[Allan Randall (930312.1200)]
Rick Marken (930310.1400) writes:
First, you say that Information Theory (IT) is to PCT as
calculus is to Newton's laws; IT is a tool like calculus.
But calculus helps us make detailed predictions...
...at the end of your post you say:
>you seemed to be asking for a *prediction* about which
>(condition 2 or 3) will be better in a real-world situation.
>This seems to be beyond the scope of information theory as it
>stands now.
Well, IT isn't much of a tool if it can't help us predict things;
looks like PCT WITH IT is no better off than Isaac's brother Phil
WITHOUT calculus.
But calculus does NOT allow you to make the kind of prediction
that Bill Powers is asking for. What Bill is asking for is like
asking calculus to predict the orbit of a planet, all by itself
WITHOUT any of Newton's Laws. Bill is specifically asking, unless
I am misunderstanding him, for a PCT-type prediction using
information theory and ONLY information theory. I agree that
this may not be possible. What I do not want to see him do is
to reject what could turn out to be a valuable tool, on the basis
that it cannot do the job all by itself. This is what I was getting
at with the Newton analogy. Contrary to what you imply, calculus
simply can't make physical predictions unless it is used in
combination with a physical model of some kind. All by itself,
it is just a mathematical technique, like information theory.
>If no information about the
>disturbance can be extracted from this data, then there is
>no way the system can translate the error from this signal into
>an action on the world that will counter the disturbance. Is this
>or is this not true?
This is NOT TRUE. Surprise!
>If you agree, then you are agreeing with an
>information theoretic analysis.
So I guess I disagree with an IT analysis -- and if I'm right
(which I am) then the IT analysis is wrong, right?
Right. Exactly. Here is something we can actually nail down. The
statement I made, which you say is not true, is the whole crux
of this controversy. It is a fundamentally information theoretic
statement. The reason why I asked whether it was true or not was
that I could not imagine a PCTer disagreeing with it (I was wrong -
you did), but at the same time I considered it an information
theoretic statement. Here you are claiming the statement is actually
false - there is no information about the disturbance in the
perceptual signal - a claim that is in direct contradiction with
Ashby's Law of Requisite Information. If you are correct, Ashby's Law
is completely unfounded. (However, I don't think you actually are
correct.)
It is this fact about control systems that nails everyone to the
wall -- and proving it to myself is what turned me into a PCT
"fanatic" ...
...In a high gain, negative feedback control loop, the
output DOES NOT depend on the sensory input; rather, SENSORY INPUT
IS CONTROLLED BY OUTPUT.
The second statement is true, but I think your first statement is
false. The output DOES depend on the sensory input, and the sensory
input DOES depend on the output. We do not have to choose between
the two. It is better to say they are interdependent, than that
one depends on the other. Isn't your response-stimulus description
just as wrong as stimulus-response?
What you do in a tracking task is NOT
caused by what you see; ...
Magic, then?
... there is a LOOP so that what you see is
both a cause AND A RESULT of your output.
Now you are back to the closed loop and admitting that they are
interdependent.
The nearly perfect
relationship between output and disturbance does NOT exist
because the system has access to information (from the sensory input)
about the disturbance.
This is silly. How can there be ANY relationship between the output and
disturbance, let alone one that is "nearly perfect," if the system has
no access to information about the disturbance? This is just physically
impossible, Rick. I think either you are misinterpreting what I mean by
"information," or you believe some kind of witchcraft is responsible
for control.
When control is good, there IS NO information
about the disturbance in the stimulus -- NONE, ZILCH, NADA.
This is true NOT when control is *good* but when control is *perfect*,
which is inherently impossible for an error-control system, as Ashby
said. Let's be clear what we mean by "disturbance." Stop me when you
disagree. The disturbance is the sum of all the various environmental
influences impinging on the CEV. This CEV is not an absolute property
of the environment, but is defined by the hierarchy. In information
theory terms, the hierarchy is an encoding scheme for representing the
environment. Each perceptual signal represents one CEV in the
environment. This does *not* mean that the disturbance exists in
the hierarchy and not in the world. In order to describe anything,
says information theory, it must be described in some language. The
disturbance is in the world, but the description that isolates it as
an entity seperate from the rest of the environment is in the
hierarchy, not the world.
Only that information which is relevant to control of the CEV is
transmitted in the percept. But to say there is NO information at all,
none, zilch, nada, is just incoherent. If I am driving my
car down the road and there is a sudden huge gust of wind from the
right and at the same time I start sliding on the ice, the
"disturbance," in PCT terms, is the disturbance to the CEV that results
from these forces. But an outside observer will tend to describe
the disturbance in a different language (a different encoding scheme).
They will probably describe the gust of wind, its force, and the sliding
motion due to the ice as seperate, complex entities. But this
description is no more an absolute depiction of reality than the
perceptual one inside the driver! The "disturbance" relevant to PCT
is the one described inside the organism that is controlling, not the
one described dispassionately by an external observer. Both use
an encoding scheme to describe the disturbance. One scheme requires
many many bits, while the other requires very few.
This is what I mean when I say that the hierarchy brings the information
content of the disturbance in line with the output capacity. An external
observer describes the disturbance in a language that requires many bits
(such as the detailed description of the molecular positions/momentums
that the compensatory thermostat requires). The internal hierarchy
describes the same real-world disturbance in a language requiring only
a small number of bits - a number that can be handled by the capacity
of the output channel (such as the much simpler description used by
the error-control thermostat). This is Ashby's Law.
The output
mirrors the disturbance because this is what the output MUST DO in order
to keep the input IN THE REFERENCE STATE; this is the magic of
closed loop control.
Yes, this does sound like magic, and not a scientific explanation at
all. There must be an explanation WHY the control system is able to
do what it MUST DO. Just to say that it MUST DO it does not explain
anything.
ยทยทยท
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Allan Randall, randall@dciem.dciem.dnd.ca
NTT Systems, Inc.
Toronto, ON