Category questions

[From Rick Marken (931105.0800)]

Bill Powers (931102.1830), Martin Taylor (931104 12:00)--

I may just be categorically challenged, but I still don't
have a clear idea of the difference between a "category"
perception (as a perceptuual type currently located at level
seven of the HPCT model) and any other categorical perception
(for example, all the perceptual "constancies" where some aspect
of a perception -- such as shape [configuration] -- remains
constant despite variations in lower level aspects of the
perception -- such as the component sensations of the shape).

Also, there has been a lot of high-powered "category perception"
model development going on here; do either of you have any
suggestions regarding experiments that might provide some data
against which the models could be evaluated?

"All modelling and no testing makes Jack a trendy scientist"
-- Poor Richard (S. Marken).

Along those lines, I'd would still appreciate any comments
(positive or negative) regarding my suggested test for category
perception (which involved testing the speed at which subjects
can control for what are hypothetically category perceptions and
comparing this to the speed at which they can control sequences,
programs, etc).

One last question:

Martin says:

Aside: there is no "contrast" between p and q [analog variables],
but there is between P and Q [discrete variables]

This "flip-flop" model of "contrast" suggests to me that any mutually
exclusive discrete perception would be considered a "contrast". So this
must include the Necker cube. In my experience, the Necker cube
alternates between two mutually exclusive (and discrete) states; one
corner of the cube is either pointing "toward" me or "away from" me.
So the cube is always in one of two (discrete) states-- "toward" or
"away from"; and never in both (mutually exclusive). This must qualify
perception of the Necker cube as one example of a non-verbal perceptual
contrast, no? (I have a feeling the answer will indeed be "no").



[Martin Taylor 931105 15:00]
(Rick Marken 931105.0800 and Bill Powers 931105.1015)

I like most of Bill's description of why "category" is more than just
the result of a many-to-one transformation. I don't agree that the
level should be called "naming," for reasons that Bill (or was it Mary?)
adduced some time ago--we and probably many animals can perceive categories
without having names for them. Consciously, I find myself often seeing
or hearing "another of those (as opposed to these or THOSE)," without
ever attempting to name them. Categories are useful perceptions, even
without their symbols. That's part of why I differentiated three classes
of perception in my discussion of labelled categories with continuous
values: "P" the label, P the category, and p the value. "P" is itself
a category perception, as is P. Each could evoke the other through the
association mechanism I propose exists within the category level. But
they are not the same. The perception of the symbol is not the perception
of the category. To quote (I think) Korzybski, "The map is not the



This "flip-flop" model of "contrast" suggests to me that any mutually
exclusive discrete perception would be considered a "contrast". So this
must include the Necker cube. In my experience, the Necker cube
alternates between two mutually exclusive (and discrete) states; one
corner of the cube is either pointing "toward" me or "away from" me.
So the cube is always in one of two (discrete) states-- "toward" or
"away from"; and never in both (mutually exclusive). This must qualify
perception of the Necker cube as one example of a non-verbal perceptual
contrast, no? (I have a feeling the answer will indeed be "no").

No. Why "no?" No, you're wrong, the answer is not "no". That's why "no."

Sure, "Necker Cube facing toward" and "Necker Cube facing away" are two
contrasting constructed categories. Contrasting as "toward" and "away"
contrast, constructed because "Necker Cube" and "toward/away" are categories.

The Necker Cube phenomenon is quite interesting. A generation ago, I did
some work on reversing figures, with a mathematically inclined colleague.
The first thing we found was that unless you instruct a person that they
should see a cube facing forward or back, that's not what they see. This
alternation is primarily the property of psychology students, not of the
general public. If you just bring someone in and ask "what do you see,"
they tell you all sorts of things--a butterfly, a chimney pointing up,
a pipe with the hole toward you, a closed box, a flat hexagon with lines
in it ... The longer they look, the more things they see, and the faster
it changes shape. The number of changes of form is proportional to k(k-1)
where k is the number of different forms they have seen. (The fit is so
close that one can't separate the data from the parabolic curve in most
cases.) This is true of almost all line drawings (all that we were able
to create), as well as of alternations of perception in other modalities.
(Rick has the paper in his possession--he commented "good data, bad theory"
at one time).

One of the theories of alternating figures at that time was that the
perceiving system "fatigues" and the fatigue of seeing one form allowed the
other to poke through, and be perceived until the first had again recovered.
To test this notion (which is incompatible with the multi-form results), we
wanted to measure the durations for which a 2-way figure would be seen in
each of its modes (we wanted 3-way, but could not generate one). The
form we wound up with was a flat piece of plasticene dented all over with
a ping-pong ball. It can look like a field of bubbles or a field of dents.
The observers looked at the plasticene, not at a flat picture of it.

We gave the observers a microswitch that they were to press when they saw
a dented surface, and to release when they saw bubbles. We ran each of
four observers for 36 minutes of observation on each of 5 consecutive days,
either 36 separate minutes separated by 15 seconds of rest, or four 9-minute
periods with 3 minutes of rest. There was no obvious difference between
these schedules in the pattern of results. (All this is reported in
Taylor and Aldridge: "Stochastic processes in reversing figure perception"
Perception and Psychophysics, 1974, 16, 9-27, if you want more detail).

To analyze the results, we modelled the process, much as PCT modellers
model the results of a tracking study. The model had two levels. At the
lower level there were a small number of "detector nodes," each of which
had the ability to decide whether it was seeing bubbles or dents. Each
fed its answer into the same upper level node, which decided on what the
actual perception would be. Each lower-level node changed its decision
randomly according to a Poisson process with a fixed rate parameter, the
same for all of them. The upper node decided that the perception was
"Bubbles" if more than B of the lower ones said so, and "Dents" if less
than D (D<B) said it was bubbles. If the number of lower ones saying
"bubbles" was between B and D, the perception stayed at whichever it had
been earlier.

Using this model, the variable parameters are: N, the number of lower-level
nodes; B and D, and the rate parameter k.

We did the analysis for each or the 20 9-minute blocks, regardless of the
schedule of observation. The timing curves looked, on the face of it,
very different from one block to another. Sometimes bubbles would be seen
preferentially, sometimes dents, sometimes they were equal. (I'm talking
about the whole shape of the survivorship curve here, not just average
timing.) The interesting thing was that the changes from one block to the
next could always be accommodated by a single unit shift in B or D, and
(once or twice) in N. The value of k increased reasonably slowly and
smoothly over the week, at least within each day and then across days.

Of the two subjects whose data we published (the most and least variable in
performance), one had 26 lower-level nodes, the other 33 most of the time,
but occasionally dropped to 32 and once went up to 34. The ability of
the model to fit drastic changes in timing data with a one-unit shift
in a small integer parameter (e.g. B goes from 14 to 15) makes me think
that these numbers represent something real, though it may not be the
two-level structure we modelled. I think that one subject really did
have 26 of "something," and not 52 or 78 of them. The other really did
have 33 usually, but might add or lose one occasionally. Perhaps if
we had tried the same subjects a year or two later, these numbers might
have changed, but I doubt that it would have ceased to be a small integer.

Anyway, the point for this discussion is that the perception of reversing
figures is more complex than it seems at first sight (sorry!). The
reversal process does seem to me to illustrate the contrast between
contrasting categories, and it does exhibit the hysteresis that I have
argued to be a necessary symptom of the existence of a contrast.


Martin Taylor has suggested association as the
result of positive-feedback cross-connections among systems at
this level; I think the concept is promising, but that memory
association may be a more general answer. Memory associations are
basically one-way; we have to create both directions
independently, as far as I know. Also, I have a problem with
positive cross-connections in that I think they would tend just
to drive all the signals either to maximum or to minimum.

It is true that a positive feedback connection in which the loop gain
is greater than unity would drive all signals to saturation. I envisage
a much lower loop gain in the associative process. In the brain, I
understand that excitatory connections tend to be much more numerous
than inhibitory ones, which must mean that the inhibitory ones individually
are more important, since not all neurons are saturated all the time
(epilepsy might be a condition in which such saturation does occur over
parts of the brain). Either the inhibitory connection or some chemical
adaptation within the individual neuron presumably counters the effect of
all the excitatory synapses that combine to make the neuron fire. So I
would extrapolate this to the integrated "neural current" metaphor, and
say that the gain of a positive cross-link is likely to be substantially
less than that of an inhibitory one; the flip-flop contrastive connection
is much more targeted and better defined than the widely distributed, but
weak, associative connections.

However, real-time association has to play a part if we can
create labels _ad libitum_.

Yes. I agree with this. The hard-linking of symbols to category perceptions
would not occur through the direct association connection I postulated,
especially if it is true that the associative cross-links are weak. On
the other hand, I am reminded of a "fact" that has stayed with me for a
long time as a minor puzzle. When people are asked to provide the first
word that comes to mind when another is spoken, adults tend to reply with
a word of the same class (I would now say with a word that has a contrastive
relationship to the first): "black" -> "white," "table"->"chair." Young
enough children don't, at least not so much. They tend to respond with
a word that in some way goes along with the original: "Black"->"night,"
"Table"->"eat." (I made up the examples).

In previous writing, I have invoked something I called a "holographic
mirror" to account for this effect. I assumed that there exist some
form of associative links among word representations, and that the
primary links are among words that go together rather than among words
of the same class. The child has few such links, and when asked for a word
that they think of after another is spoken, what comes up is the word
with the strongest associative link, there being few competitors. An
adult has many associative links to every word, so there are many that
have much the same direct linkage gain. But most of these words also
are linked to words that contrast with the first one, since the contrast
is based on the communality of context in which they appear. The combined
strength of the second-order links on that contrasted word is greater than
the strength of the links to other words of other types, making the effect
that of a mirror that refocusses the divergent rays of a light onto a
bright spot.

In the context of the present model, this proposal can be made more concrete.
Bill says "Memory associations are basically one-way." This model does not
require that to be the case. The reported associations could be one-way,
despite all of the associative links being symmetric between the associated
categories, because the mirroring effects are by no means guaranteed
to be the same between the two members of a contrasting pair. The picture
of the connections is the same as before, the output of a category
perceptual signal being fed positively to associated category PIFs
and negatively with high gain to contrasting category PIFs. There are
many low-gain associative links for every category (in an adult brain),
but few of the high-gain contrastive links.

There's a second "fact" relating to this model. There is a class of studies
in which a word is presented as a brief flash, probably masked. It is hard
to identify. If an associated word has been presented earlier, the flashed
word is easier to identify. But a second-level associate (an associate of
an associate) has no apparent effect, even if the associations both seem
to be very strong. If the association data were derived from a simple-
minded application of the idea of "spreading activation" (which is
what my proposal incorporates), the second-level associate should have
a strong effect. But if the holographic mirror model is right, there
is no reason why the second-level associate should have any special
increase in activation from the originally presented word.

The above deals with hard-linked associations. Bill muses about

let "X" be everything with drawers that have socks or shirts in
them. Maybe such fanciful categories aren't really useable until
they become habitual ways of perceiving the world, so the
apparent ease of inventing categories isn't operationally

I think it is significant, and is not caught by the associative connections.

But notice that these categories are all constructed ones, not contrastive
ones. They are at the next higher level of the logical hierarchy (logical
expression, in my model), and there is no proposal that associative links
occur at that level (though there is no proposed exclusion of the possibility,
either). Any links such categories have with symbols is likely to occur
through a mechanism different from that at the category level.


The harder this gets, the more I'm inclined to stop all this
guessing and get back to simple experiments. Although it's almost
irresistible to try to look ahead to what we might find.

The envelope with your experimental disk arrived today. I haven't tried
to load it into a computer, but probably will on Monday. So I, too, will
get back to simple experiments. As you say, the look ahead is very
tempting. There's no reason not to continue to do some of each, provided
that the speculative stuff doesn't get too far out of whack.