[From Bill Powers (920610.1900)]
Martin Taylor (920610.1830) --
Unfortunately, straightness is a property of the translation of objects
in a special abstract world, not of the projection of the movement of
objects across the retina.
This brings up an interesting point about the involvement of control in
learning perceptions. As you say, straight lines aren't preserved in
general when they move across the retina. Therefore if we try to create an
_arbitrary_ transformation, it is more likely to destroy invariances than
to create them. But suppose you take hold of an object that has a straight
edge and move it so it translates (in external space) ALONG THAT EDGE.
There are two results: one, the image on the retina, at least in its
central parts, is not altered at all, no matter what optical distortions
are involved. The second in a minute.
This means that among all the ways of moving that object across the retina
_by controlling the position of that object_, there is one that will in
fact create a striking invariance: a total lack of change in one perceived
edge of the object (and any line parallel to it), except at the ends.
Therefore if you control for the appearance of the edge, and try to keep it
the same, any freedom of movement that remains will eliminate all possible
invariances but one. This invariant image on the retina isn't itself
"straight," as an external observer would see it. But by its invariance, it
DEFINES the property of straightness.
The other effect is that a kinesthetic path will, or may, be traced by the
hand holding that object in a path that also is straight in external space.
So the feel of straight-line motion is generated at the same time as the
look of straight-line motion. In an approximate sort of way, I can see that
this may be the basis for creating Cartesian perceptual maps in both the
kinesthetic and visual modalities, at the same time.
Another figure that is invariant with respect to a specific way of
controlling that figure is a circle. However distorted its image on the
retina, and whatever the angle of view, that image will remain unchanged if
the circle is rotated about an axis normal to its center. A square is
invariant with respect to 90-degree rotations; an equilaterial triangle
with respect to 120-degree rotations. A plane in space is invariant with
respect to particular manipulations in x,y, and z.
In each case, a particular way of moving the object as part of a process of
control (and particular other ways of NOT moving it) will reveal a true
invariance that is tied to geometrical properties of the outside world. All
that is necessary is to control for a lack of change in the appearance of
the figure while manipulating it. It seems to me that there's a principle
here that could be exploited by those who are investigating perceptual
learning -- but only if they do it in the context of control theory. I
think it's essential for this kind of learning that one have the experience
of doing things to the object yet experiencing no change in the object
(that is, in the particular aspect being noticed). This shows how the
object is free to change without altering its appearance. The object's
invariances are learned both kinesthetically and visually by finding out
what aspects of vision and kinesthesia can be changed through action
without changing some particular aspect of the visual object.
···
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Re: perceptual learning, extreme position.
J.G. Taylor may not have been out of line in insisting at all perception is
learned. We have to think of two aspect of perception (which, Martin, you
have actually mentioned): the TYPE of perception to be learned, and the
PARTICULAR VARIANT of that type.
Consider the phasic stretch reflex. The rather complex physical arrangement
that allows for this reflex involves the muscle spindle, the spinal motor
neuron, and the muscle. I don't think there's much chance that the
EXISTENCE of the phasic component of the stretch reflex is learned in a
single lifetime. If the spindle arrangement and the sensory nerve aren't
there when you're born, you're out of luck. So the TYPE of perception, the
first derivative of muscle length, is present because the physical means of
detecting it is present.
However, you can't be born with a damping coefficient that's fixed, if only
because your arms and legs are going to grow, changing their masses and
moments of inertia continually. The sensitivity of this stretch perception
has to be learned; there's no other way to get the damping coeffient right.
You may even have to construct new cross-connections between motor nerves
serving opponent muscles. So these aspects of perception can't be
inherited.
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With respect to the output map I ended up using for the Little Man, I count
that as more or less of a failure. It would be far better if the
kinesthetic positions were SENSED in a space compatible with the visual
sensory space. The only reason I didn't do it that way was that I couldn't
think of a method for generating the map that would allow behavior to
progress smoothly from a flat map to a map with the required curvatures in
it.
Initially, I had thought that after comparing the kinesthetically sensed
finger position with the visually sensed position, I could use the error to
make small corrections in the map and thus create, eventually, kinesthetic
perceptual signals that agreed with visual ones. But the method I used
created bumps in the map, which then caused instabilities in the control
process, which in turn exaggerated the bumps, and so on. What was needed
was some method that would create corrections all around the position of
the fingertip at any moment, so that the curvatures of the map would
develop on a much larger scale. All the ways of doing that, however, took a
huge amount of computation (trying to imitate a parallel system with one
lonely processor). Also, the correct way of doing it would require a very
long time for building the map, so that bumps would smooth out. In trying
to get the map to form in some reasonable time I simply set the loop gain
of the correction process too high. I felt sort of pressed for time -- I
wanted to get this model into print and I didn't want to make it contingent
on solving the whole perceptual mapping problem. So I settled for an output
map, which works but isn't elegant. And probably isn't the right model.
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Best,
Bill P.