[Martin Taylor 931031 10:10]
This posting is a follow-up to my posting in which I suggested that
categories are defined by a contrast process that links perceptions of
possible category members in a flip-flop relationship. It covers some
points raised in the discussion that ensued while I was off the net, up
to Friday 931029. I have not made specific references to postings
because I am writing this at home without direct access to them.
···
==============
Three points on contrast as defining categories: (1) "natural kinds"
versus constructed categories; (2) co-existence of analogue and
categorical representation of the same perception; (3) categorical
"level-skipping" and the concept of interacting but separate analogue
and digital perceptual control hierarchies.
(1) "natural kinds" versus constructed categories"
In various posts, Bill P. and Bruce Nevin have both raised the issue of
arbitrarily constructed categories, such as "a thing to pry with" or "a
red box or a blue metal can with a hole in its top." The question is
how a perceptual input function defining such an arbitrary category can
be developed. As a practical matter, the flip-flip function I proposed
as a possible instantiation of the contrast process will not do it,
because the mutually inhibitory cross-links cannot be constructed at
will. Neither will the flip-flop function do it conceptually, for what
category contrasts with "a thing to pry with?"
The flip-flop mechanism depends on the existence of mutually exclusive
sets of category perceptions. A thing cannot readily be perceived as
being at the same time above and below another thing, or as red and
green (at the same spot), or as the phoneme /m/ and /b/. However, in
all these cases, a smooth change in an environmental variable can lead
to an abrupt change in the perceived category: slowly raising the
"thing" changes it from "below" to "above;" changing the wavelength of
the light changes the perception from red to green by way of a couple of
other categories such as "orange" and "yellow" (which are determined by
the language one speaks), slowly changing the rate of amplitude growth
of the sound changes the perception abruptly from /m/ to /b/ at a growth
rate that depends on the situational and phonetic context.
In each of these cases, a tendency to perceive the sensory input as
belonging to one category actively inhibits the ability to see it as
belonging to the contrasting category. When the balance of evidence
from the sensory input changes sufficiently toward the other category,
it overwhelms the suppression and becomes the perceived category,
actively inhibiting the one that had been perceived, as sketched in this
diagram. In the diagram, the gap between the lower and upper thresholds
is caused by mutual inhibition between the "A" and "B" perceptual input
functions.
more "A-like" | \ /\ /
> \ / \ /
sensory |----------------------------------------- upper
input | \ /| \ /| threshold
> \ / | \ / |
>----------------|----------------|-------lower
more "B-like" | |\ / | | \ / | threshold
> > \_/ | | \/ |
> > > > >
Perceived category A | B | A | B | A
---time-->
If two or more categories have this kind of mutually inhibitory
relationship, the relationship must somehow have developed prior to the
occurrence of the momentary sensory input. It reflects a property of
the perceptual control possibilities in the world--the world's
"affordances," if you like. The world never provides the sensory input
appropriate to a clear example of "A" at the same time as it provides a
clear example of "B", and no actions of the control system will generate
perceptions of both together. If reference signals are provided to the
"A" and "B" ECSs that demand both perceptions to be present at the same
time, conflict is inevitable because the world happens to be constructed
so that they cannot be present together. I would call such contrasting
categories "natural kinds." (I am aware that this use of the term is in
no better agreement with its everyday use than is the PCT use of the
word "perception." But I think my use is appropriate within the PCT
context).
There is another, less obvious, property of "natural kinds." The
contrasting category members normally occur in similar contexts. There
is no contrast between a perception of "red" and a perception of
"antique," or even of "bright." The contrasting categories are of the
same type. One could fit instead of the other in most situations. (The
linguistic consequences of this property are far-reaching, as I am sure
will not escape notice.)
In the case of an arbitrarily constructed category, there are two things
to note. Firstly, so far as I can see, every constructed category is
based on logical combinations of categories. The categories of which it
is constructed can themselves be constructed, but in the end they
resolve into "natural kinds." Secondly, there is no obvious way of
determining a category that contrasts with a constructed category, other
than by substituting a contrasting natural kind in the construction, or
by changing one of the logical operations in the definition.
Constructed categories seem to belong at a logical level of perceptual
control above the level of "natural kind" categories.
I have not forgotten the possibility of constructed categories that
contain fuzzy adjectives such as "a bluish box that is not too tall."
It seems to me that even such descriptions are built on natural kinds,
where "bluish" contrasts with "greenish", "tall" contrasts with "short,"
and so forth. The fuzziness is associated with low gain in the
inhibitory cross-links of the natural-kind categories, not with their
nonexistence. When the cross-link gain is low, the categories cease to
contrast, in the sense that the inhibition provided by one perceptual
signal has a positive feedback gain to itself of less than unity in the
steepest part of the perceptual input function. The hysteresis shown in
the diagram does not occur.
===================
(2) co-existence of analogue and categorical representation of the same
perception.
Bill P. suggests that the scheme I proposed might be modified by taking
the cross-links between copies of the perceptual signals representing
the contrasting category members, rather than between the originals. He
says that one could otherwise not simultaneously walk and perceive "I am
walking." This brings up a real issue, because I don't think Bill's
suggestion works, either. The important point is not that there is
cross-connection between the contrasting perceptual SIGNALS, but that
each of the perceptual signals is fed to the input of the other
perceptual FUNCTION. If one works with copies, the copies must be of
the entire PIFs of the ECSs concerned. Since the nature of the PIF is
determined in the course of reorganization, the PIF for a category
perception that uses the contrast process will inevitably deviate over
time from one that does not--the control actions that bring perceptual
signals to their reference values will differ. So, even if copies of
the PIFs were initially constructed, they would not continue over time
to be faithful copies, and the analogue versions would cease to
correspond to their pseudo-digital counterparts.
With Bill, I accept that there is probably is a higher analogue
hierarchy, somewhat in parallel with a logical hierarchy based on
contrastive categories. But I do not think it can be built on
perceptual signals that mimic the category signals without contrast. I
think it has to be built on PIFs whose inputs include the same kinds of
sensory signals that feed contrasting category PIFs, and quite possibly
on the outputs of category PIFs as well.
Let's consider walking while controlling for perceiving "walking." From
somewhere, a reference signal is provided that sets a high level for the
intended perception of "walking," which is contrasted to "standing,"
"running," "sitting," and the like. All these others have low values
for their reference signals.
The output of the category ECS for "walking" is high because the current
perception is of "sitting," and therefore not of "walking." That output
contributes (by prior reorganization) to reference signals in events
level ECSs for perceptions relating to what happens during walking. So
walking happens, and the category perception changes from "sitting" to
"walking." I may be naive here, but I don't see any necessary
contradiction between perceiving walking as a category and performing it
in all its analogue precision. At first glance, to see a problem here
seems analogous to the roboticist's seeing problems with inverse
kinematics in the usual underdetermined trajectory "problem".
The same is true for speech, but in a more complex way. A word can be a
pattern of sounds, references for which may be provided to event-level
ECSs by a word-level category system. But it can also be a sequence of
phoneme categories, each of which can provide references to the same
event-level ECSs. The word might at the same time be a constructed and
a natural category, though presumably not in the same ECS. Some more
exploration is required to see how this might work. Data might be
available in the literature on speech and reading.
Finally, as a gratuitous intuition, might it be true that humans are the
only species capable of forming constructed categories, and is that the
necessary foundation for the development of syntactic language?
(3) categorical "level-skipping" and the concept of interacting but
separate analogue and logical perceptual control hierarchies.
The way I look at the "natural kind" categories, one can be formed at
any level of the analogue hierarchy, but the perception of the existence
of a category member is the same no matter which analogue level it
refers to. The picture might look something like this (skipping many
analogue levels for ease of presentation):
c
principles---a
> > > t---\ -------------
events------e \ | logical | other
> > > > g------| |-----logical
configurations--o / | expressions | levels
> > > > > r---/ -------------
intensities----y
In the diagram, "logical expressions" is more or less equivalent to what
I called "constructed category" above, but might have a wider meaning,
which is why I changed the terminology. I have no thoughts on what that
"wider meaning" might be, but leave it open as a possibility.
"Category" in this representation is the base of a "logical" hierarchy
in much the same way that "intensity" is the base of the analogue
hierarchy. I use the word "logical" with some trepidation, because it
is true, as several posters have noted, that the magnitude of category
membership is not strictly all-or-none. The values of the perceptual
signals anywhere in the logical hierarchy can take on values other than
one and zero.
What is important about the "logical" hierarchy is that there is a
discontinuous break between high values and low values in the category
perceptions, allowing the higher "logical" levels to generate
"decisions." A "decision" sounds like a planning choice, but it is
intended to indicate a choice between whether the current perception
does or does not correspond with the reference level, whereas the error
signal in an analogue level indicates a continuous degree of deviation
between the current perception and the reference level. An ECS within
the logical hierarchy generates output if the current perception does
not correspond with its reference level, and not if it does correspond.
In that sense, a "decision" can be seen as a choice of whether or not to
act. At the program level, it would be a choice of how to act (see
Bill's example of "Old MacDonald"), which does sound rather like a
planning decision, even though it is based on the discontinuity of the
accessible values of the error signal.
Categories derive from every analogue level. What this means is that a
PIF at a high logical level (e.g. "program") can have as its sensory
input signals derived from categories at both low and high analogue
levels. More important, the reference signals from this high logical
level can be manifest through the category level output signals at both
low and high analogue levels. A perception of a particular category
member at a low analogue level may result in an error signal at a high
logical level, and the consequent output may generate reference signals
at high analogue levels that differ substantially from the current
perceptions at those levels. I think of wearing a blue tie at a Liberal
party meeting, for example (red would be the appropriate contrasting
category member). Error signals would be generated at the event level,
and probably higher, and the resulting actions would be likely to result
in the ejection of the wearer of the blue tie from the meeting room.
If the category level is connected as suggested in the figure, reference
signals are simultaneously output to multiple analogue levels. But the
lower analogue levels get their reference signals also from higher
analogue levels. Should not Bill P's arguments against output level-
skipping apply? The argument is that the higher level can work more
effectively through the intermediate level than by connecting directly
to the lower level, if it can work through the lower level at all.
Hence reorganization will remove all output links that skip levels. The
argument seems to me to be valid.
If Bill's argument applies, then no matter where the sensory inputs to
the category level come from, the outputs should go only to the highest
analogue level. This causes a conceptual problem. If we accept Bill's
concept that there are high analogue levels corresponding to systems and
principles and the like, as well as high logical levels such as
programs, then all actions based on "logical thought" (error signals
within the logic levels) should be executed through error signals at the
highest analogue level. A painter wanting "red" should find an error in
his perception of the current state of his principles of painting. This
does not seem reasonable to me. But I do not have a ready reason why
Bill's argument forbidding output level-skipping should not apply. I
think it should fail, but do not see how.
That's enough speculation for now, I think.
Martin