principles

[William_T_Powers2]

[From Bill Powers (941013.0705 MDT)]

Bruce Abbott (direct) -- I forgot to mention that the source code I sent
runs under Turbo Pascal 5.5.

···

------------------------------------------------------------------------
Martin Taylor (941012.1540) writing to Rick, but publicly--

In case you lost it, the argument was twofold:

1. that an external observer of any kind can test only for controlled
perceptual spaces, not for controlled perceptual variables ("controlled
perceptions"), since any scalar application of the Test within the
controlled perceptual space will result in a well-fitting scalar model,
and thus no perceptual direction within the controlled space can be
distinguished from another by the Test.

This conclusion is drawn, I think, from some assumptions that greatly
simplify the real case. If you include nonlinearities, time-delays, and
dynamical characteristics of the scalar control systems, there may be
ways to distinguish the primary axes of control. Also, and this may
ultimately prove more important, any given control system at one level
can become a component of control of many different variables at the
next level. This means that the axes of a control space may not always
consist of variables of the same kind. For example, an arm position
control system in one dimension may be joined with a gaze direction
control system in another dimension at the same level, for a specific
higher-level purpose. By looking at many different examples of control,
and hypothesizing that the nervous system will not needlessly duplicate
scalar control systems, we might be able to deduce a basic set of scalar
control systems, and from them the primary axes of control at a given
level.

But of course the primary axes may not always be the same.

In mathematical developments, one does not keep returning to a theorem
that has already been proven, to check it out in very new context. This
is because mathematical theorems are based on a few simple assumptions
which are clear, unvarying, and explicit. In modeling behavior (or any
complex system), however, there are many more assumptions than meet the
eye, many of them tacit rather than being clearly stated, and others
inadvertently changing meaning with context. All general principles must
therefore be frequently revisited, to see whether the underlying
assumptions still remain acceptable. I think you tend to forget this:
once you've come up with a principle, you seem to assume that it's valid
from then on, in all contexts. I don't think that we have any general
principles of human behavior that are so reliable that we don't need to
re-examine the assumptions at frequent intervals, to see if they are
still valid. This means keeping the assumptions in mind, and not just
remembering previous conclusions.

"Scalar" does not imply "linear," nor does it preclude temporal
properties of the control systems. I believe your argument is basically
algebraic and based on assumptions of linearity and simultaneity.
--------------------------
2. the relative gains of different controlled perceptions change over

time (not perceptual spaces, because "gain" has no meaning in that
context). Hence what the Test shows to be controlled at one moment may
not be shown to be controlled at another.

So you're saying that changes in the perceptual gain can't be detected?
Or that if the gain changes, there is no longer any control? As in any
empirical test, what you measure applies only to that test. Repeated
tests, and tests under varying conditions, can reveal changes in all
main parameters. It is true that qualitatively, all parameters "change."
But the only important question is by how much and how fast -- a
quantitative question. If we think quantitatively, the object is to
assess the way parameters change through time and with conditions. We
don't think in terms of only two choices: having control and not having
control, knowing the controlled variable and not knowing it. What the
test shows to be controlled at one time will probably not be greatly
different from what it shows to be controlled at another time not too
much separated from the first time. The test applied under one set of
conditions may show a change in the controlled variable from what is
found under other conditions; that is how we discover the effects of
changes in conditions, and learn to take them into account.

"Gain" most certainly does have meaning in the context of controlling
variables in perceptual spaces. Perceptual gain is a component of loop
gain. Anisotropic perceptual gain (as in the inverted-T experiment)
means anisotropic loop gain.

I did spend quite a while trying to argue that not all systems with
negative feedback should be called "control systems," on the ground
that the term "control system" was more fruitfully applied to negative
feedback systems with variable reference levels.

I still dispute this basis for distinguishing control systems from
equilibrium systems. We never did arrive at a conclusion about the
"vortex" example, because it boiled down to a question of the net gain
around the feedback path. My contention was that the loop gain was less
than 1. This was not settled because neither of us could do the analysis
required to calculate the loop gain. A similar disagreement exists with
respect to chaotic or self-organizing systems with attractors. I contend
that it is the loop gain that rules such systems out as being control
systems -- or rather, that would pick out any examples that are actually
control systems.

You speak of "feedback systems with variable reference levels." But the
variability of a reference level is not a property of the feedback
system in question; a control system does not vary its own reference
level. A reference level is set by an effect from a higher system that
puts a bias on the input process of a lower system. If the output of
that higher system is fixed, then according to your definition the
control system at the lower level is no longer a control system, just
because the reference signal has ceased to vary. If the reference signal
begins to vary again, the system turns back into a control system.

Also by your definition, a system with an attractor becomes a control
system iff some external system injects influences that change the
location or shape of the attractor in the phase space.

During that discussion, I did point out that a variety of self-
organized (NOT "chaotic") structures were stabilized by negative
feedback, and that I didn't like the connotations of calling them
"control systems."

If we define a control system as any negative feedback system with a
loop power gain greater than one, we can easily distinguish control
systems from negative feedback systems in general. Words like
"stabilized" are qualitative terms; what makes the difference is how
well a variable is stabilized, a quantitative question. A loop power
gain of 1 is a natural dividing criterion that doesn't depend on whether
you "like the connotations" of a definition.
-------------------------

Is the English language really so hard to understand as you often make
it appear? Or is it my English usage that is hard for everyone to
understand?

What creates the difficulties is your tendency to generalize at the drop
of a hat, and then assume that your generalization is true under all
circumstances. You are always trying to draw some grand general
principle from a few specific observations, and then extend the
principle to other untested cases which have not been shown to fall
under the same principle. Once you have decided on a generalization, no
examples that violate it have any visible effect on your conviction that
they are right. To apply the Test, you appear to have excellent and
highly disturbance-resistant control systems at the principle level.
Judging from the failure of mere observations to modify them, and your
professed distaste for mere practical examples, this level appears to
operate largely in the imagination mode.

You asked.
------------------------------------------------------------------------
Best,

Bill P.

[_Martin_Taylor]

[Martin Taylor 941014 19:00]

Bill Powers (941013.0705 MDT)

Martin Taylor (941012.1540)

I hesitated at first to respond to this posting, because I have a feeling we
are getting into a game of crossing-messages-tag. I made some observations,
Rick responded. I responded to Rick, and then I got a response to the
original from Bill, to which I responded, expanding on my response to
Rick. Now I get a comment from Bill on my response to Rick, but apparently
written before my response to Bill got to him. So I don't really know
whether my answer to Bill's earlier comment suffices to answer some of
the issues he raises in his posting of yesterday morning (such rapid
delivery may make this kind of tag obsolete if it continues :-).

Anyway, I don't think another look at the issue of testing for "THE
controlled perception" will hurt.

···

===========================

...any scalar application of the Test within the
controlled perceptual space will result in a well-fitting scalar model,
and thus no perceptual direction within the controlled space can be
distinguished from another by the Test.

This conclusion is drawn, I think, from some assumptions that greatly
simplify the real case. If you include nonlinearities, time-delays, and
dynamical characteristics of the scalar control systems, there may be
ways to distinguish the primary axes of control.

Well, yes and no. I discussed this point in my reply to your previous
comment. Nonlinearity doesn't affect the issue. Time delays and
dynamical characteristics might have an effect, in that one may anticipate
differential abilities to control rapidly fluctuating disturbances in
different directions of the space. This ties in with my Etch-a-Sketch
example, and with everyday psychophysics (but then, you don't accept that
the resolution of the perceptual function has anything to do with the
quality of control, so you won't agree with this last).

Here's the point, from the experimenter's view. If there really IS a
perceptual space, rather than a set of independent scalar perceptual
variables, then the experimenter can apply the Test along any axis of
the space, and will find that on this axis the Test shows a controlled
perception to exist. If the "true" control systems that exist within
the organism can be accurately modelled by a hypothesized control system
(say a lagged integrator, for example), then so will the result of the
experiment done on an axis that does NOT correspond to any scalar signal
within the organism.

Now the experimenter hypothesizes that there really is a perceptual space,
and doesn't trust that the Test (which fitted to 99.99% accuracy) showed
a true controlled perception. The experimenter varies the axis a little
within the hypothesized perceptual space (perhaps moving a target dot from a
little above left to a little below right, instead of left-right), and
performs the Test again. Again it fits to 99.99% accuracy. The experimenter
continues this procedure over many axes in the hypothesized space, and
always finds what appears to be a controlled perception.

Are all of these Tests to be trusted as indicating that the physical
dimension on which the test was performed actually is the CEV for some
perceptual function? Not at all. The results were obtained from a
system that WE (godlike creatures) know to have only two control systems
in it. Two of the experiments came close to testing for these truly
controlled perceptions, but how can the experimenter know which ones?

One way, as I suggested in my earlier response to Bill, which he hadn't
seen when writing the comment on my answer to Rick, is that the parameter
values of these beautifully fitting models may differ in the different
directions. I think this is what Bill may be getting at when he talks about
"non-linearities, time delays, and dynamical characteristics" to which I
would add resolution in time and whatever perceptual dimension is being
tested. If the model fits are very good, and the parameter values fitted
change in some intelligible way, then one can argue that there is something
special about the axes giving extreme parameter values, and especially about
those that give best actual control.

But this still doesn't tell you that there are, in the example case, two
and only two scalar control systems. The individual Tests done by the
experimenter might truly have been discovering individual controlled
variables that had perceptual functions very sensitive only to changes
in their specific axes, and not to changes along neighbouring axes. Human
visual orientation and movement detectors seem to be a bit like this. But
they are more like the next case.

Another possibility for the same result might be that the organism had
several control systems distributed around the various directions in the
space, with overlapping responses, all equally sensitive but a bit more
crowded near the axes that showed best control. In a robust system, this
is the optimal arrangement, but you won't know from the Test applied only
within the perceptual space that this is the arrangement of the actual
controlled perceptions.

You can't tell, at least not in any simple way, is the bottom line.

Also, and this may
ultimately prove more important, any given control system at one level
can become a component of control of many different variables at the
next level. This means that the axes of a control space may not always
consist of variables of the same kind.

Yes, and in this case you will almost certainly be able to distinguish
the real controlled perceptual inputs to the combined perceptual function
(which itself produces a one-dimensional perceptual signal if we are to
believe HPCT).

All general principles must
therefore be frequently revisited, to see whether the underlying
assumptions still remain acceptable. I think you tend to forget this:

Huh? Am I not doing EXACTLY this here, and asking you to do as much?

I don't think that we have any general
principles of human behavior that are so reliable that we don't need to
re-examine the assumptions at frequent intervals, to see if they are
still valid. This means keeping the assumptions in mind, and not just
remembering previous conclusions.

Yes, Yes, Yes!!!!!! That's so important, and often hard to do. It's an
exercise I trained myself in many years ago, and one I maintain while my
physical exercise diminishes.

"Scalar" does not imply "linear," nor does it preclude temporal
properties of the control systems.

Correct. That's what I meant by "scalar." No implications about linearity,
and an assumption that the scalar value changes over time.

I believe your argument is basically
algebraic and based on assumptions of linearity and simultaneity.

Not in the slightest.
-------------------------

2. the relative gains of different controlled perceptions change over
time (not perceptual spaces, because "gain" has no meaning in that
context). Hence what the Test shows to be controlled at one moment may
not be shown to be controlled at another.

So you're saying that changes in the perceptual gain can't be detected?
Or that if the gain changes, there is no longer any control?

No. Not at all. I'm contesting Rick's repeated claim that the goal of
PCT is to find "the controlled variable(s)". The way he puts it, it NEVER
sounds as if "the controlled variable" could change from moment to moment.
It sounds as if once you've found it, you can rely on it being there when
you want it again in some extension of the model. That's what I am pointing
out to be false.

Of course (qualified by the first part of this posting) you can find a
controlled variable if you guess right as to its CEV. But it may not
be a controlled variable the next time you look. And you say as much
in your further comments.

Repeated
tests, and tests under varying conditions, can reveal changes in all
main parameters. It is true that qualitatively, all parameters "change."
But the only important question is by how much and how fast -- a
quantitative question. If we think quantitatively, the object is to
assess the way parameters change through time and with conditions. We
don't think in terms of only two choices: having control and not having
control, knowing the controlled variable and not knowing it. What the
test shows to be controlled at one time will probably not be greatly
different from what it shows to be controlled at another time not too
much separated from the first time.

Yes, all the way down the line. I'd emphasize that "probably" in the second
last line, because there may well be rare occasions when control gain does
shift abruptly.

"Gain" most certainly does have meaning in the context of controlling
variables in perceptual spaces. Perceptual gain is a component of loop
gain. Anisotropic perceptual gain (as in the inverted-T experiment)
means anisotropic loop gain.

Hang on, now. I don't remember saying that gain didn't apply in scalar
situations. What I think I said, and what I certainly intended to say,
is that in a multidimensional perceptual space defined by two or more
non-colinear control systems, there is no valid number that can be applied
to "gain" in the space. The fitted model control system that matches the
data in any specific axis of the space certainly does have a loop gain,
but that can differ with the choice of axis. "Gain" as a scalar number
has no meaning in a multidimensional perceptual control space. Now if you
want to get mathematical, you could probably define a gain matrix or tensor
that would be valid in the space, but then you are opening the door to
Hans Blom's vector control systems. And that is something you prefer not
to do until the need has been demonstrated by experiment or simulation
(and I agree with you on that).

We never did arrive at a conclusion about the
"vortex" example, because it boiled down to a question of the net gain
around the feedback path. My contention was that the loop gain was less
than 1. This was not settled because neither of us could do the analysis
required to calculate the loop gain.

I still can't. Can you? But that wasn't why I mentioned it. I wasn't
trying to reopen that discussion, because from my end I have no more to
add. But Rick accused me of "noticing that chaotic attractors were
control systems," which was false on two counts. I responded because I
prefer factual corrections to emotional attacks (though I plead guilty
to the occasional outburst myself).

You speak of "feedback systems with variable reference levels." But the
variability of a reference level is not a property of the feedback
system in question; a control system does not vary its own reference
level.

But neither does a control system call ITSELF a control system. Someone
else observing it does. And to that someone else (namely me, but apparently
not you) it makes a difference whether the negative feedback loop might
set its controlled variable to some changeable reference, or whether the
control set point is fixed by the physics of the situation. You don't mind,
because you think (without evidence) that self-organizing structures do
not represent negative feedback loops with gain greater than unity. I mind,
because I think (without evidence) that they do, and I don't like to put
river waves and vortices in the class of control systems.

I like to think of control systems as being either alive or created by
other control systems that are alive. That's just me. I argued for that
feature (a potentially variable reference level) to be used as a criterion
for CALLING something a control system. If the community doesn't go along,
so be it. One uses the language of the community with whom one speaks.

Also by your definition, a system with an attractor becomes a control
system iff some external system injects influences that change the
location or shape of the attractor in the phase space.

If that's a consequence of my definition, I'm not sure I see it. It
seems to me that disturbances to a self-organized structure can change
the location or shape of the attractor to some degree, as they can with
the perceptual signal of a control system. The question is how hard the
structural elements (I don't want to call them feedback loops) resist the
disturbance. If there is no resistance, the external influence acts like
a reference signal; if there is strong resistance, it acts like a
disturbance. When you have no inside and no outside in a loop, you really
can't distinguish reference from disturbance in any other way. You
look to see where the gain is. And I think we do agree that there is no
inside or outside in the loop (with gain greater than or less than unity)
that consitutes a vortex.

===============

What creates the difficulties is your tendency to generalize at the drop
of a hat, and then assume that your generalization is true under all
circumstances.

I do indeed try to look for generalizations whenever I can, but then I
test them as much as I can. Most of my candidate generalizations fail
before I propose them outside of my head, but some survive.

You are always trying to draw some grand general
principle from a few specific observations, and then extend the
principle to other untested cases which have not been shown to fall
under the same principle.

Don't understand the last clause: "which have not...". The first part,
I agree with. I think it is the essence of Science, to try to make the
world make sense.

Once you have decided on a generalization, no
examples that violate it have any visible effect on your conviction that
they are right.

Quite the contrary. Any example that violates a possible generalization
signals that either the range of the generalization or the generalization
itself has to be modified. I doubt you can find an example where I have
acted otherwise.

To apply the Test, you appear to have excellent and
highly disturbance-resistant control systems at the principle level.

I hope so. The search for a consistent view of the world is one principle
I adhere to. I believe in the Unity of Science (deliberate capitalization)

Judging from the failure of mere observations to modify them,

What!!!

and your
professed distaste for mere practical examples,

As far as I am aware, I never professed any distaste for other people testing
practical examples. And sometimes I do my own, though I usually prefer not
to. My theoretical position on practical examples is that they provide
data that provide spot checks on theories. If the checks fail, you don't
know whether the failure is structural or parametric. If the checks
succeed, you know that the theory has at least one case in which it provides
a good description of the facts. The more often this happens, the better
for the theory. But if you don't know whether the theory failed the spot
check because it was a wrong theory or because you stuck in the wrong
numbers, what good did it do you other than to set you to seeking the
problem? (Which isn't a bad thing). I've always encouraged people to
look at YOUR practical examples, and I've used the Crowd demo to good
effect in a colloquium in the Netherlands. So don't think that I have
a distaste for "mere" practical examples. I'm just not very good at
making them. I contract with other people to make them, as you well know.

this level appears to
operate largely in the imagination mode.

Pfah!

You asked.

I didn't ask what you answered. Here I paraphrase the question I did ask.

Why is it that Rick so often berates me for saying something stupid that
is actually the opposite of what I did say?

That question is one I wouldn't mind having answered.

===============
Well, with the new rapidity in the mailing list, I might even see your
response to this before I leave

Martin

[William_T_Powers2]

[From Bill Powers (941015.0905 MDT)]

Martin Taylor (941014.1500) --

Thanks very much for scaring up that information about growth and
decline of muscle strength. You answered my main question; muscle fibers
are not added or lost; instead, the number of myosin and actin fibrils
within a fiber changes. This is clearly, as you say, a control process.

There are still several candidates for the controlled variable. Chemical
fatigue products might be controlled near a level of zero (but then why
would excess fibrils be lost when there is little use of the muscles?).
Or the stress per fibril might be controlled at some (long-term) average
amount that is non-zero. At this level, I think we can guess that the
controlled variable is related to the welfare of the muscle fiber. A PCT
physiochemist might have some fun comparing models built on different
hypothetical controlled variables to see which come the closest to
describing both growth and atrophy of muscles.

I have heard that every major organ responds this way to use of its
byproducts. When the body makes heavy use of the byproducts, the organ
hypertophies; when the byproducts are allowed to build up, the organ
atrophies. The one organ that I know the most about (not much) is the
thyroid gland, and it definitely behaves this way. In the old days, a
"lazy thyroid" was treated by adding thyroxin, its product, to the
bloodstream. The result of continued treatment of this sort was to
shrink the thyroid to the size of a peanut (poetic license).

···

-----------------------------------
Subj: RE: principles

Your point that multiple control systems define a control space, and
that the Test might come up with dimensions of control that do not align
with the "natural" dimensions, is valid. So is your point that the
primary axes of control may change over time, so that the controlled
variable we derive from the Test on one occasion may not be the
controlled variable we find on a later Test.

My point is the same as Tom Bourbons's: might and may also mean might
not and may not. When theory leads us to see possibilities, that is all
they are, possibilities. Possibilities are not observations. When we
apply the Test we come up with a definition of a controlled variable and
some characteristics of the associated -- hypothesized -- control
system. As long as that model continues to describe and predict control
behavior satisfactorily, it makes no difference if another model might
work equally well. The main thing the Test does is to eliminate models
that DO NOT work or that work LESS WELL than another model.

As we build up a general model of behavior, as long as the models of
specific control processes continue to work there is no reason to change
them. The only reason we would have to change them would be that when we
try to explain a more complex behavior using the existing models, there
is some failure in prediction; we find that the new level of controlled
variable can't be composed of the underying variables we had found with
the Test, so we must go back and look at other models that would also
pass the Test at the lower level. Now we have a basis for discriminating
among models that pass the Test, and we can pick the one that works best
at _both_ levels.

What we will end up with is a general model that works at many levels
and is not ruled out by the Test at any level. Along the way, we might
or might not find that multiple experimental tests narrow down the
possibilities so we can justify only one model for each control process.
It's unlikely that such a general model would work across all
individuals; at the very least, different people will show different
parameters even for control systems of the same basic organization. And
there is no reason to suppose that all people become organized alike
even in terms of gross organization: that is a matter to be decided
empirically, not theoretically. We know that adult brains are not all
wired alike; the levels of perception that I find in my own experiences
may be quite different from those that another person would experience.
One important question that can only be answered empirically is the
constancy of control organizations over time. This, too, might or might
not prove to be different in different people.

What's important about PCT is not any particular model that can be
constructed within its range of application, but the methods we develop
for characterizing control processes as we come across them. As we
become proficient in devising and testing models, it will make less and
less difference whether any particular model is the one final model, or
whether the organization of the brain changes over time. The important
thing is to be able to see and understand what is going on with
sufficient temporal resolution to see changes and sufficient accuracy to
make judgements of no change meaningful -- and not only to see and
understand, but test through experimentation.

I will even agree that it is possible that a vector or tensor
representation of complex control may be a useful way to handle multiple
control processes, even though I don't know how to do it. However, such
mathematical approaches are only computational conveniences. When you
see vector or tensor notations expanded into the elementary operations
that define them, you see what such representations are actually
proposing about the underlying processes. The brain does not do vector
or tensor operations (except symbolically, and at quite a different
level of phenomena); it does all the detailed multiplications and
additions that are implied by vector or tensor notation. The neural
systems themselves always have to operate in the fully-expanded form.
And the actual fully-expanded form will always be somewhat different
from what we would derived from the formal definitions of mathematics;
the mathematical representations are always approximations and
idealizations of the actual processes.

Now the experimenter hypothesizes that there really is a perceptual
space, and doesn't trust that the Test (which fitted to 99.99%
accuracy) showed a true controlled perception. The experimenter varies
the axis a little within the hypothesized perceptual space (perhaps
moving a target dot from a little above left to a little below right,
instead of left-right), and performs the Test again. Again it fits to
99.99% accuracy. The experimenter continues this procedure over many
axes in the hypothesized space, and always finds what appears to be a
controlled perception.

Incidentally, the "99.99% fit" is becoming a rather annoying
exaggeration of the measures we actually get and the criteria we
propose. A correlation of 0.996 (about the highest we ever see)
corresponds to a mean error of prediction of about 0.03 or so, for a
predictive accuracy of about 97%. The range of correlations we propose
as being acceptable go with prediction errors from about 10% to about
3%.

You scenario is what you imagine will happen, but we won't know whether
this will actually happen until we try it. In cases where we have tried
something like this, notably Rick's test of a model that used rho and
theta instead of x and y to model two-dimension control using a mouse,
the behavior of the model was much worse than an x-y model, in
comparison with the behavior of the person. In experiments containing a
rotation of the effect of the handle on the cursor in two dimensions,
subjects did very much worse than when the axes were horizontal and
vertical (Ray Pavloski used such rotations as a way of creating errors
to induce stress). Inserting cross-connections between axes externally
to the person, and applying disturbances at different angles, also
showed great differences in performance compared with the simple x-y
case. Just what this means about "primary" axes of control is not clear,
but it is clear that if you start actually experimenting with different
axes you can come up with differences in performance and differences in
model predictivity. If we believed your scenario, we would just try one
set of axes and assume that we'd get the same results for all other
possibilities. So far that doesn't seem to be true.

Another possibility for the same result might be that the organism had
several control systems distributed around the various directions in
the space, with overlapping responses, all equally sensitive but a bit
more crowded near the axes that showed best control.

This is indeed a possibility which may or may not prove to be the case.
I tend to think it is correct, but only experimentation can show whether
it is. One implication of this sort of arrangement would be that a
person should have no trouble changing axes of control when there is a
relative rotation between the input and the output effects. In fact,
people do have a great deal of trouble with such rotations. It is
possible that with sufficient practice, a person could learn to control
just as skilfully with a rotation present as without it. But the
question is then whether the person has added a new, rotated, control
system, or has reorganized the former control system to work with the
new conditions. The answer can be found experimentally by seeing how
rapidly the person can switch from one control situation to the other.
If a new control system has been added, then with enough practice the
person should be able to switch very rapidly from one set of axes to the
other, and back. If we are seeing a reorganization, on the other hand,
we should see an effect like that with the inverting-prism glasses:
restoring the normal conditions requires a long learning period just as
in adapting to the inverted situation.

The "vector" perceptual responses that Georgeopolis has found look like
examples of the situation you describe, but they may represent one level
below the level where directional control is actually achieved. Even
with such distributed vector responses, it is possible that the signals
from such neurons are received with weightings that project the vectors
onto one particular angular direction for two receiving systems, thus
establishing a two-axis perceptual space with specific normal axes at
the next level up.

I should think that with enough experimentation we could make some
headway on this question. And of course, we should get some useful
information from neurological investigations, which can rule out some
possibilities just by showing that the necessary pathways aren't there.

All general principles must therefore be frequently revisited, to see
whether the underlying assumptions still remain acceptable. I think
you tend to forget this:

Huh? Am I not doing EXACTLY this here, and asking you to do as much?

You are not testing assumptions, you're elaborating on them in different
ways. When I speak of testing assumptions, I mean going back to nature
and doing an experiment under new conditions that challenge the
assumptions, to see if they remain true. Simply offering possibilities
is not testing assumptions (except in the sense of seeing if your
logical is still internally consistent).

I'm contesting Rick's repeated claim that the goal of PCT is to find
"the controlled variable(s)". The way he puts it, it NEVER sounds as
if "the controlled variable" could change from moment to moment. It
sounds as if once you've found it, you can rely on it being there when
you want it again in some extension of the model. That's what I am
pointing out to be false.

"The test for the controlled variable" does sound as if there is only
one test and only one possible controlled variable, but I hope not many
people take it this way. "The controlled variable" is a class of
variables, and is to be understood in the same way as "the analysis of
variance method for determination of the response to the stimulus."

As to the controlled variable changing from moment to moment, that would
make the Test rather hard to pass. We don't generally accept a variable
as being controlled if it shows up in only one experiment and never
again. Once again, you're turning a quantitative question into a
qualitative one.

In all control-system experiments, no matter what level of organization
is involved, the control loop passes through the environment. This means
that all levels of control are always visible. Higher-level variables,
in an "extension of the model," are functions of lower-level variables
which are represented in lower levels of a multi-leveled model. If any
of the lower-level variables ceased to be controlled as we model them,
the higher-level model would fail, too. A properly-constructed multi-
leveled control model is cumulative; establishing a model of one level
is not like proving a theorem once and for all and then assuming its
truth from then on. A multileveled model would include all lower levels
that have already been established, and a test of the multileveled model
would include a test of all the levels so far built.

The first few levels of the "portable demonstrator" in the 1960 paper
were set up this way. The first level involved resisting a sudden push
on the hand. The second level involved treating the sudden push as a
signal to move the hand quickly to some other position; now visible were
the resistance to the initial push, and a rapid transition to a new
position. The third level involved responding to the push by moving the
hand to a new position aligned with a movable target. Now all three
aspects of the proposed hierarchical control system were visible: the
initial resistance to the push, the quick movement to a new
kinesthetically-defined position, and a final adjustment of that
position to match the changed position of the target.

This is how I envision the ultimate PCT model: every experiment will
explicitly test all levels up to the highest one being investigated. So
it won't matter if the definition of a controlled variable changes; we
will be able to see the change and represent it properly in the model.
Or so I imagine.

Of course (qualified by the first part of this posting) you can find a
controlled variable if you guess right as to its CEV. But it may not
be a controlled variable the next time you look. And you say as much
in your further comments.

Maybe, maybe not. We will obviously make the most progress with
controlled variables that show up again and again. However, if a
controlled variable is defined as ax1 + bx2 + cx3, and we find that a,
b, and c have changed by 5% between tests, are we to say that the system
is no longer controlling the variable it was controlling before? Or are
we to take this as evidence of some other control process that is
altering the coefficients, or as some slow process of reorganization?
When we investigate a higher-level process, one way we test it is to see
how it changes not only the reference signals for specific lower-level
systems, but how it changes from using one lower system to another. If
the changes of usage are systematic, we can characterize the higher-
level controlled variable, and at the same time come to understand why a
lower-level variable is sometimes controlled and sometimes not.

If a lower-level controlled variable proves to be approximately the same
each time we see it, but is simply not present at other times, what
would be more natural than to put the blame on a higher level of
control? What you cite as a drawback of the Test is really evidence
about higher levels of control.

Skipping around --

this level appears to operate largely in the imagination mode.

Pfah!

When you say a principle applies to a imagined case other than the one
from which it was derived, as when you said in this post ...

The experimenter varies the axis a little within the hypothesized
perceptual space (perhaps moving a target dot from a little above left
to a little below right, instead of left-right), and performs the Test
again. Again it fits to 99.99% accuracy.

... then you are imagining. The principle is that any set of orthogonal
axes is sufficient to represent control equally well in a given
perceptual space. You then imagine a case in which that is actually
found to be true. The only way to know if that generalization is valid
is to actually do what you imagined doing and show that in fact the
principle applies. It may or it may not, but the only way to know for
sure is to do the experiment.

Enough, enough. Some of our differences, it seems, will never be
resolved. But no matter. We have enough agreements to go on for quite
some time.
-----------------------------------------------------------------------
Best to all,

Bill P.

[_Martin_Taylor]

[Martin Taylor 941017 16:15]

[Martin Taylor 941014 19:00]

Bill Powers (941013.0705 MDT)

Martin Taylor (941012.1540)

A bit of a follow-up, since I have not had any comment on the original yet
(though no doubt comment has been posted!!!-(

...any scalar application of the Test within the

controlled perceptual space will result in a well-fitting scalar model,
and thus no perceptual direction within the controlled space can be
distinguished from another by the Test.

This conclusion is drawn, I think, from some assumptions that greatly
simplify the real case. If you include nonlinearities, time-delays, and
dynamical characteristics of the scalar control systems, there may be
ways to distinguish the primary axes of control.

If there really IS a
perceptual space, rather than a set of independent scalar perceptual
variables, then the experimenter can apply the Test along any axis of
the space, and will find that on this axis the Test shows a controlled
perception to exist. If the "true" control systems that exist within
the organism can be accurately modelled by a hypothesized control system
(say a lagged integrator, for example), then so will the result of the
experiment done on an axis that does NOT correspond to any scalar signal
within the organism.

[much later]

and your
professed distaste for mere practical examples,

I propose a practical example. You know EXACTLY what control systems exist
in the Little Man. I propose that you treat the LM as an unknown test
subject, and see if you can determine the various controlled perceptions.
It is NOT fair in this test to assume anything about the xyz spatial
directions of the LM's computational space, so the experimenter's xyz axes
should probably be chosen at random with respect to the LM, though I suppose
there would be no problem in assuming one axial plane to run through LM's
eyes perpendicular to the neck axis, if you want (which clearly makes
assumptions that one might make in respect of a human subject).

The claim I make is that if you do a one-dimensional test, by moving
the target dot along any curve you want in the space, the LM will counter
the disturbance effectively--how effectively will depend on the bandwidth
of the disturbance and quite possibly the curve chosen for the test.

Question 1: Without considering the relative precision of tracking, can you
determine the axes (if they exist) in the geometric space that correspond
to the LM's perceptual signals, using the Test? (In other words, can you
reconstitute not the perceptual functions themselves, though to do so
would be ideal, but the environmental variables that form the arguments
to the perceptual functions).

Question 2: When you include consideration of the relative precision of
tracking along different 1-D curves, can you determine the axes?

Question 3 and 4: If you apply the Test in 2 or 3 dimensions simultaneously,
not using (Q3) or using (Q4) information about the tracking precision,
do the tracking results then show the nature and axes of the perceptual
signals?

My guess is that the answer to Q1 is "no," and to Q2 it might be "yes" but
I'm not at all sure about it. Q3 and 4 are interesting questions, because
they allow the experimenter to probe all possible dynamical interactions
among the control systems at the same and different levels of the hierarchy,
which I'm not sure Q1 and Q2 do (though I could be wrong).

Anyway, the LM is a much simpler test subject than the human, and one for
which you know precisely the correct answer. I am betting that for any
one-dimensional track you will be able to fit the data with a single
scalar control system of some kind, thereby demonstrating that the Test
does not uniquely specify which perceptions are controlled. If you can't,
and find you need two or three or more control systems in your fit, then
I am wrong, and the Test is capable of finding "the controlled perception"
as opposed to "controlled perceptual spaces."

Would this proposal help our understanding of the issue?

Whatever the answer, I do not think that looking for controlled perceptual
spaces is any the less PCT research than is the search for controlled
perceptual scalar variables. For the latter, I think you need physiological
data to supplement the Test.

Martin

PS. I really hope that the first response to this that I see (after Nov 16)
contains answers obtained from a real test using the LM, done by some
programmer with a PC, not necessarily Bill P.

[Tom_BOURBON3]

Tom Bourbon [941017.1234]

[From Bill Powers (941015.0905 MDT)]

Martin Taylor (941014.1500) --

. . .

To summarize, Martin has written on the idea that reference perceptions
might change from moment to moment. As I mentioned in an earlier reply to
Martin, implicit in a claim like his, but typically forgotten, is the
opposite possibility: reference perceptions _might not_ change from moment
to moment. Some reference perceptions might be stable over long periods of
time and over many instances of control. Bill picked up on that theme.
Here is an example of what I mean.

At a CSG meeting a few years ago, I described some data on driving in the
USA. The following are more up-to-date versions of those data. Even if
some of the estimated values are off by factors of 2 or 3 or 10, the results
will not change very much.

Year Miles driven in USA Deaths Avg. Miles/trip Trips
1980 1,111,596,000,000 23,000 8.69 (est.) 127,916,685,800
1991 1,548,589,000,000 18,500 8.69 (est.) 178,203,567,300

That is quite a bit of driving. PCTers often use driving as an example of
perceptual control. At least we can't be accused of picking a trivial and
unrepresentative example.

How well did American drivers control their respective reference perceptions
while they drove all of those miles? The answer will give us an idea of how
well we are doing when we model control behavior. As indices of performance,
I will use the probability that, during a trip, a person in the automobile
became a traffic fatality, and the inverse -- the probability that there
was no fatality during a trip.

Year p(fatality\trip) p(no fatality\trip)
1980 .00000018 .99999982
1991 .000000104 .999999896

Not bad. Those are the levels of precision people achieve while controlling
the many perceptions that must be controlled during a trip in an automobile.
These were the kinds of data I had in mind when I wrote the following to
Martin:

···

==========================
Tom Bourbon [941013.1359]

[Martin Taylor 941012 15:40]
Point 1 suggests that no version of the Test can determine whether any
particular scalar CEV corresponds to a controlled perception, unless the
perceptual space in question is unidimensional.

You lost me on Point 1, Martin. To understand such claims as this, I
often need examples. Could you step me through your thinking by using an
example? To pull one out of the air, could you show me how those ideas
would apply were you to test for the controlled perceptual _spaces_ of a
person driving in traffic, and show why you could not test for controlled
perceptual _variables_? I would appreciate that.

Martin:

2. the relative gains of different controlled perceptions change over
time (not perceptual spaces, because "gain" has no meaning in that context).
Hence what the Test shows to be controlled at one moment may not be shown
to be controlled at another.

. . .

Point 2 suggests that
the results of the Test performed at different times will be different,
except under the same kinds of conditions as are assumed in standard
psychophysics--namely that the subject collaborates with the experimenter
to control some consistent perception.

_Never_ at another moment? Couldn't you just as easily say that, "what the
Test shows to be controlled at one moment _may be_ shown to be controlled at
another?" Point 2 also "suggests" that the results of the Test performed
at different times will be _the same_. Could you give a clue as to why you
chose to introduce this red herring? Are you saying that, because a person
_might_, or _might not_, control a different perception later, we cannot
test for the perception the person is controlling now? What difference does
it make if a person does adopt a different reference perception later? (I am
asking your opinion.) Do you think Rick (or Bill Powers or I or any other
person who has actually done the test and modeled the results) believes that
once a CV is identified, it must ever after remain the same?

I am still interested in the answers you would give, Martin. Perhaps now
you have a better idea of what I was thinking when I asked the questions.

Back to the present.

Martin:

Now the experimenter hypothesizes that there really is a perceptual
space, and doesn't trust that the Test (which fitted to 99.99%
accuracy) showed a true controlled perception. The experimenter varies
the axis a little within the hypothesized perceptual space (perhaps
moving a target dot from a little above left to a little below right,
instead of left-right), and performs the Test again. Again it fits to
99.99% accuracy. The experimenter continues this procedure over many
axes in the hypothesized space, and always finds what appears to be a
controlled perception.

Bill:

Incidentally, the "99.99% fit" is becoming a rather annoying
exaggeration of the measures we actually get and the criteria we
propose. A correlation of 0.996 (about the highest we ever see)
corresponds to a mean error of prediction of about 0.03 or so, for a
predictive accuracy of about 97%. The range of correlations we propose
as being acceptable go with prediction errors from about 10% to about
3%.

Your 99.99% _overstates_ the precision we achieve in our modeling, Martin,
but it _understates_ the precision people achieve in their "real world"
control behavior, at least people in the USA when they drive their
automobiles. It is obvious to me that we have a long way to go before our
modeling comes close to the precision people achieve. It is also obvious
that reference perceptions can be much more stable than you have implied and
that sometimes our chances of identifying them might be easier than you have
implied.

Later,

Tom

[Bill_Leach1]

<[Bill Leach 941018.15:49 EST(EDT)]

[Bill Powers (941015.0905 MDT)]

It is possible that with sufficient practice, a person could learn to
control just as skilfully with a rotation present as without it. But the
question is then whether the person has added a new, rotated, control
system, or has reorganized the former control system to work with the
new conditions.

Thinking about this one... seems to me that both are possible for the
same test but with different people. I would suggest that some people
would alter an existing control system and some people would create a new
one. Of course guessing is not the way to answer such a question,
performing the experiments IS.

-bill