# The challenge: its original form

[From Bill Powers (960627.1610 MDT)]

Martin Taylor 960627 14:15 --

Read your post again, if you want to know why we have trouble
communicating:

Let's go through these. Of the set you mention, we did not use e or
o, so drop them.

1. Fi (input function). Does this fluctuate in some way related to
the disturbing variable?

2. Fo (output function). Does this fluctuate in some way related to
the disturbing variable?

3. Fe (environmental feedback function). Does this fluctuate in
some way related to the disturbing variable?

4. r (reference signal). Does this fluctuate in some way related to
the disturbing variable?

5. p (perceptual signal). Does this fluctuate in some way related
to the disturbing variable?

If none of these do, then using them cannot result in a
reconstruction in any way correlated with the disturbing influence
(note: "influence" here, not "variable"). Let's consider them.
...
Which demonstrated the ONLY thing that was at issue: whether the
perceptual signal carried information about the fluctuations in the
disturbing influence.

So make up your mind: are you talking about the disturbing VARIABLE or
the disturbing INFLUENCE? Have we not agreed that these are different
things? All through our initial arguments, we were talking about
information in the perceptual signal about the disturbing VARIABLE. You
didn't even notice that there was a difference until I tried to make the
difference clear some time later, and you started huffing about how you
would NEVER have meant the disturbing VARIABLE, and how could we think
such a thing? Yet here you are, asking five times "Does this fluctuate
in some way related to the disturbing variable?"

Your definition of a disturbing INFLUENCE makes it nothing more than a
component of a unitary CEV or perceptual signal, having no reference to
whatever distal processes are producing that component. A disturbing
VARIABLE, however is a measurable physical variable distinct from the
CEV, which acts through some law or linkage to create a component of the
CEV attributable to the disturbing variable.

The answer to (5) is NO. The perceptual signal does not fluctuate in a
way related to ANY ONE disturbing VARIABLE. If there are two disturbing
variables acting, one might be increasing its effect (via its connecting
disturbance function) in exactly the way another is decreasing its
effect (through a different disturbance function), although the sum
might have a constant nonzero effect. If one (unopposed) disturbance is
increasing as t^3 while the other is increasing as -(t^2), the
perception will be changing as t^3 - t^2, which does not correspond to
either disturbing variable. If there are n disturbing variables acting,
each through its respective disturbance function, the net effect on the
perceptual signal can be anything, depending on the nature of the
connecting disturbance functions. And the perceptual signal need not
show a correlation with any of the disturbing variables. We aren't
talking about random variables here, but ordinary physical processes
which are quite orderly.

The disturbing INFLUENCE contains no information about how many
disturbing VARIABLES with what temporal waveforms are contributing to
it, or by what paths. Given the state of the CEV, the state of o, and
the form of the feedback function, you can compute that there is a net
influence acting independently of the output. But that is as far as you
can go. If the output is 10 kilograms of force, and the acceleration
being controlled is zero, then without knowing any more you can say that
there is a net disturbing force of -10 kilograms. But whether that net
force is due to a single physical interaction or to many, or to nearby
small influences or distant strong ones, or from one directly opposing
force or many applied at different angles, is not deducible from local
knowledge.

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.

No, that was what made it so powerful. The demonstration was done
entirely on your own ground and on your terms.

No, that is what made it so trivial.

And don't forget that at the time, you were defining
"disturbance" very differently from the way Rick and I were defining
it.

I don't think so, except that I was using the term "disturbance"
for what we have since come to label "disturbing influence". As was
made clear every time you tried to impute to me the intention of
discussing what we now call the "disturbing variable."

Well, that's a pretty monumental "except." You arbitrarily changed the
definition of "disturbance" to make your answer to the challenge
possible, and then strenuously objected when we said you had not met the
conditions of the challenge. That is not answering the challenge
"entirely on your own ground and on your own terms." It is twisting our
statement of the challenge, which you could not meet, into a different
statement which you could -- irrelevantly -- meet.

You also twisted the basic meaning of the challenge. What we maintained,
and still do, is that the control system can counteract the effects of
envirnmental disturbances on its CEV without any knowledge of what is
causing those effects. By that we did not mean "without an external
observer's having any knowledge of the disturbance." We were talking
about what the control system itself could do. But you immediately
confused that kind of knowledge with what an external observer who could
perceive all signals and functions could do, which had nothing to do
with our challenge.

···

------------

Here you seem to be wanting analytical expressions--algebra. Is
that right? Would you be happy with that?

NO. I already know how to do the algebra for simple control systems.
What I want is an analysis in terms of INFORMATION THEORY which leads to
the same results we get by other means. You're continually making
statements about what information theory says, but without ever
demonstrating that it actually says what you claim it says. You're
waving your arms but you're not writing anything on the blackboard.

What DO you want? I've tried, as you point out, to choose models
that demonstrate the essential points, from various angles.

I want you to do the demonstration, not say it could be done or that
somebody else might like to do it or that you don't have time to do it
or that it's so self-evident that it doesn't need to be done.

You quote the introduction to my proposed simulation experiment,
which was introduced with the intention of providing a testing
ground in which you, Bill Powers, would not be able to say that the
information calculations were wrong because the simulation of a
continuous system was actually discrete. It annoys you.

Yes, I'm annoyed. All you have is a PROPOSED simulation experiment. I
haven't seen a single information calculation. I want to see the
finished product, not more half-worked-out proposals. Your stated
proposal is only a sketch, as you would find out if you actually tried
to implement the "simulation" (it is not a simulation -- what physical
situation are you simulating?).

The "grandiose claims" are far from grandiose when it comes to a
single scalar control loop. They become more interesting when we
deal with multiple parallel control loops, and much more so when we
deal with a hierarchy. As you have seen.

That is complete -- well. What is grandiose is saying anything about
information theory in relation to a single scalar control loop. I don't
want to see something "more interesting". That usually means
"sufficiently more complex that any result could be obtained just by
making the right assumptions." I want to see the simple analysis of a
simple scalar control loop, in which information theory is applied to
generate a rigorous conclusion that anyone would necessarily reach given
the same theory. This is what you have never done and what you still
don't want to do. It's not "interesting." Well, Martin, I claim that you
don't know how to do it. I'm trying to call your bluff.

What really frosts me, Martin, is the clarity with which you answer
questions about PCT (960627 16:30 to >Jeff Vancouver). Why can't you do
that with information theory, too?
-----------------------------------------------------------------------
Best,

Bill P.