Vortices and feedback, again

[Cliff Joslyn 931219 24:00]

[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'd prefer to get on with talking
about real PCT.

I fail to see how this is an irrelevant thread. Maybe it's uninteresting to
you, but I think that the fundamental relation between stability, feedback,
and control is absolutely essential to all of cybernetics, and PCT in
particular. Further, I assert that these relations are not at all obvious,
at least not to me. So thank you for your continued public service to the
PCT community.

We all agree that vortices and other self-organized structures have no
purpose. As such, they are not PERCEPTUAL control systems.

Right. Don't forget my basic questions:

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

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

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

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

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

I think these are important questions.

Now, returning to the vortex.

By the time
the wave has propagated around the drain rim back to the North point, it might
augment or oppose the effect of the small lateral jet, depending on the
various factors of flow rate, viscosity, surface tension, and the like. But
with short propagation times, it will oppose the jet.

This is the key: how or why does this happen? What is the nature of this
"restoring force"? Does it always and exactly (eventually) oppose the jet?
Does it have a name? Can it be (simply) mathematically defined?

Your diagram:

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

is inadequate, because it is structural, in terms of flows, not functional,
in terms of the relations between forces/components. A functional negative
feedback diagram has the logical form:

I ----> E ----> S ----> O
        ^ |
        > >
        --- F <--

where input I goes to some effected node E, goes on to be sampled at S, and
passes to output O. The sample is fed to the feedback F, which then goes
back to the effected node E. Each of these components must be identified
functionally. If the feedback is negative, then a change at S is opposed by
a change of F at E.

I assumme that you apply the same reasoning to other complex stable
systems, like spinning tops, Benard convection cells, etc.? Again, a simple
mathematical description of such systems, where the feedback can clearly be
seen, would be helpful to me. I'm willing to go private if CSG-L is truly
getting fed up with this thread.

This is fundamentally different from the ball-in-a-bowl
or even a weight on a spring, for both of which a disturbance must add energy
to the system, energy which is dissipated into heat (or otherwise lost) as the
original state of the system is restored.

But that's not the question. Your task is to show that there is no feedback
in the ball in the bowl, but there is in the vortex. Are you claiming that
dissipation is related to feedback?

Also, damped oscillators (balls in bowls) CAN be mathematically described
as having feedback. Consider the damped spring

        d^2 x/dt^2 + dx/dt k_1/m + x (k/m)^(1/2) = 0,

where x(t) is the position of the plumb, k_1 is the damping factor, m the
plumb mass, and k the spring constant. The feedback isn't evident until you
transform into first order differential equations, letting

        x_1 = x, x_2 = dx/dt

so that

        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.

Now we all know that this isn't REAL feedback. In particular, (A) is only a
relabeling. What I'm saying is that we must be careful in identifying the
presence of feedback in a system. 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.


Cliff Joslyn, Cybernetician at Large, 327 Spring St #2 Portland ME 04102 USA
Systems Science, SUNY Binghamton NASA Goddard Space Flight Center
cjoslyn@bingsuns.cc.binghamton.edu joslyn@kong.gsfc.nasa.gov

V All the world is biscuit shaped. . .