Newsgroups: bit.listserv.csg-l
Date:         Mon, 21 Dec 1992 12:42:43 EST
From:         mmt@BEN.DCIEM.DND.CA
Subject: Re: Information theory vs control theory

[Martin Taylor 921221 12:00]
(Bill Powers 921219.0130)

Well, given last year's experience, I didn't expect my information-theory
posting to be understood, and I wasn't disappointed in my expectation.  Is
it worth trying some more?  I'll give it a little shot, and then give up if
it still doesn't work (rather like CSG papers trying to get into conventional
psychology journals, isn't it!).

>>In a choatic world, delta matters.  If delta is very small, the
>>probability distribution of states at t+delta is tightly
>>constrained by the state at t. If delta is very large, the
>>probability distribution of states at t+delta is unaffected by
>>the state at t ...
>
>It matters a heck of a lot more to a plan-then-execute model than
>it does to a control model. Remember that control of a variable
>depends only on the ability of the system to affect that
>variable, directly, in present time. It isn't necessary to
>produce an output and wait to see its future effects.

The statement is completely independent of what is acting on or looking at
the world.  It has to do only with the rate at which the world supplies
information that can be looked at.  Of course it matters "a heck of a
lot more to a plan-then-execute model than it does to a control model."
Didn't I demonstrate that adequately in my posting?

But the delta between the output and observable effects on sensory inputs
is important to the amount of information contained in the error signal
and thus valuable for higher levels of control.

>>The central theme of PCT is that a perception in an ECS should
>>be maintained as close as possible to a reference value.  In
>>other words, the information provided by the perception, given
>>knowledge of the reference, should be as low as possible.
>
>I think you'd better take one that back to the drawing board. The
>reference in no way predicts the perception by its mere
>existence. The best control requires the widest bandwidth in the
>system, including its input function, up to the point where noise
>begins to become significant. I don't see how this is consistent
>with saying that the information provided by the perceptual
>signal should be as low as possible.

The word "should" seems to be ambiguous.  It refers in my posting to the
results of having a good, properly functioning ECS.  In your comment, you
take it to refer to how a functioning ECS is to be designed, and that the
perceptual bandwidth should be low.  If the perceptual bandwidth is low,
then the ECS will have difficulty matching the perceptual signal to the
reference signal, and thus the error signal will have high information
content.  Now it is true that if the perceptual signal has lower bandwidth
than the reference signal and the same resolution, then the error signal
will in part be predictable, thus having lower information content than
would appear on the surface.  But I had the presumption that we are always
dealing with an organism with high bandwidth perceptual pathways, so I forgot
to insert that caveat.

>>It is that kind of thing that I refer to as "understanding"
>>PCT, not the making of predictions for simple linear phenomena.
>
>Dennis Delprato, here is another addition to your list of myths
>about PCT: that we can predict only simple linear phenomena.
>Martin, have you looked at the Little Man? It is chock full of
>nonlinearities.

I think you know from all my postings, including the one you are
commenting on, that I don't subscribe to that myth.  Sloppy wording.
Sorry.  But Tom specifically asked me to improve upon the numerical
predictions made by a linear model, which is why I made the posting
in the first place.

>>>And in a control
>>>model, the signals in the various paths normally carry far
>>>less information than the theoretical limits allow.
>>Dubious.  I would like to be able to figure out how to test
>>that assertion.
>
>It's easy. Most perceptions occur on a scale between 0 and
>maximum magnitude, and vary at a rate between 0 and some maximum
>cutoff frequency. To accomodate the maximum magnitude and
>frequency, the perceptual channel must have a certain information
>capacity. As perceptual signals can be controlled at any level
>within the whole range and can be varied at any rate up to the
>maximum, it follows that unless the perception is being
>controlled at maximum magnitude and the reference signal is
>changing at the maximum rate that still permits control, the
>actual information flow must be much less than the channel
>capacity. Most perceptions are not controlled at their extremes;
>hence most perceptions must use less than the whole channel
>capacity.

The last sentence is a non-sequitur.  What follows the semicolon has
no relation to what precedes it.

> My theory of perception agrees with a largely noise-free
>experienced world; yours appears to predict a world in which
>perception barely stands out over the background noise. If your
>model were correct, precise control would be impossible.

You place great store on the conscious impression of precise perception.
This impressions really has nothing to say about whether evolution has
worked well or not.  Conscious impressions can be, and probably are built
from many noisy samples which are used as rapidly as possible in the actual
perceptual processes that are involved in control.  Furthermore, if most
of the control is done in the central part of the range, most of the
channel capacity would be expected, in an efficient syste, to be devoted
to accurate perception within that region.

>Show me where Shannon's theory says there must be a comparator, a
>reference signal, and a perceptual signal.

Show me where Euclid's axioms say that the sum of the squares on the
two sides of a right-angled triangle equals the square on the hypotenuse.

I am not sure that the discrete individualized ECS is predicted by
Shannon.  What I did point out is that Shannon's theorems demonstrate
that S-R and plan-then-execute will not work in a chaotic world, whereas
perceptual control will work.  The thesis is that if a structure is to
be stable in the world, perceptual control is nessary, though it may not
always be sufficient.  I cannot prove the necessity, because it may depend
on hidden assumptions (like the relatively high sensory bandwidth) that
I have not seen.  But the only other way I can see to make a stable structure
is to have one in which the binding energies are high compared to the
thermal regime in which the structure finds itself.

>I think that information theory is by its very nature a post-hoc
>description, not a model. You can't start with information theory
>and come up with a system design. Or so sez I.

There's usually an interplay between abstract principles and practical
prototyping.  If you understand the Carnot cycle, you know that superheated
steam engines can be more efficient than ones operating at lower temperatures.
James Watt didn't know that, but he came up with a principle for making
steam engines.  Could Sadi Carnot have built Watt's steam engine from
first principles?  I doubt it, and quite probably he wouldn't have
invented his cycle either, if Watt's engine hadn't been there.  Yes,
the Carnot cycle is a description, not a model.  But it's useful.

Maybe this is an appropriate place to enter a reminder that we have a
difference of opinion about there being a qualitative distinction between
a description and a model.  I deny it, whereas you think it important.
I think Occam's razor is important, and that the difference between
what you call a "description" and a "model" is that your "model" is a
more precise description over a wider range than is your "description."
Occam's razor thereby gives more credence to your "model" than to your
"description."  It's simply a question of what is nowadays called
Kolmogorov complexity.

>One last observation:
>
>>The way around this is that category boundaries are not
>>thresholds, but fold catastrophes.
>
>That's a pretty fancy term for a Schmidt trigger. Anyway, saying
>that categories are fold catastrophes says nothing that my
>description of hysteresis didn't say. Categorizing categorizing
>doesn't tell us how it works. It doesn't work the way it does
>because it's a fold catastrophe. It's a fold catastrophe because
>of the way it works, which remains undisclosed.

Actually, I thought it did point out a necessary condition for it to
work--positive feedback.  You can't have category perception without
some form of positive feedback, whether it occurs by cross-linking and
mutual inhibition among perceptual functions at a given level, through
some kind of modelling/imagination loop, or through temporal recurrence.

A Schmidt trigger provides a very specific kind of fold catastrophe, which
loses all information other than the category.  There's no need to lose
that information, and as the fold approaches the cusp of the three-dimensional
version (stress being the third variable), the "adjectival" information begins
to dominate.  What your description didn't say was that the categorical
aspect is of variable importance, and that the degree of overrun is
affected by the amount of stress.  The cusp catastrophe, of which the
fold is a cross-section, does say that.

And yes, it is "only" a description, with a mechanism.

Martin
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