[From Bill Powers (960625.1530 MDT)]
Martin Taylor 960625 14:00 --
Writing to Rick Marken:
Actually, we used three things: (1) f(), The unvarying output-to-
CEV function (which I sometimes label the output/feedback
function), (2) The reference waveform r(t), and (3) the perceptual
signal waveform p(t).
If you are given Fi (input function), Fo (output function), Fe
(environmental feedback function), r (reference signal), and the
behavior of any signal in the loop (p,e, or o) you can then calculate
the part of the state of the perceptual signal that is due to the sum of
all independent disturbances acting through their respective disturbance
functions. This has nothing to do with information theory, Martin: it is
just plain mathematics. And this is all you showed with your "magical
mystery function." I never doubted that this could be done; I'm sure
Rick never did, either. That calculation doesn't depend on "the
information in" anything -- it's just algebra.
I think that the problem was that Rick and I were expecting you to pull
some sort of rabbit out of your hat, something that would show that the
"Information" in the perceptual signal had something fundamental to do
with the way this system works. I know I was thinking you must have some
sort of short-cut, the way dynamical equations can be magically picked
out of a simple statement of conservation of angular and linear
potential and kinetic energy. But what did you come up with? Nothing but
a solution of a set of algebraic equations in which there was only one
unknown.
This piddling result didn't seem to jibe with your grandiose claims
about the power of information theory. There wasn't even a mention of
"information" in your triumphant demonstration. The calculations didn't
involve any equations for Information, per se, or any relations
involving Information. Nothing at all was derived from which one could
calculate the information in the perceptual signal about the
disturbance. And don't forget that at the time, you were defining
"disturbance" very differently from the way Rick and I were defining it.
As later events showed, your definition of "disturbance" is simply "that
part of the value of the CEV (or perceptual signal) not attributable to
the output." Since by your own admission this conceptual subdivision of
the input plays no role in the actual operation of a control system, the
point of calculating this kind of "disturbance" is rather hard to see.
Your line of argument is something like the one I would use in showing
that information theory is irrelevant to control theory (if I believed
that).
Your position on information has changed considerably over the years
since 1993. Back then, you said things like
Throughout, I am trying to take the position that the only
probabilities that can be observed are based within the observing
entity. ...
Sometimes I slip, I acknowledge. But that's a simple mistake, not
a failure of principle. In this case, the reference signal and
the perceptual signal are both known within the ECS. If you
remember a long way back, this came up. There is no need for an
external evaluation of the probability distribution, any more than
there is a need for an evaluation of a neural current that is based
on a rate of neural impulses. I suppose it might be possible for
an external observer with a probe to make the analyses, and
sometimes it is didactically easier to posit such an observer.
But in practice there isn't one, and it is not necessary to think
of one. ...
Now, 1996, you are saying that of course the information is not known to
the system itself, and that all this is just an external observer's way
of evaluating what is going on inside the control system. But the
kicker, to me, is this passage:
... 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?
How do you know that "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?" Are you saying that you have
actually "put them in", but simply haven't shown your results to us? Or
do you mean that you can see how it would be done in principle, and are
so sure that the results would be identical that you don't see any
reason actually to do the calculations? Or do you mean that a model
based on information theory would not actually contain any calculations
of information, and would simply be the same model we already have?
I don't see how any of these possibilities lends support to your claim
that information theory shows WHY PCT WORKS. We have only your word,
your claims, that it does. The models you pick as examples are so
contrived, so obviously tailored to the special needs of informational
calculations, that they hardly seem general -- but even so, if you could
show how information theory itself -- not algebraic or sequential
calculations -- can be used to demonstrate some essential point, that
would be at least a step in the right direction. But even in the latest
round on this subject, you say
With trepidation, here's a proposed simulation experiment. I may
have time to set it up, but probably not soon, and someone else
might like to. But for now, think of it as a thought experiment,
and give me your comments on what it might show if it were ever to
be done.
I am simply not interested in thought experiments that will never
actually be done. All that thought experiments do is to reveal your
beliefs. I claim that you do not know how to do informational
calculations for a working control system and that you have no way of
showing that they in any way "explain" how a control system works. This
is just more bluffing and procrastination. I don't believe that you will
ever get around to actually setting up this model or working out the
informational calculations that would be needed to draw any conclusions.
After three years, I am still waiting to see an orderly analysis of
information in a control system that simply proceeds from A to Z without
detours for verbal explanations and arm-waving, and without heaping ad-
hoc assumptions upon assumptions to take care of problems encountered
along the way.
I hate being in this relationship to you, Martin. I don't expect that
you enjoy it, either. I feel that I'm questioning someone's religious
faith, and you've done little to relieve me of that onus. I think that
we are at an impasse, and that communication between us on this subject
is so poor that there is no hope of resolving the problem. I suppose
that all I can do is find the guts just to stay out of it. I hope I can
do that, although the present post makes me a liar.
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Best,
Bill P.