[From Bill Powers (960617.1500 MDT)]
Martin Taylor 960617 15:45 --
What was said in 1992 seems to be mostly a matter of what you now think
were your most important points then, and thus what you select from the
stream of communications to show that you were right all along. One
great difficulty is that your arguments then did not impress me any more
than they do now, yet you cite them as if they settled the matter once
and for all -- and as if I had agreed that they did. Let's just look at
a few of them.
In fact, [the discussion] arose out of my 921218 analysis of the
informational basis of PCT:
"The central theme of PCT is that a perception in an ECS should be
maintained as close as possible to a reference value. In other
words, the information provided by the perception, given knowledge
of the reference, should be as low as possible."
This is not and never was the central theme of PCT as I see it. The
central theme of PCT is that organisms control their perceptions by
acting on the environment. How well they control them depends on the
parameters of the control system. There is no "should" involved.
Organisms control as well as they control, neither better nor worse.
I have no idea what you mean by saying "the information provided by the
perception, given knowledge of the reference". Information and knowledge
are not the same thing, and anyway what is there in a control system
that can evaluate the information in a perception, with or without
"knowledge" of the reference? You're talking gobbledygook.
Later, dogmatic assertions were made that there is no information
about the disturbance in the perceptual signal, assertions that we
proved false, using experimental simulations agreed to be effective
for the purpose.
They were not adequate for the purpose except in your own mind. You and
Randall agreed they were effective; Rick and I did not. In fact there is
no way to tell what the disturbing variable is from knowledge of the
variables in the control loop (perception, reference, error, output) or
from the forms of the functions in the loop (perceptual, comparison,
output, feedback). The reason is very simple: exactly the same
perturbation of the loop can arise from an infinity of different
disturbing variables acting (singly or together) through an infinity of
different disturbance functions.
In your first demonstration, you employed a step-disturbance acting
through a unity disturbance function. This led to a step-change in the
perceptual signal, which you then assumed represented the true
disturbance. But it did not. The same step-change in the perceptual
signal could have been created by an infinity of different disturbances
acting through different disturbance functions. There is no possibility
that one could work backward from knowledge of the perceptual signal to
deduce the nature of an unknown disturbing variable or variables acting
via unknown functions. There is simply no information (in any sense of
the word) about the disturbing variables in the perceptual signal.
Every now and then you seem to wake up and say "Oh, OF COURSE there is
no information about the CAUSE of a perturbation in the perceptual
signal. How could you ever have thought I would suggest such a silly
thing? Please read what I say and you will not attribute such foolish
ideas to me." And then you turn right back to the same theme and claim,
as above, that there really is information in the perceptual signal
about the disturbance, and that you proved it.
I can't account for this except by guessing that you are shifting
meanings of "disturbance" between one set of statements and the other.
One sense refers to the proximal perturbation of the input to the
perceptual function that results from whatever distal disturbing
variables happen to be acting. The other sense (which I always mean by
"the disturbance") refers to the changes in the distal disturbing
variables themselves. Your statement about information in the perceptual
signal about "the disturbance" cannot apply to the distal disturbing
variable. It applies trivially to the proximal variable, because the
proximal variable is exactly what we mean by a CEV. To say that the
perceptual signal contains information about the state of the CEV is a
tautology, because that relationship defines the nature of the
perceptual input function. As I tried to point out four years ago, if y
is the sum of a, b, c ... d, then there is no way to work backward from
knowledge of y to the state of a, b, c, and so on. You could have
exactly the same value of y arising from an infinity of combinations of
a, b .. d. A control system can control y if it can vary one of the
variables on which y depends. To do so, it does not need to know
anything about the states of the other variables on which y depends.
Nothing. NADA.
At least, they were agreed to be effective until the results showed
the dogma to be false. Then, and only then, were irrelevant
objections raised.
This somewhat scurrilous allegation rests on our initial difference in
conceiving the conditions of the "challenge." Rick and I were assuming
that you would be given only the state of the perceptual signal. You
then proceeded to use your own assumptions about the forms of all the
functions, including the disturbing function, and the values of all the
variables and signals, including the reference signal, to deduce the
only remaining unknown, the disturbing variable.
Rick sent you some lists of numbers on several occasions, representing
the state of the perceptual signal in a working control model, and
challenged you to deduce the behavior of the disturbing variable from
knowledge of the behavior of the perceptual signal (I see that he is
offering to do this again). If the perceptual signal had contained
information about the disturbance, you should have been able to use that
information to deduce the behavior of the disturbance. Obviously, you
could not do this. Rick's challenge should have been completely
sufficient to show you how we conceived of the challenge in general.
What you did was to permit yourself to use all kinds of knowledge that
Rick and I were ruling out. Our objections were quite relevant to our
understanding of the phrase "information in the perceptual signal about
the disturbance."
You citing you:
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.
You citing me:
You forgot to mention the form of the input function, the function
relating the disturbing variable to the controlled variable, and the
setting of the reference signal, all of which you must also know.
You now:
And could you now, after three years of consideration, tell me
which of these varies in a manner coordinated with variations in
the disturbing influence on the CEV? If you can correctly assert
that any one of these contains information about the fluctuations
of the disturbance, then and only then can you criticize the
demonstration experiment and the derived conclusion.
Wait a minute. You're saying that I can't criticize your experiment and
its conclusion if I can't correctly assert that any variable or function
in the control loop but the perceptual signal "varies in a manner
coordinated with variations in the disturbing influence on the CEV." If
I've untangled this set of nested negatives correctly, you're saying
that the perceptual signal _does_ vary in a "coordinated" way (whatever
that means) with the disturbing influence.
But this is exactly what I am trying to tell you is your primary
mistake. The perceptual signal does NOT vary in a way that correlates
with any particular disturbing variable. At one moment there might be a
single disturbing variable acting through a simple linear function; at
the next there might be twelve disturbing variables acting through a set
of functions ranging from square to square root to exponential. The
control system will behave no differently in any case. It simply senses
the controlled variable and acts according to deviations of its
perception from the momentary setting of the reference signal.
Furthermore, given complete knowledge of everything in the control loop,
but not of the environment beyond the input quantities themselves, you
could certainly deduce the state of a hypothetical disturbing variable
based on assuming a hypothetical disturbance function. But this would be
a complete fiction; it would not be a "reconstruction" of the true
disturbing variable. Your chances of guessing correctly what the actual
number of disturbances is, and what their individual waveforms are, and
how each one is linked to have an effect on the controlled variable, are
essentially zero. And the control system can't do this, either.
But (as I said those long years ago as well), is it not absurd to
ask the control system, which has but a single scalar value for its
perceptual signal, to _know_ (perceive, understand,...) anything
other than the value of the CEV. Is it not a red herring to suggest
that anything in the discussion hinges on this absurdity?
I use "know" in a loose way, to be sure. I say that a system "knows"
about something outside it if there is a variable inside the system that
covaries with the external something. A photocell "knows" about light
intensity, but not about color. In a simple control system, the only
"knowledge" that exists is the perceptual signal. And it is "knowledge"
only in the sense that it represents the value of a function of some set
of input quantities.
Since this is the only knowledge that the system itself has, it is
absurd to say (as you have said) that the system "uses information" that
is "contained in" the perceptual signal. All the control system needs is
the perceptual signal itself. It does not have to perform any operations
to detect or manipulate measures of information. So who is being absurd
here?
You should be stating that "as the precision of opposition to the
disturbance increases, so the information about the disturbance
remaining in the perceptual signal decreases" and then you would
see it as a perfectly straightforward, self-evident proposition, in
place of a paradox contrary to reason.
But that is contrary to the idea that the control system uses the
information in the perceptual signal to construct an output that
precisely opposes the effects of the disturbance on the input quantity.
The paradox lies in claiming that control -- the precise opposition to
the effects of an unknown disturbing variable or variables -- relies on
information in the perceptual signal, and also to say that the better
the control, the less information there is in the perceptual signal. In
the limit, according to this way of looking at the system, control would
be perfect if there were NO information in the perceptual signal. But in
that case, what would be the basis for constructing the output?
···
---------------------------------
Well, let's move on.
Firstly, consider a predictable world. PCT is not necessary,
because the desired effects can be achieved by executing a
prespecified series of actions.
I thought this was silly in 1992 and I still do. If the world is
predictable, this does not mean that any organism is capable of
predicting it. Furthermore, as I pointed out back then, even if the
world is predictable, a control system is still the fastest and least
complex way to control it. Suppose the muscles were calibrated perfectly
and the organism somehow could carry out the calculations necessary to
generate the muscle tensions required to produce any position of the
limbs. Yes, in principle one could do an open-loop calculation involving
all the inverse kinematics and dynamics, but at what cost? Probably a
large portion of the brain would have to be devoted to performing this
calculation over and over in real time. But the same result can be
achieved, for all practical purposes, using a few very simple negative
feedback control systems which do only a few elementary calculations. So
even in a perfectly predictable world, the control system is still the
system of choice. To say that the world is predictable is not to say
that it is simple or that a given organism is capable of predicting it.
Your assumption is not tenable. Unfortunately, you insist that it is
correct, and go on from there.
At the other extreme, consider a random world, in which the state
at t+delta is unpredictable from the state at t. PCT is not
possible. There is no set of actions in the world that will change
the information at the sensors.
There is no information at the sensors. Information, as you have said a
number of times, depends on the nature of the receiver. It does not
exist independently in the environment. If the receiver is monitoring
the mean noise level of the sensor signals, acting at random can raise
or lower that noise level, since random acts imposed on a random world
will add in quadrature to the net effect. Control would still be
possible, if not very useful.
Now consider a realistic (i.e. chaotic) world.
Fine. But you are assuming at this point that PCT would not be necessary
in a predictable world, which is false. That vitiates the strength of
this orderly argument. You are equating "predictable" with "simple" or
"understandable." In fact, you are attributing predictableness to the
environment, as if it were a property of the environment and not a
function of the organism's capacities to predict.
At time t one looks at the state of the world, and the
probabilities of the various possible states at t+delta are thereby
made different from what they would have been had you not looked at
time t. If one makes an action A at time t, the probability
distributions of states at time t+delta are different from what
they would have been if action A had not occurred, and moreover,
that difference is reflected in the probabilities of states of the
sensor systems observing the state of the world. Action A can
inform the sensors. PCT is possible.
When you start talking like a quantum physicist you lose me. This whole
way of dealing with phenomena strikes me as awkward and ugly. And
anyway, I don't have to follow your arguments any further, since you
have made a basic mistake in saying that in a predictable world, PCT
would not be necessary.
----------------------------------
Things become more interesting when we go up a level in the
hierarchy. Now we have to consider the source of information as
being the error signals of the lower ECSs, given that the higher
level has no direct sensory access to the world
Not the error signals: the perceptual signals. These are not the same
thing, even though you try to make them the same:
Even though the higher ECSs may well take as sensory input the
perceptual signals of the lower ECSs, nevertheless the information
content (unpredictability) of those perceptual signals is that of
the error, since the higher ECSs have information about their
Actions (the references supplied to the lower ECSs) just as the
lower ones have information about their Actions in the world.
This is patching up your argument as you go. The error is the difference
between the reference signal and the perceptual signal. If the higher
system is in the imagination mode, it is not receiving the perceptual
signal. If it is in the action mode, it is not receiving a copy of its
own output. When you try to design a system can can operate in both
modes at once, you run into all sorts of problems. But I don't expect
that such niggling details will deflect you.
(Unexpected events provide moments of high information content, but
they can't happen often, or we are back in the uncontrollable
world.)
So you are still assuming that disturbances have to be predictable for
control to work?
What does this mean? Firstly, the higher ECSs do not need one or
both of high speed or high precision. The lower ECSs can take care
of things at high information rates, leaving to the higher ECSs
precisely those things that are not predicted by them--complexities
of the world, and specifically things of a KIND that they do not
incorporate in their predictions. In other words, the information
argument does not specify what Bill's eleven levels are, but it
does make it clear why there should BE level of the hierarchy that
have quite different characteristics in their perceptual input
functions.
If information theory could really, out of its own premises, come up
with these predictions, that would be impressive. But it can't because
it didn't. You're solving a problem to which you already know the
answer, and throwing in all the assumptions needed to make your
"prediction" come out right. Those assumptions are not contained in
information theory. What does information theory have to say about
"kinds" of perceptions? Nothing.
---------------------------
Another item
In your comment, you take it to refer to how a functioning ECS is
to be designed, and that the perceptual bandwidth should be low.
If the perceptual bandwidth is low, then the ECS will have
difficulty matching the perceptual signal to the reference signal,
and thus the error signal will have high information content.
First I have never said that the perceptual bandwidth should be low.
They are what they are. And second, if the perceptual bandwidth is low,
the ECS will have an easier time in matching the perceptual signal to
the reference signal, and the error signal, in your parlance, will have
a low information content. Your deduction here is exactly the opposite
of what would happen. Of course if the reference signal varied rapidly,
the error signal would also vary rapidly and contain more information --
but why would a reference signal from a higher, slower system vary more
rapidly than the perceptual signal of a lower, faster system?
Now it is true that if the perceptual signal has lower bandwidth
than the reference signal and the same resolution, then the error
signal will in part be predictable, thus having lower information
content than would appear on the surface. But I had the
presumption that we are always dealing with an organism with high
bandwidth perceptual pathways, so I forgot to insert that caveat.
By your argument, a completely random error signal would have the lowest
predictability of all, and thus contain the most information. But so
what? The control system would not work with a random error signal.
Well, given last year's experience, I didn't expect my information-
theory posting to be understood, and I wasn't disappointed in my
expectation. Is it worth trying some more?
No, it is not. You don't have a clear and rigorous argument that can be
built up from basic principles without any outside assumptions to carry
you across the rough spots. If you knew what you were talking about, you
would be able to explain it clearly.
------------------------------
Lastly:
The situation is different if we take a full-blooded outside view
of the action of a CEV. It is from this kind of view that we argue
that the disturbance provides information that passes through the
perceptual signal to the output signal. From the outside we can
see the disturbing variable do whatever it does to affect the CEV,
and we can see the ECS modifying its output to bring the perceptual
signal back to its controlled value. From outside we can see the
reference signal of the ECS changing, and the ouput changing to
move the CEV so that the perceptual signal comes to its new
controlled value. From outside, the arguments about there being no
information from the disturbance in the perceptual signal lose
their force.
So from the outside view, it is the information from the disturbance
that passes through the perceptual signal to the output signal, with the
result of modifying the output to bring the perceptual signal back to
its controlled value? This takes us back to the original information-in-
perception argument. If the information in the perception decreases as
the output comes to oppose the effects of the disturbance more
precisely, how can it be the information passing through the perception
to the output that is responsible for the increase in precision? Does
precision improve as the amount of information on which it is based
decreases? What you are saying may make perfect sense to you, but to me
is is nonsense.
--------------------
One more peanut:
[Allan Randall 930325 12:40] to Rick Marken
> >Are we also agreed that this disturbance, while defined in this
> >external point of view, is nonetheless defined in terms of the
> >CEV, which is defined according to the internal point of view?
>
> Say what? Why not just say CEV(t) = d(t) + o(t). If that's what
> the above sentence means then I agree with it.
The point is that the disturbance d(t), if separated out from o(t),
is not a meaningful quantity to the ECS. It is meaningful only to
the external observer. By drawing an arrow marked d(t) you are
talking about something the ECS has no direct access to. From the
perspective of the ECS, only the variation in the CEV matters. It
cannot separate out its own output from the disturbance. On the
other hand, this disturbance is defined in terms of the CEV, since
only things in the world that affect the CEV can be said to be
disturbance.
It is not the disturbance that is defined in terms of the CEV, but the
effect of the disturbance. As you say, all that matters is the value of
the CEV itself. Words like "meaningful" are just noises. Talking about
the ECS "having access to" something is just a noise. My whole point is
that the ECS does NOT have "access" to the disturbance d(t). Nor does it
have "access" to the form of the function relating d(t) to its effect on
the CEV. Nor is the linking function or the nature and number of d(t)
variables necessarily the same from one moment to the next.
-------------------------------
The basic problem in the "information about disturbance" argument is
that you keep forgetting that a given fluctuation of the CEV can be
produced by many different independent variables in the environment,
acting through many different paths, even from one moment to the next.
All your arguments are based on the (often apparently unconscious)
assumption that there is a _single_ disturbing variable acting through a
_known and invariant_ disturbance function on the CEV. When that
assumption is true, your conclusions follow trivially, but you are
dealing only with a special case set up to MAKE your arguments true. In
general, a control system _however intelligent and complex_ cannot know
what is causing a CEV to vary at any given time. All it can know -- that
is, all that can be represented by its perceptual signal -- is the
current state of the CEV. And that is all that it needs to know.
---------------------------------
If Signal X matches the disturbance, the perceptual signal must be
the route from which the mystery function M(r, p) gets the
information about the disturbance. Right?
Now let the function M be indentical to O(R-P). Signal X will then
be the negative of the output signal, which is the disturbance.
The only question here is whether O(error) is a function or a
magical mystery tourgoodie. I prefer to think we are dealing with
physical systems, and that O is a function. Therefore, information
about the disturbance is in the perceptual signal, and moreover, it
is there in extractable form.
QED.
See what I mean? This sloppy analysis omits two things: the form of the
function through which even a single disturbance acts on the CEV, and
the number of such functions with disturbing quantities operating
simultaneously. What you have shown is that if you assume a single
disturbance acting through a unity transfer function, you can deduce its
value from knowledge of all other signals and functions in the system.
Big surprise! But you have not shown that there is only one disturbance,
or that the form of the disturbance function is a simple multiplier of
1. You're in such a hurry to get to your triumphant "QED" that you
overlook an elementary omission in setting up your imaginary experiment.
Enough. I'm just not up to following through all these arguments which
are made up on the spur of the moment to meet a particular case and then
forgotten about when the same principle comes up in a different context.
What I am hearing are arguments for the sake of arguing, for the sake of
appearing to win an argument. I've been picking holes in your arguments
for a good four years now, with no discernible effect. I know when I am
trying to alter a controlled variable that is being maintained by a
strong and active system, although I may be somewhat slow to admit that
I can't budge it.
This time I am going to stick to my oft-broken resolution: no more
participation in this line of discussion.
-----------------------------------------------------------------------
Best,
Bill P.