# Briefly: vortices and perceptual control systems

[From Bill Powers (931220.1830 MST)]

Martin Taylor (931220.1400) --

I think we are slowly getting to the nitty-gritty of what is and
is not a "perceptual control system." I want to make some points,
but I'll try to be very brief in the hopes that I can get them
across without too much blather.

You say, "No perception, no perceptual control." I have probably
never said this crucial statement out loud, but I am saying it
now: a perception is a representation of an external variable
DERIVED BY A MEANS THAT DOES NOT AFFECT THE EXTERNAL VARIABLE.
When you see your finger pointing to a target your eye absorbs
some of the light reflected from the pointing finger. I think I
told you of my calculation: the energy in the light used to
observe a moving finger is something like 10^-18 of the energy
required to move the finger, in ballpark numbers. In general this
is true of all controlled variables. Sensing the state of the
controlled variable has no effect on the controlled variable.
This is many orders of magnitude different from the energy levels
involved in the "feedback" in a vortex.

You bring up use of the Test in situations like that of the
vortex. In fact, applying the Test is impossible, as far as I can
see. The basic procedure is to calculate the effect that a
disturbing variable would have on the proposed controlled
variable _in the absence of feedback control_, using only
physical principles. Then you apply the disturbance, and measure
the actual effect. How do you calculate the effect that the
disturbance would have had on the vortex if there had been no
negative feedback? It's probably not possible to eliminate the
effects you're calling feedback without violating physical
principles. This is just another way of saying that the forward
effects and the feedback effects can't be separated; they can't
even exist without each other. You can't even calculate the state
of the vortex without computing the balance of forces in both
directions. Come on, Martin, if you put your mind to it you could
say this much better than I can.

One of the consequences of true feedback control is that the
operation of a control system is almost entirely insensitive to
variations in its own power supply. In a control system, the
control action regulates the flow of energy from the power
supply, not vice versa. If there is no disturbance causing an
error, no energy is expended. If the capacity of the power supply
is increased, there is essentially no effect on behavior.

In the vortex, the size, spin rate, and flow rate are determined
directly by the power supply. The greater the head, the faster
the vortex spins, the greater its size, and the greater the flow
rate. Nothing is stabilized against changes in the amount of
incoming energy. The vortex seems to lack major aspects of the
control system's ability to control. It is created by an external
force; it does not create that force.

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.

You've said this, but you haven't proven it. The problem is that
you've picked a complex physical system that is extremely hard to
analyze. You're guessing that certain relationships between
disturbances and effects on the vortex exist, but until you show
exactly what those effects are, your argument could be wrong. The
only way to settle the issue is to set up the equations and find
out what the effective loop gain actually will be. As this has
not been done, and I don't know how to do it, all my arguments
have to be indirect, based on characteristics of what I think of
as control systems that are different from the characteristics of
a passive system (as I see it) like a vortex. General principles
won't hack it here, because they have not been tied to the level
of observation. You haven't even said what attribute of the
vortex (if any) is resistant to disturbance. The whole question
revolves around WHAT is resistant to disturbance, and HOW
RESISTANT it is. Mere nonlinearity isn't the critical issue; you
can put a marble into any shape of bowl you like, and it's still
a marble in a bowl, not a control system.

It would be very helpful if you could think of a different
example, one that we could actually analyze.

ยทยทยท

---------------------------------------------------------------
Best,

Bill P.

[Martin Taylor 931221 11:00]
(Bill Powers 931220.1830)

Ok, we seem to have got off top dead centre, and maybe we are going somewhere.
I'll try to be brief, too.

You say, "No perception, no perceptual control." I have probably
never said this crucial statement out loud, but I am saying it
now: a perception is a representation of an external variable
DERIVED BY A MEANS THAT DOES NOT AFFECT THE EXTERNAL VARIABLE.

I think the key is not what you capitalize, but the words "representation
of an external variable." What the simple negative feedback system
(whether a votex be one or not) lacks is an external variable. It has
no inside and outside. One could construct an artificial negative feedback
loop in which an observer could identify an inside and an outside, but
I think it would be a very determined observer who could find an inside
and outside are in a natural self-organized system.

If there is no outside, there is no external variable, and no internal
"representation," no "perceptual signal," no PERCEPTUAL control. It might
be argued that a contrived negative feedback system with lumped components
--environmental variable, perceptual sensor-transform, and amplifier--
is a control system, though I would raise a mild objection to doing so.
I don't think it can be argued that a self-organized system with no such
separation of components, and more importantly of signal paths, can be
so labelled, no matter what the gain in its feedback loop.

Your capitalized line is excessive as written. I should like to replace
it with something like:

"derived by a means that has substantially less effect on the external
variable than does the control output."

But that formulation ties the nature of perception immediately to the
construct of control. This may not be a bad thing. Consider the
alternative. In the absence of control, all there is "inside" the system
is a signal. The system has nothing to indicate where this signal comes
from, and assuming that the signal derives from some interaction involving
an "external" variable, there is nothing to indicate whether the "observing"
interaction destroyed the thing observed. Passive observation can provide
statistical regularities of the things observed, but it cannot determine
the degree to which those regularities are a property of the observation
process itself, the effects of the observation process on the things
observed, or the "unaffected" properties of the things observed.

Only if one includes the "thing observed" as an element in a control loop,
and is able to control the corresponding perceptual signal, can one determine
that the observation process is not materially affecting the thing observed.
"Materially affecting" here means "in comparison with the effect of the
control actions," and "one" could mean either an external observer or a
monitor of only the internal states of the control system.

I think I
told you of my calculation: the energy in the light used to
observe a moving finger is something like 10^-18 of the energy
required to move the finger, in ballpark numbers. In general this
is true of all controlled variables. Sensing the state of the
controlled variable has no effect on the controlled variable.
This is many orders of magnitude different from the energy levels
involved in the "feedback" in a vortex.

"No effect" is too strong. But the "many order of magnitude" is quite
right. Over four billion years of evolution, control systems have evolved
to maximize their ability to control, which includes minimizing the
effect of sensing on the thing controlled. Nevertheless, some sensing
mechanisms do require "tangible" effects on the thing perceived (I use
quotes because I am thinking of touch in particular). It has happened
that people have broken delicate things trying to feel their surface and
bulk properties. Control is lost, because the effects of sensing on the
thing acted upon are of the same order of magnitude as the output actions
would be.

The way I see it, a self-organized structure was the start of the evolution
toward life. It wasn't what I would like to call a "control system," but
it was a negative feedback system. It had no inside and outside, no
representation of external variables. It just existed until a disturbance
came along that took enough energy from it to shift the flow into some other
structure (also self-organized). It didn't take much of a disturbance to
kill such a structure. At some point, a complex enough structure came
about by chance that its effects on its local neighbourhood reduced the
disturbances that would otherwise have killed it ("oil on troubled waters"),
and that structure tended to last longer than others. Also, the existence
of this self-organized structure tended to generate others of its kind
in the same general neighbourhood, much as one vortex enhances the likelihood
of another in a downstream vortex train.

I wouldn't say that a disturbance-calming structure was a control system
either. But at some point one must have arisen that did more than simply
affecting the local environment in a way that reduced its disturbances. The
effect on the local environment simply begins to specify an "inside" and
an "outside." Control comes closer when a structure evolves in which
something in the structure itself alters as a response to something that
changes "outside," and that internal change causes a greater effect on
the thing "outside" that tends to bring the "inside" back to its original
state. Finally, I think by the relation I called "mutuality," heterogeneous
collections of such structures arise in which the internal changes are
themselves reflected in resisted changes in the larger structure. A
control system has emerged with reference levels in the lower-level
structures set by resisted changes in the higher-level structure.

The upper level in the organized complex is not what I would call a
"control system," though the two-level system as a whole IS a hierarchic
control system. The upper level is a simple dynamically stable structure,
whose stability is engendered by negative feedback. And so it remains
today in all living systems.

Didn't we talk about all this a couple of years ago?

You bring up use of the Test in situations like that of the
vortex. In fact, applying the Test is impossible, as far as I can
see. The basic procedure is to calculate the effect that a
disturbing variable would have on the proposed controlled
variable _in the absence of feedback control_, using only
physical principles. Then you apply the disturbance, and measure
the actual effect. How do you calculate the effect that the
disturbance would have had on the vortex if there had been no
negative feedback?

I suggested applying a mild jet of water oriented circunferentially
at some point near the drain rim. It should be easy to compute the
expected change in lateral momentum of the water directly affected
by the jet if there were no feedback from effects around the drain rim.

One of the consequences of true feedback control is that the
operation of a control system is almost entirely insensitive to
variations in its own power supply.

This is true only if the power supply is strong enough. It ties in with
Gain. If the gain is low, the action of the control system does vary
with changes in gain. If it is high, even quite large proportional
changes in gain have negligible effects. Gain is limited--or at least
the power to affect the environmental variable is limited--by the power
supply. If you have enough power, it doesn't matter how much more you
have, but if you don't, every little bit extra gives you the possibility
of better control. Your amplifier can output only as much as the power
source gives it.

In the vortex, the size, spin rate, and flow rate are determined
directly by the power supply. The greater the head, the faster
the vortex spins, the greater its size, and the greater the flow
rate. Nothing is stabilized against changes in the amount of
incoming energy. The vortex seems to lack major aspects of the
control system's ability to control. It is created by an external
force; it does not create that force.

I guess you still miss the point here. The shape of the vortex is determined
directly by the energy flow (among other things). But the energy flow
that does this determination is not the _modulation_ energy that is
always the signal in a control system. The modulation energy is what
counts. Ask Does a small disturbance get countered by a larger output
modulation? Not Does changing the carrier energy change the enviromental
variable?

The whole point about ALL self-organized systems is that they are created
by energy flows and are aspects of those flows. It is their structure, not
their content, that matters. We interchange most of our atoms with our
enviroment many times over our lives, but "we" are our structures, not our
atoms, so "we" survive the interchange. We would not survive a factor of two
change in the sun's output. Neither would the vortex (probably) survive
a factor of two change in the flow rate.

It would be very helpful if you could think of a different
example, one that we could actually analyze.

I agree. I'll see if I can. But all nonlinear systems are hard
to analyze, and nonlinearity is crucial, as are far from equilibrium
conditions, in the development of a self-organized structure. As you say:

you can put a marble into any shape of bowl you like, and it's still
a marble in a bowl, not a control system.

And it isn't a self-organized structure, either.

Martin