Speech and Chaos

Harry Erwin erwin at trwacs.fp.trw.com
Sat Feb 6 12:24:55 EST 1993


Dr. Huberman got on my case for being too vague, so I posted the
following to him:

If we look at what Freeman did we see the following: He postulated an
underlying high-dimensional quasi-periodic process--imagine (this is how I
see it) a field of dots, with the darkness of each dot varying
periodically (at different periodicities) and now superimpose a scene
additively, so the dots of the scene vary in darkness, each with their own
period. Over time the scene is apparent in the average value of each dot,
but at any given instant, the image is filtered through an ergodic haze.
(I envision the activity of virtual particles around a bare electron in
similar terms, although the haze is not quasiperiodic.) If this haziness
lasts long enough, the cortex eventually picks up on it and performs an
orienting action.

Now supplement this system with a collection of patterns downloaded to the
olfactory bulb from the cortex. Each pattern consists of a set of neuronal
connections that are mutually excitory and that compete with other patterns.
These perturb the quasiperiodic system described above non-linearly.
If any pattern matches the current state of the image+ergodic haze, it is
amplified, and, if it fails to match, it is weakened. This causes the overall
state of the system to evolve, with the components of the scene that match
patterns in the set becoming more and more distinct.  Eventually the system
converges to one of the patterns and that is what is reported back to the
cortex. 

Another way I envision this system is to ignore the high dimensionality,
and instead imagine the state of the system as evolving along a path.
Sometimes I'm on the inside of the path and sometimes I'm on the outside.
In part this results from the quasiperiodicity of the system and in part
from my interaction with the downloaded patterns. Sensitive dependence on
initial conditions and the other characteristics of chaos means that I'm
not stuck in a minimum energy rut, but rather can swing from side to side
easily. The downloaded patterns tend to attract me if there's a match.
If I'm attracted enough I discover that the path I was following has a
branching and I end up following it rather than the original path.
In Freeman's olfactory bulb model, I end up at a specific destination,
which gets reported back to the cortex, and the system is reset for
the next sniff. In the cortex, the new path is like the old path,
and I continue along indefinitely. Each decision point is like a gate or a
"y" where I can continue on the old path or choose the new. 

The point is that the chaos is associated with the sequence of gates
(hyperbolic points) and the choice of "right or left" at each gate.
I should be able to replicate a train of thought by reporting "and here,
I decided this rather than that." Both speech and mental plans (as in
Paul Werbos' Heuristic Dynamic Programming) seem to have something of
this structure. 

(I've also been told that scientists in the former Soviet Union have
studied this type of system extensively, but little has been published
in English.)

Cheers,
-- 
Harry Erwin
Internet: erwin at trwacs.fp.trw.com



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