[Martin Taylor 941013 15:15]
Bill Powers (941008.1650 MDT)
More generally, Rick often pleads that the only legitimate aim of PCT
research is to find "the controlled variable." If one is to believe
the premises of PCT, this search is doomed to fail, because which
variables are controlled, and the "insistence" on each (to use a word
introduced to the discussion long ago as a generalization of "gain")
changes from moment to moment. What is a controlled perception one
moment is not one the next.That sounds like a wonderful excuse for not doing any research at all.
According to that view, we shouldn't even try to do tracking
experiments; people are just so variable that you couldn't hope to get
the reference signals to stay still long enough to get a one-minute run
in.
In what way does this follow? When one does a tracking study, one has a
collaborator as subject. If the subject chooses to shift randomly the
tracking reference difference between cursor and target, there's nothing the
experimenter can do to make the model fit better. When the subject
cooperates, and agrees to take a reference level for the cursor-target
difference and to control a perception against that reference, THEN you
can get a consistent experiment with a model that fits pretty well
(correlation between model and data of between 0.6 and 0.98 or so in our
sleep deprivation experiments, before the subjects got sleepy).
You may do experiments such as those Chuck Tucker proposed, in which the
subjects are not willing collaborators, but then you should be prepared
to find that the perceptions controlled at one moment may not be controlled
at another. Often they will be, but sometimes something else may distract
the subjects, or "it just doesn't matter so much today."
Furthermore, if the perceptual functions of the living system are
distributed and not mutually orthogonal, as must be the case in a
robust system ...Who says that must be the case? The only way to prove that it is is to
SHOW that is is, in real people, in real experiments.
Two answers:
(1) I was wrong to restrict the problem to non-orthogonal
controlled perceptions; the situation is worse, in that if the space
can be taken as a Minkowski space (distance = (x^k + y^k +...)^-k)
then any direction in the space may be tested and found to correspond
to a controlled perception (though if k != 2, you may get better results
in some directions than in others--try drawing circles with an "Etch-a
Sketch"!).
(2) "as must be the case in a robust system"
is correct, whether it applies to real people or not; if you lose one of
an orthogonal set of sensors, you lose that component of the space ENTIRELY.
That is not a robust system.
... then there are no identifiable, discrete, "controlled perceptions,"
but rather there are controlled "perceptual spaces" of indeterminate
dimensionality.In that case I had better stop trying to brush my teeth, type letters,
drive a car, buy groceries, design experiments, and so on.
Huh?!? This is a pretty wild non-sequitur. I point out that you can
control, say, blue-to-red variation, or aqua-to-lime, even though you
have only red, green, and blue sensors, and you take it to mean that
you can't control ANY colour perception???
The ultimate
authority on what variables we can perceive and control, and the
dimensions in which we do so, is our own experience. It is our own
experience that tells us how to set up experiments that will work.
Yes, and I was pointing out that experiments WILL work, even though the
quantities controlled do not necessarily correspond to any SINGLE controlled
perception internal to the organism. My point was that the experiments
cannot tell you which neural signals exist and are controlled, if they
combine in such a way as to form multidimensional spaces. The experiments
allow you to generate unidimensional or multidimensional models that fit
the data well, provided that the modelled perceptual signals are formed
from combinations within the space covered by the really controlled
perceptual signals.
Try it on a model of a model. Set up a "subject" system of two parallel
control systems, one of which perceives the x location of a dot and the
other the y location (velocity, acceleration). Then observe it controlling
against a disturbance that always acts equally in x and y. You will be
able to model the data with a model that has one control system, which
perceives location (velocity, acceleration) in the direction x=y.
If you then disturb the dot in a random direction in the x-y plane, you will
be able to model the result by adding another control system that perceives
and acts in the direction x=-y. You will also be able to model the same
data equally well by using two control systems that control in directions
x=2y and 2x=-y, for example. And you will model pretty well, but less
accurately, by using two control systems with perceptual functions
p1=(x+y)^3, p2=(x-y)^3. You should be able to tell that this last model
is worse than the others, but you won't be able to tell between the other
two.
Can't you think of a way to establish what the right dimensions are?
If the combination is non-Euclidean, as it would be, for example, if the
x-direction perceptual signal was sensitive only to movements within 60
degrees of the x-direction and gave no response to the 60 degree sector
centred on the y-direction, then you may well find parametric value changes
when you fit your pair of orthogonal Euclidean control systems. Those
changes may clue you into the existence of preferred perceptual directions
in the test system (or person). In effect, that's the kind of thing that
is done in testing for auditory or visual filter bandwidths (orientation
sensitivities).
Rick has shown quite clearly, for example, that a polar
coordinate system doesn't work as a model of two-dimensional mouse
tracking.
Yes, that's the kind of thing that can work. And when he asks for a
collaborative subject to control "size," he is depending on the subject
to have a consistent idea of what "size" means. And then he can determine
whether a model fits better if it uses a perceptual function that sees
a total perimeter, an area, or something else. The "Etch-a-Sketch" example
I mentioned above is similar. People control in x and in y in such a
way that the combination is far from Euclidean, and even without looking
at the physical control medium an application of the Test in different
directions would show up the x and y directions as special (better control
in those directions than in diagonal directions). None of which relates
to the issue I raised.
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The question of whether individual control systems "know what each
other is doing" is independent of whether the controlled signals are
scalar. One ECU could "know what the other is doing" if, say, the
output of one affected the gain of another, or if the perceptual signal
on one contributed to the sensory input of the other.I really don't like speaking so metaphorically, at least before we know
what we are talking about in literal terms. All that one ECU can ever
know is the state of its own perceptual signal. It can't know that it
has a perceptual input function, a comparator, and an output function.
It can't know the gain of its own output function.
Right. What I meant by "knowing" is that there is an input signal
corresponding to the thing known. A "canonical" ECU has two sets of
input signals--the sensory signals and the contributors to the reference
signal. I suggested the possibility of a third, contributors to a "gain
control" signal.
The only quantum of "knowing" that exists in an ECU is the
magnitude of its perceptual signal, a scalar quantity.
I do not think the ECU can be said to "know" the state of its own perceptual
signal, because that is an internal signal within the ECU. To allow that
the ECU "knows" the state of its perceptual signal is to allow it to "know"
the state of any other signal internal to itself. The choice of metaphor
is, of course, free to the writer, but I think that the only reason to use
the metaphor of "knowing" the perceptual signal and not the other signals
is that the perceptual signal corresponds to the state of something in the
outer world AS SEEN BY AN ANALYST. To the ECU, the perceptual signal is
special only insofar as it is stabilized when the reference signal is stable.
Other than that, it is only a signal among several others, and of no special
significance.
I used the metaphor "one ECU knowing what the other is doing" as a statement
equivalent to "the output of the other ECU contributes to the input of
the one ECU," largely because this was how I understood Hans Blom to have
used "knowing."
Bill Williams' simulation of the Giffen Effect was an example of real-
world control involving conflicting goals. ... There are lots
of possibilities. It would be nice to see more of them being tested.
Yes, indeed. If only someone would, and could get our economy-killing
economists to understand. But what's the hope? 
But your summary of the E. coli method of steering is misleading.
Sorry; you are right. My stupidity (or hurry?).
E. coli neither moves faster nor in bigger jumps
when error is large. It always travels at the same speed, and in fact
travels LESS far between tumbles when the error is larger, because the
time-interval between tumbles is decreased.
Has anyone tried my wrongly described method? It seems to me that it
ought to work, too. But maybe not.
Martin