[Martin Taylor 921221 20:00]
(Bill Powers 921221.1500)
···
From: Tom Bourbon (921222 10:10 CST)
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Martin:
Bill, your posting just arrived, as I was on the way out to go
home, so this must be short (our phone lines have got very bad
recently, and I can no longer try to do it from home).
As usual, you are an acute observe, especially in relation to the
question of model types. But I really do think that I can use
information theory to identify that the PCT structure was correct,
at least feasible. When you put in the appropriate perceptual
input functions, gains, and delays, you get the same model that you
and/or Tom would produce without information theory, so it should
make the same predictions in any specific case. So why should I
try to do better, when I anticipate the result being identity?
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Me (now):
Martin, I think this is the heart of the misunderstanding that
seems to emerge in a regular cycle on csg-l, concerning your ideas.
You are convinced that you can work from first principles in
information theory and (necessarily?) arrive at an architecture
identical to that in the PCT model. Further, you say that your
model would behave identically to a PCT model. I certainly would
not question or challenge your convictions -- they are yours and
you undoubtedly have good reasons to hold them. What I would like
to see is a demonstration that things work the way you believe they
do.
I am not saying you are wrong. I am not even offering a challenge,
although that is the way my offer has been characterized on the
net, just as it was when I first made it over a year ago. Then and
now, my posts were motivated by concern that the discussion about
information theory and PCT was becoming supercharged and an
opportunity for clearer understanding on both sides might be
slipping away. I thought of my posts more as requests, or offers,
or attempts to encourage you to try a different style of
presentation.
Obviously, on csg-l part of the group with which you converse
relies heavily on modeling and simulation as strategies to test
ideas about behavior and perception. The emphasis is clearly on
generative models, not descriptive ones. For a variety of reasons,
the generative modelers on the net think of information theory and
signal detection theory as descriptive. In contrast, you
frequently appeal to both of those theories and say they provide
you a deeper understanding of PCT. As you said in your post:
"What I do want to do is to get some deductions about the structure
and its behaviour that are not obvious, even though they may
(should) agree with what you have found to work in practice. I
find that it makes much more sense to me to have a good theoretical
underpinning that allows me to generalize from a practical result
than just to see the practical result and wonder what might happen
if some little thing were changed."
Who could possibly see a problem with those thoughts? The
difficulty arises when, probably through misinterpretation by your
readers, you seem to argue that information theory *obviously*
offers a superior, or clearer, understanding of the phenomenon of
control and that readers on the net who do not see that fact, on
their own, have an inferior understanding of control. Whether
their interpretation of your intent is right or wrong, it is clear
that some readers begin to take those remarks personally. That is
why I offer this suggestion: Demonstrate that you can work from
first principles in information theory and (necessarily?) arrive at
an architecture identical to that in the PCT model. If the model
you derive is identical to the PCT model, you are right; there is
no need to simulate it -- to run it. But if it differs in any
details, run it, to confirm that it behaves as you think it will.
That step should satisfy any questions, doubts or criticisms I have
seen directed toward your posts about information theory and PCT.
The following exchange between Bill and you leads me to doubt that
you will try the approach I suggest.
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Bill to Martin:
Martin, the difference that Tom is talking about, I believe, is
between a descriptive model and a generative model. A descriptive
model provides a general picture of which a specific behavior is
only one example. A generative model actually generates (simulated)
behavior for direct point-by-point comparison with real behavior.
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Martin replies to Bill:
Yes, I understand. I have a bit of a problem with limiting myself
to either kind of model exclusively, though, and it is a problem
that has been with me since undergraduate days. If a generative
model does predict reality well, without excessive use of
parameters, then it produces strong evidence of the plausibility of
the theory that underlies it. But if the generative model fails,
it does not give evidence against the underlying theory, because
the failure could have been only in the choice of parameters. So
the generative model is a one-sided kind of support.
On the other hand, the theory by itself is only plausible unless it
can be shown to predict reality, and that can be done only through
generative models or mathematical analysis. In the case of your
and Tom's models, the prediction is very good. So I see little
point in trying to create generative models from what I see as a
theoretical support for the same structure on which your models are
based. It is conceivable that in some situations the information-
theoretic approach might produce numerical statements of more
precision or using fewer parameters, but those situations probably
will not be easy to find. They will be at higher levels in the
hierarchy, most probably. I'm not even going to look for them at
present, at least not until I can see some problems with your
practical approach that are resolved in the information-theoretic
approach.
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Me (now):
I believe a major question that is unresolved for some of the
modelers is whether you would necessarily arrive at the PCT
structure. Couldn't you just as easily arrive at other, sometimes
implausible, structures? I have seen information theory used to
justify or explain many varieties of theory in behavioral and
cognitive science. Why should one person arrive at a PCT
structure, when so many others did not? I am not saying that you
will not, just that I do not see the necessity that you will.
Also, the act of producing and simulating a model does not require
that the modeler limit herself or himself to that model over some
other(s). Modeling and simulating are tests, nothing more. In
"Models and their worlds," when Bill and I constructed and ran a S-
R model, a plan model and a PCT model, we did just that. The act
itself need say nothing about the preferences or beliefs of the
modeler. (Of course, our reviewers thought otherwise!)
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Martin:
I've been playing with information at an intuitive level for as
long as you've been playing with control systems. It's hard for me
to get back to basics (or even to exact formulae, since I don't use
them much), but it will be a good exercise for me to try.
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Me (now):
Try it! You might like it! Even should the task prove daunting
(which, for you, I doubt), the least you can expect is that your
personal insights about PCT and information theory will be more
easily digested by readers on the net -- the discussion will be
much more likely to remain on a technical level.
Just to clarify my "challenge" .... For me to more easily
understand your personal insights about PCT and information theory,
I would like to see whether principles in information theory
necessarily imply and produce a generative control model and
whether a model so produced can assume the role of a person or a
PCT model in a real-time interactive task. The person who
accomplishes that demonstration will have made clear a relationship
that is not obvious to some people on the net, including me. I am
willing to be taught.
Until later,
Tom Bourbon e-mail:
Magnetoencephalography Laboratory TBOURBON@UTMBEACH.BITNET
Division of Neurosurgery, E-17 TBOURBON@BEACH.UTMB.EDU
University of Texas Medical Branch PHONE (409) 763-6325
Galveston, TX 77550 USA FAX (409) 762-9961