# More vortex questions

[From Rick Marken (931220.0830)]

Martin Taylor (931219 17:30)--

I apologize in advance for continuing this irrelevant thread on vortices, but
several posters have asked me to do so.

I agree with Cliff Joslyn (931219 24:00) and Bill Powers (931219.1830 MST)
that this is NOT an irrelevant thread at all. It seems to me that we are
honing in on a fundemental point -- characterizing the difference between
purposive and non-purposive systems. You say that the difference
is NOT based on negative feedback. In fact, you said:

There exist in nature many, many negative feedback systems that
stabilize structures, sometimes structures of considerable complexity.

and gave the vortex as one example of a negative feedback system that is
NOT purposive. I agree that the vortex is not purposive; but I believe
that this is because it is not organized as a negative feedback system.
You seem to think that the vortex IS a negative feedback system that is
not purposive becuase it has no "reference level". Is this correct?

Your post (931219 17:30) helped to clear things up a bit for me. The
replies from Powers and Joslyn were also helpful. But I would still like
to see a diagram of what you think is the negative feedback relationship
between variables in a vortex. The diagram you provided was not very
clear to me:

-------->- | Main flow (power supply)
> > V
> Gain
> > >
--<-------| -----> Flow down drain
deviation from V
stable vortex shape | vortex

I see the power supply as one variable. The Gain is apparently a
function that transforms the power into another variable -- but what?
The circle of arrows seems to represent the vortex itself, which has
varable parameters but is not a variable. Where is the negative
feedback in your diagram? Does the amplified power get turned into a
motion that reduces the power? Is this a reasonable rewrite of your
diagram:

power supply -->Gain --> vortex
^ motion
> >
>---------neg f-------

where the line labelled "neg f" is the negative feedback path back
to the power supply. Is this right?

Thanks

Rick

[Martin Taylor 931220 14:00]
(Rick Marken 931220.0830) (Bill Powers 931219.1830 and 931220.0710) and
(Cliff Joslyn 931219 24:00)

All of you think the thread about vortices is relevant to PCT. I don't see
how, but I guess I'm willing to consider continuing it. I'd really like
Gary Cziko to say he thinks it isn't irrelevant, but since he seems to have
moved his throne elsewhere, we'll have to do without.

Before continuing with the physics of a vortex, let me see if I can sort out
what it is that could be relevant about it.

To me, the only issue, and a trivial one at that, is whether the word
"purpose" implies that there is a goal or reference level. Away back,
when I was a PCT neophyte, I asked whether it was correct to say that
the existence of a reference level defined "purposiveness" and the value
of that reference level define the actual purpose. Rick Marken said that
was a very good statement, and I have come over the years to take this as
one of the foundational concepts of PCT.

At some point recently, someone equated the concept "control" with that
of simple negative feedback. Inasmuch as it seems to me to be useful to
tie together the notions of "control" and "purpose," I proposed restricting
the use of the word "control" to negative feedback systems with a variable
reference input, in other words to control with the purpose of bringing a
perception to a reference level. It was purely a question of the extension
of the use of words that have a technical meaning within PCT.

To illustrate the difference between purposive control and simple negative
feedback system, I used what seemed to me to be the simplest natural example
of a purposeless negative feedback system I could think of on the spur of
the moment: a vortex in a sustaining energy stream. So, instead of
discussion of the use of technical terms in PCT, there resulted a series
of postings about whether a vortex, in particular, was actually a negative
feedback system. THAT's where I think the thread became irrelevant to
PCT, unless you are arguing one of (a) there are no natural negative
feedback systems that lack reference inputs, or (b) all negative feedback
systems should be called "control systems" and should be said to have
"purpose."

Argument (a) is relevant to PCT, because I think that biological control
systems with reference inputs originally evolved from self-organized systems
(later, Bill--I've read your comment on that and will respond). And I
remain convinced that self-organized systems are precisely negative feedback
systems with gain that is sometimes quite high. So if you want to pursue
argument (a), you have to provide an alternative origin for the first
control systems with reference inputs.

Argument (b) is one of word usage. I just happen to find it more natural
to take "control" and "purpose" as having a common domain of reference,
which excludes negative feedback systems that lack reference inputs. If
the net concensus is that all negative feedback systems should be called
"control systems" with a purpose of maintaining whatever it is that the
feedback maintains, I won't argue very strongly. I just think that the
other, more restricted, usage is preferable.

···

-----------------------
(Bill Powers 931220.0710)

I really object to calling a vortex a "self-organizing" system in
the context of any quantitative discussion. Organization is a
perception; who is to say whether a vortex impresses everyone as
more organized than a laminar flow, or less? The "organized-ness"
is based on the familiarity of the vortex shape. Equating
organization to a function of entropy is gratuitous; One might
as well just compute entropy and leave "organization" out of it
because that, in effect, is what is done.

This paragraph suggests why we have such difficulty communicating. A
self-organized structure has nothing to do with "impressing everyone" or
with familiarity. For us to identify a self-organized structure, we do
have to do the equivalent of the Test on it, and to that degree it IS
a matter of perception as to whether we see one that exists or not.
But the shape itself has nothing to do with the self-organization. That
has to do with stability against disturbance.

A self-organized structure comes into existence in a strong non-equilibrium
energy flow, and vanishes if the flow stops or becomes too weak. The
signature of a self-organized structure is that equipartition of energy
among the degrees of freedom in the flow is violated and the violation is
maintained while the material content of the structure may change. The
energy per degree of freedom in the self-organized structure is substantially
different from the energy per degree of freedom in the driving flow, and
stays that way rather than returning toward equipartition, as would happen
in a closed system. Entropy is continually being exported by way of the
flow, compensating the entropy gain involved in the dissipation mentioned
by most posters on the "vortex" thread. (Yes, Bob. I did check not only
"Physics Today"--the magazine of the Americal Physical Society--but also
my introductory thermodynamics text, and I still can find no reference to
entropy being defined only in a closed system, either in elementary or
less elementary thermodynamics).

A self-organized system retains its organization against the continual
buffeting of the energy in the "disorganized" degrees of freedom of the
flow, and may do so against organized disturbances introduced from outside.
It is the stability of the energy in the particular degrees of freedom in
the structure that determines the self-organization, not the recognizability
of any particular shape or structure. It happens in all kinds of energy
flows, not just mechanical.

Symmetry is at the heart of many physical principles. A structure is a
broken symmetry. The equipartition of energy among the degrees of freedom
of a physical system is a symmetry. Each degree of freedom is interchangable
with each other, as regards energy. If some degrees of freedom have and
retain more energy than others, the symmetry of the energy flow is broken.
A self-organized structure can be seen as a stable way in which the
symmetry has been broken. The flow as a whole sustains it.

When a symmetry is broken, it may be broken in many ways. Consider a
pencil balancing on its point. So long as there is no tiny push to one side,
it will stay balanced, but any little push will break the symmetry.
In a self-organized structure, some little push has happened at some
point, perhaps just the random motion of molecules happening to put a
little bias one way or the other, perhaps the Coriolis force on a radial
fluid flow. The effect of that little push changes the flow in some
manner such that a bigger push in the same direction returns to the
original point, increasing the effect in a positive feedback loop.
I hope that in this group I don't have to point out that all this
is happening simultaneously around the loop, rather than in the discrete
elements that the language requires us to use.

This positive feedback loop would expand without limit, except that
some nonlinearity stops it eventually. That nonlinearity might be in
the configuration of the structure, in the material substrate, or anywhere.
Now the structure is continually extracting energy from the main flow,
slowly perhaps, but at exactly the rate that balances the dissipation.
Bill got this far in his nice analysis of angular momenta and the like
in a vortex.

To recapitulate: a small force at some point in the flow breaks the symmetry,
and results in a further reapplication of the small force. The result is
the eventual extraction of a possibly large amount of energy from the main
flow into a structure whose main characteristic is the reapplication of
the symmetry-breaking force. The rate at which the symmetry-breaking force
redirects energy into the structure balances the rate at which energy
is to dissipation. This is the positive feedback loop that creates the
structure and that is limited by the balance of forces that has been
mentioned by various posters.

I suppose, hesitantly, that this positive feedback loop corresponds to
Rick's rewrite of my negative feedback diagram:

power supply -->Gain --> vortex
^ motion
> >
>---------neg f-------

where the line labelled "neg f" is the negative feedback path back
to the power supply. Is this right?

The "neg f" should be "pos f" and at the limiting condition the loss
round that part of the loop, in the "vortex motion" just balances the Gain.

The interesting question now can be asked. If the self-organized structure
is disturbed, does its restoration involve negative feedback, and if so,
with what gain. Rick's picture does not apply to this question. It is
this question to which the answer seemed to me intuitively obvious, that
"of course" it has to involve negative feedback, in a mechanism quite
unlike the ball-in-a-bowl or the weight-on-a-spring. The positive
feedback loop itself involves only a very low-level return path as compared
to the energy in the structure--just enough to counter dissipative losses.

The modulation energy on this small amount HAS to be even smaller, and
yet its effects are large, restoring the structure to nearly its undisturbed
state. This says to me "high-gain negative feedback" for the modulation
signal that is the change in the state of the self-organized structure.
The largest that the signal could possibly be is the rate of dissipation
of energy within the structure (unless the disturbance is biased toward
adding energy to the structure), but the change of energy that it induces
may be orders of magnitude larger, depending on factors such as viscosity
if the structure is in a fluid flow.

The diagram that I think describes the situation is the one Rick redrew:

-------->- | Main flow (power supply)
> > V
> Gain
> > >
--<-------| -----> Flow down drain
deviation from V
stable vortex shape | vortex

Rick did not understand it initially. I'll try to answer the questions
superfluous and redundant.

I see the power supply as one variable.

No, the power supply is just that. It's a power supply, such as is needed
by every amplifier, including the output function in every normal ECS.

The Gain is apparently a
function that transforms the power into another variable -- but what?

This is an interesting question that could start a thread in itself. I
see every amplifer as a mechanism that diverts part of an energy flow
into "useful work." What it does is to take the small amount of energy
introduced at the input as a modulation on some small flow, and replicate
that modulation as a variation on a larger flow. A small signal is made
into a big signal of the same kind. The word "replicate" is not
strictly accurate, but it is convenient and carries the essence of the
idea, which is that the input modulation affects in a cause-effect
way the output modulation. The energy in the modulation of the output
is larger than that of the input. (In electronics, one can get larger
output voltages than input without modulating any new energy flow. The
effective device is called a "transformer." here we are talking about
amplifiers, not transformers.)

The circle of arrows seems to represent the vortex itself, which has
varable parameters but is not a variable.

No. The "vortex itself" does not appear in the diagram, except as the
side-effect shown leaving the figure at the bottom. The structure
of the vortex does appear, and perhaps should have been labelled, but
even small ASCII diagrams are time-consuming to make. Put it at the
bottom-left corner of the feedback-loop square.

Where is the negative

It is the modulation energy associated with the deviation from the stable
vortex shape.

Does the amplified power get turned into a
motion that reduces the power?

I don't understand this question. The modulation of the flow in the
amplifier reduces the modulation energy associated with the disturbance
(which isn't shown in the diagram and probably should have been; it would
go in the normal place, coming in from the bottom-left to affect the
vortex structure, which correesponds to the CEV in a control system).

================
(Cliff Joslyn 931219 24:00)

Some questions raised. I'll try to see if I can answer them.

1) What is the simplest, and evolutionary first, system which shows
negative feedback? (Martin: vortex?)

I wouldn't know, but I assume it would be some kind of chemical system, if
by "evolutionary first" you mean "leading directly to life." If you just
mean "in the universe" it could be the kind of symmetry-breaking that led
to the first split of the four forces. To come down a level or three,
one way of looking at the stability of fundamental particles such as
photons or quarks is as the stable points of transformation loops in the
vacuum. (This was, in fact, the analogy I was using before I found out
about PCT, to deal with stable ideas and momentary cognitive flashes).

2) Is feedback necessary for perceptual control? (Martin: yes)

Yes.

3) Is feedback sufficient for perceptual control? (Martin: no)

No perception, no perceptual control. I take it more as a definition
than as a technical statement that a perception is a signal created
by some function of more than one input variable, and that perceptual
control involves the comparison of this signal with a reference value.

4) If feedback is necessary but not sufficient, then what further
conditions are sufficient? (Martin: ?)

See (3). As much as anything, it is a question of the agreed use of words.

5) What is the simplest, and evolutionary first, system which meets these
conditions, and thus shows control?

I have no idea, but it seems to require that there be at least a 2-level
system, so it isn't a simple negative feedback system. The upper of the
two levels can be a simple negative feedback system, but the lower would
receive reference signals from the upper, qualifying them as perceptual
control systems. At present, we do not consider the system of control of
intrinsic variables to be perceptual control, because there are no perceptual
signals corresponding to them. They are kept in control by means of
the control of other perceptions.

I assumme that you apply the same reasoning to other complex stable
systems, like spinning tops, Benard convection cells, etc.?

Of course not spinning tops. Convection cells, yes; they are self-organized
structures.

On the damped spring:

d x_1/dt = f_1(x_1,x_2)
d x_2/dt = f_2(x_1,x_2),

where

f_1(x_1,x_2) = x_2 (A)
f_2(x_1,x_2) = - x_1 k/m - x_2 k_1/m

What's this? Feedback! x_2 affects x_1 through f_1, and vice versa x_1
affects x_2 through f_2. The faster you go, the more your position changes;
but the farther out you are, the faster you go, the "restoring force" of
the spring brings you back.

Where did the energy of this motion come from? The disturbance, right?
There may well be feedback, but there sure isn't high gain. There is
no amplifier extracting energy into that motion from an energy flow.
I reserve judgment about whether a spring excited by jiggling its support
randomly would qualify. The feedback (if any) would have to restore the
amplitude of motion given some imposed disturbance that extracted or added
energy to the oscillation.

Just because there are a bunch of forces
acting to affect each other doesn't mean that actual feedback, a factor
which acts SPECIFICALLY to oppose a disturbance, is present.

# Right.

(Bill Powers 931219.1830)

An interesting objection:

The problem with treating a vortex or any similar system as a
negative feedback system, I have finally realized, is that you
can't separate the forward path from the feedback path. These
paths are not physically distinct, even though you might be able
to manipulate the equations to give the appearance of distinct
paths. The so-called feedback effects are simply the inverse of
the forward effects; you are separating action and reaction, but
only through the artifice of mathematics (using superposition to
treat the two paths as if they were independent). In fact, the
"reaction" is identical with the "action," and separating them is
a conceptual mistake -- unless they are in fact physically, not
just conceptually, separate as they are in all true control
systems.

I can see that there is a psychological problem in thinking about the
feedback loops in the vortex (taken as an example of a self-organized
structure). I am not at all sure that there is any technical need
for the paths to be physically separate "as they are in all true
control systems." I hope that the discussion above has shown that
the "so-called feedback effects" are not "simply the inverse of
the forward effects," and that true feedback and true gain are involved.

It is, I grant, MUCH easier to see what is going on when the elements
are physically separated, just as it is much easier to follow discrete
packets of effects around a control loop than to conceive of all the
effects happening simultaneously and continuously. But that doesn't
mean it is wrong to see the effects happening simultaneously and continuously
or that it is wrong to see the feedback circuits in physically continuous
structures.

If the state of motion of the vortex were truly a controlled
variable in a control system, then increasing the head of the
water in the bathtub would have no effect on the vortex.

I think that's a non-sequitur. The very structure of the vortex is determined
by the energy flow rates. At low rates you get laminar (radial) flow
and self-organized structures cannot occur, At high rates you get
turbulence, and self-organized structures that might have existed get
destroyed. What you have to test against is a disturbance that comes
from elsewhere, just as it does when you test a living control system.
The disturbance does not, by its nature, affect the power source for
the living control system, and neither should the disturbance that tests
whether the vortex involves a negative feedback loop.

The vortex's spin rate could be made independent of the head if we
simply stirred with our fingers in the direction and by the
amount needed to keep the spin rate constant.

Sure, and if you impose overpowering force on the external variable whose
perception is controlled by a living control system, you can make it
take on a value of your choosing. That doesn't mean that the other
living control system wasn't controlling, beforehand.

Control systems work by using a feedback path that does not enter
significantly into the energetics of the output process,

Welllll, I think that depends on what you mean by "significantly." The
most it can is determined by the energy gain in the output amplifier,
which in a neural system is probably about the same as the amplitude
gain squared. If the output gain is 10, and my analysis is right (which
I won't bet on too heavily), the feedback energy cannot be more than 1%
of the energy it influences, and is likely to be much less. Is this
"not significant?" Am I agreeing with you or disagreeing?

and that is physically distinct from the output process.

Physically, yes. Geometrically, not necessarily. I'm not sure what
you mean by "physically distinct" here, and therefore whether to agree
or to disagree.

In a vortex, the
forces that restore the vortex to its equilbrium state after a
perturbation arise from the perturbation itself.

I hope I have shown this not to be the case. It has been at the head of
almost all my postings on this thread that this is not the case for the
vortex, whereas it is for the ball-in-the-bowl.

Control systems create abnormal physics. The four major classes
of amplifiers (vacuum tubes, transistors, neurons, and enzymes)
create a strong assymetry, preventing actions from producing
equal and opposite reactions directly against their causes.

# Why is this abnormal physics? I don't understand what's abnormal about it. In fact, of the four, transistors were discovered through the application of mathematics to the then-known physics of electron transfer in semiconductors. Vacuum tubes were not predicted, but are easily analyzed using normal physics (it used to be one of the first things done in introductory electrical engineering, but I don't suppose it is nowadays). The many actions and interactions of neurons are not now well known, but that is more a chemical than a physical problem, I think. I'd be very surprised if any abnormal physics appeared. As with enzymes, which I thought were catalysts rather than amplifiers, but I'll take your word that they aren't.

(Bill Powers (931220.0710)

You are incorrect, by the way, in saying that a tendency to
loop gain greater than 1. It requires only a loop gain greater
than zero. A control system with a loop gain of 0.5 will produce
an output that is 0.5/1.5 or 1/3 the magnitude of a disturbance.
When the disturbing influence is removed, the output will restore
the system to equilbrium.

You are right, of course. Silly of me. I hope that the rest now seems
less silly.

I see I have spent 3 1/2 hours composing this, even without going back over
it to see what I have written. I really don't want to do any more on this
thread unless I can be shown how it is properly relevant to PCT. The only
thing I anticipate getting out of this whole discussion is some notion of
whether to use "control" and "purpose" in reference to isolated negative
feedback loops that occur in nature rather than just to those that have
variable reference inputs. I'll use the terms in whatever way the net
concensus goes, but I do say that we need some form of language that allows
us to distinguish the two kinds. I don't think an engineer designing a
negative feedback loop would find much use for one that had no "input,"
and I don't think life has, either.

Martin

From Tom Bourbon [931221.0959]

[Martin Taylor 931220 14:00]
(Rick Marken 931220.0830) (Bill Powers 931219.1830 and 931220.0710) and
(Cliff Joslyn 931219 24:00)

All of you think the thread about vortices is relevant to PCT. I don't see
how, but I guess I'm willing to consider continuing it. I'd really like
Gary Cziko to say he thinks it isn't irrelevant, but since he seems to have
moved his throne elsewhere, we'll have to do without.

Martin, it's CZIKO who is irrelevant, not the discussion on vortices! ;-))

I also voted for keeping the discussion of vortices "on the net." My
interest in keeping it here stems from the fact that, when I talk about PCT
with new people, I am often confronted with a remark like, "Oh yeah? Well
what about ________?" The blank is filled in with some example or another
the person believes is proof that control exists without control systems.
One of the more popular items for filling the blank is "self-organizing
systems." Vortices have been mentioned in that regard. Another frequent
blank filler is the example of "balls in bowls." Naturally, when I see
exchanges like the following:

Bill P.:

In a vortex, the
forces that restore the vortex to its equilbrium state after a
perturbation arise from the perturbation itself.

Martin T.:

I hope I have shown this not to be the case. It has been at the head of
almost all my postings on this thread that this is not the case for the
vortex, whereas it is for the ball-in-the-bowl.

I am interested in seeing the discussion remain in full view.

The following exchange between Rick and you raises a new question for me:

Martin:

To recapitulate: a small force at some point in the flow breaks the symmetry,
and results in a further reapplication of the small force. The result is
the eventual extraction of a possibly large amount of energy from the main
flow into a structure whose main characteristic is the reapplication of
the symmetry-breaking force. The rate at which the symmetry-breaking force
redirects energy into the structure balances the rate at which energy
is to dissipation. This is the positive feedback loop that creates the
structure and that is limited by the balance of forces that has been
mentioned by various posters.

I suppose, hesitantly, that this positive feedback loop corresponds to
Rick's rewrite of my negative feedback diagram:

power supply -->Gain --> vortex
^ motion
> >
>---------neg f-------

where the line labelled "neg f" is the negative feedback path back
to the power supply. Is this right?

The "neg f" should be "pos f" and at the limiting condition the loss
round that part of the loop, in the "vortex motion" just balances the Gain.

The interesting question now can be asked. If the self-organized structure
is disturbed, does its restoration involve negative feedback, and if so,
with what gain.

Tom, now:
Up to that point, Martin, I had apparently been misinterpreting your ideas
about negative feedack, vortices and control. Previously, I thought you
were saying the emergence and the continuation of a vortex were examples of
non-purposive negative-feedback control. Here, you seem to be saying that
the creation and continuation of a vortex provide examples of *positive*
feedback (without control?), but that the restoration of the vortex after it
is disturbed is a demonstration of *negative* feedback control. Was I right
before, or am I right now -- or have I been hopelessly wrong from the start?

Martin to:

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

(Cliff Joslyn 931219 24:00)

Cliff:

5) What is the simplest, and evolutionary first, system which meets these
conditions, and thus shows control?

Martin:

I have no idea, but it seems to require that there be at least a 2-level
system, so it isn't a simple negative feedback system. The upper of the
two levels can be a simple negative feedback system, but the lower would
receive reference signals from the upper, qualifying them as perceptual
control systems. At present, we do not consider the system of control of
intrinsic variables to be perceptual control, because there are no perceptual
signals corresponding to them. They are kept in control by means of
the control of other perceptions.

Tom, now:
I'm not sure I exactly follow you here: "we do not consider the system of
control of intrinsic variables to be perceptual control, because there are
no perceptual signals corresponding to them. They are kept in control by
means of the control of other perceptions." Perhaps I am not clear on
which meaning you attach here to "perceptual signals." Are you using the
phrase in reference to perception-as-contents-of-human-subjective-awareness?
In that case, it probably follows that the control of intrinsic variables
does not (necessarily) entail perceptual control.

On the other hand, a PCT reading of research on the "signalling systems" in
individual cells, as an example, suggests that much of the activity of a
single cell can be modeled as "perceptual control;" that was the approach
taken in the PCT modeling of "chemotactic behavior" in E. coli. And work is
under way on a PCT rendering of phenmomena in molecular biology. Maybe you
can clarify just a bit more the sense in which you intended the passage I
quoted; I seem to be missing something.

By the way, that was a nice post yesterday on pull-pull systems. At CSG, I
never got around to showing you the "pull-pull" versions of the tracking
tasks -- strings tied to the control handles. One person *must* use two
hands (or the equivalent), and a literal *gang* of participants can join in,
given enough string. With broom sticks for handles and ropes instead of
string, we could probably have a PCT tug-of-war at the meeting next year.
Interestingly, the results can be modeled with one simple PCT loop, or as
two pull-pull models. Would that be an example of "real" social systems
organized as control systems? ;->

Until later,

Tom

[Martin Taylor 931221 13:30]
(Tom Bourbon 931221.0959)

Spinning around again...

[Following a discussion of the initial positive feedback system that
establishes the vortex...]

Up to that point, Martin, I had apparently been misinterpreting your ideas
about negative feedack, vortices and control. Previously, I thought you
were saying the emergence and the continuation of a vortex were examples of
non-purposive negative-feedback control. Here, you seem to be saying that
the creation and continuation of a vortex provide examples of *positive*
feedback (without control?), but that the restoration of the vortex after it
is disturbed is a demonstration of *negative* feedback control. Was I right
before, or am I right now -- or have I been hopelessly wrong from the start?

The emergence of a self-organized structure is an example of symmetry-breaking.
I think that the departure from symmetry has to involve a positive
feedback system (I used a pencil falling after being balance on its point
as an example, but it is not a good example for the development of a
structure). A positive feedback system will run away to infinity unless
it is limited by some nonlinearity. At some point the energy extracted
from the power source into the few degrees of freedom of the structure
will just balance the dissipative losses, and that's where I see a
"balance of forces" existing. If there's no disturbance, that's where
things will stand.

Now I look at a different phenomenon, a distortion of the structure, caused
by some externally powered disturbance. The question is whether this
distortion is resisted in a negative feedback loop, not whether the
emergence and continuation of the structure itself is part of such a
loop. Bill P has suggested a search for an example easier to analyze, to
see whether we can tie down more closely the actual gain in the restorative
process, something that I don't know how to do quantitatively in the vortex.
I second Bill's motion, but haven't thought of a suitable example. It
might be easier if my background had been chemistry rather than physics,
but may that's an example of "the grass is greener on the other side."

At present, we do not consider the system of control of
intrinsic variables to be perceptual control, because there are no perceptual
signals corresponding to them. They are kept in control by means of
the control of other perceptions.

Tom, now:
I'm not sure I exactly follow you here: "we do not consider the system of
control of intrinsic variables to be perceptual control, because there are
no perceptual signals corresponding to them. They are kept in control by
means of the control of other perceptions." Perhaps I am not clear on
which meaning you attach here to "perceptual signals."
...
Maybe you
can clarify just a bit more the sense in which you intended the passage I
quoted; I seem to be missing something.

I was thinking about the conceptual separation between control of intrinsic
variables through reorganization of the perceptual control hierarchy.
The perceptual control hierarchy works by direct control of variables
that are ultimately functions of sensory variables. The intrinsic variables
are controlled by manipulating the perceptual control, not by direct actions
on things that affect functions of sensory signals. I may say that I'm
not 100% happy with this distinction, but I understand it to be one of
the accepted conceptual structures of PCT, and that's how I intended the
passage that bothered you.

···

================
Tom,

On tracking tasks: I have still not figured out how to keep the three
cursors aligned and not have them go offscreen. I'm not sure I have even
figured out how to keep them aligned effectively. What is clear is that
we will have to give hints or instructions to the subjects during the
sleep study, or they will still be learning at the end of the week. Do
you have any useful verbal description of how to do it?

Martin