Still no information about perception

Marken_Richard_S1 · April 2, 1993, 10:08pm

[From Rick Marken (930404.1200)]

Sorry to keep at this but it's pretty fundemental, from my perspective.
If behavior is the control of perception, then perception is CONTROLLED;
this means that perception is not in a position to tell (inform) the
controller about how to control it. There is no information about the
disturbance in the controlled perceptual input to a control system; not
even information about the derivative of the disturbance. Bill Powers
showed that in a control system that computes output as the integral
of error, the perceptual signal is proportional to the derivative of
the disturbance: ie. p = d(d)/dt. But this is only true when when ko
is optimal and p = o + d precisely. And unless the system KNOWS that
these conditions hold (ie. it has some other source of information about
itself and/or the state of the world) there is no way that the system
can know that integrating p will result in d.

Rather than try to answer Martin's and Allan's last posts, let me
just try to explain again EXACTLY what I mean when I say "there is
no information about the distrubance in controlled perceptual input".
I mean that given a string of values of perceptual input there is
NO WAY to reconstruct with ANY confidence the disturbance that was
present when the perception was occurring. I consider it unfair to
use, as part of the process of extracting d values from p values, any
information that the control system itself could not possibly have . I am
willing to assume that the system can know r, the value of its reference
signal; I'll even allow that it can know O(), the output function (I'm
being REAL liberal here), and, of course, it can know p (and any function
thereof). What it can't know is d (of course), anything about d (like when
it starts or stops). It also cannot know the functions relating d or o to
p; ie, it cannot know that p = g(o) + f(d), and it cannot know g()
or f(). If there is information about d in p THAT IS RELEVANT TO THE
OPERATION OF A CONTROL SYSTEM then the control system MUST be able to
extract that information knowing only what the control system itself can
know.

With these caveats, I again say that there is no information about the
disturbance in perception. This means that the outputs that compensate
for the disturbance (and result in the controlled value of the perception)
CANNOT be viewed as being caused by (or based on information
provided by) the perceptual signal -- the perceptual signal is NOT
informative about "what to do" (what output to produce) in order to
control the perception. Perception is controlled -- it does not control.

Below is a sequence of 50 values of p obtained in a simulation of
a compensatory tracking task. I claim that there is NO INFORMATION
ABOUT THE DISTURBANCE IN THIS SEQUENCE (of perceptual values). If
there is such information then, by now, Martin and/or Allan should
be able to know how to extract it and present it to me in a table of
numbers that represent the distrubance (I have the table of dist-
urbance numbers right here in my pocket). I'll believe their claim that
there IS information about the disturbance in perception when they
give me the last 40 or so values of the disturbance (since they might
want to use up some of the initial values computing first or second
derivatives). According to Bill Powers' analysis this morning, each
of the numbers below is proportional to the derivative of the dist-
urbance. This information should be enough to recover a sequence of
numbers that is highly correlated with the actual disturbance. I will also
tell Martin and Allan that this sequence of perceptual inputs was experienc-
ed by a control system that had a constant reference signal corresponding
to 0 in units of the perceptual variable. I will also tell them that the
output function, O( ), was an integrator -- O := O + ko *(-p)*dt -- where
dt = 0.1 and ko = 10. That's about all that (and, really, MUCH more than)
the control system could conceivably know about itself or the world. Now,
all you have to do to prove to me that there is information about the dist-
urbance in perception is send me back the list of 50 numbers that
constitute the disturbance (or a list of numbers that correlate very
highly with the actual disturbance numbers).

If, for some reason, you are lucky enough to send me back a sequence
of 40 or so numbers that matches (or even closely approximates) the
disturbance then I would like to do it a couple more times just
to make sure that this wasn't a fluke and you really KNOW how to extract
information about disturbances from perceptual signals. But I don't
think that this will really be necessary. I think it is highly unlikely
that you will find a sequence of numbers that comes close to the actual
disturbance. By the way, just to keep this fair, I am sending the 50 values
of the disturbance to Bill Powers and Gary Cziko; they will be the referees,
OK?

Happy disturbance hunting. Here'e the sequence of 50 p values:

1.005025
0.005025
1.000025
0.005
1.080427
0.010804
0.085966
1.087577
0.021752
0.09227
1.094603
0.228376
0.108046
0.104313
-.894812
0.141782
0.105423
-.799151
0.121545
0.197632
0.114098
-.798209
0.090034
-.714653
-.924469
-.972333
-.998959
0.050113
-.843603
-.956468
-1.071734
-.05817
-.836931
-1.099776
-.138254
-.892406
-.12657
-.908274
-1.173942
-.294174
-1.008277
-.288462
-.034383
0.061136
0.1007
1.119942
0.586718
1.369701
1.767049
2.006814

Best

Rick

Allan_F_Randall · April 7, 1993, 8:36pm

[Allan Randall (930407.1600 EDT)]

Rick Marken --
(930404.1200) (930402.1800) (930403.1000) (930403.1600) (930406.1200)

I'll believe their claim that
there IS information about the disturbance in perception when they
give me the last 40 or so values of the disturbance ... Now,
all you have to do to prove to me that there is information about the dist-
urbance in perception is send me back the list of 50 numbers that
constitute the disturbance (or a list of numbers that correlate very
highly with the actual disturbance numbers).

The fact that you would issue such a challenge shows that you are still
missing our point. Why must we produce a "very high" correlation with
the disturbance? I have tried to emphasize more than once that no one
is claiming there is 100% of the disturbance information in the percept.
You have sincerely stated that you understood this and were not expecting
such a demonstration. But now you say that we must produce a "very high"
correlation to satisfy you. I repeat, yet again, the principles put
forth by Ashby: the goal of the ECS is for there to be *no* information
about disturbances in the percept. However, the control system's only
source of information is via this percept, so perfect control is not
possible. I still don't think you've responded to this point. The
percept is the only information source the control system has. I would
really really like to know how you view this. Where do you think the
information is coming from to allow the system to control against
the disturbance? Do you think the system needs *any* information
at all about the world in order to control? If not, I just have to shake
my head. Magic.

Rather than asking for a near-perfect reconstruction of D, a more
reasonable request would be for a demonstration that P allows a
reconstruction of D using *fewer* additional bits of information than
required without P (rather than *no* additional bits, as you are
currently requiring). I will try to put together some kind of
simulation to demonstrate this, when I can find the time (you may
have to be patient - I have other work to do). If you will send me
the complete information about the system you used to produce the P
sample, I could use that. Or, send me a description of some similar
system for which a demonstration would satisfy you. I don't want to
just make up my own, since you are now attributing the lack of
information to nonlinearities. I would prefer to use a system that
is as simple as possible, while still having the characteristics that
you think are required.

Although you say that we are not allowed to use f() to reconstruct
d, this should not strictly be the case. To be in line with
information theory, you should simply stipulate that f(), while it
may be used, is not "free."

Also, some kind of external language, say the C programming language
or something similar, should be allowed "for free". Some kind of
external point of view is implied by even including D in our model
of what is happening. However, if the C programming language had
f() as a built-in function, then I would agree that this is cheating.

You seem to include the output function "for free" only reluctantly.
I'm not sure why. The output function is as much a part of the
hierarchy as the input function or the comparator. To exclude it,
you would need to draw your system boundary lines differently.

So to summarise, would you be satisfied with a demonstration that
takes only the C programming language and the hierarchy as "free"?
I would attempt to show that knowing the percept allows a shorter
C program to be written that outputs the disturbance than could be
written without knowing the percept. Would you accept that *if* this
is the case, there is information about the disturbance in the
percept?

I've tried to
be linear about this -- but now it's no more mister straight guy.

The nonlinearity may further mask the nature of the disturbance, yes.
But if you are claiming it destroys *all* of the information about the
disturbance, then I think you have a problem with explaining how
successful control is possible. If the feedback function was to
completely block the flow of information from disturbance to percept,
then control against said disturbance would not be possible.

1) There IS information in the perceptual signal of an ECS!
...
2) The information in the perceptual signal is about the REFERENCE

Wow! We actually agree! This is the second channel that Ashby talked
about. There is one channel, from disturbance to percept, that is
blocked by successful control (so far, we disagree on this point).
The second channel is *not* blocked by successful control, and goes
from reference to percept. While this is really a separate issue from
the one we have been debating, it is still an important point, and
its nice to see we can at least agree on one aspect of information
in control systems!

[to Martin Taylor]
So what you are claiming is that given the equation o = int(p) and
p you can compute o. If that's all you meant by "there is information
about the disturbance in p" then I must admit that you are correct:
if y = 2 * x and I give you the value of x, you probably could
determine the value of y. IT sure gives some incredible insights.

The experiments Martin and I proposed were not intended to be
"incredible insights." We initially thought the results simply
followed logically, and did not expect to have to implement anything.
We only implemented something because we couldn't seem to get the
point across any other way. Now that you have removed the assumption
of information about D in the output, the Mystery function is no
longer needed. It really doesn't show anything at all exciting.
It's all exactly as blindingly obvious as you state above. We
should now be able to move on.

That stack will show
how the correlation between d and o can range from nearly 0.0
to nearly 1.0 ...

I'm not really interested in such demonstrations of correlation.
I'm trying to build a case for applying Information Theory to HPCT,
not Correlation Theory.

1) p = r

2) o = -g(d)

The second equation says that output (the proximal, environmental
effect of the system) depends on the disturbance (d) and the nature
of the relationship is determined by the feedback function, g(),
...
Note that p NEVER APPEARS
IN EQUATION 2); output does not depend on perception at all;

This is a bit of misdirection on your part. These "equations" are
not descriptions of the operation of a control system. They are
conditions which are closely approximated in a well-controlling
system. In the actual equations that describe the control system's
operation, the output does indeed depend on p.

[NB. that in the two equations above,
p is already busy being a dependent variable; it can't be
an independent variable, too. In other words, in a control loop,
r tells p what to do; p can't, at the same time, be telling o
what to do].

Now who is thinking in stimulus-response terms? Why does a variable
*have* to be either dependent or independent? Why can't r tell p
what to do, while p tells o what to do, while o tells the
environment what to do, while the environment tells p what to do,
while p tells o what to do...et cetera? You are denying the very
essence of a closed loop here. You're talking in terms of
dependent and independent variables only. In a closed loop,
interdependence is the name of the game.

···

-----------------------------------------
Allan Randall, randall@dciem.dciem.dnd.ca
NTT Systems, Inc.
Toronto, ON