[From Bill Powers (950717.1030 MDT)]
Hans Blom (950717) --
Let me try to rephrase this. According to PCT and any other control
theory, you wouldn't do anything ELSE THAN WHAT YOU ARE DOING RIGHT
NOW if all your references are satisfied: all references are
satisfied precisely because your actions are exactly appropriate.
The possible occurrence of disturbances doesn't much play a role.
Yes, and that says it very well. Nice to find we are in such close
agreement about this.
If the actions are exactly appropriate, I don't consider it correct
to talk about "error" existing in the system. The problem is that
Bill calls a difference between reference level and perception an
"error". I consider that an incorrect phraseology; it is just a
difference, not an error (with all the connotations that the word
"error" implies), particularly not when the actions are exactly
appropriate. A lot of my misunderstan- dings with Bill originate
here. The perfection or not of integrators only confuses the issue.
I agree that this is a source of disputes between us. I have no
objection to calling an error a "difference" -- "error" is simply the
term that has been common in control theory since the 1940's, but you
are not the first to dislike the connotations of that word.
The substance of our disagreement really comes from our difference over
the main kind of control that goes on in organisms. You prefer to use
the model-based control system as the default; I prefer to use the
negative feedback control system as the default.
Under a model-based control system, once convergence is complete, it is
possible in principle for differences to be completely removed, so that
behavior is _exactly_ appropriate for making the controlled perception
_exactly_ match the reference signal. A negative feedback control
system, however, will never be able to remove that last tiny bit of
difference between reference and perception, so (without considering
integrating output functions) perfection is unattainable.
However, this difference in approaches really has no practical
significance. The model-based control system, in a real organism, will
never attain perfection, and there will always be a difference between
the behavior of the model and that of the real environment. Models are
always approximations of and abstractions from the physical world; the
only completely accurate "model" is the physical world itself. Errors in
the model (and here I think you will accept the term "error") will
always exist, and the adaptive functions will always be working to try
to remove them -- an impossible task, as the model's parameters are not
a complete set of the parameters that matter.
That is only because it's under active control. Active control is
error-driven. Always.
The same problematic phraseology again. If the action is exactly
appropriate, how can we talk about control being ERROR-driven?
In the negative feedback control system, the action can never be
_exactly_ appropriate, because some difference between perception and
reference, however small, is required to drive the behavior. In a model-
based control system, the action will also never be exactly appropriate,
because of unmodeled dynamics and imperfections and limitations in the
system identification. If you really want to compare my approach and
yours, you should subject your model to the same realistic limitations
that apply to mine. I could easily say that in a control system with
infinite gain, the error/difference goes to zero within any arbitrarily
small difference epsilon, and thus make my model as perfect as yours.
But I don't do that, because I am trying to model real systems, not
mathematical idealizations.
What you have to understand is that _small_ errors can lead to _large_
behaviors. That is what keeps the errors small.
The physiologist Guyton, in his textbook on physiology, often gives
numbers for loop gains of the control systems that control
(influence?) things like blood pressure, heart rate, cardiac
output, breathing rate, tidal volume and such. Surprisingly, loop
gains are often around 3 to 5 only. Thus, large "errors"
(differences between reference and perception) must exist in most
of these systems. ERRORS?
Please, get it out of your mind that when I speak of errors I mean
"mistakes." I am simply using an old and widely-used term that means
nothing more than the difference between perception and reference.
Measuring loop gains for such things as "blood pressure, heart rate,
cardiac output, breathing rate, tidal volume and such" is probably too
simple an approach, as all these variables interact. Disturbing any one
of them to measure loop gain will result in compensating actions by the
other control systems, leading to a spuriously low apparent loop gain.
If you arbitrarily raise heart-rate, you will be increasing blood
pressure, and vasodilation will take place to reduce the pressure, and
that will feed back through the baroreceptors to reduce heart rate.
All those variables are probably under control, but in a way susidiary
to controlling more important variables like blood CO2, nutrient
concentrations around the muscles, and so forth.
Reconsider this sentence. Only DISTURBANCES can cause ZERO ERROR?
Isn't this usage of the term "error" idiosyncratic in the extreme?
It is your usage of "error" that is ideosyncratic in connection with
control theory. And, in a negative feedback control system, a
disturbance that aids the output can not only bring the error exactly to
zero (at which point the system's output would become zero), but can
cause an excess of perception over reference, leading (if control is
two-way) to a reversal of the output. In your idealized model-based
control system, where perception is maintained mathematically equal to
reference, all disturbances would _cause_ differences between perception
and error. But that is only in a ideal model-based control system, not
in the kind of control system I normally assume -- the ordinary kind.
···
--------------------------------
If you are looking for the "elements" of the history that are
important, you can look forever. It is the CORRELATIONS between
what you do and what you observe that carry the importance (even if
you don't actively do something, you still act, of course).
I express the same thought by saying that what adaptive control systems
learn are _properties_ of the environment, not specific responses to
specific events. Any number of quite different histories can reveal the
same properties. When control systems adapt, their parameters change, so
that the physical properties of the control system become appropriate to
the properies of the part of the environment that lies between output
and input. The values of signals and variables that happen to exist
during any particular interactions with the environment are almost
irrelevant, except as they reveal properties of the environment.
-----------------------------
RE: pinball machine
Do you think that this historical record would do you any
good as an explanation the next time you found the ball in the 5000
slot?
In principle, yes. It is just such a complex explanation!
But the particular events that took place, which you recorded the first
time, could not be invoked as explanations the second time the ball
landed in the same slot. (1) It is extremely unlikely that repeating all
those events would result in the same outcome: the smallest
uncertainties at each stage would multiple and rapidly turn into large
variations in the outcome. (2) Furthermore, there are innumerable other
histories that could also put the ball into the 5000 slot. Simply
knowing where the ball landed would not tell you which of those possible
histories actually took place, so your "explanation" would most probably
be entirely wrong.
I preach a different kind of discipline to PCTers: never defend
control theory. Attack it.
From which solid ground?
From the grounds that if control theory applies, certain outcomes should
be seen under specific variations in conditions. In other words, we
attack on the basis of control theory itself. If control is actually
going on, then when we apply disturbances in every way that could affect
the controlled variable, we can calculate from the model how the model
will behave. If that behavior doesn't match the behavior of the real
system subjected to the same disturbances, then the model is wrong. I
preach that all experiments should be set up so that if control theory
doesn't apply, it will make wrong predictions.
How are you ever going to conclude logically -- and isn't that what
we want in science -- that control theory is the only correct
explanation if all you have is a set of observations taking the
form
IF control going on THEN the Test failed ?
You misunderstand the Test. When the Test is failed, that shows that the
variable hypothesized to be under control is NOT under control. The Test
does not confirm that a particular control model is unique; all it can
do is reject incorrect control models. When the Test is passed, we can
conclude only that the hypothesis of control (the particular model being
used) is consistent with the observations -- not that it is the only
hypothesis that would be consistent. It is possible for more than one
model to pass the Test. In that case we would have to choose among the
models using other criteria: goodness of fit, simplicity, ability to
apply over a broad range of circumstances, and so forth.
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Best,
Bill P.