[From Bruce Abbott (2012.12.08.1500 EST)]
Rick Marken (2012.12.08.1045) --
RM: I'm moving this to a new subject head which I think better reflects the
subject of the debate.
Well, it's incorrect so I've changed it to something more suitable.
I noticed that you didn't address any of the points I raised in the post to
which this is supposed to be a reply. I really would like to know how you
think the output pattern matches the disturbance pattern, thus demonstrating
that information has been passed from disturbance to output, without that
information passing through the mechanism of the control system.
Bruce Abbott (2012.12.07.1830 EST)
RM: You are assuming that the only way for information about the
disturbance to appear at the output is for this information to have gone
through the organism.
BA: How else could it get there? Magic?
RM: Actually, there is no "it" (information) to get there. The information
about the disturbance in output is in the mind of the observer who sees a
correlation between disturbance and output. So when I say that there is
information about the disturbance in the output of a control system I just
mean that we do see a correlation between disturbance and output when a
system is controlling a controlled variable. But that doesn't mean that
there is really something called "information" that is telling the system
how to vary its output in a way that compensates for the disturbance. And we
know from the equations of PCT that there is no such information becaust the
observed relationship between disturbance and output depends not on
characteristics of the organism but on characteristics of the feedback
connection between system outputs and controlled variable.
Rick, you just aren't getting the concept of information. Let's see if this
makes it any clearer: I have a time-varying signal that you can display on
an oscilloscope. However, instead of sending you that signal, I use the
signal to disturb a controlled variable (the reference is being held
constant), then hook up a device that converts the control system's output
to a time-varying voltage, inverts the waveform, and displays it on the
oscilloscope. I assert that I have transmitted information to you about the
values of the original signal as they varied over time (with some minor
distortion due to the fact that the control system's output doesn't exactly
track the effect of the disturbance on the CV). To say that the two signals
are "highly correlated" is equivalent to saying that the information carried
by the original signal has been transmitted (with some slight loss of
fidelity) to the second signal, via the communication channel established by
the signal pathways within the control system. It's similar to the process
involved when I talk to you on the phone: In that case the auditory waveform
of my voice gets transduced to an electrical signal that is transmitted by a
communication channel (the phone lines), and transduced back to an auditory
waveform by your receiver. To the extent that you can understand me, the
information carried by the signal of my voice has now been successfully
transmitted to the airwaves entering your ear.
It's information in the information-theoretic sense because the sound you
hear reduces uncertainty about the waveform variations taking place at the
sending end.
I've deleted much of the remainder of your post because it has no relevance
to the question. It's like "proving" that rockets can't propel spacecraft by
demonstrating that the air is too thin up there -- under the
misunderstanding that the rocket exhaust needs something to push against.
Given that you don't understand what information -- in the information
theoretic sense -- is, your counterargument completely misses the mark.
RM: I care about you guys getting this right -- understanding that
information about the disturbance is not what "guides" the output in control
-- only because I think not getting this right takes your eye off what I
think is the main "ball" in PCT: controlled variables.
You still misunderstand the concept. Information is not something separate
from the time-varying variables and signals involved in minimizing the
effects of a changing disturbance on a controlled variable. It is just a
measure of how well variation in one variable or signal gets impressed upon
another that is in communication with (influenced by) it. Information is not
a property of the observer, but of the signal.
I've tried to explain the information concept more clearly in my reply to
Bill's (2012.12.08.1043 MSRT) post. See if that doesn't help clear up the
misunderstanding.
That said, I really don't care about applying information theory to the
analysis of control system performance -- mainly because I'm not equipped to
do it, but also because any possible advantages (if any) of such an analysis
over the traditional approach have yet to be demonstrate. But I do recognize
that such an application is possible and perhaps may even prove fruitful.
Therefore I don't disparage those who make the attempt.
Bruce