[From Bill Powers (931219.1830 MST)]
Martin Taylor (931219.1730) --
I apologize in advance for continuing this irrelevant thread on
vortices, but several posters have asked me to do so. I'd
prefer to get on with talking about real PCT.
It's not an irrelevant thread if there really is a difference
between control systems and vortices that is not just a matter of
a variable reference signal. I am still convinced that there is a
difference, and that therefore control theory is not continuous
with the "dynamical systems" approach to attractors etc.. Your
well-organized post on vortices, for which thanks, may get us
closer to settling this question, which is an important one. I
think I may now have the means of saying what I've been trying to
get across with "unidirectionality" and other less-than-clear
arguments.
We all agree that vortices and other self-organized structures
have no purpose. As such, they are not PERCEPTUAL control
systems.
We can't agree on this, because if vortices and such are control
systems, they are purposive. The existence of a reference input
is irrelevant to my concept of purpose, because even if there is
such an input, the signal entering it can be zero. That case is
indistinguishable from the case in which the reference input is
missing. If the closed-loop organization is not sufficient to
define purpose, then neither is a reference signal, because a
reference signal means nothing without the closed loop.
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.
Using this artificial separation of paths, you can treat a simple
spring as a negative feedback system. When you disturb the
position of one end of the spring (with the other end anchored),
you apply a certain force. The spring quickly comes to a state in
which it is applying a precisely equal and opposite force at the
same point, so the net force becomes zero. The reaction force
could be imagined to be a negative feedback phenomenon. The
deviation of the end of the spring from its undisturbed state
gives a measure of the loop gain: if k is the spring constant in
stretch per unit force, then the loop gain is, by inference,
approximately 1/k. The greater the stretch, the lower the loop
gain.
But a spring is not a negative feedback system. Or do you say
that it is one?
Or consider another case, a bucket with a hole in it, being
supplied with water from a running spigot. The forward path
consists of the incoming water, which increases the height of
water in the bucket at a certain rate. The feedback path consists
of the fact that as the height of the water increases, the
outflow through the hole increases, reducing the rate at which
the height of the water increases. This outflow effect tends to
offset the inflow effect and bring the height of the water to a
specific level. If you scoop out a little water, the water level
will decrease, but will increase again to the original level; if
you add a scoop of water, the water level will increase and then
decrease again to the original level. You can show that there is
an incoming flow of energy and an outgoing flow of energy, and
that the correction process is powered by that energy.
But the bucket with a hole in it is not a negative feedback
system. Or do you say that it is one?
My judgment in each case is justified by the fact that the
forward and so-called feedback paths are one and the same path.
The outflow in the bucket is produced by the inflow, not by a
separate path that detects water height and independently acts to
adjust the outflow. The reaction force in the spring is
identically the applied force; the applied force, which stretches
the spring, also creates the reaction force. In neither case is
there a separate feedback path.
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. In the
bucket example, increasing or decreasing the inflow rate would
have no effect on the final water level. In the spring example,
applying a force to the end of the spring would have no effect on
the final length of the spring. That is how you can tell that a
control system is present: the physical system does not respond
normally to changes in energy or force inputs. It comes close to
not responding to them at all.
A physicist presented with these claims would object that each
one is impossible. That is precisely the point. A control system
creates impossible relationships among the variables familiar to
the physicist. And when it is explained how each control system
would work, the physicist would object that we are cheating. 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. The water level in
the bucket would remain constant despite changes in the inflow if
we manipulated a faucet inserted at the hole in the bottom, in
the way needed to counteract changes in the inflow. The length of
the spring would remain constant if we pulled on its end through
another spring, in the appropriate direction and by the amount
needed to keep the end from moving, while the disturbing force
was applied.
Control systCSG-L@UIUCVMD.BITNET
Status: O
[Martin Taylor 931005 14:00]
(Hal Pepinsky Tue, 5 Oct 1993 12:41:55)
Sorry if I used "referent". It should read "reference" or "reference
signal" or "reference level" depending on the context.
do you see my point
about the importance of modeling two or more actors' control in
relation to one another?
Absolutely. That's been more or less the focus of my work for the last
10 or 12 years, both before and after learning about PCT. That's ems work by using a feedback path that does not enter
significantly into the energetics of the output process, and that
is physically distinct from the output process. In a vortex, the
forces that restore the vortex to its equilbrium state after a
perturbation arise from the perturbation itself. The forces
downstream subtract from or add to the upstream forces to create
the final effect; they are part of the reaction forces, not
separately generated forces. The vortex is simply a complex
version of the bucket with the hole in it, complex enough to make
the reasoning more difficult and the relationship between action
and reaction harder to work out. But only normal physics is
involved; only action and reaction, two ways of looking at a
single relationship.
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.
Disturbing the output of a unity-gain amplifier has no
the output of a unity-gain amplifier has no
Status: RO
significant effect on the input of the amplifier. This allows the
effect of an action to alter the action without reflecting
directly against it; the opposing effect arises through a
physically different pathway in which actions produce effects
without reactions.
This is the difference between all equilibrium systems and all
negative feedback control systems -- all purposive systems.
ยทยทยท
Subject: Re: Hal to Martin
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Best,
Bill P.