From: tomh.bbs@cybernet.cse.fau.edu
Newsgroups: comp.ai.philosophy
Subject: Re: Categories: bounded or graded?
Date: 17 Apr 92 19:35:23 GMT
Organization: Florida Atlantic University, Boca Raton

christo@psych.toronto.edu (Christopher Green) writes:

> In article <1992Apr15.010721.17700@organpipe.uug.arizona.edu> bill@NSMA.AriZo
> >
> >  In my opinion the belief that natural categories are defined
> >by invariant features leads to all kinds of nasty problems.  
> 
> No more nasty than those lead to by the idea that they're graded.
> See Osherson & Smith.

Using concepts from Synergetics (Haken) and Dynamical Systems Theory,
we (and others) view categorical phenomena as the result of self-
organization of patterns in non-linear systems.  For example, the
"gaits" of running animals such as horses are normally defined as
certain patterns of relative phase among the limbs; in the dynamical
view, the limbs are seen as non-linear oscillators, which couple
together to produce the characteristic gait patterns as stable
attractors of the oscillator dynamics.

A 'gait space' is really a continuous space, where any possible phasing
of the limbs is representable.  In nature, only a few gait patterns
are actually observed;  this is the categorical nature of gait patterns.
What defines when you are in a particular gait pattern?  How close to
the 'cannonical pattern' do you have to be?  In the dynamical view,
closeness is irrelevant - the category (the gait pattern) is defined
as a stable attractor - and the existence of the category is related
to the *stability* of the attractor.

So concepts like "invariant feature" are too discrete, while concepts
like "graded" are too continuous.  The view here is that the reality
is a self-organized, stable state of a non-linear system.  Such a
theory has certain predictions having to do with (in the case of
animal gaits) non-linear oscillators, such as hysteresis.  Many
experiments have been done (refs. available on request) which show
such non-linear phenomena in 4 limb and 2 limb patterns in humans,
wing patterns in locusts, fin and tail coordination in fish, auditory
perception of tones in humans, apparent motion, muscles of the jaw
and face during speech, etc. etc.  The list is very long.  All of
these very high-dimensional systems exhibit low-dimensional dynamics
characteristic of simple non-linear systems.

Again, I would say that neither "invariant feature" nor "continuous"
hits the mark - one needs to refer to the process that creates the
category in the first place, specifically to the stability of the
pattern.  A very stable pattern might be viewed as an invariant
feature, and a somewhat less stable pattern might be seen as being
more continuous.  Both are really two sides of the same coin.

Viewed this way, it becomes possible to sensibly address issues of
development - how does categorical perception develop, for example?
There is an underlying system which, through exposure to patterns,
self-organizes stable attractors which correspond to those patterns.
This explains how we can become sensitive to one set of phonemes while
losing the ability to distinguish certain sounds.  The range of
possible sets of "features" is potentially very large, and precisely
which patterns become stable is dependent upon the environment.
All this can be put in a precise mathematical framework involving
non-linear dynamics.

A few of us here at FAU have coined the term "digilog" to be an icon
for this type of thing:  neither the discrete, digital, invariant
feature, nor the continuous, analog representation is quite right.
Such dual concepts almost always have a common underlying reality.

Tom Holroyd
Center for Complex Systems and Brain Sciences
Florida Atlantic University, Boca Raton, FL
tomh@bambi.ccs.fau.edu (or the address I'm posting from)
Newsgroups: comp.ai.philosophy