Dynamical systems, information solution

[Martin Taylor 931116 12:00]
(Rick Marken 931115.2100)

I get a little wary, having so often written that we are converging, or
getting close to agreement. But here I'm going to say it again, in the
hope that it might be true.

But first:

A PCT person sees the dynamic view as lacking intentionality and purpose,

You betcha. Unless you know of a dynamical system that resists disturbances
we're looking at systems that DON'T CONTROL.

Tautology. A control system is the type of dynamical system that resists
disturbances. There are others. A marble in a bowl resists disturbances
to its resting position in the bottom of the bowl, but is not a control
system. A control system is just a particular kind of dynamical system,
for which a necessary characteristic is resistance to disturbances.

Now:

But I still have one little problem: where do I insert the
filter, quantizer and noise generator so that it influences ONLY the
information about the disturbance? If I filter, quantize or add noise
to the perceptual function, am I not filtering, quantizing or adding
noise to information about the effects of BOTH disturbance(s) and
output(s) on perception?

You can't, for all the reasons we all know about and have always agreed on.
The only thing that affects the perceptual signal is the CEV, which is
defined by the PIF. The information about the disturbance that is
manifest in the perceptual signal cannot be segregated from the effects
of other influences on the CEV (i.e. the output of the ECS). I don't
think there has ever been a question about that, though in the past
discussions I have had a hard job fighting to keep out the words you have
stuffed in my figurative mouth to the contrary.

Maybe you are still confusing your terminology. As Bill Powers
(931115.1130 MST) points out:

Repeating myself, I remind you that we have agreed to distinguish
between "disturbance" (an external variable that contributes to
the state of the CEV via some physical link) and "fluctuation"
(the actual change in the CEV regardless of its cause).

I meant "the effect of the disturbance on the CEV," not "the fluctuation"
and not "the disturbing variable."

So, given the now agreed on terminology,
I think we can see that there is NO information in perception about
disturbances but there IS information in perception about fluctuations (in
the CEV).

I still can't agree with this. Numerically, there is mutual information
between the influence of the disturbing variable (IDV) on the CEV and the
fluctuations in the CEV. Hence there is mutual information between
the IDV and the perceptual signal. (Mutual information is a generalization
of the concept of information transmission, which does not carry any
connotation of a "channel" between the variables).

This must be what you meant all along, right Martin? Perception carries
information about the CEV, NOT about the disturbance.

Perception carries information about the CEV, and THEREFORE about the
effect on the CEV of everything that influences the CEV, whether it be
a disturbance or the ECS output. The question as to whether the different
effects can be segregated has no bearing on the question of how much
mutual information there is.

(Oded Maler 931116 09:30)

the intuiuition that, I think, Martin has,
about *why* it works in the world, is related to gross properties of
systems in general, to information. That was mu guess.

A good guess. Maybe the problem of communication has been related to
a mismatch of messages between people talking about HOW control works
and people talking about WHY it works that way.

Martin