Kicking the Information Habit

[From Rick Marken (960608.1600)]

Martin Taylor (960608 1221) --

the initial and basic prediction from information theory is
that the better the control, the less information from the disturbance
will be found in the perceptual signal, and that's the result that
showed up.

As I recall, you made that "basic prediction" after you saw the data; I
guess that's the kind of prediction you get to make when you have two
watches :wink: It's a pretty strange prediction, too, since it says that
the less information you have about the disturbance, the more precisely
you can reproduce it. Is that _really_ what you thought the information
theory prediction was, at first?

However, in the presence of good control, a good reproduction
of the disturbance waveform can be constructed from the perceptual
signal, which is not possible when control is attempted but poor.

Yes. And this was true because the "information" you used to reconstruct
the disturbance was the output of the control system; you didn't use the
perceptual signal because there is no information in the perceptual signal
about the disturbance. There can't be. The perceptual signal always
represents a mix of disturbance and output effects on the controlled
variable: p = o + d. There is no information about the disturbance in
perception, no matter how well or how badly the perceptual signal is
being controlled. The whole idea of information in perception is
completely inconsistent with the facts of closed loop behavior.

There is also no information about the disturbance in the output variable;
the output variable mirrors the _net_ effect of all disturbances to the
controlled variable. So the most you can learn about "the" disturbance
from the output variable is the net effect of what might be one or many
disturbances to the controlled variable. And even this "information"
hinges on you knowing two things that the control system itself could
not possibly know: 1) the disturbance function, h(), that determines the
effect of disturbance variables on the controlled variable and 2) the
feedback function, g(), that determines the effect of the control system's
own output variations on the controlled variable. That is,

p = g(o)+ h(d1, d2...dn).

You were able to determine d based on o when you knew that g() and h()
were 1.0 and there was only one distrubance variable so that p = o+d.
Then, given o you were able to find d (this reconstruction was more
accurate when control was very good becuase, in that case, p is essentially
a constant). Your reconstruction of d based on o was not done with
information theory; it was done with (simple) algebra.

If analysis of the information processing that is inevitable any time an
influence at one place has an effect at another can be helpful in
understanding control,then use it.

Information processing is _inevitable_ any time an influence at one place has
an effect at another?!?!? The earth influences the position of the moon and
vice versa; is information processing going on here? Is the earth getting
gravitational information from the moon? (I have the scary feeling that
you're going to say "yes").

So far, I accept that I have not demonstrated it [information theory] to be
useful to you, though I find it useful to me. I have no problem with that,
and I don't understand why you do.

I spent a lot of time a couple years ago trying to explain why I have
a problem with information theory. My main problem wih it is that it
points behavioral researchers down a blind alley. If you think that
the brain is processing information about events in the world you will
do research aimed determining how these events are processed. That is, you
don't do the kind of research that helps you understand the behavior of
living systems; research aimed determining the kinds of perceptual
variables (events) that people perceive and control.

One of the tough things for people getting into PCT is confronting the
fact that their old, beloved theories are not consistent with PCT. This
is particularly tough when those theories were what led people to PCT
in the first place. But the fact is that PCT is a whole new ballgame;
you can't play it well if you keep trying to throw in rules from other
games.

Best

Rick

[Martin Taylor 960608 19:15]

Rick Marken (960608.1600)

I'm away for a week starting Monday, and it isn't so easy searching the
archives from home, so a proper reply will have to wait at least until
June 17 and probably later. I don't want to restart the "information
theory" thread as a technical discussion, but there are a couple of
points to be made, which _have been_ redocumented from the archives
the last time these statements were made.

the initial and basic prediction from information theory is
that the better the control, the less information from the disturbance
will be found in the perceptual signal, and that's the result that
showed up.

As I recall, you made that "basic prediction" after you saw the data;

False. It was this that started the whole thing. The rationale seemed to
me to be obvious, and to provide a sound basis for the claim that
control was essential to life. That whole notion seemed to scare some
people on CSGnet, and led to the entire information-theory discussion.

I started to rewrite the rationale, and then realized it would probably
restart the entire discussion. Instead, I'll find the original in the
archives, if I can, and quote it when I get back.

However, in the presence of good control, a good reproduction
of the disturbance waveform can be constructed from the perceptual
signal, which is not possible when control is attempted but poor.

Yes. And this was true because the "information" you used to reconstruct
the disturbance was the output of the control system; you didn't use the
perceptual signal because there is no information in the perceptual signal
about the disturbance. There can't be.

Wrong again. I used certain fixed functions plus the varying perceptual
signal. The fact that the fixed functions were the output function and the
feedback function of the control loop is neither here nor there.
The fact that they don't vary as a function of the waveform of the
disturbance is what matters. The only varying item used was the perceptual
signal.

The original question was put in words something like: If, using nothing
that contains information about the disturbance, plus the perceptual
signal, one can reconstitute the disturbance waveform, would you agree
that the perceptual signal carries information about the disturbance?
Marken said "yes" and said that when I did what I described I would do, the
disturbance would _not_ be reproduced. But it was, so Marken claimed "foul".

Why "foul"? Because I used the form of the output function. Does the
form of the output function carry any information about the moment-by-
moment fluctuations of the disturbance waveform? No, it does not. I used
the form of the feedback function. Does the form of the feedback function
carry any information about the moment-by-moment fluctuations of the
disturbance waveform? No, it does not. Where, then, cometh the information
that allows the reconstruction of the disturbance waveform to the
accuracy permitted by the precision of control? The only thing left
is the waveform of the perceptual signal.

Let's recap. The issue was whether there is any information about the
disturbance waveform in the waveform of the perceptual signal. Nothing
that is fixed over time, or that varies independently of the disturbance
waveform carries any information about the disturbance waveform. A fixed
reference level conveys no information about the disturbance waveform.
A fixed output function conveys no information about the disturbance
waveform. A fixed feedback function carries no information about the
disturbance waveform. So, to use any of these in any way along with
other candidates is legitimate when we are looking to see if a
candidate signal carries information about the disturbance waveform.

When we use these supporting functions and values, along with the
perceptual signal, lo and behold, we can reconstruct the disturbance
waveform. Before we produced the data, Marken said that the test was
legitimate. After we produced the data, and for all the subsequent years,
he said it was not. I cannot see any reason why it is not legitimate
to use the height of Salisbury Cathedral and the phase of the moon
in such a test, so long as it is clear that they are not affected by
the moment-by-moment fluctuations of the disturbance waveform. The issue
is not whether the control system "knows" these things. The issue is
whether information about the disturbance waveform is present in the
perceptual signal. The result is crystal clear. It is.

But, perhaps paradoxically, the correlation between the perceptual signal
and the disturbance appraoches zero as control appraoches perfection. And
that apparent paradox seems to be the point that leads some people to
argue that the perceptual signal does not--can not--carry information
about the disturbance waveform.

Now back to our regularly scheduled program.

More on this, if you insist--which I don't--, in 10 days or so.

Martin

[From Rick Marken (960608.1745)]

Martin Taylor (960608 19:15)--

The fact that the fixed functions were the output function and the
feedback function of the control loop is neither here nor there.

I think the fact that you had to use the feedback and output functions
to reconstruct the disturbance is quite a bit more _here_ than
_there_:slight_smile:

But don't worry. I don't want to start the information theory debate
again. Those who were there and understood it know the true value of
information theory in psychology; those who didn't -- or who want to
believe that all those smart, famous psychologists just couldn't be
wrong -- don't.

Best

Rick