[From Bill Powers (931021.1130 MDT)]
Martin Taylor (931020.1440), Rick Marken (931020.1500) --
Rick is correct in pointing out that any perceptual function of
multiple lower-level perceptions CAN BE SEEN as creating what we
call a category. Martin is correct in pointing out that when
lower-level aspects of perceptions are perceived as aspects of
categorization, great confusion results. But we are still left
with problems.
If a category-perception is a signal that is a function of any of
several sets of lower-level contributors, then in that respect it
is just like a perception at any other level. The relation
between elements of a category and the category signal is not
unique to the category level, and so is not sufficient to define
what we mean by category.
If all that distinguishes the category level from lower levels is
the (proposed) fact that the signal is binary, being either ON or
OFF, then there is nothing about the actual perceptual function
itself that characterizes the category level. The binary-ness can
be accomplished by a simple threshold trigger mechanism; this
does not tell us what kind of function is producing the
perceptual signal, but only what is done with the signal. The
question is whether the existence of a binary flip-flop situation
is itself sufficient to define a category level.
The possibility of cross-connections between different perceptual
functions is reasonable; I have suggested this before, as has
Martin. Mutual lateral inhibition, with the perceptual signal of
one system reducing the gain of "neighboring" input functions,
can be adjusted to any degree from a slight suppression effect to
a complete catastrophic flip-flop effect. The magnitude of the
mutual lateral inhibition can be estimated from the magnitude of
hysteresis effects. Those effects, while easily measurable, are
not always so large as to create a total flip-flop situation. The
boundary is shifted, but not all the way toward the unselected
perception.
Mutual lateral inhibition can create the appearance of a binary
choice, or something near it, but is this sufficient to
characterize a category level? In fact, if mutual lateral
inhibition were to occur at ANY level of perception, the same
effect would be seen. We know that mutual lateral inhibition
exists as low in the nervous system as the retina, and that it
does have the effect of "edge enhancement." We can conjecture
that it probably exists at the configuration level, too, as in
the reversible cube and staircase, and in the figure-ground
phenomena of the face and the vase or the hag and the rabbit.
Some interpretations of configurations (in three dimensions) are
simply ambiguous and depend on what part of a figure one imagines
to be farthest away. But one must imagine one or the other
situation; it is impossible (or at least very rare) to imagine
both at once.
Other configuration perceptions, for no discernible a priori
reason, are simply mutually exclusive; one sees a face or a vase
but never both; a hag or a rabbit, but never both. This mutual
exclusiveness is not just a matter of categorizing; it is
inherent in the perception of the configuration, and one simply
does not see more than one of the mutually-exclusive
configurations at a time. You can feel the shift occurring, and
it is clearly a flip-flop effect. This phenomena is handily
explained by mutual lateral inhibition at the configuration
level. It may be possible for a person to learn to eliminate or
weaken this mutual inhibition (I believe Greg said he could do
it), but in general I think it exists willy-nilly, and is a very
strong effect where there is mutual exclusiveness.
So we lose the uniqueness of mutual lateral inhibition, and the
resulting binary effects on perception, as a determinant of the
category level.
There is still another problem. In the PCT model, a difference
between two categories is not carried by different values of a
single category-perception signal, but by presence of a category
signal in the output of one perceptual function rather than the
output of a physically different perceptual function. This means
that at the category level, there is no necessary constraint
(except through possible mutual lateral inhibitions) that
prevents two categories from being perceived at the same time. In
fact the most common case is for MANY categories to be perceived
in the same set of lower-level perceptions. If I say "The red
ball in the northeast corner and with a string attached to it," I
am specifying multiple categories to which the item that I am
trying to distinguish belongs.
The fact that categories are involved here is clear when we
examine each element. "Ball" by itself indicates a category that
includes many very different items, from a doll's ball to a
beach-ball to a ball-bearing, in many different locations, with
many different relationships to other objects, and so forth.
"Red" is a category that includes many hues and saturations and
occurs in conjuction with many objects. A "corner" is any of many
configurations that differ in orientation and other attributes; a
"string" is certainly no specific piece of string, and "attached"
covers many kinds of attachments. So this phrase really evokes
many category signals at the same time. Only a few sets of
categories are mutually exclusive, such as "face" and "vase",
and many of those may be mutually exclusive because of lateral
inhibition at a lower level rather than the category level. They
DO not occur at the same time, but there is nothing at the
category level that says they MUST NOT occur at the same time. We
can perceive that A is inside of B and at the same time outside
of C; the categories "inside" and "outside" can certainly be
perceived at the same time -- but some relationship perceptions
may be mutually-exclusive, for example because A cannot be
perceived as both inside and outside of B. Other categories such
as "mine" and "yours" may seem mutually exclusive at first, until
we remember that there is also a case called "ours," meaning
"yours" AND "mine."
I am working toward the point that there can be confusion about
category perceptions not only through mixing them up with lower
levels of perception, but through confusing them with higher
levels, particularly the logic level.
When we talk about "intersecting categories" as a means of
narrowing down a specification, what is it that we imagine to be
carrying out this intersection process? The category level would
be concerned only with providing signals standing for categories
perceived in the current world of specific lower-level signals.
Are we to propose that this level also does the intersecting of
the categories? I say no, intersection is a different process
from categorizing; it is a logical process, and belongs to the
logic or program level.
Note how we can recast the statement about the ball in the
corner. Ungrammatically (an irrelevant dimension for now) we can
say "ball AND red AND corner AND northwest AND string AND string-
attached...". We are saying by that logical expression that we
require the presence of all of these category signals at the same
time, in an either-or way for each of them. The logical
expression is a simple Boolean conjunction of multiple logical
variables.
What this suggests to me is that the conversion to binary
variables occurs at the input of the logic level as a
thresholding process and is not necessarily present at the output
of the category level. This allows the phenomenon that Rick
mentioned: the appreciation of particular perceptual fields as
better or worse examples of a given fixed category.
We can now explain a phenomenon that would be difficult to
explain if categories were actually binary in nature. Consider
the process now called, happily, "morphing." Here one visual
pattern is converted into a very different one (in a different
category) by a graphical algorithm that slowly and simultaneously
alters the positions of points in one picture to become points in
another picture, each transition being scaled so that all
transitions are uniform and start and end at the same times.
If we morph a picture of an elephant into a picture of a mouse,
two things happen. At the category level, the impressions of
mouse and elephant change magnitude, I propose, in a smooth way:
each becomes a better or worse example of its category. We can
say of the same image, "that's a poor mouse and an even worse
elephant."
The other thing that happens beside this smooth change in
category, with both category signals being present to varying
degrees, is the imposition at the logic level of an exclusive-or
way of perceiving. At some point we stop describing the picture
as "elephant" and start describing it as "mouse." Going from
mouse to elephant, the boundary might shift toward mouse, the
hysteresis effect. But the logic level imposes a new condition
that is not a constraint at the category level: (mouse AND NOT
elephant) OR (elephant AND NOT mouse). We say "the same thing
can't be both an elephant and a mouse." Unwittingly, we also
impose the condition, "the same thing can't be both NOT an
elephant and NOT a mouse," unless experience has taught us not to
apply the exclusive-or too casually. In learning to perceive
logical variables, we often make mistakes, as in assuming that A-
implies-B is the same as B-implies-A.
So all the processes that are binary in nature are imposed by the
way the logic level thresholds the continuous input signals that
reach it, and the way the input functions convert the states of
the resulting on-off signals into values of logical expressions.
I realize that I've skipped the sequence level, and that what I
have proposed here doesn't yet sound like a program level. Never
mind. These levels need a more careful look anyway; quite likely
a different and finer breakdown is needed.
I realize, too, that I may have left the category level with
nothing to do, but I don't really think so. In the past, I've
spoken of the configuration level as perceiving the degree to
which a given configuration is present. That sounds a lot like
the category level I've just described. However, I think the
problem is that I've been putting category-like properties into
the configuration level, and they should be removed. For a nice
example, see BCP, p. 126.
One idea is to speak of configuration-type variables rather than
configurations as classes. Variables like orientation, size, and
position are configuration-type variables, although they don't
specify any _particular_ configuration-class. Variables like
amplitude and frequency are event-type variables, but can be
combined to produce any specific event. Etc.
When a reference signal reaches a category-level system, it
signifies that an input is to be created for that system that
means presence of something in that category. As these reference
signals are generated by a logic-type system, they are either ON
or OFF: there are no reference signals specifying degrees of
membership in a given category.
Some inputs may create more category signal than others, but only
one input signal is needed. A signal standing for my mother's
face, or one very like it, and a signal standing for my sister's
face, are each sufficient to create a perception in the category
I call "a relative." To have enough signal to let the logic level
accept that "relative" is true, I might need a good likeness of
mother or sister to be present, or to have both present at once.
I'm sure Martin would like to offer another interpretation, if
we'd let him.
So we get some inkling of the kind of perceptual function that is
needed at the category level-- an inkling, but still not a very
good definition.
When a couple more generations of desktop computers have gone by,
we might be able to implement real-time morphing and do some
relevant experiments. Right now I don't think that even a 586
(Pentium) would produce interesting graphics in real time. But
maybe someone will think (or has thought) of simpler ways to do
this. Line-drawings? Maybe.
Too long, too long. But there was a lot to think about.
···
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Best,
Bill P.