[Martin Taylor 950315 11:00]
Trying to catch up on a whole lot of interesting stuff, with no time to
do it in....
Rick Marken (950305.2000)
Martin Taylor (950304 18:00) --
The outside observer can determine the "information about;" the
control system only uses it.But you have never shown that the control system uses "information about";
you just say it does. An outside observer can also determine the Laplace
transform of the perceptual signal, for example. Does that mean that the
control system uses this transform too? In fact, a control system uses the
difference between two signals (p and r) to continuously drive it's output.
Why don't we leave it at that?
Did Newton's apple know that it was being pulled by a gravitational force
proportional to the product of its mass and that of the whole Earth?
Did it know that it was describing a geodesic in a non-Euclidean space-time
manifold? Did it use the geodesic to decide where to fall? Or did it
use the calculus of variations to find a minimum in the force-time equations
determining its route to the ground?
In fact, an apple just falls until it hits the ground. It uses the ground
to know when to stop. Why don't we just leave it at that?
There's a serious point here. All the systems we talk about are our
own perceptions. We are outside them looking in. The control system
is a "system" that consists of several components, no one of which in
isolation IS the system. When we look from outside, we can choose to
look in any way that suits our personal modes of perception, and we can
choose to look at any element of the system or at the whole thing.
Rick is happy to look at the comparator and the error signal that serves
as input to the output function, and to "leave it at that," because
the control system does not know enough maths to compute its own Laplace
transforms (or informational parameters).
The Laplace view is of the functioning of the system as a whole, but
applies only to linear systems. The information view looks less precisely
han the Laplace view at the whole system, but applies to a wider range of
systems, including sets of interacting scalar control systems, whether they
be in one hierarchy or in a whole society. To say that information theory
does not apply to control is only to say that you have an antimathetic (no
typo) set of perceptual functions. To say that it is not useful to apply
information theory to control is legitimate and arguable.
Rick can "leave it at that" without disturbing me. I prefer to look
in more than one way at what the systems do. To get an apple to eat, I
shake the tree and let it fall--and "leave it at that," as so many did
before Newton. But for other purposes, I might look at it as an example
of many related things, like space shuttles and baseballs. I might think
of other influences, none of them "known" to the apple, such as wind speed
and direction. I might think of the apple's time-lines in a locally
Euclidean 4-space, wrong though that might be in detail.
No, the apple "uses" none of these. They exist in the way we see the fall
of the apple, and the more of them we see, the better we understand the
apple's fall--and much else, beside. Years ago, I started off the information
theory discussion with a provocative statement that one couldn't properly
understand the control system without understanding the role of information.
Now, I would retract that claim, and replace it with the statement that
I can't properly understand ... Other people perceive differently, and
information theory may not aid their understanding. It no longer disturbs
me to realize that.
So I was wrong in saying that the control system "uses" information about
the disturbance (and other things) in going about its business. It no
more uses that information than it uses the difference between p and r.
It's all in how we choose to look at the control system.
ยทยทยท
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There's no point in going over yet another repetition of how we have shown
the correctness of the information-theoretic description. If you don't
have a perceptual function that allows you to see something, you won't
see it. It's much like high-level colour-blindness, and there's no point
in giving a colour-blind person ever more red and green patches and saying
"See, there's a BIG difference between them." For the colour-blind person,
there isn't.
If and when I find a quite different way of showing the usefulness of the
IT approach, we can address separately at that time whether it is useful.
We can also address at any time whether my procedures in using it were
correct. What makes no sense to discuss is whether it is applicable,
because that is simply a question of asking whether arithmetic is applicable
when there are a number if objects lying around. If you want to shovel
them into a pit, arithmetic isn't useful. If you want to determine how
many of them somebody just removed, it may be.
Martin