1.06 - Gestalt and Universals

classes ::: Cybernetics, Cybernetics, or Control and Communication in the Animal and the Machine, Norbert Wiener, chapterAmong other things which we have discussed in the previous,
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object:1.06 - Gestalt and Universals
subject class:Cybernetics
book class:Cybernetics, or Control and Communication in the Animal and the Machine
author class:Norbert Wiener
class:chapterAmong other things which we have discussed in the previous
chapter is the possibility of assigning a neural mechanism to
Locke’s theory of the association of ideas. According to Locke,
this occurs according to three principles: the principle of conti-
guity, the principle of similarity, and the principle of cause and
effect. The third of these is reduced by Locke, and even more
definitively by Hume, to nothing more than constant concomi-
tance, and so is subsumed under the first, that of contiguity. The
second, that of similarity, deserves a more detailed discussion.
How do we recognize the identity of the features of a man,
whether we see him in profile, in three-quarters face, or in full
face? How do we recognize a circle as a circle, whether it is large
or small, near or far; whether, in fact, it is in a plane perpendicu-
lar to a line from the eye meeting it in the middle, and is seen as
a circle, or has some other orientation, and is seen as an ellipse?
How do we see faces and animals and maps in clouds, or in the
blots of a Rorschach test? All these examples refer to the eye,
but similar problems extend to the other senses, and some of
them have to do with intersensory relations. How do we put into
words the call of a bird or the stridulations of an insect? How do
we identify the roundness of a coin by touch?184
Chapter VI
For the present, let us confine ourselves to the sense of
vision. One important factor in the comparison of form of dif-
ferent objects is certainly the interaction of the eye and the
muscles, whether they are the muscles within the eyeball, the
muscles moving the eyeball, the muscles moving the head, or
the muscles moving the body as a whole. Indeed, some form of
this visual-muscular feedback system is important as low in the
animal kingdom as the flatworms. There the negative phototro-
pism, the tendency to avoid the light, seems to be controlled by
the balance of the impulses from the two eyespots. This balance
is fed back to the muscles of the trunk, turning the body away
from the light, and, in combination with the general impulse to
move forward, carries the animal into the darkest region acces-
sible. It is interesting to note that a combination of a pair of
photocells with appropriate amplifiers, a Wheatstone bridge for
balancing their outputs, and further amplifiers controlling the
input into the two motors of a twinscrew mechanism would
give us a very adequate negatively phototropic control for a little
boat. It would be difficult or impossible for us to compress this
mechanism into the dimensions that a flatworm can carry; but
here we merely have another exemplification of the fact that
must by now be familiar to the reader, that living mechanisms
tend to have a much smaller space scale than the mechanisms
best suited to the techniques of human artificers, although, on
the other hand, the use of electrical techniques gives the artifi-
cial mechanism an enormous advantage in speed over the living
organism.
Without going through all the intermediate stages, let us
come at once to the eye-muscle feedbacks in man. Some of these
are of purely homeostatic nature, as when the pupil opens in
the dark and closes in the light, thus tending to confine theGestalt and Universals
185
flow of light into the eye between narrower bounds than would
otherwise be possible. Others concern the fact that the human
eye has economically confined its best form and color vision to
a relatively small fovea, while its perception of motion is bet-
ter on the periphery. When the peripheral vision has picked
up some object conspicuous by brilliancy or light contrast or
color or above all by motion, there is a reflex feedback to bring
it into the fovea. This feedback is accompanied by a compli-
cated system of interlinked subordinate feedbacks, which tend
to converge the two eyes so that the object attracting attention
is in the same part of the visual field of each, and to focus the
lens so that its outlines are as sharp as possible. These actions
are supplemented by motions of the head and body, by which
we bring the object into the center of vision if this cannot be
done readily by a motion of the eyes alone, or by which we
bring an object outside the visual field picked up by some
other sense into that field. In the case of objects with which
we are more familiar in one angular orientation than another—
writing, human faces, landscapes, and the like—
there is also
a mechanism by which we tend to pull them into the proper
orientation.
All these processes can be summed up in one sentence: we
tend to bring any object that attracts our attention into a stan-
dard position and orientation, so that the visual image which
we form of it varies within as small a range as possible. This does
not exhaust the processes which are involved in perceiving the
form and meaning of the object, but it certainly facilitates all
later processes tending to this end. These later processes occur in
the eye and in the visual cortex. There is considerable evidence
that for a considerable number of stages each step in this pro-
cess diminishes the number of neuron channels involved in the186
Chapter VI
transmission of visual information, and brings this information
one step nearer to the form in which it is used and is preserved
in the memory.
The first step in this concentration of visual information
occurs in the transition between the retina and the optic nerve.
It will be noted that while in the fovea there is almost a one-one
correspondence between the rods and cones and the fibers of the
optic nerve, the correspondence on the periphery is such that
one optic nerve fiber corresponds to ten or more end organs.
This is quite understandable, in view of the fact that the chief
function of the peripheral fibers is not so much vision itself as
a pickup for the centering and focusing-directing mechanism of
the eye.
One of the most remarkable phenomena of vision is our abil-
ity to recognize an outline drawing. Clearly, an outline drawing
of, say, the face of a man, has very little resemblance to the face
itself in color, or in the massing of light and shade, yet it may
be a most recognizable portrait of its subject. The most plausible
explanation of this is that, somewhere in the visual process, out-
lines are emphasized and some other aspects of an image are
minimized in importance. The beginning of these processes is in
the eye itself. Like all senses, the retina is subject to accommo-
dation; that is, the constant maintenance of a stimulus reduces
its ability to receive and to transmit that stimulus. This is most
markedly so for the receptors which record the interior of a large
block of images with constant color and illumination, for even
the slight fluctuations of focus and point of fixation which are
inevitable in vision do not change the character of the image
received. It is quite different on the boundary of two contrasting
regions. Here these fluctuations produce an alternation between
one stimulus and another, and this alternation, as we see in theGestalt and Universals
187
phenomenon of after-images, not only does not tend to exhaust
the visual mechanism by accommodation but even tends to
enhance its sensitivity. This is true whether the contrast between
the two adjacent regions is one of light intensity or of color. As
a comment on these facts, let us note that three-quarters of the
fibers in the optic nerve respond only to the flashing “on" of
illumination. We thus find that the eye receives its most intense
impression at boundaries, and that every visual image in fact has
something of the nature of a line drawing.
Probably not all of this action is peripheral. In photography, it
is known that certain treatments of a plate increase its contrasts,
and such phenomena, which are of non-linearity, are certainly
not beyond what the nervous system can do. They are allied to
the phenomena of the telegraph-type repeater, which we have
already mentioned. Like this, they use an impression which
has not been blurred beyond a certain point to trigger a new
impression of a standard sharpness. At any rate, they decrease
the total unusable information carried by an image, and are
probably correlated with a part of the reduction of the num-
ber of transmission fibers found at various stages of the visual
cortex.
We have thus designated several actual or possible stages
of the diagrammatization of our visual impressions. We cen-
ter our images around the focus of attention and reduce them
more or less to outlines. We have now to compare them with
one another, or at any rate with a standard impression stored
in memory, such as “circle" or “square." This may be done in
several ways. We have given a rough sketch which indicates how
the Lockean principle of contiguity in association may be mech-
anized. Let us notice that the principle of contiguity also covers
much of the other Lockean principle of similarity. The different188
Chapter VI
aspects of the same object are often to be seen in those processes
which bring it to the focus of attention, and of other motions
which lead us to see it, now at one distance and now at another,
now from one angle and now from a distinct one. This is a gen-
eral principle, not confined in its application to any particular
sense and doubtless of much importance in the comparison of
our more complicated experiences. It is nevertheless probably
not the only process which leads to the formation of our specifi-
cally visual general ideas, or, as Locke would call them, “complex
ideas." The structure of our visual cortex is too highly organized,
too specific, to lead us to suppose that it operates by what is
after all a highly generalized mechanism. It leaves us the impres-
sion that we are here dealing with a special mechanism which is
not merely a temporary assemblage of general-purpose elements
with interchangeable parts, but a permanent sub-assembly like
the adding and multiplying assemblies of a computing machine.
Under the circumstances, it is worth considering how such a
sub-assembly might possibly work and how we should go about
designing it.
The possible perspective transformations of an object form
what is known as a group, in the sense in which we have already
defined one in Chapter II. This group defines several sub-groups
of transformations: the affine group, in which we consider
only those transformations which leave the region at infinity
untouched; the homogeneous dilations about a given point, in
which one point, the directions of the axes, and the equality of
scale in all directions are preserved; the transformations preserv-
ing length; the rotations in two or three dimensions about a
point; the set of all translations; and so on. Among these groups,
the ones we have just mentioned are continuous; that is, the
operations belonging to them are determined by the values ofGestalt and Universals
189
a number of continuously varying parameters in an appropri-
ate space. They thus form multidimensional configurations in
n-space, and contain sub-sets of transformations which consti-
tute regions in such a space.
Now, just as a region in the ordinary two-dimensional plane
is covered by the process of scanning known to the television
engineer, by which a nearly uniformly distributed set of sam-
ple positions in that region is taken to represent the whole,
so every region in a group-space, including the whole of such
a space, can be represented by a process of group scanning. In
such a process, which is by no means confined to a space of
three dimensions, a net of positions in the space is traversed
in a one-dimensional sequence, and this net of positions is so
distributed that it comes near to every position in the region, in
some appropriately defined sense. It will thus contain positions
as near to any we wish as may be desired. If these “positions,"
or sets of parameters, are actually used to generate the appro-
priate transformations, it means that the results of transform-
ing a given figure by these transformations will come as near
as we wish to any given transformation of the figure by a trans-
formation operator lying in the region desired. If our scanning
is fine enough, and the region transformed has the maximum
dimensionality of the regions transformed by the group consid-
ered, this means that the transformations actually traversed will
give a resulting region overlapping any transform of the original
region by an amount which is as large a fraction of its area as
we wish.
Let us then start with a fixed comparison region and a region
to be compared with it. If at any stage of the scanning of the
group of transformations the image of the region to be com-
pared under some one of the transformations scanned coincides190
Chapter VI
more perfectly with the fixed pattern than a given tolerance
allows, this is recorded, and the two regions are said to be alike.
If this happens at no stage of the scanning process, they are
said to be unlike. This process is perfectly adapted to mecha-
nization, and serves as a method to identify the shape of a fig-
ure independently of its size or its orientation or of whatever
transformations may be included in the group-
region to be
scanned.
If this region is not the entire group, it may well be that
region A seems like region B, and that region B seems like
region C, while region A does not seem like region C. This cer-
tainly happens in reality. A figure may not show any particular
resemblance to the same figure inverted, at least in so far as the
immediate impression—
one not involving any of the higher
processes—is concerned. Nevertheless, at each stage of its inver-
sion, there may be a considerable range of neighboring positions
which appear similar. The universal “ideas" thus formed are not
perfectly distinct but shade into one another.
There are other more sophisticated means of using group
scanning to abstract from the transformations of a group. The
groups which we here consider have a “group measure," a prob-
ability density which depends on the transformation group itself
and does not change when all the transformations of the group
are altered by being preceded or followed by any specific trans-
formation of the group. It is possible to scan the group in such
a way that the density of scanning of any region of a consider-
able class—that is, the amount of time which the variable scan-
ning element passes within the region in any complete scanning
of the group—is closely proportional to its group measure. In
the case of such a uniform scanning, if we have any quantity
depending on a set S of elements transformed by the group, andGestalt and Universals
191
if this set of elements is transformed by all the transformations
of the group, let us designate the quantity depending on S by
Q(S), and let us use TS to express the transform of the set S by the
transformation T of the group. Then Q(TS) will be the value of
the quantity replacing Q(S) when S is replaced by TS. If we aver-
age or integrate this with respect to the group measure for the
group of transformations T, we shall obtain a quantity which we
may write in some such form as
∫ Q ( TS ) dT
(6.01)
where the integration is over the group measure. Quantity 6.01
will be identical for all sets S interchangeable with one another
under the transformations of the group, that is, for all sets S
which have in some sense the same form or Gestalt. It is pos-
sible to obtain an approximate comparability of form where the
integration in Quantity 6.01 is over less than the whole group,
if the integrand Q(TS) is small over the region omitted. So much
for group measure.
In recent years, there has been a good deal of attention to the
problem of the prosthesis of one lost sense by another. The most
dramatic of the attempts to accomplish this has been the design
of reading devices for the blind, to work by the use of photo-
electric cells. We shall suppose that these efforts are confined to
printed matter, and even to a single type face or to a small num-
ber of type faces. We shall also suppose that the alignment of
the page, the centering of the lines, the traverse from line to line
are taken care of either manually or, as they may well be, auto-
matically. These processes correspond, as we may see, to the part
of our visual Gestalt determination which depends on muscular
feedbacks and the use of our normal centering, orienting, focus-
ing, and converging apparatus. There now ensues the problem192
Chapter VI
of determining the shapes of the individual letters as the scan-
ning apparatus passes over them in sequence. It has been sug-
gested that this be done by the use of several photoelectric cells
placed in a vertical sequence, each attached to a sound-making
apparatus of a different pitch. This can be done with the black of
the letters registering either as silence or as sound. Let us assume
the latter case, and let us assume three photocell receptors above
one another. Let them record as the three notes of a chord, let
us say, with the highest note on top and the lowest note below.
Then the letter capital F, let us say, will record
——————
Duration of upper note
———— Duration of middle note
—
Duration of lower note
The letter capital Z will record
——————
—
——————
the letter capital O
—
—
—
—
and so on. With the ordinary help given by our ability to inter-
pret, it should not be too difficult to read such an auditory code,
not more difficult than to read Braille, for instance.
However, all this depends on one thing: the proper relation
of the photocells to the vertical height of the letters. Even with
standardized type faces, there still are great variations in the sizeGestalt and Universals
193
of the type. Thus it is desirable for us to be able to pull the ver-
tical scale of the scanning up or down, in order to reduce the
impression of a given letter to a standard. We must at least have
at our disposal, manually or automatically, some of the transfor-
mations of the vertical dilation group.
There are several ways we might do this. We might allow for a
mechanical vertical adjustment of our photocells. On the other
hand, we might use a rather large vertical array of photocells
and change the pitch assignment with the size of type, leaving
those above and below the type silent. This may be done, for
example, with the aid of a schema of two sets of connectors, the
inputs coming up from the photocells, and leading to a series
of switches of wider and wider divergence, and the outputs a
series of vertical lines, as in Fig. 8. Here the single lines repre-
sent the leads from the photocells, the double lines the leads to
the oscillators, the circles on the dotted lines the points of con-
nections between incoming and outgoing leads, and the dotted
lines themselves the leads whereby one or another of a bank of
oscillators is put into action. This was the device, to which we
have referred in the introduction, designed by McCulloch for
the purpose of adjusting to the height of the type face. In the
first design, the selection between dotted line and dotted line
was manual.
Fig. 8194
Chapter VI
This was the figure which, when shown to Dr. von Bonin, sug-
gested the fourth layer of the visual cortex. It was the connect-
ing circles which suggested the neuron cell bodies of this layer,
arranged in sub-layers of uniformly changing horizontal density,
and size changing in the opposite direction to the density. The
horizontal leads are probably fired in some cyclical order. The
whole apparatus seems quite suited to the process of group scan-
ning. There must of course be some process of recombination in
time of the upper outputs.
This then was the device suggested by McCulloch as that
actually used in the brain in the detection of visual Gestalt. It
represents a type of device usable for any sort of group scanning.
Something similar occurs in other senses as well. In the ear, the
transposition of music from one fundamental pitch to another
is nothing but a translation of the logarithm of the frequency,
and may consequently be performed by a group-
scanning
apparatus.
A group-scanning assembly thus has well-defined, appropri-
ate anatomical structure. The necessary switching may be per-
formed by independent horizontal leads which furnish enough
stimulation to shift the thresholds in each level to just the proper
amount to make them fire when the lead comes on. While we do
not know all the details of the performance of the machinery, it
is not at all difficult to conjecture a possible machine conform-
ing to the anatomy. In short, the group-scanning assembly is
well adapted to form the sort of permanent sub-assembly of the
brain corresponding to the adders or multipliers of the numeri-
cal computing machine.
Lastly, the scanning apparatus should have a certain intrin-
sic period of operation which should be identifiable in the per-
formance of the brain. The order of magnitude of this periodGestalt and Universals
195
should show in the minimum time required for making direct
comparison of the shapes of objects different in size. This can be
done only when the comparison is between two objects not too
different in size; otherwise, it is a long-time process, suggestive
of the action of a non-specific assembly. When direct compari-
son seems to be possible, it appears to take a time of the order
of magnitude of a tenth of a second. This also seems to accord
with the order of magnitude of the time needed by excitation
to stimulate all the layers of transverse connectors in cyclical
sequence.
While this cyclical process then might be a locally deter-
mined one, there is evidence that there is a widespread synchro-
nism in different parts of the cortex, suggesting that it is driven
from some clocking center. In fact, it has the order of frequency
appropriate for the alpha rhythm of the brain, as shown in elec-
troencephalograms. We may suspect that this alpha rhythm
is associated with form perception, and that it partakes of the
nature of a sweep rhythm, like the rhythm shown in the scan-
ning process of a television apparatus. It disappears in deep sleep,
and seems to be obscured and overlaid with other rhythms,
precisely as we might expect, when we are actually looking at
something and the sweep rhythm is acting as something like a
carrier for other rhythms and activities. It is most marked when
the eyes are closed in waking, or when we are staring into space
at nothing in particular, as in the condition of abstraction of a
yogi, 1 when it shows an almost perfect periodicity.
We have just seen that the problem of sensory prosthesis—
the problem of replacing the information normally conveyed
through a lost sense by information through another sense
still available—
is important and not necessarily insoluble.
What makes it more hopeful is the fact that the memory and196
Chapter VI
association areas, normally approached through one sense, are
not locks with a single key but are available to store impressions
gathered from other senses than the one to which they normally
belong. A blinded man, as distinguished perhaps from one con-
genitally blind, not only retains visual memories earlier in date
than his accident but is even able to store tactile and auditory
impressions in a visual form. He may feel his way around a room,
and yet have an image of how it ought to look.
Thus, part of his normal visual mechanism is accessible to
him. On the other hand, he has lost more than his eyes: he has
also lost the use of that part of his visual cortex which may be
regarded as a fixed assembly for organizing the impressions of
sight. It is necessary to equip him not only with artificial visual
receptors but with an artificial visual cortex, which will translate
the light impressions on his new receptors into a form so related
to the normal output of his visual cortex that objects which ordi-
narily look alike will now sound alike.
Thus the criterion of the possibility of such a replacement
of sight by hearing is at least in part a comparison between the
number of recognizably different visual patterns and recog-
nizably different auditory patterns at the cortical level. This is a
comparison of amounts of information. In view of the some-
what similar organization of the different parts of the sensory
cortex, it will probably not differ very much from a comparison
between the areas of the two parts of the cortex. This is about
100:1 as between sight and sound. If all the auditory cortex were
used for vision, we might expect to get a quantity of reception of
information about 1 per cent of that coming in through the eye.
On the other hand, our usual scale for the estimation of vision is
in terms of the relative distance at which a certain degree of reso-
lution of pattern is obtained, and thus a 10/100 vision meansGestalt and Universals
197
an amount of flow of information about 1 per cent of normal.
This is very poor vision; it is, however, definitely not blindness,
nor do people with this amount of vision necessarily consider
themselves as blind.
In the other direction, the picture is even more favorable. The
eye can detect all of the nuances of the ear with the use of only
1 per cent of its facilities, and still leave a vision of about 95/100,
which is substantially perfect. Thus the problem of sensory pros-
thesis is an extremely hopeful field of work.

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