RM: How do you know this? Since the controlled perception (p) is a theoretical construct that explains the observation that an aspect of the environment (q.i) is controlled, how do you know that this construct does not always correspond to any aspect of the environment that can be perceived by an external observer? I'd like to see a demonstration or model showing how this works.
Â
RM: The source of the dispute is whether PCT is approached from the scientific or mathematical-logical perspective. From the scientific perspective -- the one that Bill and I take -- the perceptual signal, p, is a theoretical construct that accounts for the observed fact that some variable aspect of the environment, q.i, is being controlled; the goal of PCT research from this perspective is to discover what aspects of the environment organisms control, how they control them and why. From the mathematical-logical perspective -- the one that you and many others take -- the perceptual signal is a fact -- an axiom from which conclusions are derived by logical deduction; the goal of PCT research from that perspective is to derive new facts (theorems) from the axioms that are assumed to make up PCT. The dispute exists because I (like Bill, as described in his 1994 post to you, which I have copied again below for your enlightenment) think the mathematical -logical approach to PCT is a barrier to progress in the development of a science of living control systems.Â
MT: Actually, not according to Powers, for whom ones own perceptions were the only reliable truth.
RM: Bill knew that our observations are our perceptions. Your constant attempts to make it seem like what I say is not consistent with what Bill said are really deplorable. Compare Bill's post below to his Foreword to " Mind Readings" and see whose approach to PCT was the one Bill preferred.Â
Â
RM: Please explain how observations differ from perceptions. No, on second though, don't bother.Â
MT: It's not a "yes-no" proposition. Control comes in degrees between perfect (impossible for physically realizable systems) and no control.
RM: It's true that control comes in degrees but the identity of the variable being controlled is, indeed, a yes-no proposition. For example, in the "What is size" demo (<http://www.mindreadings.com/ControlDemo/Size.html>http://www.mindreadings.com/ControlDemo/Size.html\) the variable controlled is either area ("yes", q.i = h * w) or it is something else ("no" it is not area, it is perimeter, h + w). The primary concern of PCT research is figuring out what variable is being controlled; that's what the test for the controlled variable is all about. Only after that "yes-no" question is answered can you start trying to determine why the quality of control is good or poor.Â
MT: No, it IS true that the perceptual signal MAY correspond to the observer's notion of q.i, and not only because of the possible contribution of imagined components to the perceptual function's input.
RM: Only in the non-scientific armchair of the mathematical-logical approach to PCT.Â
Â
RM: Here again is Bill's post. Enjoy.
···
========================================
Date: Wed, 17 May 1995 05:24:50 -0600
Subject: Friction
Hello, Martin -- (no CCs)
I have become increasingly frustrated with our communications and have been
trying to figure out what is wrong. In the middle of the night a possibility
occurred to me. A bit of browsing through the archives -- not exhaustive --
has brought up a number of topics all of which have led me to the same
frustration with your approach that I am currently experiencing. The ones I
recall now, which are probably not all of them, are (in no particular order)
----------------------------------
Information about the disturbance flowing through the perceptual signal to
enable control to take place.
The perceptual function composed of an S-shaped response followed by an
integrator.
A discussion on bandwidth in relation to maximum realizable gain in a control
system.
The "bomb" effect.
Flip-flops or cross-connections as explanations of category perceptions,
association, contrast.
Categories as existing parallel to the analogue hierarchy.
Control system organization as being a model of the environment.
----------------------------------
I finally realized that there is a common element in your treatment of all
these subjects. It is very much like the way you took off on the basis of
assuming that my limitation of the disturbance magnitude in Hans' set of
disturbances was due to insufficient output strength in my model, which in
turn was caused by too short a word length. Having assumed the truth of your
premise without particularly checking to see if it was true, you then built a
series of plausible deductions from the assumption, which happened to support
a general principle you were trying to get across. Unfortunately, the premise
was false. I would not be surprised, however, if you decided that even if the
premise happened to be false in that case, the deductions you made from it
were probably true.
Â
In each of the above subjects, you began with a theoretical possibility and
developed it just far enough to see some possible implications of it. Then you
quickly built a plausible and ever-more-detailed series of deductions from
those implications, and arrived at what seemed to you an interesting new
phenomenon. You could see in your mind's eye how the Bomb would sit there
ticking, ready to go off if the right combination of disturbances occurred.
You could imagine information flowing from the disturbance through the
perceptual system to the output, where it got used up in producing the effects
that would counteract the disturbance. You could see the s-shaped curves and
integrators acting like a perceptron for the input part of a control system.
You could see a whole hierarchy of discrete categories with hysteresis,
running in parallel to the analog hierarchy. And the fact that you could see
in principle how certain other phenomena might flow from the initial
conceptualizations was enough to convince you that the initial
conceptualizations must be correct.
Â
So what happens is that the tail wags the dog: the attractiveness and richness
of the conclusions drawn from the initial assumptions convinces you that the
initial assumptions must have been right. And once that has happened, you
forget completely that the initial assumptions were never established as true,
and you speak of the conclusions as if they were now established facts; you
even start using them to prove other conclusions.
Â
The name of this type of reasoning process, or one name, is of course
"mathematics." In mathematics (including logic, or is it the other way
around), it doesn't matter whether the initial assumptions are factually true
or in some way supportable by evidence. The assumptions are simply the initial
process of setting up the chessboard with a problem, so you can work out a
solution to it. Once the field of play is established, you can then start
working out the theorems and proofs, encountering beauty and entertainment at
many stages along the way. You begin to get a feel for the system you have
created, so its major conclusions become familiar parts of that conceptual
world. These major conclusions become theorems on which to build further; they
get names like "information about the disturbance" and "The Bomb" andÂ
"crossconnections."Â Since they have been derived by correct reasoning from the
premises, there is no reason to doubt them any more; they become real. The
premises drop out of sight; they were never very important anyway, except as a
way to get the game started. The real fun is in building the structure of
ideas on those premises.
Â
Judging from various comments you have made about your interests and
preferences, I don't think that this is a completely inappropriate assessment
of your modus operandi. Your approach is not the engineering approach to a
physical system, but the mathematical-logical approach to a hypothetico-deductive
system.
Â
This hypothesis explains to me your disdain for "mere demonstrations." If you
have worked out the logic correctly, what is the point in doing an actual
demonstration of it, and doing different demonstrations to bring out one point
or another? If you understand addition, what is the point of demonstrating
that 9 + 1 = 10, and 8 + 2 = 10, and so forth? If you understand the complete
structure of information theory from Shannon on up, what is the point in
demonstrating what you already know to be true: that the signals inside a
control system must contain or pass along information about the disturbance,
and that it is this information that makes control (and everything else)
possible? And most important, if you have shown that there are no logical
errors in reaching a conclusion about real behavior, what is the point in
going through the labor of showing by direct experiment that the conclusion
actually fits the data? If the data do not agree with the conclusion, there
must have been some error or something unaccounted for in the experiment.
That last if-then is the only way I can explain your reaction to difficulties
when we actually try out some of your proposals. In the long information
-in-perception debacle, we tried computing the reduction in the uncertainty in
The perception, then in its first derivative, then both again with temporal
shifts, and in every case the results disagreed with your deductions about
what we should find. By rights, this should have brought you up short and
caused you to question the very basis on which you built your deductions. But
that didn't occur: you simply abandoned the attempt to make a correct
deduction that would fit the data and turned to other subjects.
Â
If I had been in your shoes, I would have had to backtrack through the logic
trying to find the error, and eventually (if no logical mistake could be found
that would fix the problem) I would have gone all the way back to the simple
starting premises on which the whole logical structure is built: if there are
no mistakes in the logic, yet the conclusions do not fit observation, then the
only place left to find an error is in the premises. And for me, however
painful the decision, the only conclusion I could then reach is that the
entire system is built on false-to-reality premises.
Â
When I went through the process of computing reduction in uncertainty about
the disturbance due to the perceptual signal, under your tutelage, I noticed a
fact, and mentioned it, that seemed significant to me. In the process of
computing the conditional probabilities, I noticed that I would get the same
conditional probabilities no matter in what order I did the sampling of the
disturbance waveform. So in principle there was an infinity of different
waveforms that would allow me to compute the same quantity of information in
the perception. This made it very hard for me to see how the outcome could be
an output waveform based on the "information" that was arranged in the same
sequence as the elements of the disturbance waveform, which of course is
necessary if the effect of the disturbance is to be canceled.
Your reply was brief and dismissive: you just compute the conditional
probabilities on pairs of successive values of the waveform, and get the
probabilities of the first derivatives. But after thinking that over, I
realized that the same problem still existed: one could rearrange the pairs
and get the same conditional probabilities. So how could the information
passed in the perceptual signal possibly be responsible for producing the
RIGHT output waveform?
Â
When I mentioned this (I am pretty sure I mentioned it), there was no reply
that I recall. The failure to get the right results when we used the first
derivatives as elements, even time-shifted, reinforced my doubts about the
process, but not being an expert in information theory I did not feel
competent to ferret out the cause of the problem.
I now realize that you did not search for the cause of the problem by
backtracking through information theory. You just gave up on it. This did not
solve the problem, but it left the intellectual structure of information
theory in your head undisturbed. If PCT is correct, we can use this phenomenon
to guess at the nature of the variable you were -- and are -- controlling.
I remember getting a frantic phone call from Chris Love shortly after the
start of the Little Baby project. He had tried to set up a big complex
hierarchy of control systems in which, per the boss's suggestion, the
perceptual function was an S-shaped curve followed by an integrator. The
reason he called was that he hadn't been able to get even a single elementary
control system to work. I tried to explain to him that a control system
organized that way would be trying to control a variable that was the inverse
function of the proposed form, namely a nonlinear first derivative that went
to infinity at zero and maximum perceptual signal. He was not then
knowledgeable about control theory, so I just suggested that he move the
integrator to the output function, and preferably make the input function
linear. He tried that, and got a working control system for the first time,
several months into the project. I felt very sorry for Chris, because he had
to try to make the suggested model work, and it could not work.
On other occasions, I have pointed out to you a shortcoming of the perceptron
approach, in that it doesn't yield perceptual signals which are continuous
representations of controlled variables. The nonlinearities and other
properties limit the output to a yes-no signal, which is good only for
discrete control. However, in the fairly recent past, I noticed that you were
still referring to the S-shaped input function with an integrator as part of
the model. Chris' problems do not seem to have shaken your faith one bit. Or
perhaps they have simply led you to abandon that problem, and go to modeling
discrete systems. Obviously it has not led you to re-examine the premises
behind the perceptron approach.
--------------------------------------
I think that in deciding to be an abstract theoretician, you have simply cut
off your higher level systems from lower-level perceptions, operating the
higher-level systems in the imagination mode. And I think that this is a
mistake. If you don't continually check your higher-level models against
experiences by interacting with the outside world at the lowest levels, you
run the risk of creating a systematic delusion about the nature of the world;
one that is internally consistent, but which is not consistent with what your
senses could tell you if you consulted them. Abstract thought alone is simply
not a reliable way to learn about nature.
Â
This is why I am so adamant about demonstrations and experiments. You have to
close the loop through the external environment if you're to achieve real
control. No matter how self-evident or obvious or logically necessary a
conclusion may seem, it is still necessary to find a way to test it by
interacting with the world. And when you do such tests, it is necessary to pay
attention to the outcome, because if the outcomes don't agree with the logic,
it says that something is wrong with the logic or with the premises on which
it's founded. No matter how convinced you are that you have the right idea,
nature is perfectly capable of contradicting you.
Â
And this says something else, too. It says that there is really very little
point in building up big deductive structures on premises that have not been
experimentally demonstrated. Your cross-connection ideas about category
perception may prove to be quite right, but you have no way to verify that
such cross connections exist or work in the ways you assume they work.
Technology has simply not reached the stage where we can do this in a living
working brain. Perhaps it would be possible to do experiments to check, at
least, the conclusions, to see if people actually work in the way that your
hypothetical model works. But unless you can also check the premises, you are
on very uncertain ground. For any circuit that accomplishes a given result,
there are a dozen different ones that would do the same thing. There will
always be uncertainties in our models, but why deliberately make them as large
as possible?
---------------------------------
I have no illusions about changing your style to correct what I see as
mistakes. What you make of what I say is in your hands alone. But if you want
to understand where our frictions come from, you have to know how I perceive
the way you work, and how limited it looks to me. You have to understand that
even where you think you see agreement, you may be considering only a narrow
range of meanings of what I or others say, meanings that fit your world-view
but that may only represent one point of intersection of trajectories that are
headed in different directions. And you have to realize that you often read
hastily, making assumptions that a more careful reading would quickly set
straight and then leaping ahead to draw unwarranted conclusions -- largely,
seeing agreement where there is actually no agreement, or only a very partial
agreement. This is another penalty for working in the imagination mode. You
are far from the only person to work this way, of course.
Obviously, I have considered only YOUR problems, not my own. I am sure that
all of this looks quite different to you. If you want to turn the tables, you
have every right.
Bill
--
Richard S. MarkenÂ
"Perfection is achieved not when you have nothing more to add, but when you
have nothing left to take away.�
                --Antoine de Saint-Exupery
. Bruce has a point but I have a feeling that he doesn’t know how to prove it in scientific way. His view upon “environmental control problem” is totaly different from Ricks.
