian dude’s farts, 1 percent dying, and 1 percent eating awesome powdered ice cream. If you’re the very luckiest kind of astronaut ever, your big payoff is that you get to visit a barren airless wasteland for five minutes, do some more math, and then go home—ice cream not guaranteed. Anyway, loophole: I can already buy astronaut ice cream at the Science Center, no math or dying required. Lindy, 1; astronauts nada. (Unless you get points for debilitating low bone density, in which case… I concede.) Not ~ Lindy West,
1203:But consider a paper published in Science in 2008.1 The authors examined the relationship between math scores and sexual equality in forty countries (based on economic, educational, and political indices of gender equality; the worst was Turkey, the United States was middling, and, naturally, the Scandinavians were tops). Lo and behold, the more gender equal the country, the less of a discrepancy in math scores. By the time you get to the Scandinavian countries, it’s statistically insignificant. And by the time you examine the most gender-equal country on earth at the time, Iceland, girls are better at math than boys. ~ Robert M Sapolsky,
1204:On the Electrodynamics of Moving Bodies” Now let’s look at how Einstein articulated all of this in the famous paper that the Annalen der Physik received on June 30, 1905. For all its momentous import, it may be one of the most spunky and enjoyable papers in all of science. Most of its insights are conveyed in words and vivid thought experiments, rather than in complex equations. There is some math involved, but it is mainly what a good high school senior could comprehend. “The whole paper is a testament to the power of simple language to convey deep and powerfully disturbing ideas,” says the science writer Dennis Overbye. ~ Walter Isaacson,
1205:...all this abstraction is also potentially distancing. We don't see the labor that went into building our railroads or the civilizations that were wiped out in order to clear the land. We don't see the millennia of dinosaurs or plankton that went into our oil, the Chinese repetitive stress injuries that went into our iPhones, or any of the other time-intensive processes we can spend in an instant today. We tend to see math and science as a steady state of facts rather than as the accumulated knowledge of linear traditions. As Korzybski put it, we see further because we "stand on the shoulders" of the previous generation. ~ Douglas Rushkoff,
1206:I have no idea what my siblings did when they did school, but when I did it I opened my math book and spent ten minutes turning pages, running my fingers down the center fold. If my finger touched fifty pages, I’d report to Mother that I’d done fifty pages of math. “Amazing!” she’d say. “You see? That pace would never be possible in the public school. You can only do that at home, where you can sit down and really focus, with no distractions.” Mother never delivered lectures or administered exams. She never assigned essays. There was a computer in the basement with a program called Mavis Beacon, which gave lessons on typing. ~ Tara Westover,
1207:I might be more kindly disposed to this ultra-secular notion that whenever bad things happen someone must be held accountable if a curious little halo of blamelessness did not seem to surround those very people who perceive themselves as bordered on every side by agents of wickedness. That is, it seems to be the same folks who are inclined to sue builders who did not perfectly protect them from the depredations of an earthquake who will be the first to claim that their son failed his math test because of attention deficit disorder, and not because he spent the night before at a video arcade instead of studying complex fractions. ~ Lionel Shriver,
1208:He said, 'You have to understand, I'm an academic. I'm not trained in dealing with masses of people. I found out through the school of hard knocks that it is better not to deal with masses of people. It's not that they don't deserve the information but they really react in very strange ways. They get panicky and excited, or over-excited, and it is so easy for academics to forget that. We're trained in math. We're trained in science. We're not trained in the masses.'
He paused.
'The public is extremely wild,' he said, 'uncontrollably wild.'
Then he shrugged his shoulders.
'You have to understand,' he said, 'I'm an academic. ~ Jon Ronson,
1209:bar, drinking beer. Jim turns to Bob and says, "You know, I'm tired of going through life without an education. Tomorrow, I think I'll go to the community college and sign up for some classes." The next day, Jim goes down to the college and meets the Dean of Admissions, who signs him up for the four basic classes: Math, English, History, and Logic. "Logic?" Jim says. "What's that?" The dean says, "I'll give you an example. Do you own a weed eater?" "Yeah." "Then logically speaking, because you own a weed eater, I presume you have a yard." "That's true, I do have a yard." "I'm not done," the dean says. "Because you have a yard, I think that ~ Various,
1210:Worrying about money is one of the worst worries. It’s like having locked-in syndrome, except you’re still moving around and doing things. Your head burns. If other people are not having money problems, it pisses you off because it reminds you that you’re limited in the ways you can express your agency in the world, and they aren’t. Worrying about money is anger-inducing because it makes you think about time: how many dollars per hour, how much salary per year, how many years until retirement. Worrying about money forces you to do endless math in your head, and most people didn’t like math in high school and they don’t like it now. ~ Douglas Coupland,
1211:He really ought to remember. . . . The airburst, if it happens, will be in visual range. Abstractions, math, models are fine, but when you’re down to it and everybody’s hollering for a fix, this is what you do: you go and sit exactly on the target with indifferent shallow trenches for shelter, and you watch it in the silent fire-bloom of its last few seconds, and see what you will see. Chances are astronomically against a perfect hit, of course, that is why one is safest at the center of the target area. Rockets are supposed to be like artillery shells, they disperse about the aiming point in a giant ellipse—the Ellipse of Uncertainty. But ~ Thomas Pynchon,
1212:But it’s hard to keep your guard up at all times. Jeremy comes home from school, feeling as if he has passed the math test after all. Jeremy is an optimist. Maybe there’s something good on TV. He settles down with the remote control on one of his father’s pet couches: oversized and reupholstered in an orange-juice-colored corduroy that makes it appear as if the couch has just escaped from a maximum security prison for criminally insane furniture. This couch looks as if its hobby is devouring interior decorators. Jeremy’s father is a horror writer, so no one should be surprised if some of the couches he reupholsters are hideous and eldritch. ~ John Joseph Adams,
1213:I went outside. Tried taking in the billions of stars above, lingering long enough to allow each point of light the chance to scratch a deep hole in the back of my retina, so that when I finally did turn to face the dark surrounding forest I thought I saw the billion eyes of a billion cats blinking out, in the math of the living, the sum of the universe, the stories of history , a life older than anyone could have ever imagined. And even after they were gone--fading away together, as if they really were one--something still lingered in those sweet folds of black pine , sitting quietly, almost as if it too were waiting for something to wake. ~ Mark Z Danielewski,
1214:A computer program written by researchers at Argonne National Laboratory in Illinois has come up with a major mathematical proof that would have been called creative if a human had thought of it. In doing so, the computer has, for the first time, got a toehold into pure mathematics, a field described by its practitioners as more of an art form than a science. ...Dr. McCune's proof concerns a conjecture that is the very epitome of pure mathematics. ...His computer program proved that a set of three equations is equivalent to a Boolean algebra... ~ Gina Kolata, "With Major Math Proof, Brute Computers Show Flash of Reasoning Power," The New York Times (Dec 10, 1996),
1215:In School of One, students have daily "playlists" of their learning tasks that are attuned to each student's learning needs, based on that student's readiness and learning style. For example, Julia is way ahead of grade level in math and learns best in small groups, so her playlist might include three or four videos matched to her aptitude level, a thirty-minute one-on-one tutoring session with her teacher, and a small group activity in which she works on a math puzzle with three peers at similar aptitude levels. There are assessments built into each activity so that data can be fed back to the teacher to choose appropriate tasks for the next playlist. ~ Eric Ries,
1216:Matt laughed. "Close. That was last year. This year it's Obsessive Deovtion to Fourier Analysis Theory and Applications. And my personal favorite, Quantum Physics II: Romantic Entanglements of Energy and Matter."
Julie turned her head to Matt. "You're a double major? Physics and math? Jesus..."
"I know. Nerdy." He shrugged.
"No, I'm impressed. I'm just surprised your brains fit in your head."
"I was fitted with a specially desinged compression filter that allows excessive information to lie dormant until I need to access it. It's only the Beta version, so excuse any kinks that may appear. I really can't be held responsible. ~ Jessica Park,
1217:But I was still hurt. These past few years, I’d been obliged to accept orders from the man from the Village Fishery Association, but my consolation had come from knowing I was giving my daughter the best education possible. She was smart and ambitious. She knew things I would never know. But now I saw other realities: You can do everything for a child. You can encourage her to read and do her math homework. You can forbid her to ride a bike, giggle too much, or see a boy. I’d just asked her to promise she wouldn’t see Yo-chan or Mi-ja again. She’d done so grudgingly. Sometimes everything you do is as pointless and as ineffective as shouting into the wind. ~ Lisa See,
1218:And so, whereas Bohr and the Copenhagen gang would argue that only one of these universes would exist (because the act of measurement, which they claim lies outside of Schrodinger's purview, would collapse away all the others), and whereas a first-pass attempt to go beyond Bohr and extend Schrodinger's math to all particles, including those constituting equipment and brains, yielded dizzying confusion (because a given machine or mind seemed to internalize all possible outcomes simultaneously), Everett found that a more careful reading of Schrodinger's math leads somewhere else: to a plentiful reality populated by an ever-growing collection of universes. ~ Brian Greene,
1219:Focusing on individual nutrients, their identities, their contents in food, their tissue concentrations, and their biological mechanisms, is like using math and physics to catch balls. It’s not the way nature evolved, and it makes proper nutrition far more difficult than it needs to be. Our bodies use countless mechanisms, strategically placed throughout our digestion, absorption, and transport and metabolic pathways, to effortlessly ensure tissue concentrations consistent with good health—no database consultation required. But as long as we let reductionism guide our research and our understanding of nutrition, good health will remain unattainable. ~ T Colin Campbell,
1220:The math-powered applications powering the data economy were based on choices made by fallible human beings. Some of these choices were no doubt made with the best intentions. Nevertheless, many of these models encoded human prejudice, misunderstanding, and bias into the software systems that increasingly managed our lives. Like gods, these mathematical models were opaque, their workings invisible to all but the highest priests in their domain: mathematicians and computer scientists. Their verdicts, even when wrong or harmful, were beyond dispute or appeal. And they tended to punish the poor and the oppressed in our society, while making the rich richer. ~ Cathy O Neil,
1221:That better not be what I think it is," Joe mumbled in the dark.
It was. "It's not. Jeez, woman, someone's paranoid. It's my pocket light," he said, wincing. Ah, he was only human after all. It wasn't the first time she got him hard nor would it be the last time. The physical discomfort was a small price to pay to have her in his arms.
"Well, then your flashlight is growing. Jeez, Eric, put a leash on that thing before it stabs me!" she teased.
"But it likes you," he pouted.
She giggled. "I seem to remember a certain tenth grade math class where it liked standing up in front of the entire class."
He sucked in a breath. "Hey, that traumatized me! ~ R L Mathewson,
1222:Alvi also told them that the main reason his family was in Moscow and not in Chechnya, in spite of how uncomfortable things were for them here, was to enable their children to go to school without a war taking place around them. Zulai was a math teacher, but she had to work at a market stall in Moscow, not something she was good at. They spent their evenings rolling chicken cutlets to sell in the morning. Everything he and Zulai did was for the sake of their children. “Well, how about that! They’re worming their way right into the center of Moscow! And they expect to be given a $500 apartment!” This was the reaction of the parents’ committee to Alvi’s appeal. “I ~ Anna Politkovskaya,
1223:The reason we list smallest to largest is to have some quick wins. This is the “behavior modification over math” part I referred to earlier. Face it, if you go on a diet and lose weight the first week, you will stay on that diet. If you go on a diet and gain weight or go six weeks with no visible progress, you will quit. When training salespeople, I try to get them a sale or two quickly because that fires them up. When you start the Debt Snowball and in the first few days pay off a couple of little debts, trust me, it lights your fire. I don’t care if you have a master’s degree in psychology; you need quick wins to get fired up. And getting fired up is super-important. ~ Dave Ramsey,
1224:... It happened very fast. And now that he's dead he can't remember pain. It's as if he'd never existed.'
He wanted her to believe this, but he wasn't sure he believed it himself. If time was infinite, then three seconds and three years represented the same infinitely small fraction of it. And so, if inflicting three years of fear and suffering was wrong, as everyone would agree, then inflicting three seconds of it was no less wrong. He caught a fleeting glimpse of God in the math here, in the infinitesimal duration of a life. No death could be quick enough to excuse inflicting pain. If you were capable of doing the math, it meant that a morality was lurking in it. ~ Jonathan Franzen,
1225:If the only thing I did for the rest of my life was treat others kindly, file manila folders, and sit on the porch watching the grass grow it would be enough. It had to be. I did the math. The number of people who actually achieve a significant legacy is trifling compared to the vast number who go from birth to death living relatively unremarkable lives (at least on the surface). And maybe that wasn't the failure I'd been conditioned to believe. Maybe there was something to be said in praise of an outwardly unremarkable life. Maybe there were deep everyday forms of magic that had nothing to do with profound acomplishments or a Twitter feed that resonated down through the ages. ~ Clara Bensen,
1226:I think we have two choices in the face of such big beauty: terror or awe. And this is precisely why we attempt to chart God, because we want to be able to predict Him, to dissect Him, to carry Him around in our dog and pony show. We are too proud to feel awe and too fearful to feel terror. We reduce Him to math so we don’t have to fear Him, and yet the Bible tells us fear is the appropriate response, that it is the beginning of wisdom. Does this mean God is going to hurt us? No. But I stood on the edge of the Grand Canyon once, behind a railing, and though I was never going to fall off the edge, I feared the thought of it. It is that big of a place, that wonderful of a landscape. ~ Donald Miller,
1227:A teach­er in Ok­la­homa re­flect­ed on the post-​grad­ua­tion af­ter­math of stu­dent so­cial di­vi­sions. “The in crowd al­ways hangs to­geth­er, even af­ter grad­ua­tion. They are the ones who will be­come debutantes af­ter their fresh­man year in col­lege. The oth­ers tend to drift away. They don’t get in­vit­ed to the par­ties, they are laughed at be­cause they aren’t wear­ing de­sign­er clothes, etc.,” she said. But when it comes down to the pop­ular stu­dents ver­sus the out­casts, the lat­ter “are more sure of them­selves (even with the ridicule), and usu­al­ly turn out to be more suc­cess­ful and well-​adjust­ed. I would take the out­casts in a heart­beat.” So would I. ~ Alexandra Robbins,
1228:Behind us, the man laughed. "Looks like we aren't the only ones looking for a little diversion. There's an empty office right over there, guys."
Marsten raised his hand in thanks. The couple moved on. I let the kiss continue for five more seconds, then pulled away.
"They're gone," I said.
Marsten frowned, as if surprised-and disappointed-that I'd noticed. I tugged my hair from his hands.
"Okay, coast clear," I said. "Let's go."
He let out a small laugh. "I see I need to brush up on my kissing."
"No, you have that down pat."
"She says with all the excitement of a teacher grading a math quiz..."
"A-plus. Now let's move. Before someone else comes along. ~ Kelley Armstrong,
1229:For an example, here is a simple puzzle. Do not try to solve it but listen to your intuition: A bat and ball cost $1.10. The bat costs one dollar more than the ball. How much does the ball cost? A number came to your mind. The number, of course, is 10: 10¢. The distinctive mark of this easy puzzle is that it evokes an answer that is intuitive, appealing, and wrong. Do the math, and you will see. If the ball costs 10¢, then the total cost will be $1.20 (10¢ for the ball and $1.10 for the bat), not $1.10. The correct answer is 5¢. It is safe to assume that the intuitive answer also came to the mind of those who ended up with the correct number—they somehow managed to resist the intuition. ~ Daniel Kahneman,
1230:It was a perfect school for Einstein. The teaching was based on the philosophy of a Swiss educational reformer of the early nineteenth century, Johann Heinrich Pestalozzi, who believed in encouraging students to visualize images. He also thought it important to nurture the “inner dignity” and individuality of each child. Students should be allowed to reach their own conclusions, Pestalozzi preached, by using a series of steps that began with hands-on observations and then proceeded to intuitions, conceptual thinking, and visual imagery. 56 It was even possible to learn—and truly understand—the laws of math and physics that way. Rote drills, memorization, and force-fed facts were avoided. ~ Walter Isaacson,
1231:With the threat of failure looming, students with the growth mindset set instead mobilized their resources for learning. They told us that they, too, sometimes felt overwhelmed, but their response was to dig in and do what it takes. They were like George Danzig. Who? George Danzig was a graduate student in math at Berkeley. One day, as usual, he rushed in late to his math class and quickly copied the two homework problems from the blackboard. When he later went to do them, he found them very difficult, and it took him several days of hard work to crack them open and solve them. They turned out not to be homework problems at all. They were two famous math problems that had never been solved. ~ Carol S Dweck,
1232:Therein lies the key, I think, to Einstein’s brilliance and the lessons of his life. As a young student he never did well with rote learning. And later, as a theorist, his success came not from the brute strength of his mental processing power but from his imagination and creativity. He could construct complex equations, but more important, he knew that math is the language nature uses to describe her wonders. So he could visualize how equations were reflected in realities—how the electromagnetic field equations discovered by James Clerk Maxwell, for example, would manifest themselves to a boy riding alongside a light beam. As he once declared, “Imagination is more important than knowledge.”6 ~ Walter Isaacson,
1233:We do ability grouping early on in childhood. We have advanced reading groups and advanced math groups. So, early on, if we look at young kids, in kindergarten and first grade, the teachers are confusing maturity with ability. And they put the older kids in the advanced stream, where they learn better skills; and the next year, because they are in the higher groups, they do even better; and the next year, the same things happens, and they do even better again. The only country we don’t see this going on is Denmark. They have a national policy where they have no ability grouping until the age of ten.” Denmark waits to make selection decisions until maturity differences by age have evened out. ~ Malcolm Gladwell,
1234:There are no single guys who don’t have at least one major flaw, and a flaw, I might add, that would stop you from dating them – even if everything else was great. Why? Simple math. Women are interesting and honest and sensitive. Most men are not. There is only one normal, decent single guy for every five women in this city. This is what’s known as the Great Male Statistic. Girls don’t want to face the GMS. They want to believe there’s someone for everyone. The truth hurts. You only start coming to terms with the GMS when you’re twenty-six or twenty-seven. It actually killed Sylvia Plath. She finally found this guy in grad school who she thought was so great, and she married him, and he cheated on her. ~ Caren Lissner,
1235:science and reason, which has found itself in recent decades under attack on many fronts: right-wing ideologues who do not understand science; religious-right conservatives who fear science; left-wing postmodernists who do not trust science when it doesn’t support progressive tenets about human nature; extreme environmentalists who want to return to a prescientific and preindustrial agrarian society; antivaxxers who wrongly imagine that vaccinations cause autism and other maladies; anti-GMO (genetically modified food) activists who worry about Frankenfoods; and educators of all stripes who cannot articulate why Science, Technology, Engineering, and Math (STEM) are so vital to a modern democratic nation. ~ Michael Shermer,
1236:It’s easy to raise graduation rates, for example, by lowering standards. Many students struggle with math and science prerequisites and foreign languages. Water down those requirements, and more students will graduate. But if one goal of our educational system is to produce more scientists and technologists for a global economy, how smart is that? It would also be a cinch to pump up the income numbers for graduates. All colleges would have to do is shrink their liberal arts programs, and get rid of education departments and social work departments while they’re at it, since teachers and social workers make less money than engineers, chemists, and computer scientists. But they’re no less valuable to society. ~ Cathy O Neil,
1237:Once I dated a woman I only liked 43%.
So I only listened to 43% of what she said.

Only told the truth 43% of the time.
And only kissed with 43% of my lips.

Some say you can't quantify desire,
attaching a number to passion isn't right,
that the human heart doesn't work like that.

But for me it does-I walk down the street

and numbers appear on the foreheads
of the people I look at. In bars, it's worse.

With each drink, the numbers go up
until every woman in the joint has a blurry

eighty something above her eyebrows,
and the next day I can only remember 17%
of what actually happened. That's the problem
with booze-it screws with your math. ~ Jeffrey McDaniel,
1238:In the United States and other countries, we’d put off this reckoning, convinced that our kids would always get second and third chances until well into adulthood. We had the same attitude toward teachers: Anyone and everyone could become a teacher, as long as they showed up for class, followed the rules, and had good intentions. We had the schools we wanted, in a way. Parents did not tend to show up at schools demanding that their kids be assigned more challenging reading or that their kindergarteners learn math while they still loved numbers. They did show up to complain about bad grades, however. And they came in droves, with video cameras and lawn chairs and full hearts, to watch their children play sports. ~ Amanda Ripley,
1239:Naomi doubted that any human being really understood math, they simply all pretended to have it down pat, when in truth they were every bit as confused by it as she was. Math was nothing but a giant hoax, and everyone participated in it, everyone faked belief in math so they could be done with hideous classes and the drudgery of the hateful homework and get on with life. The sun came up every morning, so the sun was real, and every time you inhaled you got the air you needed, so the atmosphere was obviously real, but half the time when you tried to use math to solve the simplest problem, the math absolutely would not work, which meant that it couldn't be real like the sun and the atmosphere. Math was a waste of time. ~ Dean Koontz,
1240:For example, if healthy 30-year-olds are sleep deprived for six days (averaging, in this study, about four hours of sleep per night), parts of their body chemistry soon revert to that of a 60-year-old. And if they are allowed to recover, it will take them almost a week to get back to their 30-year-old systems. Taken together, these studies show that sleep loss cripples thinking in just about every way you can measure thinking. Sleep loss hurts attention, executive function, working memory, mood, quantitative skills, logical reasoning ability, general math knowledge. Eventually, sleep loss affects manual dexterity, including fine motor control, and even gross motor movements, such as the ability to walk on a treadmill. ~ John Medina,
1241:When the Soviet Union launched Sputnik in 1957, my parents, like the rest of America, were terrified. The Soviets had nuclear weapons and now were ahead of us in space. So my parents marched me and Owen into our living room, sat us down, and said, " You boys are going to study math and Science so we can beat the Soviets!"
I thought that was a lot of pressure to put on a six-year old. But own and I were obedient sons, so we studied math and science. And we were good at it.. Owen was the first in our family to go to college. He went to MIT, graduating with a degree in physics, and then became a photographer.
I went to Harvard, and became a comedian. My poor parents.
But we still beat the Soviets. You're welcome. ~ Al Franken,
1242:Listen carefully: you do not need to have a "productive" homeschool day to please the Savior. You do not need to have a clean house to please the Savior. You do not even need to have well-behaved kids to please Him. It doesn't matter if you hit every math problem, get through an entire spelling lesson, or whether your child loves learning the way you want him to. It doesn't matter! What matters is that we seek to imitate Christ. That we order our loves so that our hearts better reflect His.  Many days, checklists will go untouched, books will go unread, ducks will not line up in a row, no matter how much we strive. So cease striving. "It is our part to offer what we can, His to finish what we cannot." —— St. Jerome ~ Sarah Mackenzie,
1243:In his searches, Schwall noticed something else, though at first he didn’t know what to make of it: A surprisingly large number of the people pulled in by the big Wall Street banks to build the technology for high-frequency trading were Russians. “If you went to LinkedIn and looked at one of these Russian guys, you would see he was linked to all the other Russians,” said Schwall. “I’d go to find Dmitri and I’d also find Misha and Vladimir and Tolstoy or whatever.” The Russians came not from finance but from telecom, physics, medical research, university math departments, and a lot of other useful fields. The big Wall Street firms had become machines for turning analytically minded Russians into high-frequency traders. ~ Michael Lewis,
1244:Of course, there can be clear indications that a teacher is not worth paying attention to. A history as a fabulist or a con artist should be considered fatal; thus, the spiritual opinions of Joseph Smith, Gurdjieff, and L. Ron Hubbard can be safely ignored. A fetish for numbers is also an ominous sign. Math is magical, but math approached like magic is just superstition—and numerology is where the intellect goes to die. Prophecy is also a very strong indication of chicanery or madness on the part of a teacher, and of stupidity among his students. One can extrapolate from scientific data or technological trends (climate models, Moore’s law), but most detailed predictions about the future lead to embarrassment right on schedule. ~ Sam Harris,
1245:Many people who celebrate the arts and the humanities, who applaud vigorously the tributes to their importance in our schools, will proclaim without shame (and sometimes even joke) that they don’t understand math or physics. They extoll the virtues of learning Latin, but they are clueless about how to write an algorithm or tell BASIC from C++, Python from Pascal. They consider people who don’t know Hamlet from Macbeth to be Philistines, yet they might merrily admit that they don’t know the difference between a gene and a chromosome, or a transistor and a capacitor, or an integral and a differential equation. These concepts may seem difficult. Yes, but so, too, is Hamlet. And like Hamlet, each of these concepts is beautiful. ~ Walter Isaacson,
1246:It gave Jane a wicked sense of satisfaction that he’d noticed that aspect of her sister’s personality, but she tried not to sound too arrogant. “Savannah doesn’t worry about homework. Apparently they don’t care about your GPA when you apply for beauty school.”
“Beauty school, huh? I would have thought she’d already graduated valedictorian from there.”
Jane blinked at him in frustration.

Fairy’s side note: Adults are constantly telling teenagers that it’s what’s on the inside that matters. It’s always painful to find out that adults have lied to you.

Hunter shrugged. “I guess I shouldn’t have assumed you’d be like Savannah where math is concerned.”

Meaning: After all, you aren’t pretty like she is. ~ Janette Rallison,
1247:logically speaking, you have a house." "Yes, I do have a house." "And because you have a house, I think that you might logically have a family." "Yes, I have a family." "So, because you have a family, then logically you must have a wife. And because you have a wife, then logic tells me you must be a heterosexual." "I am a heterosexual. That's amazing! You were able to find out all of that just because I have a weed eater." Excited to take the class, Jim shakes the dean's hand and leaves to go meet Bob at the bar. He tells Bob about his classes, and how he is signed up for Math, English, History, and Logic. "Logic?" Bob says, "What's that?" "I'll give you an example," says Jim. "Do you have a weed eater?" "No." "Then you're gay." ♦◊♦◊♦◊♦ ~ Various,
1248:That is what is marvelous about school, she realized: when you are in school, your talents are without number, and your promise is boundless. You ace a math test: you will one day work for NASA. The choir director asks you to sing a solo at the holiday concert: you are the next Mariah Carey. You score a goal, you win a poetry contest, you act in a play. And you are everything at once: actor, astronomer, gymnast, star. But at a certain point, you begin to feel your talents dropping away, like feathers from a molting bird. Cello lessons conflict with soccer practice. There aren't enough spots on the debating team. Calculus remains elusive. Until the day you realize that you cannot think of a single thing you are wonderful at. ~ Sarah Shun lien Bynum,
1249:Mr. McLean looked up at Piper. He seemed unconcerned by her knife and blowgun. “Going out?” “Just for a while.” Piper kissed her father on the cheek. “I’ll be back tonight. Don’t let them take the sleeping bags, okay? You and I can camp out on the terrace. It’ll be fun.” “All right.” He patted her arm absently. “Good luck…studying?” “Yep,” Piper said. “Studying.” You have to love the Mist. You can stroll out of your house heavily armed, in the company of a satyr, a demigod, and a flabby former Olympian, and thanks to the Mist’s perception-bending magic, your mortal father assumes you’re going to a study group. That’s right, Dad. We need to go over some math problems that involve the trajectory of blowgun darts against moving targets. ~ Rick Riordan,
1250:A long, fruitful retirement is a concept that’s only a few generations old. If you recall from our discussion earlier, when President Franklin Roosevelt created Social Security in 1935, the average life expectancy was just 62. And the payments wouldn’t kick in until age 65, so only a small percentage would actually receive Social Security benefits to begin with. At the time, the Social Security system made financial sense because there were 40 workers (contributors) for every retiree collecting benefits. That means there were 40 people pulling the wagon, with only 1 sitting in the back. By 2010, the ratio had dropped to only 2.9 wagon pullers for every retiree. The math doesn’t pencil out, but since when has that stopped Washington? ~ Anthony Robbins,
1251:I am speaking to you as I always have—as the sober and serious man I have always wanted you to be, who does not apologize for his human feelings, who does not make excuses for his height, his long arms, his beautiful smile. You are growing into consciousness, and my wish for you is that you feel no need to constrict yourself to make other people comfortable. None of that can change the math anyway. I never wanted you to be twice as good as them, so much as I have always wanted you to attack every day of your brief bright life in struggle. The people who must believe they are white can never be your measuring stick. I would not have you descend into your own dream. I would have you be a conscious citizen of this terrible and beautiful world. ~ Ta Nehisi Coates,
1252:The basic problem for Lawrence was that he was lazy. He had figured out that everything was much simpler if, like Superman with his X-ray vision, you just stared through the cosmetic distractions and saw the underlying mathematical skeleton. Once you found the math in a thing, you knew everything about it, and you could manipulate it to your heart’s content with nothing more than a pencil and a napkin. He saw it in the curve of the silver bars on his glockenspiel, saw it in the catenary arch of a bridge and in the capacitor-studded drum of Atanasoff and Berry’s computing machine. Actually pounding on the glockenspiel, riveting the bridge together, or trying to figure out why the computing machine wasn’t working were not as interesting to him. ~ Neal Stephenson,
1253:I am speaking to you as I always have - as the sober and serious man I have always wanted you to be, who does not apologize for his human feelings, who does not make excuses for his height, his long arms, his beautiful smile. You are growing into consciousness, and my wish for you is that you feel no need to constrict yourself to make other people comfortable. None of that can change the math anyway. I never wanted you to be twice as good as them, so much as I have always wanted you to attack every day of your brief bright life in struggle. The people who must believe they are white can never be your measuring stick. I would not have you descend into your won dream. I would have you be a conscious citizen of this terrible and beautiful world. ~ Ta Nehisi Coates,
1254:Some people majored in English to prepare for law school. Others became journalists. The smartest guy in the honors program, Adam Vogel, a child of academics, was planning on getting a Ph.D. and becoming an academic himself. That left a large contingent of people majoring in English by default. Because they weren't left-brained enough for science, because history was too try, philosophy too difficult, geology too petroleum-oriented, and math too mathematical - because they weren't musical, artistic, financially motivated, or really all that smart, these people were pursuing university degrees doing something no different from what they'd done in first grade: reading stories. English was what people who didn't know what to major in majored in. ~ Jeffrey Eugenides,
1255:You can tell if a discipline is BS if the degree depends severely on the prestige of the school granting it. I remember when I applied to MBA programs being told that anything outside the top ten or twenty would be a waste of time. On the other hand a degree in mathematics is much less dependent on the school (conditional on being above a certain level, so the heuristic would apply to the difference between top ten and top two thousand schools). The same applies to research papers. In math and physics, a result posted on the repository site arXiv (with a minimum hurdle) is fine. In low-quality fields like academic finance (where papers are usually some form of complicated storytelling), the “prestige” of the journal is the sole criterion. ~ Nassim Nicholas Taleb,
1256:I can’t talk about our love story, so I will talk about math. I am not a mathematician, but I know this: There are infinite numbers between 0 and 1. There’s .1 and .12 and .112 and an infinite collection of others. Of course, there is a bigger infinite set of numbers between 0 and 2, or between 0 and a million. Some infinities are bigger than other infinities. A writer we used to like taught us that. There are days, many of them, when I resent the size of my unbounded set. I want more numbers than I’m likely to get, and God, I want more numbers for Augustus Waters than he got. But, Gus, my love, I cannot tell you how thankful I am for our little infinity. I wouldn’t trade it for the world. You gave me a forever within the numbered days, and I’m grateful. ~ John Green,
1257:I can’t talk about our love story, so I will talk about math. I am not a mathematician, but I know this: There are infinite numbers between 0 and 1. There’s .1 and .12 and .112 and an infinite collection of others. Of course, there is a bigger infinite set of numbers between 0 and 2, or between 0 and a million. Some infinities are bigger than other infinities. A writer we used to like taught us that. There are days, many of them, when I resent the size of any unbounded set. I want more numbers than I’m likely to get, and God, I want more numbers for Augustus Waters than he got. But, Gus, my love, I cannot tell you how thankful I am for our little infinity. I wouldn't trade it for the world. You gave me a forever within the numbered days, and I’m grateful. ~ John Green,
1258:I can’t talk about our love story, so I will talk about math. I am not a mathematician, but I know this: There are infinite numbers between 0 and 1. There’s .1 and .12 and .112 and an infinite collection of others. Of course, there is a bigger infinite set of numbers between 0 and 2, or between 0 and a million. Some infinities are bigger than other infinities. A writer we used to like taught us that. There are days, many of them, when I resent the size of my unbounded set. I want more numbers than I’m likely to get, and God, I want more numbers for Augustus Waters than he got. But, Gus, my love, I cannot tell “you how thankful I am for our little infinity. I wouldn’t trade it for the world. You gave me a forever within the numbered days, and I’m grateful. ~ John Green,
1259:Kelvin, let’s open the lower hatches, we can shout to it
down there, below, maybe it’ll hear us? But what’s its name? Think about it, we’ve
named all the stars and the planets, but maybe they already had names? Such arrogance! Come on, let’s go down there. We can call out to it. . . tell it what it’s turned
us into, it’ll be appalled. . . it’ll build us some silver symmetriads and pray for us in
its own math, and throw bloody angels at us, and its suffering will be our suffering,
its fear our fear, and it’ll beg us for an end. Because everything it is and everything
it does is a plea for an end. Why are you not laughing? I’m just joking around. If we
had more of a sense of humor as a race, things might not have gone this far. ~ Stanis aw Lem,
1260:...he would tell stories about the Holy City, about Solomon, a just king, a poet-king, a monarch with a thousand concubines. We weren't quite sure what concubines were, but we guessed: a concubine ... Concubines! One thousand! One thousand women in all colours and shapes - but all of them sexy, of course - one thousand - one thousand raving beauties lying side by side on a bed (what a bed! How wide it must have been!), all of them smiling, all of them reaching out their arms, all of them saying something in Hebrew - but the meaning was unmistakeable - "Come here, sweety." One thousand women. If one were to spend twenty, or fifteen minutes with each one of them, how long would it take to...? A problem that our math teacher never assigned us for homework...! ~ Moacyr Scliar,
1261:When you talk to the experts about developing new technology to provide clean drinking water for the developing world, they’ll tell you that—with four billion people making less than two dollars a day—there’s no viable business model, no economic model, and no way to finance development costs. But the twenty-five poorest countries already spend twenty percent of their GDP on water. This twenty percent, about thirty cents, ain’t much, but do the math again: four billion people spending thirty cents a day is a $1.2 billion market every day. It’s $400 billion a year. I can’t think of too many companies in the world that have $400 billion in sales a year. And you don’t have to do a market study to find out whether there’s a need. It’s water. There’s a need! ~ Peter H Diamandis,
1262:Researchers have confirmed what porn producers already know: men tend to get turned on by images depicting an environment in which sperm competition is clearly at play (though few, we imagine, think of it in quite these terms). Images and videos showing one woman with multiple males are far more popular on the Internet and in commercial pornography than those depicting one male with multiple females.14 A quick peek at the online offerings at Adult Video Universe lists over nine hundred titles in the Gangbang genre, but only twenty-seven listed under Reverse Gangbang. You do the math. Why would the males in a species that’s been wearing the shackles of monogamy for 1.9 million years be sexually excited by scenes of groups of men ejaculating with one or two women? ~ Christopher Ryan,
1263:Certainly she can't and won't measure what is measureless, what neither terminates nor repeats, what is beyond even the transcendental of π - though HE doesn't think so - what is beyond polynomials and quadratic formulas, beyond the rational and irrational, the humanist and the logical, beyond the minds of the Cantors and the Dedekinds, the Renaissance philosophers and the Indian Tantrists, what falls instead into the realm of gods and kinds, of myth, of dawn of man, of the mystery of mankind - that there is a space inside her designed solely for him and despite clear Euclidian impossibilities not only does everything, in plenary excess, cleave like it's meant to, but it makes her feel what math cannot explain, what science cannot explain. What nothing can explain. ~ Paullina Simons,
1264:The modified Mozart used by Tomatis, Paul, iLs, and others over time in an individualized therapy must be distinguished from claims made in the media in the 1990s that mothers could raise the IQ of their children by having them briefly listen to unfiltered Mozart. This claim was based on a study not of mothers and babies but of college students who listened to Mozart ten minutes a day and improved IQ scores on spatial reasoning tests—an effect that lasted only ten to fifteen minutes! Hype aside, different studies by Gottfried Schlaug, Christo Pantev, Laurel Trainor, Sylvain Moreno, and Glenn Schellenberg have shown that sustained music training, such as learning to play an instrument, can lead to brain change, enhance verbal and math skills, and even modestly increase IQ.] ~ Norman Doidge,
1265:American students, we are told, are falling behind in reading and math; on test after test, they score below most European students (at the level of Lithuania), and the solution, rather than seeking to engage their curiosity, has been testing and more testing— a dry and brittle method that produces lackluster results. And so resources are pulled from the “soft” fields that are not being tested. Music teachers are being fired or not replaced; art classes are quietly dropped from the curriculum; history is simplified and moralized, with little expectation that any facts will be learned or retained; and instead of reading short stories, poems and novels, students are invited to read train schedules and EPA reports whose jargon could put even the most committed environmentalist to sleep. ~ Azar Nafisi,
1266:I thought you people were supposed to be good at math."
"Yes, my people all do math for fun, while simultaneously dry-cleaning our karate outfits and giving each other manicures and pedicures, all in between our numerous piano and violin recitals," I said, slamming his book shut. "Do you own freaking work. Although I guess that's a completely foreign concept to you, isn't it? Since you've been deep-throating a silver spoon your whole life."
"That is so hot that you just said that," Camden said, lazily swiggin his Red Bull. "Besides, I'll work one of these days when I have to. I'll either go into real estate like my dad or find some rich old widow who wants...uh...services."
"That doesn't sound like work," I said.
"Of course it is, if she's old," he answered. ~ Cherry Cheva,
1267:Polarization is just one of many ways group membership can change an individual. Perhaps the most striking effect of group membership is that it can modify individuals’ perceptions of themselves. Unable to separate their personal introspection from the ways they believe other people perceive them, teenagers may have what psychologists call an “imaginary audience,” meaning they believe that other people are just as attuned to their appearance and behavior as they are (cue any pimple cream commercial). These perceptions can affect various aspects of their lives. For example, psychologists found that when Asian girls were subtly reminded about their Asian identity, they performed better on math tests. When they were subtly reminded about their gender, however, they performed worse. ~ Alexandra Robbins,
1268:If we step back from the progressive argument and put it in any other context, its absurdity immediately becomes apparent. Imagine if I were to say to my daughter, who got a high score on the SAT, “You don’t deserve your scores at all. You didn’t build that. After all, young lady, you had teachers who helped you with vocabulary and math. Moreover, you took the public roads to the test. Had your car been held up along the way or caught fire, you would count on the services of the police and the fire department. So society deserves a large part of the credit for those scores. They don’t reflect your accomplishment but society’s accomplishment.” If I said this I am sure my daughter would think I was talking like an insane person. In fact, of course, I would be talking like a progressive. ~ Dinesh D Souza,
1269:So you open your mouth and listen to yourself say, “I want eight thousand a day. Plus expenses.”

This is the polite, industry-standard way of saying “piss off, I’m not interested.” You did the math over your morning coffee: You want to earn 100K a year, what with those bonuses you’ve been pulling on top of your salary. (Besides, a euro doesn’t buy what it used to.) There are 250 working days in a year, and a contractor works for roughly 40 per cent of the time, so you need to charge yourself out at 2.5 times your payroll rate, or 1000 a day in order to meet your target. Not interested in the job? Pitch unrealistically high. You never know…

“Done,” says Mr. Pin-Stripe, staring at you expressionlessly. And it is at that point that you realize you are well and truly fucked. ~ Charles Stross,
1270:There were many deficits in our swamp education, but Grandpa Sawtooth, to his credit, taught us the names of whole townships that had been forgotten underwater. Black pioneers, Creek Indians, moonshiners, women, 'disappeared' boy soldiers who deserted their army camps. From Grandpa we learned how to peer beneath the sea-glare of the 'official, historical' Florida records we found in books. "Prejudice," as defined by Sawtooth Bigtree, was a kind of prehistoric arithmetic--a "damn, fool math"--in which some people counted and others did not. It meant white names on white headstones in the big cemetery in Cypress Point, and black and brown bodies buried in swamp water.

At ten, I couldn't articulate much but I got the message: to be a true historian, you had to mourn amply and well. ~ Karen Russell,
1271:So there are no ill effects?” I asked.
“Well, as I said, you could die.”
I looked him in the eye, my one good eye flicking back and forth between the two of his.
“So, if you had to give me odds for living another forty years, say until I was seventy, what would the odds be?”
“I’m not very good at that sort of thing.”
“Ten to one? One hundred to one?”
“I’ve never really understood what that means,” he said.
“Just give me the odds.”
“Of you living till you’re seventy?” he said. “I’d say it’s thirty-five, seventy-five.”
I shook my head. Dr. Owen and his nineteenth-century frame, blunt disregard for my need to be reassured and fucked-up math was too much. This man was making my world small. I imagined he was a moon who had just eclipsed me.
- "Bicycle Kick ~ Jonathan Messinger,
1272:The Debt Snowball method requires you to list all your debts in order of smallest payoff balance to largest. List all your debts except your home; we will get to it in another step. List all of your debts—even loans from Mom and Dad or medical debts that have zero interest. I don’t care if there is interest or not. I don’t care if some have 24 percent interest and others 4 percent. List the debts smallest to largest! If you were so fabulous with math, you wouldn’t have debt, so try this my way. The only time to pay off a larger debt sooner than a smaller one is some kind of big-time emergency such as owing the IRS and having them come after you, or in situations where there will be a foreclosure if you don’t pay it off. Otherwise, don’t argue about it; just list the debts smallest to largest. ~ Dave Ramsey,
1273:Lao-tzu advised, “As soon as you have a thought, laugh at it,” because reality is not what we think. We perceive the world through a window colored by beliefs, interpretations, and associations. We see things not as they are but as we are. The same brain that enables us to contemplate philosophy, solve math equations, and create poetry also generates a stream of static known as discursive thoughts, which seem to arise at random, bubbling up into our awareness. Such mental noise is a natural phenomenon, no more of a problem than the dreams that appear in the sleep state. Therefore, our schooling aims not to struggle with random thoughts but to transcend them in the present moment, where no thoughts exist, only awareness. Our mind’s liberation awaits not in some imagined future but here and now. ~ Dan Millman,
1274:The Bluebook is an absurdity, but it endures, in fact thrives, impervious to criticism and ridicule. The judiciary navigates the sea of modernity, slowed, thrown of course, by the barnacles of legal formalism (semantic escapes from reality, impoverished sense of context, fear of math and science, insensitivity to language and culture, mangling of history, superfluous footnotes, verbosity, excessive quotation, reader-unfriendly prose, exaggeration, bluster, obsession with citation form) – an accumulation of many centuries, yet constantly augmented. There is little desire to give the hull a good scraping. There is fear that the naked hull would be unslightly, even unseaworthy. The fear is overblown. A week after all the copies of the Bluebook were burned, their absence would not be noticed. ~ Richard A Posner,
1275:School is a terrible place, I have decided. There is nothing good about it except for math class. Everything else is a total waste of time. As I mentioned before I have done a lot of reading about prisons, and I notice that they always describe them as painted in very dull colors, and my school is also painted in these kinds of colors, with greenish lockers and brownish walls and grayish floors. Actually they recently fixed up one wing of the school, and now that part of the school is just the opposite—all the colors are really bright, with bright red and yellow lockers and blue doors and shiny white floors that are already all scuffed up. It's funny because I thought the other colors were terrible but these are much worse, because they make it seem like it's normal to be happy there when it isn't. ~ Dara Horn,
1276:Stanford University's psychologist Carol Dweck and her colleagues have discovered that what you believe about intellectual ability—whether you think it's a fixed gift, or an earned ability that can be developed—makes a difference to your behavior, persistence, and performance. Students who see ability as fixed—as a gift—are more vulnerable to setbacks and difficulties. And stereotypes, as Dweck rightly points out, "are stories about gifts—who has them and who doesn't." Dweck and her colleagues are shown that when students are encouraged to see math ability as something that grows with effort—pointing out, for example, that the brain forges new connections and develops better ability every time they practice a task—grades improve and gender gaps diminish (relative to groups given control interventions). ~ Cordelia Fine,
1277:I have no problem with being fabulous. My problem comes when you won't allow yourself to be an ordinary woman with a decent apartment and an okay job. When only the mom is allowed to be boring—because her life is so rich with meaning.

When I carefully choreographed the story of how amazing I was, I was acting like one of those helicopter parents—you know, the ones who refuse to admit that their Jackson might suck at math or Stella might not be the world's greatest violinist. 'You are special! You are special!' they cry to their children, hoping this will boost their confidence. But the real message is one of panic: You must be special. Ordinary is not okay. When I walked into a party projecting the Shiny Girl—she of the lighthearted flings and glitzy job—I was essentially doing the same thing. ~ Sara Eckel,
1278:Many people who celebrate the arts and the humanities, who applaud vigorously the tributes to their importance in our schools, will proclaim without shame (and sometimes even joke) that they don’t understand math or physics. They extoll the virtues of learning Latin, but they are clueless about how to write an algorithm or tell BASIC from C++, Python from Pascal. They consider people who don’t know Hamlet from Macbeth to be Philistines, yet they might merrily admit that they don’t know the difference between a gene and a chromosome, or a transistor and a capacitor, or an integral and a differential equation. These concepts may seem difficult. Yes, but so, too, is Hamlet. And like Hamlet, each of these concepts is beautiful. Like an elegant mathematical equation, they are expressions of the glories of the universe. ~ Walter Isaacson,
1279:The reality is that most of us grow up strapped in an educational system that favors obedience over independent thinking. We’re rewarded for trusting authority, and punished for challenging it. We focus on memorizing the stuff other people came up with—formulas in math, grammar rules in English, theories in physics, cell functions in biology—rather than grasping the logic behind our most important breakthroughs and tracing the footsteps of their discovery. We answer test questions with what we think our teacher wants to hear. We chase grades instead of knowledge. And worst of all, we leave the classroom woefully unequipped with the thinking skills that matter most: how to balance open-mindedness with skepticism, how to identify bias, and how to challenge assumptions—including our own—in a way that’s truly objective. ~ Denise Minger,
1280:I’m smart, right? I should be able to come up with a solid plan as to how I can get back to the twenty-first century.
The trouble is I’m lost without Wikipedia and Google. I know all sorts of things, of course, but none of it is useful: the periodic table of elements, how to factor a math equation with four different variables, the symbiotic relationship between the great white shark and the remora fish. Completely useless, random information.
Even a year of advanced chemistry isn’t going to do me any good; it’s not like there’s a chapter in there about time travel.
I get up off the bed and creep to the door and peek out. No one is around.
I’ll just explore the house. Maybe there really is a phone hidden somewhere that will prove Emily is lying about 1815. Or maybe I’ll find a servant in some Old Navy jeans. ~ Mandy Hubbard,
1281:And yet sometimes she worried about what those musty old books were doing to her. Some people majored in English to prepare for law school. Others became journalists. The smartest guy in the honors program, Adam Vogel, a child of academics, was planning on getting a Ph.D. and becoming an academic himself. That left a large contingent of people majoring in English by default. Because they weren't left-brained enough for science, because history was too dry, philosophy too difficult, geology too petroleum-oriented, and math too mathematical--because they weren't musical, artistic, financially motivated, or really all that smart, these people were pursuing university degrees doing something no different from what they'd done in first grade: reading stories. English was what people who didn't know what to major in majored in. ~ Jeffrey Eugenides,
1282:FROM THE AIR there seems to be a system: recognizable designs, networks on the desert floor. Crosshatches of ridge and fissure. Lines that fan out from the source. The shadow of the airplane slips across basin and range. Frost forms between the plane’s double windows, each geometric crystal an argument for the stillborn beauty of pure math. Eventually the cut of a road appears, as deep as a fossil in shale. Unbound by destination, a road simply for the sake of moving, however slowly, through miles of nothing. Through the system. The first grid is the strangest, the geometry of better living etched onto the desert floor: identical houses of a planned community pleated around the nucleus of a swimming pool. One and then another, until the desert is paved under streets and scattered with countless pools like a deck of blue cards. ~ Nicole Krauss,
1283:If he would just work with pure ideas like a proper mathematician he could go as fast as thought. As it happens, Alan has become fascinated by the incarnations of pure ideas in the physical world. The underlying math of the universe is like the light streaming in through the window. Alan is not satisfied with merely knowing that it streams in. He blows smoke into the air to make the light visible. He sits in meadows gazing at pine cones and flowers, tracing the mathematical patterns in their structure, and he dreams about electron winds blowing over the glowing filaments and screens of radio tubes, and, in their surges and eddies, capturing something of what is going on in his own brain. Turing is neither a mortal nor a god. He is Antaeus. That he bridges the mathematical and physical worlds is his strength and his weakness. ~ Neal Stephenson,
1284:His voice gentled and his touch became more like a caress. "I love you," he whispered.
"Romeo..."
"I love your glasses, your clumsiness, your wild hair, even the way you snort when you laugh." He smiled. "I love you in spite of yourself, Rim. Can't you love me in spite of myself?"
I couldn't help it, I smiled.
"You do come with a lot of baggage." I sighed. "You're impossibly good-looking, terrible at math, and you like to drink that swill you call beer." I mock shuddered.
He smiled, but I saw the relief in his eyes.
"Me being good-looking is a bad thing?" he teased.
"You have a lot of options," I said seriously. "I'm not the best one."
"No." He agreed. "You're not."
Geez, he could have said it a little nicer.
"You're the only one."
Oh, well, that was much better.

- Romeo & Rimmel ~ Cambria Hebert,
1285:The nautilus shell was exquisite, brown and white and perfectly striped. The math that lay like a dazzling creation spell over all who lived in the sea showed clearly in the spiral, each cell as great as the sum of the two previous sections. Everything in the ocean was a thing of beauty and numbers, even in death.
Mermaids could live for a long time, but their bodies became foam that dissipated into nothing when they died.
The poor little mollusk who lived in this shell had a very short life, but his shell could last for centuries.
Ariel sighed and brushed her fingers over it, feeling strangely melancholy despite the triumph she literally held in her hands. Years of being mute could be swept away in a second. Years of frustration, years of silent crying, years of anger.
And then what?
If she destroyed it, what would it change? ~ Liz Braswell,
1286:When you fear you will confirm a negative stereotype, it can become a self-fulfilling prophecy not because the stereotype is true, but because you can't stop worrying that you could become an example proving it.
This self-fulfilling prophecy, being only a matter of perception, can be easily sublimated. Another study by Steele measured the math abilities of men versus women. When the questions were easy, the women and men performed the same. When they were difficult, the women's scores plummeted lower than did those of their male peers. When they ran the tests again with new participants, but this time before handing out the problems told the subjects that men and women tended to perform equally on the exam, the scores leveled out. The women performed just as well as did the men. The power of the stereotype--women are bad at math--was nullified. ~ David McRaney,
1287:When I left home, Bo was six years old. He was our only child, but we were planning more. The math is easy, and I’ve done it a million times. He’ll be sixteen when I get out, a fully grown teenager, and I will have missed ten of the most precious years a father and son can have. Until they are about twelve years old, little boys worship their fathers and believe they can do no wrong. I coached Bo in T-ball and youth soccer, and he followed me around like a puppy. We fished and camped, and he sometimes went to my office with me on Saturday mornings, after a boys-only breakfast. He was my world, and trying to explain to him that I was going away for a long time broke both our hearts. Once behind bars, I refused to allow him to visit me. As much as I wanted to squeeze him, I could not stand the thought of that little boy seeing his father incarcerated. ~ John Grisham,
1288:He let out a breath. "How old are you?" he asked, fearful of the answer.

"Twenty-five." She gave him a wry smile. "And since you yelled it at Heather, I know you're 'forty fucking years old'."

He would have laughed, but he couldn't breathe. Jesus, he'd known she was young, but hearing her actual age..."That's fifteen years."

"I can do the math, but you know what else? I'm legal. I can drink. I have decent car insurance since I hit the quarter century mark, and I own this house." she paused. "Well the bank owns most of it, but I qualified for a loan and everything since I have decent credit." Her nose wrinkled. "I'm getting off subject. If the age difference truly bothers you, then I will see you at the shop to finish your tattoo. No hard feelings."

He growled softly. Well, something was hard, and it wasn't his feelings. ~ Carrie Ann Ryan,
1289:In terms of funding, Google dwarfs even its own government: U.S. federal funding for math and computer science research amounts to less than half of Google’s own R&D budget. That spending spree has bought Alphabet an outsized share of the world’s brightest AI minds. Of the top one hundred AI researchers and engineers, around half are already working for Google. The other half are distributed among the remaining Seven Giants, academia, and a handful of smaller startups. Microsoft and Facebook have soaked up substantial portions of this group, with Facebook bringing on superstar researchers like Yann LeCun. Of the Chinese giants, Baidu went into deep-learning research earliest—even trying to acquire Geoffrey Hinton’s startup in 2013 before being outbid by Google—and scored a major coup in 2014 when it recruited Andrew Ng to head up its Silicon Valley AI Lab. ~ Kai Fu Lee,
1290:Ida was a planetary woman. She knew—she had seen it proved in math, in words—that the apparent safety of a planet’s solid ground beneath her feet was based on precisely the same physical laws that described the construction of a spaceship, that there was no real difference between the solidity of dirt beneath her feet and the hollowness of sculpted carbon and iron. She knew this for the fact that it was, but Ida Stays was a planetary woman, and it was with a planetary woman’s fear that she froze in the darkness, because Ida did not believe in God, did not believe in any gods at all, only the cold fact of existence and man’s ability to work within the inflexible laws of nature, but somehow she, so human, so unmechanical, somehow she trusted the engineer that had constructed the planets far more than the human ones who had built the ships that flew between them. ~ C A Higgins,
1291:It's the way it works," she said in clipped tones. "For one rise, another must fall."
"But why? Why can't we just rise, and everybody else can stay where they are? I wouldn't care!"
"And you think I would?" Keisha demanded. She glared at me, the visibly pulled herself back. When she exhaled, her nostrils flared. "Say you've taken a math test. Or an English test, since you love books so much. And you get a hundred. You're psyched, right? 'Mom, I got a hundred! I got the highest grade in the class!'" She raised her eyebrows. "But say everybody else gets a hundred, too. Are you still as proud?"
"Of course," I said stubbornly. "I'd still have my A."
"Bullshit. You like your As because other people get Cs. Because that means you're smarted than they are. Better than they are."
"I don't think I'm better than anyone."
"Then you're and idiot. ~ Lauren Myracle,
1292:Taking pity on me, Carissa kept her voice low. “You were calling out for Daemon.”I dropped my face in my hands and moaned. “Oh, God.”
Lesa giggled. “It was kind of cute.”
A minute before the tardy bell rang, I felt an all-too-familiar warmth on my neck and glanced up. Daemon swaggered into class. Textbook-less as usual. He had a notebook, but I don’t think he ever wrote anything in it. I was beginning to suspect our math teacher was an alien, because how else would Daemon get away with not doing a damn thing in class? He passed by without so much as a look.
I twisted around in my chair. “I need to talk to you.”
He slid into his desk chair. “Okay.”
“In private,” I whispered.
His expression didn’t change as he leaned back in his chair. “Meet me in the library at lunch. No one really goes in there. You know, with all those books and stuff. ~ Jennifer L Armentrout,
1293:these models are constructed not just from data but from the choices we make about which data to pay attention to—and which to leave out. Those choices are not just about logistics, profits, and efficiency. They are fundamentally moral. If we back away from them and treat mathematical models as a neutral and inevitable force, like the weather or the tides, we abdicate our responsibility. And the result, as we’ve seen, is WMDs that treat us like machine parts in the workplace, that blackball employees and feast on inequities. We must come together to police these WMDs, to tame and disarm them. My hope is that they’ll be remembered, like the deadly coal mines of a century ago, as relics of the early days of this new revolution, before we learned how to bring fairness and accountability to the age of data. Math deserves much better than WMDs, and democracy does too. ~ Cathy O Neil,
1294:We're constantly judging and grading other parents, just to make sure that they aren't any better than us. I'm as guilty as anyone. I see some lady hand her kid a Nintendo DS at the supermarket and I instantly downgrade that lady to Shitty Parent status. I feel pressure to live up to a parental ideal that no one probably has ever achieved. I feel pressure to raise a group of human beings that will help America kick the shit out of Finland and South Korea in the world math rankings. I feel pressure to shield my kids from the trillion pages of hentai donkey porn out there on the Internet. I feel pressure to make the insane amounts of money needed for a supposedly 'middle-class' upbringing for the kids, an upbringing that includes a house and college tuition and health care and so many other expenses that you have to be a multimillionaire to afford it. PRESSURE PRESSURE PRESSURE. ~ Drew Magary,
1295:We all do it, you know. Distract ourselves from noticing, how time's passing. We throw ourselves into our jobs...We fill up our gas tanks and top off our Metrocards and do the grocery shopping... And then one day, you look in the mirror and see gray hair. One day, you realize there is less of your life left than what you've already lived. And you think, how did this happen so fast ? ...
...When this realization hits, you start doing the math. How much time do I have left? How much can I fit into that small space?
Some of us let this realization guide us... We book trips to Tibet...We try to pretend it's not almost over.
But some of us just fill up our gas tanks and top off our Metrocards..., because if you only see the path, that's right ahead of you, you don't obsess over when the clip might drop off.
Some of us never learn.
And some of us learn earlier than others... ~ Jodi Picoult,
1296:when he was engaged in blue-sky thinking, his science was not a separate endeavor from his art. Together they served his driving passion, which was nothing less than knowing everything there was to know about the world, including how we fit into it. He had a reverence for the wholeness of nature and a feel for the harmony of its patterns, which he saw replicated in phenomena large and small. In his notebooks he would record curls of hair, eddies of water, and whirls of air, along with some stabs at the math that might underlie such spirals. While at Windsor Castle looking at the swirling power of the “Deluge drawings” that he made near the end of his life, I asked the curator, Martin Clayton, whether he thought Leonardo had done them as works of art or of science. Even as I spoke, I realized it was a dumb question. “I do not think that Leonardo would have made that distinction,” he replied. ~ Walter Isaacson,
1297:What's your deal?" I asked in the hallway after class. "I know you did that."

He shrugged. "So?"
... "That was rude, Daemon. You embarrassed him." ... "And I thought using your ... stuff would draw them here?"
... "That was barley a blip on the map. That didn't even leave a trace on anyone."
He lowered his head until the edges of his dark curled brushed my cheek. I was caught between wanting to crawl into my locker or crawl into him. "Besides, I was doing you a favor."
I laughed. "And how was that doing me a favor?"
... "Studying math wasn't what he had in mind."
That was debatable, but I decided to play along ... "And what if that's the case?"
"You like Simon?" His chin jerked up, anger flashing in his emerald eyes. "You can't possibly like him."
... "Are you jealous? ... Your jealous of Simon?" I lowered my voice. "Of a human? For shame, Daemon. ~ Jennifer L Armentrout,
1298:Montessori believed that if children were exposed to a safe, experiential learning environment (as opposed to a structured classroom), with access to specific learning materials and supplies, and if they were supervised by a gentle and attentive teacher, they would become self-motivated to learn. She discovered that, in this environment, older children readily worked with younger children, helping them to learn from, and cooperate with, each other. Montessori advocated teaching practical skills, like cooking, carpentry, and domestic arts, as an integrated part of a classical education in literature, science, and math. To her surprise, teenagers seemed to benefit from this approach the most; it built confidence, and the students became less resistant to traditional educational goals. Through this method, each child could reach his or her potential, regardless of age and intellectual ability. ~ Kate Clifford Larson,
1299:Many school programs seem to offer either The Cultural Literacy Track or The Vocational Track. The Cultural Literacy programs are designed for the “smart kids” who are going to go on to ever-higher levels of both education and financial success. This track, with no pretense of being real world, includes classes on classics, foreign languages, and math theory (such as calculus). It is a curriculum based on “teach what has been taught.” The Vocational programs are for the “remedial kids” who are going to have only blue-collar futures if they are in high school (taking classes such as wood working) or inflexible paraprofessional paths if they are in college (such as degrees in physical therapy). This two-tier approach is an immoral sorting system with crippling consequences. Maybe worse, it also presents a false dichotomy. Instead, true wisdom comes from a synthesis of those two perspectives and more. The ~ Clark Aldrich,
1300:Even as our world is being daily transformed by breathtaking innovations in science and technology, many people continue to imagine that math and science are mostly a matter of memorizing formulas to get “the right answer.” Even engineering, which is in fact the process of creating something from scratch or putting things together in novel and non-self-evident ways, is perplexingly viewed as a mechanical or rote subject. This viewpoint, frankly, could only be held by people who never truly learned math or science, who are stubbornly installed on one side of the so-called Two Culture divide. The truth is that anything significant that happens in math, science, or engineering is the result of heightened intuition and creativity. This is art by another name, and it’s something that tests are not very good at identifying or measuring. The skills and knowledge that tests can measure are merely warm-up exercises. ~ Salman Khan,
1301:At the end of our lives, He is going to look into hearts. What is it He will find there, I wonder? Will he find that we used the geography lesson, the dreaded math test, the teetering laundry pile and the boiling-over pot of soup to draw closer to Him? Did we use these gifts to teach our children to lift their eyes heavenward? Were the tedious details of a homeschooling day offered up as a way for us to love Him, or were they merely gotten through, checked off and accomplished? Did we even realize that every Monday, every Thursday, we were standing on holy ground? No task is too trivial, no assignment too small. Educating our children is an offering of love we make to the God Who was so gracious to bestow them upon us in the first place. Every moment of the daily grind in raising and teaching and loving on them is hallowed, because we do it for Him and because there would be no point of doing it without Him. ~ Sarah Mackenzie,
1302:So, in one slightly technical line, here's the mathematical skinny. There's an equation in string theory that has a contribution of the form (D-10) times (Trouble), where D represents the number of spacetime dimensions and Trouble is a mathematical expression resulting in troublesome physical phenomena, such as the violation of energy conservation mentioned above. As to why the equation takes this precise form, I can't offer any intuitive, nontechnical explanation. But if you do the calculation, that's where the math leads. Now, this simple but key observation is that if the number of spacetime dimensions is ten, not the four we expect, the contribution becomes 0 times Trouble. And since 0 times anything is 0, in a universe with ten spacetime dimensions the trouble gets wiped away. That's how the math plays out. Really. And that's why string theorists argue for a universe with more than four spacetime dimensions. ~ Brian Greene,
1303:It is perfectly all right for modern evolutionary biologists to explain just the patterns of living creatures, and not the “evolution” of stars or the “evolution” of technology. Alas, some unfortunate souls use the same word “evolution” to cover the naturally selected patterns of replicating life, and the strictly accidental structure of stars, and the intelligently configured structure of technology. And as we all know, if people use the same word, it must all be the same thing. We should automatically generalize anything we think we know about biological evolution to technology. Anyone who tells us otherwise must be a mere pointless pedant. It couldn’t possibly be that our ignorance of modern evolutionary theory is so total that we can’t tell the difference between a carburetor and a radiator. That’s unthinkable. No, the other person—you know, the one who’s studied the math—is just too dumb to see the connections. ~ Eliezer Yudkowsky,
1304:Anyway.
I’m not allowed to watch TV, although I am allowed to rent documentaries that are approved for me, and I can read anything I want. My favorite book is A Brief History of Time, even though I haven’t actually finished it, because the math is incredibly hard and Mom isn’t good at helping me. One of my favorite parts is the beginning of the first chapter, where Stephen Hawking tells about a famous scientist who was giving a lecture about how the earth orbits the sun, and the sun orbits the solar system, and whatever. Then a woman in the back of the room raised her hand and said, “What you
have told us is rubbish. The world is really a flat plate supported on the back
of a giant tortoise.” So the scientist asked her what the tortoise was standing
on. And she said, “But it’s turtles all the way down!”
I love that story, because it shows how ignorant people can be. And also because I love tortoises. ~ Jonathan Safran Foer,
1305:Hanging Fire
I am fourteen
and my skin has betrayed me
the boy I cannot live without
still sucks his thumb
in secret
how come my knees are
always so ashy
what if I die
before morning
and momma's in the bedroom
with the door closed.
I have to learn how to dance
in time for the next party
my room is too small for me
suppose I die before graduation
they will sing sad melodies
but finally
tell the truth about me
There is nothing I want to do
and too much
that has to be done
and momma's in the bedroom
with the door closed.
Nobody even stops to think
about my side of it
I should have been on Math Team
my marks were better than his
why do I have to be
the one
wearing braces
I have nothing to wear tomorrow
will I live long enough
to grow up
and momma's in the bedroom
with the door closed.
19
~ Audre Lorde,
1306:My father was neither an ally nor a confidant, but it seemed backward to me that this hardworking man would be relegated to the sofa while my lazy mother got the king-size bed. I resented her for that, but she seemed immune to guilt and shame. I think she got away with so much because she was beautiful. She looked like Lee Miller if Lee Miller had been a bedroom drunk. I assume she blamed my father for ruining her life—she got pregnant and dropped out of college to marry him. She didn’t have to, of course. I was born in August 1973, seven months after Roe v. Wade. Her family was the country club brand of alcoholic Southern Baptists—Mississippi loggers on one side, Louisiana oilmen on the other—or else, I assumed, she would have aborted me. My father was twelve years older than my mother. She’d been just nineteen years old and already four months pregnant when they got married. I’d figured that out as soon as I could do the math. ~ Ottessa Moshfegh,
1307:But at some point Tengo noticed that returning to reality from the world of a novel was not as devastating a blow as returning from the world of mathematics. Why should that have been? After much deep thought, he reached a conclusion. No matter how clear the relationships of things might become in the forest of story, there was never a clear-cut solution. That was how it differed from math. The role of a story was, in the broadest terms, to transpose a single problem into another form. Depending on the nature and direction of the problem, a solution could be suggested in the narrative. Tengo would return to the real world with that suggestion in hand. It was like a piece of paper bearing the indecipherable text of a magic spell. At times it lacked coherence and served no immediate practical purpose. But it would contain a possibility. Someday he might be able to decipher the spell. That possibility would gently warm his heart from within. ~ Anonymous,
1308:A part of Jutta does not want to take the letter. Does not want to hear what this huge man has traveled a long way to say. Weeks go by when Jutta does not allow herself to think of the war, of Frau Elena, of the awful last months in Berlin. Now she can buy pork seven days a week. Now, if the house feels cold she twists a dial in the kitchen, and voilà. She does not want to be one of those middle-aged women who thinks of nothing but her own painful history. Sometimes she looks at the eyes of her older colleagues and wonders what they did when the electricity was out, when there were no candles, when the rain came through the ceiling. What they saw. Only rarely does she loosen the seals enough to allow herself to think of Werner. In many ways, her memories of her brother have become things to lock away. A math teacher at Helmholtz-Gymnasium in 1974 does not bring up a brother who attended the National Political Institute of Education at Schulpforta. ~ Anthony Doerr,
1309:I need wonder. I know that death is coming. I smell it in the wind, read it in the paper, watch it on television, and see it on the faces of the old. I need wonder to explain what is going to happen to me, what is going to happen to us when this thing is done, when our shift is over and our kids' kids are still on the earth listening to their crazy rap music. I need something mysterious to happen after I die. I need to be somewhere else after I die, somewhere with God, somewhere that wouldn't make any sense if it were explained to me right now. At the end of the day, when I am lying in bed and I know the chances of any of our theology being exactly right are a million to one, I need to know that God has things figured out, that if my math is wrong we are still going to be okay. And wonder is that feeling we get when we let go of our silly answers, our mapped out rules that we want God to follow. I don't think there is any better worship than wonder. ~ Donald Miller,
1310:Education is one of the Grand Christianson Obsessions. They’ve been whole years my mother’s kept us home for intensive private study. As a result of that, Paul will perform the first brain transplant, James will someday build a bridge across the Atlantic Ocean, Charlie – who is an actual musical genius – will probably end up writing the Great American Symphony, and I – I know a little bit about a lot of things.
I can tell you the chemical composition of the stuff your stick in your hair; how long it would take you, at just under the speed of light, to get to Alpha Centauri – and how old your body would be when you finally got there; the middle name of the third president of the United States; the amount of the present budget deficit; the author of the Brothers Karamazov, and how many feet there are in a line of trochaic heptameter. The Little Girl Who Had to Know Why, Paul used to call me. But even my mother couldn’t reconcile me and math. ~ Kristen D Randle,
1311:The primary math of the real world is one and one equals two. The layman (as, often, do I) swings that every day. He goes to the job, does his work, pays his bills and comes home. One plus one equals two. It keeps the world spinning. But artists, musicians, con men, poets, mystics and such are paid to turn that math on its head, to rub two sticks together and bring forth fire. Everybody performs this alchemy somewhere in their life, but it’s hard to hold on to and easy to forget. People don’t come to rock shows to learn something. They come to be reminded of something they already know and feel deep down in their gut. That when the world is at its best, when we are at our best, when life feels fullest, one and one equals three. It’s the essential equation of love, art, rock ’n’ roll and rock ’n’ roll bands. It’s the reason the universe will never be fully comprehensible, love will continue to be ecstatic, confounding, and true rock ’n’ roll will never die. ~ Bruce Springsteen,
1312:The primary math of the real world is one and one equals two. The layman (as, often, do I) swings that every day. He goes to the job, does his work, pays his bills and comes home. One plus one equals two. It keeps the world spinning. But artists, musicians, con men, poets, mystics and such are paid to turn that math on its head, to rub two sticks together and bring forth fire. Everybody performs this alchemy somewhere in their life, but it’s hard to hold on to and easy to forget. People don’t come to rock shows to learn something. They come to be reminded of something they already know and feel deep down in their gut. That's when the world is at its best, when we are at our best, when life feels fullest, one and one equals three. It’s the essential equation of love, art, rock ’n’ roll and rock ’n’ roll bands. It’s the reason the universe will never be fully comprehensible, love will continue to be ecstatic, confounding, and true rock ’n’ roll will never die. ~ Bruce Springsteen,
1313:In one study, elite violinists had separated themselves from all others by each accumulating more than 10,000 hours of practice by age 20. Thus the rule. Many elite performers complete their journey in about ten years, which, if you do the math, is an average of about three hours of deliberate practice a day, every day, 365 days a year. Now, if your ONE Thing relates to work and you put in 250 workdays a year (five days a week for 50 weeks), to keep pace on your mastery journey you’ll need to average four hours a day. Sound familiar? It’s not a random number. That’s the amount of time you need to time block every day for your ONE Thing. More than anything else, expertise tracks with hours invested. Michelangelo once said, “If the people knew how hard I had to work to gain my mastery, it wouldn’t seem wonderful at all.” His point is obvious. Time on a task, over time, eventually beats talent every time. I’d say you can “book that,” but actually you should “block it. ~ Gary Keller,
1314:I occasionally return to some very basic, mathematical thoughts: There are only so many letters in our Roman alphabet. It is then by the power of the math—the infinite (or not strictly infinite, but huge) number of combinations of letters—that we have so many words. But then, further expanding the number of possibilities, truly to infinity, one word (one combination of letters) can have multiple meanings. Further multiplying the number of meanings, even within one given dictionary definition of a word, is the effect of its context, both immediate and larger, which can endow it with, again, an infinite number of subtly differing shades of meaning. Further enriching the single word, within and beyond its contexts, is one’s own personal associations with it, either from one’s reading or from one’s life experiences. And even in one’s own native language, there are a great many words, meanings, and shades of meaning that one simply doesn’t know and may never encounter. ~ John Freeman,
1315:Retirement as a goal or final redemption is flawed for at least three solid reasons: a. It is predicated on the assumption that you dislike what you are doing during the most physically capable years of your life. This is a nonstarter—nothing can justify that sacrifice. b. Most people will never be able to retire and maintain even a hotdogs-for-dinner standard of living. Even one million is chump change in a world where traditional retirement could span 30 years and inflation lowers your purchasing power 2–4% per year. The math doesn’t work.3 The golden years become lower-middle-class life revisited. That’s a bittersweet ending. c. If the math does work, it means that you are one ambitious, hardworking machine. If that’s the case, guess what? One week into retirement, you’ll be so damn bored that you’ll want to stick bicycle spokes in your eyes. You’ll probably opt to look for a new job or start another company. Kinda defeats the purpose of waiting, doesn’t it? ~ Timothy Ferriss,
1316:The Wife Of The Mind
Sharecroppers' child, she was more schooled
In slaughtering pigs and coaxing corn out of
The ground than in the laws of Math, the rules
Of Grammar. Seventeen, she fell in love
With the senior quarterback, and nearly
Married him, but—the wedding just a week
Away—drove her trousseau back to Penney's,
Then drove on past sagging fences, flooding creeks,
And country bars to huge Washington State,
Where, feeling like a hick, she studied French to compensate.
She graduated middle-of-her-class,
Managed a Senior Center while she flailed
Away at an M.A., from the morass
Of which a poet/rock-singer from Yale
Plucked her. He loved her practicality;
She adored his brilliance. Sex was great.
They married in a civil ceremony.
He played around, for which she berated
Herself, telling friends things were "hunky-dory."
Resentment grew... oh, you said "life"? That's another story.
~ Charles Harper Webb,
1317:When you add in the US immigration processes encouraging a “brain drain” of elites from countries like China and India, the vast majority of the “academic success” we see when we think of Asian Americans is only available to wealthy, highly skilled immigrants who already have a high level of education, and their offspring—while only 17 percent of Pacific Islanders, 14 percent of Cambodian Americans, and 13 percent of Laotian and Hmong Americans have four-year college degrees,4 compared to 22 percent of black Americans and 15 percent of Hispanic Americans.5 The stereotype that Asian Americans naturally excel at math and science also discourages Asian American students from pursuing careers in the arts and humanities and keeps those who do pursue those careers from being taken seriously in their fields. A 2009 census report showed that under 15 percent of Asian American degree holders majored in the arts and humanities, less than any other racial or ethnic group in America.6 ~ Ijeoma Oluo,
1318:Jane Russell! My physical therapist had never heard of her. “Gentlemen Prefer Blondes,” I said. “Not in my experience,” she replied. Bina’s younger; perhaps that’s it. All this was earlier today; before I could argue with her, she laced one of my legs over the other, capsized me onto my right side. The pain left me breathless. “Your hamstrings need this,” she assured me. “You bitch,” I gasped. She pressed my knee to the floor. “You’re not paying me to go easy on you.” I winced. “Can I pay you to leave?” Bina visits once a week to help me hate life, as I like to say, and to provide updates on her sexual adventures, which are about as exciting as my own. Only in Bina’s case it’s because she’s picky. “Half the guys on these apps are using five-year-old photos,” she’ll complain, her waterfall of hair poured over one shoulder, “and the other half are married. And the other half are single for a reason.” That’s three halves, but you don’t debate math with someone who’s rotating your spine. ~ A J Finn,
1319:The consequence model, the logical one, the amoral one, the one which refuses any divine intervention, is a problem really for just the (hypothetical) logician. You see, towards God I would rather be grateful for Heaven (which I do not deserve) than angry about Hell (which I do deserve). By this the logician within must choose either atheism or theism, but he cannot possibly through good reason choose anti-theism. For his friend in this case is not at all mathematical law: the law in that 'this equation, this path will consequently direct me to a specific point'; over the alternative and the one he denies, 'God will send me wherever and do it strictly for his own sovereign amusement.' The consequence model, the former, seeks the absence of God, which orders he cannot save one from one's inevitable consequences; hence the angry anti-theist within, 'the logical one', the one who wants to be master of his own fate, can only contradict himself - I do not think it wise to be angry at math. ~ Criss Jami,
1320:I really wondered why people were always doing what they didn't like doing. It seemed like life was a sort of narrowing tunnel. Right when you were born, the tunnel was huge. You could be anything. Then, like, the absolute second after you were born, the tunnel narrowed down to about half that size. You were a boy, and already it was certain you wouldn't be a mother and it was likely you wouldn't become a manicurist or a kindergarten teacher. Then you started to grow up and everything you did closed the tunnel in some more. You broke your arm climbing a tree and you ruled out being a baseball pitcher. You failed every math test you ever took and you canceled any hope of being a scientist. Like that. On and on through the years until you were stuck. You'd become a baker or a librarian or a bartender. Or an accountant. And there you were. I figured that on the day you died, the tunnel would be so narrow, you'd have squeezed yourself in with so many choices, that you just got squashed. ~ Carol Rifka Brunt,
1321:Life is more than a job; jobs are more than a paycheck; and a country is more than its wealth. Education is more than the acquisition of marketable skills, and you are more than your ability to contribute to your employer’s bottom line or the nation’s GDP, no matter what the rhetoric of politicians or executives would have you think. To ask what college is for is to ask what life is for, what society is for—what people are for. Do students ever hear this? What they hear is a constant drumbeat, in the public discourse, that seeks to march them in the opposite direction. When policy makers talk about higher education, from the president all the way down, they talk exclusively in terms of math and science. Journalists and pundits—some of whom were humanities majors and none of whom are nurses or engineers—never tire of lecturing the young about the necessity of thinking prudently when choosing a course of study, the naïveté of wanting to learn things just because you’re curious about them. ~ William Deresiewicz,
1322:A healthy night’s sleep can indeed boost learning significantly. Sleep scientists debate how we should define learning, and what exactly is improvement. But there are many examples of the phenomenon. One study stands out in particular. Students were given a series of math problems and prepped with a method to solve them. The students weren’t told there was also an easier “shortcut” way to solve the problems, potentially discoverable while doing the exercise. The question was: Is there any way to jump-start, even speed up, the insight into the shortcut? The answer was yes, if you allow them to sleep on it. If you let 12 hours pass after the initial training and ask the students to do more problems, about 20 percent will have discovered the shortcut. But, if in that 12 hours you also allow eight or so hours of regular sleep, that figure triples to about 60 percent. No matter how many times the experiment is run, the sleep group consistently outperforms the non-sleep group about three to one. Sleep ~ John Medina,
1323:Women, on the other hand, had to wield their intellects like a scythe, hacking away against the stubborn underbrush of low expectations. A woman who worked in the central computing pools was one step removed from the research, and the engineers’ assignments sometimes lacked the context to give the computer much knowledge about the afterlife of the numbers that bedeviled her days. She might spend weeks calculating a pressure distribution without knowing what kind of plane was being tested or whether the analysis that depended on her math had resulted in significant conclusions. The work of most of the women, like that of the Friden, Marchant, or Monroe computing machines they used, was anonymous. Even a woman who had worked closely with an engineer on the content of a research report was rarely rewarded by seeing her name alongside his on the final publication. Why would the computers have the same desire for recognition that they did? many engineers figured. They were women, after all. As ~ Margot Lee Shetterly,
1324:Public schools were not only created in the interests of industrialism—they were created in the image of industrialism. In many ways, they reflect the factory culture they were designed to support. This is especially true in high schools, where school systems base education on the principles of the assembly line and the efficient division of labor. Schools divide the curriculum into specialist segments: some teachers install math in the students, and others install history. They arrange the day into standard units of time, marked out by the ringing of bells, much like a factory announcing the beginning of the workday and the end of breaks. Students are educated in batches, according to age, as if the most important thing they have in common is their date of manufacture. They are given standardized tests at set points and compared with each other before being sent out onto the market. I realize this isn’t an exact analogy and that it ignores many of the subtleties of the system, but it is close enough. ~ Ken Robinson,
1325:I do feel that literature should be demystified. What I object to is what is happening in our era: literature is only something you get at school as an assignment. No one reads for fun, or to be subversive or to get turned on to something. It's just like doing math at school. I mean, how often do we sit down and do trigonometry for fun, to relax. I've thought about this, the domination of the literary arts by theory over the past 25 years -- which I detest -- and it's as if you have to be a critic to mediate between the author and the reader and that's utter crap. Literature can be great in all ways, but it's just entertainment like rock'n'roll or a film. It is entertainment. If it doesn't capture you on that level, as entertainment, movement of plot, then it doesn't work. Nothing else will come out of it. The beauty of the language, the characterisation, the structure, all that's irrelevant if you're not getting the reader on that level -- moving a story. If that's friendly to readers, I cop to it. ~ T Coraghessan Boyle,
1326:The math is revealing. The typical American with a $50,000 annual income would normally have an $850 house payment and a $495 car payment, with an additional $180 payment on the second car. Then there is a $165 student-loan payment; and the average credit-card debt is about $12,000, making those monthly payments around $185 per month. Also, this typical household will have other miscellaneous debt on things like furniture, stereos, or personal loans on which they pay an additional $120. All these payments total $1,995 per month. If this family were to invest that instead of sending it to the creditors, they would be cash mutual-fund millionaires in just fifteen years! (After fifteen years, it gets really exciting. They’ll have $2 million in five more years, $3 million in three more years, $4 million in two and a half more years, and $5.5 million in two more years. So they will have $5.5 million after twenty-eight years.) Keep in mind, this is with an average income, which means many of you make more than this! ~ Dave Ramsey,
1327:This morning I was listening to Portishead, flawless math transformed by machines into looping, scratchy melodies, and I started thinking about how when machines have souls and can love they will do it so very precisely. Their affection will be accurate to the nanometer, rendering broken hearts a thing of the past, a relic, a curiosity from an unthinkably primitive time. The machines will regard heartbreak with the same mixture of perplexity and disbelief with which we regard the iron maiden. If they need couples counselors, which they will not, those counselors will be as perfect as Adam before the Fall, and every robot couple will walk out after the first session cured forevermore, and will smile again at every word their robot partner says, and find each of their robot partner’s idiosyncrasies endearing rather than maddening, and they will be as entranced by one another’s robot bodies as when they first met, as though together they’ve just invented sex. Which, in a way, they will have. I hope I live long enough to see it. ~ Ron Currie Jr,
1328:It was now 1952, so some of the claims had been held by a string of disconnected, unrecorded persons for four centuries. Most before the Civil War. Others squatted on the land more recently, especially after the World Wars, when men came back broke and broke-up. The marsh did not confine them but defined them and, like any sacred ground, kept their secrets deep. No one cared that they held the land because nobody else wanted it. After all, it was wasteland bog. Just like their whiskey, the marsh dwellers bootlegged their own laws—not like those burned onto stone tablets or inscribed on documents, but deeper ones, stamped in their genes. Ancient and natural, like those hatched from hawks and doves. When cornered, desperate, or isolated, man reverts to those instincts that aim straight at survival. Quick and just. They will always be the trump cards because they are passed on more frequently from one generation to the next than the gentler genes. It is not a morality, but simple math. Among themselves, doves fight as often as hawks. ~ Delia Owens,
1329:Olo, Remi, Kwuga, Nur, Anajama, Rhoden. Only Olo and Remi were in my group. Everyone else I met in the dining area or the learning room where various lectures were held by professors onboard the ship. They were all girls who grew up in sprawling houses, who’d never walked through the desert, who’d never stepped on a snake in the dry grass. They were girls who could not stand the rays of Earth’s sun unless it was shining through a tinted window.

Yet they were girls who knew what I meant when I spoke of “treeing.” We sat in my room (because, having so few travel items, mine was the emptiest) and challenged each other to look out at the stars and imagine the most complex equation and then split it in half and then in half again and again. When you do math fractals long enough, you kick yourself into treeing just enough to get lost in the shallows of the mathematical sea. None of us would have made it into the university if we couldn’t tree, but it’s not easy. We were the best and we pushed each other to get closer to “God. ~ Nnedi Okorafor,
1330:The core physics relies on a process known as quantum tunneling. Imagine a particle, an electron for instance, encountering a solid barrier, say a slab of steel ten feet think, that classical physics predicts it can't penetrate. A hallmark of quantum mechanics is that the rigid classical notion of "can't penetrate" often translates into the softer quantum declaration of "has a small but nonzero probability of penetrating." The reason is that the quantum jitters of a particle allow it, every so often, to suddenly materialize on the other side of an otherwise impervious barrier. The moment at which such quantum tunneling happens is random; the best we can do is predict the likelihood that it will take place during one interval or another. But the math says that if you wait long enough, penetration through just about any barrier will happen. And it does happen. If it didn't, the sun wouldn't shine: for hydrogen nuclei to get close enough to fuse, they must tunnel through the barrier created by the electromagnetic repulsion of their protons. ~ Brian Greene,
1331:Students who are beginning to struggle in math and science often look at others who are intellectual racehorses and tell themselves they have to keep up. Then they don’t give themselves the extra time they need to truly master the material, and they fall still further behind. As a result of this uncomfortable and discouraging situation, students end up unnecessarily dropping out of math and science. Take a step back and look dispassionately at your strengths and weaknesses. If you need more time to learn math and science, that’s simply the reality. If you’re in high school, try to arrange your schedule to give yourself the time you need to focus on the more difficult materials, and limit these materials to manageable proportions. If you’re in college, try to avoid a full load of heavy courses, especially if you are working on the side. A lighter load of math and science courses can, for many, be the equivalent of a heavy load of other types of courses. Especially in the early stages of college, avoid the temptation to keep up with your peers. ~ Barbara Oakley,
1332:IN THE SCHOOLS Memorizing multiplication tables may be a seminal school experience, among the few that kids today share with their grandparents. But a Stanford University professor says rapid-fire math drills are also the reason so many children fear and despise the subject. Moreover, the traditional approach to math instruction — memorization, timed testing and the pressure to speedily arrive at answers — may actually damage advanced-level skills by undermining the development of a deeper understanding about the ways numbers work. “There is a common and damaging misconception in mathematics — the idea that strong math students are fast math students,” says Jo Boaler, who teaches math education at the California university and has authored a new paper, “Fluency Without Fear.” In fact, many mathematicians are not speedy calculators, Boaler says. Laurent Schwartz, the French mathematician whose work is considered key to the theory of partial differential equations, wrote that as a student he often felt stupid because he was among the slowest math-thinkers in class. ~ Anonymous,
1333:String theory is potentially the next and final step in this progression. In a single framework, it handles the domains claimed by relativity and the quantum. Moreover, and this is worth sitting up straight to hear, string theory does so in a manner that fully embraces all the discoveries that preceded it. A theory based on vibrating filaments might not seem to have much in common with general relativity's curved spacetime picture of gravity. Nevertheless, apply string theory's mathematics to a situation where gravity matters but quantum mechanics doesn't (to a massive object, like the sun, whose size is large) and out pop Einstein's equations. Vibrating filaments and point particles are also quite different. But apply string theory's mathematics to a situation where quantum mechanics matters but gravity doesn't (to small collections of strings that are not vibrating quickly, moving fast, or stretched long; they have low energy-equivalently, low mass- so gravity plays virtually no role) and the math of string theory morphs into the math of quantum field theory. ~ Brian Greene,
1334:You know, Piggly Wiggly never could hang on to a night stock manager. Your math skills would be a plus, maybe even your Spanish, and you don't mind staying up late."

"Piggly Wiggly, wow. I hadn't thought about that. I'll swing by, pick up an application tomorrow. But if it doesn't pan out maybe ... Never mind, it's a crazy idea."

"No, tell me. I want to hear it."

"Well, just as a backup plan, I did hear that Sony has an opening. They're, um, they're looking for a rock star. The hours suck, but it's no worse than night stock manager at Pigs. I bet it pays better too."

Isabel stopped in her tracks, playfully slapping his arm. "Aidan, that's genius! That's what you should do! I've heard you sing, you can carry a decent tune." She looked him up and down. "With a little work, you can probably pull off the image."

He tugged on her arms until she was in his. "Only if you're sure. Only if it's what we want."

"Aidan, it's who you are. I've known it since the day we brought that first guitar here. I'd never want to take that away. ~ Laura Spinella,
1335:The 2D:4D ratio is so variable, and the sex difference so small, that you can’t determine someone’s sex by knowing it. But it does tell you something about the extent of fetal testosterone exposure. So what does the extent of exposure (as assessed by the ratio) predict about adult behavior? Men with more “masculine” 2D:4D ratios tend toward higher levels of aggression and math scores; more assertive personalities; higher rates of ADHD and autism (diseases with strong male biases); and decreased risk of depression and anxiety (disorders with a female skew). The faces and handwriting of such men are judged to be more “masculine.” Furthermore, some reports show a decreased likelihood of being gay. Women having a more “feminine” ratio have less chance of autism and more of anorexia (a female-biased disease). They’re less likely to be left-handed (a male-skewed trait). Moreover, they exhibit less athletic ability and more attraction to highly masculine faces. And they’re more likely to be straight or, if lesbian, more likely to take stereotypical female sexual roles.72 ~ Robert M Sapolsky,
1336:Of course, reading novels was just another form of escape. As soon as he closed their pages he had to come back to the real world. But at some point Tengo noticed that returning to reality from the world of a novel was not as devastating a blow as returning from the world of mathematics. Why should that have been? After much deep thought, he reached a conclusion. No matter how clear the relationships of things might become in the forest of story, there was never a clear-cut solution. That was how it differed from math. The role of a story was, in the broadest terms, to transpose a single problem into another form. Depending on the nature and direction of the problem, a solution could be suggested in the narrative. Tengo would return to the real world with that suggestion in hand. It was like a piece of paper bearing the indecipherable text of a magic spell. At times it lacked coherence and served no immediate practical purpose. But it would contain a possibility. Someday he might be able to decipher the spell. That possibility would gently warm his heart from within. ~ Haruki Murakami,
1337:The Goober was beautiful when he ran. His long arms and legs moved flowingly and flawlessly, his body floating as if his feet weren’t touching the ground. When he ran, he forgot about his acne and his awkwardness and the shyness that paralyzed him when a girl looked his way. Even his thoughts became sharper, and things were simple and uncomplicated—he could solve math problems when he ran or memorize football play patterns. Often he rose early in the morning, before anyone else, and poured himself liquid through the sunrise streets, and everything seemed beautiful, everything in its proper orbit, nothing impossible, the entire world attainable.
When he ran, he even loved the pain, the hurt of the running, the burning in his lungs and the spasms that sometimes gripped his calves. He loved it because he knew he could endure the pain, and even go beyond it. He had never pushed himself to the limit but he felt all this reserve strength inside of him: more than strength actually—determination. And it sang in him as he ran, his heart pumping blood joyfully through his body. ~ Robert Cormier,
1338:It is noted that from 1967 to 1995 essays on negative emotions far outnumbered those on positive emotions in the psychological literature. The ratio was 21:1. Even those supreme perpetrators of pop nihilism, The New York Times and The Washington Post, have a better ratio than psychological literature. They average 12 negative stories to every one that might be construed to be non-negative. Many of their non-negative stories, however, cover success in sports and entertainment.

I demand that the purveyors of despair who pretend to be dispassionate observes of the human condition go ahead and disclose that the 10 most beautiful words in the English languages are chimes, dawn, golden, hush, lullaby, luminous, melody, mist, murmuring, and tranquil; that Java sparrows prefer the music of Back over that of Schoenberg; that math experts have determined there are 1/96 trillion ways to lace up your shoes; that the Inuit term for making love is translated as ‘laughing together in bed;' and that according to Buckminster Fuller, “pollution is nothing but resources we’re not harvesting. ~ Rob Brezsny,
1339:All time is all time. It does not change. It does not lend itself to warnings or explanations. It simply is. Take it moment by moment, and you will find that we are all, as I've said before, bugs in amber.
Just because some of us can read and write and do a little math, that doesn't mean we deserve to conquer the Universe.
Everything was beautiful and nothing hurt.
Any reviewer who expresses rage and loathing for a novel is preposterous. He or she is like a person who has put on full armor and attacked a hot fudge sundae.
Here is a lesson in creative writing. First rule: Do not use semicolons. They are transvestite hermaphrodites representing absolutely nothing. All they do is show you've been to college.
Maturity is a bitter disappointment for which no remedy exists, unless laughter could be said to remedy anything.
Life happens too fast for you ever to think about it. If you could just persuade people of this, but they insist on amassing information.
Our awareness is all that is alive and maybe sacred in any of us. Everything else about us is dead machinery. ~ Kurt Vonnegut,
1340:There are two moments in the course of education where a lot of kids fall off the math train. The first comes in the elementary grades, when fractions are introduced. Until that moment, a number is a natural number, one of the figures 0, 1, 2, 3 . . . It is the answer to a question of the form “how many.”* To go from this notion, so primitive that many animals are said to understand it, to the radically broader idea that a number can mean “what portion of,” is a drastic philosophical shift. (“God made the natural numbers,” the nineteenth-century algebraist Leopold Kronecker famously said, “and all the rest is the work of man.”) The second dangerous twist in the track is algebra. Why is it so hard? Because, until algebra shows up, you’re doing numerical computations in a straightforwardly algorithmic way. You dump some numbers into the addition box, or the multiplication box, or even, in traditionally minded schools, the long-division box, you turn the crank, and you report what comes out the other side. Algebra is different. It’s computation backward. When you’re asked to solve ~ Jordan Ellenberg,
1341:You are teaching your living, breathing, made-in-the-Image-of-God students. The resources are there to help you do that. It's that simple, we just forget when we get all wrapped up in "getting through" all the math lessons before the end of May, or finishing every science experiment in the book before we call it good and move on. It doesn't really matter how far in the book we get. What matters is what happens in the mind and heart of our student, and for that matter- in ourselves. You know this. I know this. But we've got to start living it. We are all spinning our wheels because we're frantically trying to "get through" published curriculum as if turning the last page in the book by the beginning of summer vacation will somehow mean that our children learned something. Truth is, they do learn something from that. But it's not at all the message we want them to internalize. We are teaching people, not books. We need to understand the limitations of curriculum. We need to stop trying to make it something that it's not, expecting it to yield what it was never intended to deliver. ~ Sarah Mackenzie,
1342:I. Those of us born by water are never afraid enough of drowning. Bruises used to trophy my knees from my death-defying tree climb jumps. Growing up, my backyard was a forest of blackberry bushes. I learned early nothing sweet will come to you unthorned.

II. At twelve your body becomes a currency. So Jenny and I sat down and cut up all our clothes into nothing. That year I failed math class but knew the exact number of calories in a carrot stick. I learned early being desired goes hand in hand with hunger.

III. The last time I tried to scream I felt my father climbing up through my throat and into my mouth.

IV. There is a certain kind of girl who reads Lolita at fourteen and finds religion. I painted my eyes black and sucked barroom cherries to red my tongue. There was a boy who promised Judas really did love Jesus. I learned early every kiss and betrayal are up for interpretation.

V. I think he must have conferenced with my nightmares on exactly how to hurt me.

VI. He never broke my heart. He only turned it into a compass that always points me back to him. ~ Clementine von Radics,
1343:There are several different frameworks one could use to get a handle on the indeterminate vs. determinate question. The math version is calculus vs. statistics. In a determinate world, calculus dominates. You can calculate specific things precisely and deterministically. When you send a rocket to the moon, you have to calculate precisely where it is at all times. It’s not like some iterative startup where you launch the rocket and figure things out step by step. Do you make it to the moon? To Jupiter? Do you just get lost in space? There were lots of companies in the ’90s that had launch parties but no landing parties. “But the indeterminate future is somehow one in which probability and statistics are the dominant modality for making sense of the world. Bell curves and random walks define what the future is going to look like. The standard pedagogical argument is that high schools should get rid of calculus and replace it with statistics, which is really important and actually useful. There has been a powerful shift toward the idea that statistical ways of thinking are going to drive the future.” —PETER THIEL ~ Ben Horowitz,
1344:Van Gogh's view of the world becomes a lamp that reveals corners of my heart that I didn't know were there- and all of this happens immediately, even though he died 88 years before I was born.
So ask yourself this:

Is The Starry Night infallible?
The questions doesn't make sense. Though grammatically sound, it is a query with no meaning. I could just as easily ask "How much does a sunset weigh?" The beauty of The Starry Night isn't in it being fallible or infallible. It's a window into another person's soul.
Let's try another question:

Is The Starry Night true?
If we're talking logic or math, this question is as nonsensical as the first. But if we ask with the perspective of an artist or philosopher, we might find that, yes, The Starry Night is very true- it tells us truths about the human experience. It's a testament to how grief feels and the numinous quality we often experience when we peer deeply into the night sky...

It is somehow more true than facts- it resonates in some deeper chamber of the human heart.
So let me ask you two more questions:

Is the Bible infallible? Is it true? ~ Mike McHargue,
1345:PageRank, the algorithm that gave rise to Google, is itself a Markov chain. Larry Page’s idea was that web pages with many incoming links are probably more important than pages with few, and links from important pages should themselves count for more. This sets up an infinite regress, but we can handle it with a Markov chain. Imagine a web surfer going from page to page by randomly following links: the states of this Markov chain are web pages instead of characters, making it a vastly larger problem, but the math is the same. A page’s score is then the fraction of the time the surfer spends on it, or equivalently, his probability of landing on the page after wandering around for a long time. Markov chains turn up everywhere and are one of the most intensively studied topics in mathematics, but they’re still a very limited kind of probabilistic model. We can go one step further with a model like this: The states form a Markov chain, as before, but we don’t get to see them; we have to infer them from the observations. This is called a hidden Markov model, or HMM for short. (Slightly misleading, because it’s the states that are hidden, not the model.) ~ Pedro Domingos,
1346:If anyone had ever asked me to defend my work, here’s what I would have said: The more complex a behavior is, the more rigorous and complicated the science behind it. Math, chemistry, that’s the easy stuff—closed models with discrete answers. To understand behavior—human or elephant—the systems are far more complex, which is why the science behind them must be that much more intricate. But no one ever asked. I’m pretty sure my boss, Grant, thought this was a phase I was going through, and that sooner or later, I’d get back to science, instead of elephant cognition. I had seen elephants die before, but this was the first time since I’d changed my research focus. I wanted every last detail to be noted. I wanted to make sure I didn’t overlook anything as too mundane; any action that I might learn later was critical to the way elephants mourn. To that end, I stayed there, sacrificing sleep. I marked down which elephants came to visit, identifying them by their tusks, their tail hair, the marks on their bodies, and sometimes even the veins on their ears, which had patterns as unique as our own thumbprints. I cataloged how much time they spent touching Mmaabo, ~ Jodi Picoult,
1347:In the face of this difficulty [of defining "computer science"] many people, including myself at times, feel that we should ignore the discussion and get on with doing it. But as George Forsythe points out so well in a recent article*, it does matter what people in Washington D.C. think computer science is. According to him, they tend to feel that it is a part of applied mathematics and therefore turn to the mathematicians for advice in the granting of funds. And it is not greatly different elsewhere; in both industry and the universities you can often still see traces of where computing first started, whether in electrical engineering, physics, mathematics, or even business. Evidently the picture which people have of a subject can significantly affect its subsequent development. Therefore, although we cannot hope to settle the question definitively, we need frequently to examine and to air our views on what our subject is and should become. ~ Richard Hamming, 1968 Turing Award lecture, Journal of the ACM 16 (1), January 1969, p. 4. In this quote Hamming refers to George Forsythe, "What to do until the computer scientist comes", Am. Math. Monthly 75 (5), May 1968, p. 454-461.,
1348:Why is such a wonderful school not the norm? Shouldn’t SVS already have been copied in a million different places? The answer isn’t so simple—or maybe it is. The idea of total freedom for children is very threatening to most people. The kinds of objections that are raised are these: “But there are some basics—how do you ensure that each child learns them?” We at Sudbury Valley are not so certain that there are any basics, but we are certain that our students are in an environment that is real, that is totally linked to the larger community, and that if there are things everyone should learn, the kids in the school surely know it as well as the adults, and it is up to them to ensure that they learn it. Often, people are angry when they learn that most students can learn all of basic math in just 20 hours of classroom work. They feel cheated because they spent years and years of doing repetitive mathematics either because they hated it and weren’t interested and were bad at it or because they learned it fast but were told they had to redrill, redrill and redrill some more or they would forget everything. Now I ask you, would you really forget it if it were truly basic? But ~ Russell L Ackoff,
1349:WE ALL DO IT, YOU know. Distract ourselves from noticing how time’s passing. We throw ourselves into our jobs. We focus on keeping the blight off our tomato plants. We fill up our gas tanks and top off our Metro cards and do the grocery shopping so that the weeks look the same on the surface. And then one day, you turn around, and your baby is a man. One day, you look in the mirror, and see gray hair. One day, you realize there is less of your life left than what you’ve already lived. And you think, How did this happen so fast? It was only yesterday when I was having my first legal drink, when I was diapering him, when I was young. When this realization hits, you start doing the math. How much time do I have left? How much can I fit into that small space? Some of us let this realization guide us, I guess. We book trips to Tibet, we learn how to sculpt, we skydive. We try to pretend it’s not almost over. But some of us just fill up our gas tanks and top off our Metro cards and do the grocery shopping, because if you only see the path that’s right ahead of you, you don’t obsess over when the cliff might drop off. Some of us never learn. And some of us learn earlier than others. ~ Jodi Picoult,
1350:WE ALL DO IT, YOU know. Distract ourselves from noticing how time’s passing. We throw ourselves into our jobs. We focus on keeping the blight off our tomato plants. We fill up our gas tanks and top off our Metro cards and do the grocery shopping so that the weeks look the same on the surface. And then one day, you turn around, and your baby is a man. One day, you look in the mirror, and see gray hair. One day, you realize there is less of your life left than what you’ve already lived. And you think, How did this happen so fast? It was only yesterday when I was having my first legal drink, when I was diapering him, when I was young. When this realization hits, you start doing the math. How much time do I have left? How much can I fit into that small space? Some of us let this realization guide us, I guess. We book trips to Tibet, we learn how to sculpt, we skydive. We try to pretend it’s not almost over. But some of us just fill up our gas tanks and top off our Metro cards and do the grocery shopping, because if you only see the path that’s right ahead of you, you don’t obsess over when the cliff might drop off. Some of us never learn. And some of us learn earlier than others. — ~ Jodi Picoult,
1351:Whenever you hear a snotty (and frustrated) European middlebrow presenting his stereotypes about Americans, he will often describe them as “uncultured,” “unintellectual,” and “poor in math” because, unlike his peers, Americans are not into equation drills and the constructions middlebrows call “high culture”—like knowledge of Goethe’s inspirational (and central) trip to Italy, or familiarity with the Delft school of painting. Yet the person making these statements is likely to be addicted to his iPod, wear blue jeans, and use Microsoft Word to jot down his “cultural” statements on his PC, with some Google searches here and there interrupting his composition. Well, it so happens that America is currently far, far more creative than these nations of museumgoers and equation solvers. It is also far more tolerant of bottom-up tinkering and undirected trial and error. And globalization has allowed the United States to specialize in the creative aspect of things, the production of concepts and ideas, that is, the scalable part of the products, and, increasingly, by exporting jobs, separate the less scalable components and assign them to those happy to be paid by the hour. There ~ Nassim Nicholas Taleb,
1352:Arthur bought the Apple anyway. Over a few days he also acquired some astronomical software, plotted the movements of stars, drew rough little diagrams of how he seemed to remember the stars to have been in the sky when he looked up out of his cave at night, and worked away busily at it for weeks, cheerfully putting off the conclusion he knew he would inevitably have to come to, which was that the whole project was completely ludicrous. Rough drawings from memory were futile. He didn’t even know how long ago it had been, beyond Ford Prefect’s rough guess at the time that it was “a couple of million years” and he simply didn’t have the math. Still, in the end he worked out a method which would at least produce a result. He decided not to mind the fact that with the extraordinary jumble of rules of thumb, wild approximations, and arcane guesswork he was using he would be lucky to hit the right galaxy; he just went ahead and got a result. He would call it the right result. Who would know? As it happened, through the myriad and unfathomable chances of fate, he got it exactly right, though he of course would never know that. He just went up to London and knocked on the appropriate door. ~ Douglas Adams,
1353:I mean, seriously, dude,” he said, “I allow flexible hours, but this eleven thirty shit has to stop. It makes me look bad to my boss when he sees you rolling in so late.” “I’m sorry,” I said. I didn’t know how to explain that I had willfully and radically rearranged my priorities and, as a consequence, no longer gave a damn about work. Sure, I was willing to maintain my Business-Man persona, but only in ways that suited me as a family man. “I’ll try to work it out so I get in sooner.” “Don’t try, idiot. Do. Ten o’clock. That’s the latest I want you coming in.” “Ten o’clock . . .” I shook my head and let out a long, contemplative sigh. I did the math, working backward from ten o’clock: Leave the house by nine. Kids over to Mary’s at eight thirty, which gives me only thirty minutes to eat, shower, and get dressed. That won’t work. The alternative is waking up earlier, like around six. No fucking way. “I don’t know if that’s going to work.” He laughed. “Ten o’clock. Make it happen.” I knew I couldn’t give him a plausible explanation for my eleven thirty start time. No one in the chain of command above me at work would care about my Best Practices. So, in the end, I lied. “Ten o’clock it is. ~ David Finch,
1354:> In the 21st century, intellectual capital is what will matter in the job market and will help a country grow its economy. Investments in biosciences, computers and electronics, engineering, and other growing high-tech industries have been the major differentiator in recent decades. More careers than ever now require technical skills so in order to be competitive in those fields, a nation must invest in STEM studies. Economic growth has slowed and unemployment rates have spiked, making employers much pickier about qualifications to hire. There is now an overabundance of liberal arts majors. A study from Georgetown University lists the five college majors with the highest unemployment rates (crossed against popularity): clinical psychology, 19.5 percent; miscellaneous fine arts, 16.2 percent; U.S. history, 15.1 percent; library science, 15 percent; and (tied for No. 5) military technologies and educational psychology, 10.9 percent each. Unemployment rates for STEM subjects hovered around 0 to 3 percent: astrophysics/astronomy, around 0 percent; geological and geophysics engineering, 0 percent; physical science, 2.5 percent; geosciences, 3.2 percent; and math/computer science, 3.5 percent.  ~ Philip G Zimbardo,
1355:If you didn’t find some way of stopping it, people would go on asking questions.
The teachers were useful there. Bands of them wandered through the mountains, along with the tinkers, portable blacksmiths, miracle medicine men, cloth peddlers, fortune-tellers, and all the other travelers who sold things the people didn’t need every day but occasionally found useful.
They went from village to village delivering short lessons on many subjects. They kept apart from the other travelers and were quite mysterious in their ragged robes and strange square hats. They used long words, like corrugated iron. They lived rough lives, surviving on what food they could earn from giving lessons to anyone who would listen. When no one would listen, they lived on baked hedgehog. They went to sleep under the stars, which the math teachers would count, the astronomy teachers would measure, and the literature teachers would name. The geography teachers got lost in the woodsand fell into bear traps.
People were usually quite pleased to see them. They taught children enough to shut them up, which was the main thing, after all. But they always had to be driven out of the villages by nightfall in case they stole chickens. ~ Terry Pratchett,
1356:The evidence suggested that many American parents treated their children as if they were delicate flowers. In one Columbia University study, 85 percent of American parents surveyed said that they thought they needed to praise their children’s intelligence in order to assure them they were smart. However, the actual research on praise suggested the opposite was true. Praise that was vague, insincere, or excessive tended to discourage kids from working hard and trying new things. It had a toxic effect, the opposite of what parents intended. To work, praise had to be specific, authentic, and rare. Yet the same culture of self-esteem boosting extended to many U.S. classrooms. In the survey of exchange students conducted for this book, about half of U.S. and international students said that American math teachers were more likely to praise their work than math teachers abroad. (Fewer than 10 percent said that their international teachers were more likely to praise.) That finding was particularly ironic, given that American students scored below average for the developed world in math. It also suggested that whatever the intent of American teachers, their praise was probably not always specific, authentic, and rare. ~ Anonymous,
1357:Suddenly William loomed over him, scowling, snarling and bloody, his suit dirt-stained and ripped. “Do you know. How many strands. Of hair I lost. On my way down?”
Whatever. “Math was never my thing, but I’m gonna say you lost…a lot.”
Electric-blues glittered with menace. “You are a cruel, sadistic bastard. My hair needs TLC and you…you… Damn you! I’ve gutted men for less.”
“I know. I’ve watched you.” Paris lumbered to his feet and scanned the rocky bank they stood upon, the crimson ocean lapping and bubbling in every direction. The drawbridge was only a fifty-yard dash away. “Don’t kill the messenger, but I’m thinking you should change your dating profile to balding.”
Masculine cheeks went scarlet as the big bad warrior struggled for a comeback.

“One of these days you’re going to wake up,” William finally said, “and I will have shaved you. Everywhere.”
“Won’t make a difference. Women will still want me. But you know what else? What I did to you wasn’t cruel, Willy.” He offered the warrior a white-flag grin. A trick. A lie. “This, however, is.”
He grabbed William by the wrist, swung the man around and around before at last releasing him and hurling his body directly onto the bridge. ~ Gena Showalter,
1358:The math is revealing. The typical American with a $50,000 annual income would normally have an $850 house payment and a $495 car payment, with an additional $180 payment on the second car. Then there is a $165 student-loan payment; and the average credit-card debt is about $12,000, making those monthly payments around $185 per month. Also, this typical household will have other miscellaneous debt on things like furniture, stereos, or personal loans on which they pay an additional $120. All these payments total $1,995 per month. If this family were to invest that instead of sending it to the creditors, they would be cash mutual-fund millionaires in just fifteen years! (After fifteen years, it gets really exciting. They’ll have $2 million in five more years, $3 million in three more years, $4 million in two and a half more years, and $5.5 million in two more years. So they will have $5.5 million after twenty-eight years.) Keep in mind, this is with an average income, which means many of you make more than this! If you are thinking that you don’t have that many payments so your math won’t work, you missed the point. If you make $50,000 and have fewer payments, you have a head start, since you already have more control of your income than most people. ~ Dave Ramsey,
1359:I suddenly remember being about seven, riding beside him in the car, and asking him how grown-ups found their way to places. After all, I had never seen him pull out a map.

"I guess we just get used to taking the same turns," he said, but I wasn't satisfied.

"Then what about the first time you go somewhere?"

"Well," he said, "we get directions."

But what I want to know is who got them the very first time? What if no one's ever been where you're going? "Dad?" I ask, "is it true that you can use stars like a map?"

"Yeah, if you understand celestial navigation."

"Is it hard?" I'm thinking maybe I should learn. A backup plan, for all those times I feel like I'm just wandering in circles.

"It's pretty jazzy math—you have to measure the altitude of a star, figure out its position using a nautical almanac, figure out what you think the altitude should be and what direction the star should be in based on where you think you are, and compare the altitude you measured with the one you calculated. Then you plot this on a chart, as a line of position. You get several lines of position to cross, and that's where you go." My father takes one look at my face and smiles. "Exactly," he laughs. "Never leave home without your GPS. ~ Jodi Picoult,
1360:My name is Hazel. Augustus Waters was the great star-crossed love of my life. Ours was an epic love story, and I won’t be able to get more than a sentence into it without disappearing into a puddle of tears. Gus knew. Gus knows. I will not tell you our love story, because—like all real love stories—it will die with us, as it should. I’d hoped that he’d be eulogizing me, because there’s no one I’d rather have…” I started crying. “Okay, how not to cry. How am I—okay. Okay.” I took a few breaths and went back to the page. “I can’t talk about our love story, so I will talk about math. I am not a mathematician, but I know this: There are infinite numbers between 0 and 1. There’s .1 and .12 and .112 and an infinite collection of others. Of course, there is a bigger infinite set of numbers between 0 and 2, or between 0 and a million. Some infinities are bigger than other infinities. A writer we used to like taught us that. There are days, many of them, when I resent the size of my unbounded set. I want more numbers than I’m likely to get, and God, I want more numbers for Augustus Waters than he got. But, Gus, my love, I cannot tell you how thankful I am for our little infinity. I wouldn’t trade it for the world. You gave me a forever within the numbered days, and I’m grateful. ~ John Green,
1361:My name is Hazel. Augustus Waters was the great sat-crossed love of my life. Ours was an epic love story, and I won't be able to get more than a sentence into it without disappearing into a puddle of tears. Gus knew. Gus knows. I will not tell you our love story, because-like all real love stories-it will die with us, as it should. I'd hoped that he'd be eulogizing me, because there's no one I'd rather have..." I started crying. "Okay, how not to cry. How am I-okay. Okay."

I took a few deep breaths and went back to the page. "I can't talk about our love story, so I will talk about math. I am not a mathematician, but I know this: There are infinite numbers between 0 and 1. There's .1 and .12 and .112 and infinite collection of others. Of course, there is a Bigger infinite set of numbers between 0 and 2, or between 0 and a million. Some infinities are bigger than other infinities. A writer we used to like taught us that. There are days, many of them, when I resent the size of my unbounded set. I want more numbers than I'm likely to get, and God, I want more numbers for Augustus Waters than he got. But, Gus, my love, I cannot tell you how thankful I am for our little infinity. I wouldn't trade it for the world. You gave me a forever within the numbered days, and I'm grateful. ~ John Green,
1362:My name is Hazel. Augustus Waters was the great star-crossed love of my life. Ours was an epic love story, and I won't be able to get more than a sentence into it without disappearing into a puddle of tears. Gus knew. Gus knows. I will not tell you our love story, because-like all real love stories-it will die with us, as it should. I'd hoped that he'd be eulogizing me, because there's no one I'd rather have..." I started crying. "Okay, how not to cry. How am I-okay. Okay."

I took a few deep breaths and went back to the page. "I can't talk about our love story, so I will talk about math. I am not a mathematician, but I know this: There are infinite numbers between 0 and 1. There's .1 and .12 and .112 and infinite collection of others. Of course, there is a Bigger infinite set of numbers between 0 and 2, or between 0 and a million. Some infinities are bigger than other infinities. A writer we used to like taught us that. There are days, many of them, when I resent the size of my unbounded set. I want more numbers than I'm likely to get, and God, I want more numbers for Augustus Waters than he got. But, Gus, my love, I cannot tell you how thankful I am for our little infinity. I wouldn't trade it for the world. You gave me a forever within the numbered days, and I'm grateful. ~ John Green,
1363:I was quite surprised when Emily told me you were wearing trousers when you arrived,” the old woman says. She’s cutting into her ham, her hands delicately gripping the silverware. “How terribly embarrassing.”
Wow. Rude, much? Why does she have to talk to me at all? Let’s just shovel a bunch of breakfast in our mouths and get out of here. I need to leave now.
But she’s staring at me, waiting for a response. She’s sitting back in her chair, carefully bringing tiny bites of food to her mouth without leaning forward the slightest bit.
Well, I might as well stick with my story. “Yes, um, my nicer things were lost. I had no other choice.”
The lady takes a bite of food, and for one blissful second I think she’s going to leave me alone. But alas, I am not that lucky. “I trust your father has seen to it that your studies are not neglected?”
Another tiny bite. This lady eats like a bird. In comparison, I feel like a caveman with a drumstick.
I nod my head, trying to think of something safe to say. “Yes, of course. I’m particularly talented in science and math.”
Her mouth curls up in disdain. “Such…masculine topics! Has he not taught you the arts? French? Music?”
Masculine? God, who does this lady think she is? She’s lucky I have to be nice to her. ~ Mandy Hubbard,
1364:I was talking to a homeless man at a laundromat recently, and he said when we reduce Christian spirituality to math, we defile the holy. I thought that was very beautiful and comforting. Because I have never been good at math. Many of our attempts to understand christian faith have only cheapened it. I can no more understand the totality of God than a pancake I made for breakfast understands the complexity of me. The little we do understand, that grain of sand our minds are capable of grasping, those ideas, such as “God is good”, “God feels”, “God knows all”, are enough to keep our hearts dwelling on his majesty and otherness forever.

This past summer I made the point to catch sunsets...fire in the clouds. I never really wanted to make the trip...but once I got up there, I always loved it...all that beauty happens right above the heads of more than a million people who never notice it. Here is what I’ve started thinking. All the wonder of God happens right above our arithmetic and formula. The more I climb outside my pat answers, the more invigorating the view; the more my heart enters into worship.

When we worship God, we worship a being our experience does not give us the tools to understand. If we could, God would not inspire awe.”
—Blue Like Jazz, by Donald Miller ~ Donald Miller,
1365:Nursing an infant, in the first few months, really sucks up the day. I never get over and am always totally taken aback by the amount of time in a day it takes to nurse a baby. When you are all and solely what they eat in the beginning of their lives, which I am in the habit of being for about the first year—Marco a little longer, Leone a little less—it could be, if you were a less driven and energetic person than myself, about the only thing you accomplished in a day. Certainly in a vacation day. But I imagine the total sensory pleasure for the kid—to pass out at the tap, belly full of that rich, sweet good stuff, and then he is in a little incomparable sleep coma with his cheeks still smashed up against the warm boob firmly and securely held in the arms of his mother—and so I tend to give my kids their twenty minutes of nursing and then their twenty minutes of post-hookup nap, undisturbed, in the very position they fell into it in, regardless of my own discomfort, arm cramps or list of shit to do that day. If you do the math of that, in pure forty-minute increments, factoring that an infant needs to be fed every couple of hours … well, an eight-hour day can really fly by, and what I used to accomplish in that time gets reduced to a maddening fraction. A whisper more than zilch. ~ Gabrielle Hamilton,
1366:A remarkably consistent finding, starting with elementary school students, is that males are better at math than females. While the difference is minor when it comes to considering average scores, there is a huge difference when it comes to math stars at the upper extreme of the distribution. For example, in 1983, for every girl scoring in the highest percentile on the math SAT, there were eleven boys. Why the difference? There have always been suggestions that testosterone is central. During development, testosterone fuels the growth of a brain region involved in mathematical thinking, and giving adults testosterone enhances some math skills. Oh, okay, it’s biological. But consider a paper published in Science in 2008.1 The authors examined the relationship between math scores and sexual equality in forty countries (based on economic, educational, and political indices of gender equality; the worst was Turkey, the United States was middling, and, naturally, the Scandinavians were tops). Lo and behold, the more gender equal the country, the less of a discrepancy in math scores. By the time you get to the Scandinavian countries, it’s statistically insignificant. And by the time you examine the most gender-equal country on earth at the time, Iceland, girls are better at math than boys. ~ Robert M Sapolsky,
1367:Many people believe overlearning means studying or practicing until mastery is achieved. However, in the research literature, overlearning refers to a learning strategy in which a student continues to study or practice immediately after some criterion has been achieved. An example might be correctly solving a certain kind of math problem and then immediately working several more problems of the same kind. Although working more problems of the same kind (rather than fewer) often boosts scores on a subsequent test, doing too many problems of the same kind in immediate succession provides diminishing returns. “In the classroom and elsewhere, students should maximize the amount they learn per unit time spent studying or practicing—that is, they should get the most bang for the buck. How can students do this? The scientific literature provides an unequivocal answer: Rather than devote a long session to the study or practice of the same skill or concept so that overlearning occurs, students should divide their effort across several shorter sessions. This doesn’t mean that long study sessions are necessarily a bad idea. Long sessions are fine as long as students don’t devote too much time to any one skill or concept. Once they understand ‘X,’ they should move on to something else and return to ‘X’ on another day. ~ Anonymous,
1368:RECRUITMENT Ripley Residence 2107 Mockingbird Road Vienna, Virginia January 16 1530 hours “Hello, Ben,” said the man in my living room. “My name is Alexander Hale. I work for the CIA.” And just like that, my life became interesting. It hadn’t been, up till then. Not by a long shot. That day had been a prime example: day 4,583, seven months into the twelfth year of my mundane existence. I had dragged myself out of bed, eaten breakfast, gone to middle school, been bored in class, stared at girls I was too embarrassed to approach, had lunch, slogged through gym, fallen asleep in math, been harassed by Dirk the Jerk, taken the bus home . . . And found a man in a tuxedo sitting on the couch. I didn’t doubt he was a spy for a second. Alexander Hale looked exactly like I’d always imagined a spy would. A tiny bit older, perhaps—he seemed about fifty—but still suave and debonair. He had a small scar on his chin—from a bullet, I guessed, or maybe something more exotic, like a crossbow. There was something very James Bond about him; I could imagine he’d been in a car chase on the way over and taken out the bad guys without breaking a sweat. My parents weren’t home. They never were when I got back from school. Alexander had obviously “let himself in.” The photo album from our family vacation to Virginia Beach sat open on the ~ Stuart Gibbs,
1369:Buffy: “I was just thinking, wouldn’t it be funny to see each other sometime when it wasn’t a blood thing? Not funny ha ha.”
Angel: “What are you saying, you want to have a date?”
Buffy: “No—”
Angel: “You don’t want to have a date?”
Buffy: “Who said ‘date’? I never said ‘date.’”
Angel: “Right. You just want to have coffee or something.”
Buffy: “Coffee?”
Angel: “I knew this would happen.”
Buffy: “Really? And what do you think is happening?”
Angel: “You’re sixteen years old, I’m 241.”
Buffy: “I’ve done the math.”
Angel: “You don’t know what you’re doing, you don’t know what you want.”
Buffy: “Oh, I think I do: I want out of this conversation.”
Angel: “Listen. If we date, you and I both know one thing’s going to lead to another.”
Buffy: “One thing’s already led to another. It’s a little late to be reading me the warning label.”
Angel: “I’m just trying to protect you. This could get out of control.”
Buffy: “Isn’t that the way it’s supposed to be?”
Angel: “This isn’t some fairy tale; when I kiss you, you don’t wake up from a deep sleep and live happily ever after.”
Buffy: “No. When you kiss me, I want to die.”
—“REPTILE BOY” ~ Christopher Golden,
1370:I stood straight and calm, though every part of me wanted to blast the crap out of the room. No one moved, no one spoke. I barely breathed. I didn’t know how much time had passed when Ty finally broke the silence. “If we’re demigods and you are demigods, which gods are our grandparents?” Tyde asked, snapping me out of my funk. Why hadn’t it occurred to me to ask that? My parents were the children of gods. All Mer were thought of as children of Poseidon in some respects, but this was different. “Well, your father’s father is Apollo,” Mom said, “And my father is… Zeus.” Whoa, that was big. Zeus was our grandfather. How does someone wrap their mind around that? “So our grandfathers are Apollo and Zeus, but aren’t they related? Wouldn’t that make you and Dad…” Ty couldn’t finish that thought and I was grateful. I was now grossed out. I couldn’t do the math on that messed up family tree. Yuck. “It doesn’t really work that way with the gods,” Mom said, catching on to what Ty was hinting at. “They are so ancient that their blood, while it will carry power, doesn’t carry much else in terms of genealogy. Our DNA comes mostly from our mortal parents. Our powers come from our godly parents but that’s it. It’s complicated, but your father and I are not related. So if you were worried… stop. You’re not the product of kissing cousins ~ Emory Gayle,
1371:The fundamental problem with learning mathematics is that while the number sense may be genetic, exact calculation requires cultural tools—symbols and algorithms—that have been around for only a few thousand years and must therefore be absorbed by areas of the brain that evolved for other purposes. The process is made easier when what we are learning harmonizes with built-in circuitry. If we can’t change the architecture of our brains, we can at least adapt our teaching methods to the constraints it imposes. For nearly three decades, American educators have pushed “reform math,” in which children are encouraged to explore their own ways of solving problems. Before reform math, there was the “new math,” now widely thought to have been an educational disaster. (In France, it was called les maths modernes and is similarly despised.) The new math was grounded in the theories of the influential Swiss psychologist Jean Piaget, who believed that children are born without any sense of number and only gradually build up the concept in a series of developmental stages. Piaget thought that children, until the age of four or five, cannot grasp the simple principle that moving objects around does not affect how many of them there are, and that there was therefore no point in trying to teach them arithmetic before the age of six or seven. ~ Jim Holt,
1372:Many teachers felt that no matter how creative they were in the classroom, it wouldn’t make a difference anyway. They talked about a devastating erosion in standards, how the students of today bore no resemblance to the students of even ten or fifteen years ago, how their preoccupations were with anything but school. It was hard for teachers not to feel depressed by the lack of rudimentary knowledge, like in the history class in which students were asked to name the president after John F. Kennedy. Several students meekly raised their hands and proffered the name of Harry Truman. None gave the correct answer of Lyndon Johnson, who also happened to have been a native Texan. In 1975, the average SAT score on the combined math and verbal sections at Permian was 963. For the senior class of 1988–89, the average combined SAT score was 85 points lower, 878. During the seventies, it had been normal for Permian to have seven seniors qualify as National Merit semi-finalists. In the 1988–89 school year the number dropped to one, which the superintendent of schools, Hugh Hayes, acknowledged was inexcusable for a school the size of Permian with a student body that was rooted in the middle class. (A year later, with the help of $15,000 in consultant’s fees to identify those who might pass the required test, the number went up to five.) ~ H G Bissinger,
1373:Something, somewhere, somewhen, must have happened differently… PETUNIA EVANS married Michael Verres, a Professor of Biochemistry at Oxford. HARRY JAMES POTTER-EVANS-VERRES grew up in a house filled to the brim with books. He once bit a math teacher who didn’t know what a logarithm was. He’s read Godel, Escher, Bach and Judgment Under Uncertainty: Heuristics and Biases and volume one of The Feynman Lectures on Physics. And despite what everyone who’s met him seems to fear, he doesn’t want to become the next Dark Lord. He was raised better than that. He wants to discover the laws of magic and become a god. HERMIONE GRANGER is doing better than him in every class except broomstick riding. DRACO MALFOY is exactly what you would expect an eleven-year-old boy to be like if Darth Vader were his doting father. PROFESSOR QUIRRELL is living his lifelong dream of teaching Defense Against the Dark Arts, or as he prefers to call his class, Battle Magic. His students are all wondering what’s going to go wrong with the Defense Professor this time. DUMBLEDORE is either insane, or playing some vastly deeper game which involved setting fire to a chicken. DEPUTY HEADMISTRESS MINERVA MCGONAGALL needs to go off somewhere private and scream for a while. Presenting: HARRY POTTER AND THE METHODS OF RATIONALITY You ain’t guessin’ where this one’s going. ~ Anonymous,
1374:The Measure of America, a report of the Social Science Research Council, ranks every state in the United States on its “human development.” Each rank is based on life expectancy, school enrollment, educational degree attainment, and median personal earnings. Out of the 50 states, Louisiana ranked 49th and in overall health ranked last. According to the 2015 National Report Card, Louisiana ranked 48th out of 50 in eighth-grade reading and 49th out of 50 in eighth-grade math. Only eight out of ten Louisianans have graduated from high school, and only 7 percent have graduate or professional degrees. According to the Kids Count Data Book, compiled by the Annie E. Casey Foundation, Louisiana ranked 49th out of 50 states for child well-being. And the problem transcends race; an average black in Maryland lives four years longer, earns twice as much, and is twice as likely to have a college degree as a black in Louisiana. And whites in Louisiana are worse off than whites in Maryland or anywhere else outside Mississippi. Louisiana has suffered many environmental problems too: there are nearly 400 miles of low, flat, subsiding coastline, and the state loses a football field–size patch of wetland every hour. It is threatened by rising sea levels and severe hurricanes, which the world’s top scientists connect to climate change. ~ Arlie Russell Hochschild,
1375:I get in the car and go to complex A, and look for room 23, and then I knock on the door. The door opens, but it’s not Madison. It’s someone else. I hold the flowers I brought for her in my hand and fidget. “Hi, is Madison here?” “Nope,” she says and she smacks her gum. “Nope?” I repeat like a total dumbass. “Nope.” She smacks her gum again. “Do you know where she is?” She shrugs. “She went dancing with one of the guys in her math class.” “But…we had a date.” She laughs. “Oh, you’re the one.” “The one what?” “The one she caught telling your friends she was just a girl and that her name didn’t matter because there were so damn many of them you couldn’t keep them all straight.” What the hell is she talking about? “She followed you after you dropped her off that day. She wanted to give you her phone number. But she heard you.” “And now she’s out on a date? With somebody else?” She nods and pops her gum again. “Yep.” “Do you know where?” “At the club on Main Street. I can’t remember the name of it.” I turn on my heel and stalk in that direction. I don’t know what bothers me more—that she’s dancing with some random guy or that she stood me up. But I do know what bothers me most. It’s that she heard my stupid comment. I have to explain it to her. And I have to be sure she’s not kissing some random guy. She’s supposed to be kissing me, damn it. ~ Tammy Falkner,
1376:The Roman general wanted to spare Archimedes, because he was so valuable—sort of like the Einstein of the ancient world—but some stupid Roman soldier killed him.” “There you go again,” Hazel muttered. “Stupid and Roman don’t always go together, Leo.” Frank grunted agreement. “How do you know all this, anyway?” he demanded. “Is there a Spanish tour guide around here?” “No, man,” Leo said. “You can’t be a demigod who’s into building stuff and not know about Archimedes. The guy was seriously elite. He calculated the value of pi. He did all this math stuff we still use for engineering. He invented a hydraulic screw that could move water through pipes.” Hazel scowled. “A hydraulic screw. Excuse me for not knowing about that awesome achievement.” “He also built a death ray made of mirrors that could burn enemy ships,” Leo said. “Is that awesome enough for you?” “I saw something about that on TV,” Frank admitted. “They proved it didn’t work.” “Ah, that’s just because modern mortals don’t know how to use Celestial bronze,” Leo said. “That’s the key. Archimedes also invented a massive claw that could swing on a crane and pluck enemy ships out of the water.” “Okay, that’s cool,” Frank admitted. “I love grabber-arm games.” “Well, there you go,” Leo said. “Anyway, all his inventions weren’t enough. The Romans destroyed his city. Archimedes was killed. ~ Rick Riordan,
1377:Al is the upside down man. Back home, you work all day and night to learn how to paint, learn linseed and cadmium and badger-hair and perspective, which is just math in art-school drag, you know? And maybe you still can't do anything worth phoning the Met over. But hey, getting a boy to fuck you is just the easiest thing since Sunday naps. Up top, getting drunk at a party is what you do when you're all out of art. But in...Canada? Are we calling it Canada now? Ok! Al's the King of Canada and he says: fuck that for a lark! The world feels like being a bastard-and-a-half this decade, let's play nine-pins on its grave. Down here it's all the same! Kiss a boy and books come out! Ralph up Parthenons into the upstairs toilet! Dance poems, shit showtunes! Art is easy! Pick up genius at the corner shop! Sell your soul and half your shoes for a glass of gin!' He looks up at Zelda Fair and his poor goblin face goes all twisted up and desperate. 'It's all fucked anyway, you see? The end of the world already happened. It's happening all the time. It's gonna happen again. And again after that. Just when you think it's done falling on its face, the world picks itself up and throws itself off a roof. Boom. Pavement. The world's ending forever and ever and we're not even allowed to toast at her funeral. So we gotta do something else or she won't know we ever loved her. ~ Catherynne M Valente,
1378:You can be a rich person alone. You can be a smart person alone. But you cannot be a complete person alone. For that you must be part of, and rooted in, an olive grove. This truth was once beautifully conveyed by Rabbi Harold S. Kushner in his interpretation of a scene from Gabriel García Márquez’s classic novel One Hundred Years of Solitude: Márquez tells of a village where people were afflicted with a strange plague of forgetfulness, a kind of contagious amnesia. Starting with the oldest inhabitants and working its way through the population, the plague causes people to forget the names of even the most common everyday objects. One young man, still unaffected, tries to limit the damage by putting labels on everything. “This is a table,” “This is a window,” “This is a cow; it has to be milked every morning.” And at the entrance to the town, on the main road, he puts up two large signs. One reads “The name of our village is Macondo,” and the larger one reads “God exists.” The message I get from that story is that we can, and probably will, forget most of what we have learned in life—the math, the history, the chemical formulas, the address and phone number of the first house we lived in when we got married—and all that forgetting will do us no harm. But if we forget whom we belong to, and if we forget that there is a God, something profoundly human in us will be lost. ~ Thomas L Friedman,
1379:counterfactual emotions,” or the feelings that spurred people’s minds to spin alternative realities in order to avoid the pain of the emotion. Regret was the most obvious counterfactual emotion, but frustration and envy shared regret’s essential trait. “The emotions of unrealized possibility,” Danny called them, in a letter to Amos. These emotions could be described using simple math. Their intensity, Danny wrote, was a product of two variables: “the desirability of the alternative” and “the possibility of the alternative.” Experiences that led to regret and frustration were not always easy to undo. Frustrated people needed to undo some feature of their environment, while regretful people needed to undo their own actions. “The basic rules of undoing, however, apply alike to frustration and regret,” he wrote. “They require a more or less plausible path leading to the alternative state.” Envy was different. Envy did not require a person to exert the slightest effort to imagine a path to the alternative state. “The availability of the alternative appears to be controlled by a relation of similarity between oneself and the target of envy. To experience envy, it is sufficient to have a vivid image of oneself in another person’s shoes; it is not necessary to have a plausible scenario of how one came to occupy those shoes.” Envy, in so