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.
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
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
> > >
--<-------| -----> Flow down drain
deviation from V
stable vortex shape | vortex
Rick did not understand it initially. I'll try to answer the questions
about it, but I hope that the preceding discussion has made these answers
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
feedback in your diagram?
It is the modulation energy associated with the deviation from the stable
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)
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
On the damped spring:
d x_1/dt = f_1(x_1,x_2)
d x_2/dt = f_2(x_1,x_2),
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.
(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
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
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
return to equilibrium after a disturbance is removed requires a
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
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.