[Martin Taylor 950222 12:00]
Bill Powers (950221.2210 MST)
Maybe we are on the way to getting an agreed basis on which to have a
fruitful discussion about information. First, I (almost) agreed with
Rick, and now I (almost, perhaps more than that) agree with Bill P.
In order to detect the
information in the perceptual signal that corresponds to variations in
the disturbing variable, it seems to me that it would be necessary to
know the behavior of the disturbing variable by some means other than
through the perceptual signal. Something like synchronous detection
would be needed -- otherwise there would be no way to detect a component
correlated with variations in the disturbing variable.
Put "for the analyst" after "in order" at the start of this, and I'm in
full agreement.
This means that while the _analyst_ might be able to calculate what
proportion of the perceptual signal's variations are due to the
variations in the disturbing variable, the control system itself could
not do that because it has no separate channel that tells it what the
disturbance variations actually are.
Right. Fully agree.
So even if the information exists,
somehow, in the perceptual signal, there is no way the control system -
can find out what it is.
The connotations of this remark, rather than what it says directly, are
where I think our problem lies. I agree totally with what actually says.
There is no way the control system can find out what information in the
perceptual signal is due to the disturbance (either waveform or variable).
But there seems to be a connotation that because the control system does
not segregate the information relating to the disturbance, it therefore
does not use that information. As I noted on previous occasions, using
something is not the same as knowing it. The control system (as Rick said
so well only yesterday) knows nothing about what the perceptual signal
is about in the real world, or what an observer might say the perceptual
signal is "doing" for the control system. Within the control system, the
perceptual signal is simply a value. If the value differs from the
reference signal, the error signal differs from zero. And that's ALL.
This lack of "knowledge" about what the perceptual signal is doing, and
how it relates to the real world, is irrelevant to the facts of how well
the control system controls it. It controls as it controls, depending on
the real state of all the elements of the loop. But the analyst who wants
to explain or predict how the control system will behave must know
something about the bandwidths and delays in the control loop, both within
the ECU and in the environment. The analyst must also know about the
statistics of the disturbance, and stuff like that, stuff that the control
system can "know" nothing about. But it is that stuff that determines the
actual behaviour of the control system.
An old General Semantics motto is "The map is not the territory." The
control system is the territory, and in that territory rivers flow in
particular paths. The map describes the territory, and shows certain
directions as being maximally downhill--and that's where we usually
find the rivers flowing. "Downhill" here is analogous to "information"
or "bandwidth" or "loop delay." The rivers flow where and however fast
they do, and the control system controls as well or as poorly as it does,
whether or not we choose to make maps or descriptions and to think of
reasons why the rivers flow or how the control systems control. We don't
know what is in their real world, and they don't know how we are describing
them.
Rivers know nothing of "downhill" and control systems know nothing of
"information." But if we know which way is downhill, we may be able to
say something about the rivers, and if we know about the information flows
in a control system we may be able to say something about its manner of
control or failure to control. Exactly the same applies to Laplacian
analysis of the control system. The control system knows nothing of where
the poles and zeros are, but it behaves as their locations predict,
nevertheless.
Martin