[Martin Taylor 2014.12.09.23.05]

[From Rick Marken (2014.12.09.1930)

`RM: ... As I've`

said before, I think PCT is a discipline, like calculus,

that has to be learned. And the best way to learn PCT is by

reading the texts, running the models, and doing the demos. Like calculus, I think

one has to have a grasp of at least algebra to really

understand how the PCT model works. And like calculus, there

are right and wrong answers to questions about how the PCT

model works and how it applies to behavior.

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One thing Bill said from
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time to time was that when control systems become more than a

simple loop, it is often quite hard to intuit what they will do.

Algebra isn’t enough to understand anything much more than

steady-state, asymptotic, or near-equilibrium conditions in linear

systems. You need dynamic analysis, but to get closed-form

solutions for non-linear systems (which real biological systems

almost surely are) is next to impossible except in the simplest

cases. So, although, in principle, I support Rick in what he says

here, yet there is a lot of possible variation right at the

heart of PCT.

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Demonstrations and parametric model comparisons with observable
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behaviour are an approach that can help intuition, and Bill and

Rick, among others, have a lot of experience with them, but again

largely in very simple structures. So far as I know, Arm2 is the

largest set of parameters to have been reorganized by the e-coli

method, and we are dealing with tens rather than the millions or

trillions of weights in a human brain.

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Even using the "neural current on a wire" simplification used in all
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the diagrams, there are many largely unexplored directions of

variation for even a single control loop. For example, is there a

standard form of the output of a comparator as a function of (r-p)?

Is there normally a tolerance zone for which the output error is

zero for |r-p| small enough? Is the error output linear,

logarithmic, or even non-monotonic, with |r-p|? It takes

high-precision experimentation to distinguish these possibilities

with ordinary tracking studies (as I know from experience), and

although such questions have been raised, and non-linear errors with

a tolerance zone seem likely, how will we learn whether they occur

always, usually, often, or never in living systems?

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Then let's ask about the output function. In most demo studies the
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environmental feedback path that contains the output function has

been assumed to be linear, and the output function a simple linear

leaky integrator. But the real world contains its own integrators,

in the simplest case as when an output force only accelerates a

free-moving weight. Our friends who have been building real live

robots have had to consider this. The environmental feedback

function is almost always nonlinear, for example when static

friction has been overcome, the dynamic friction is less.

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The environmental feedback function has its own dynamics. Bill
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invented the Artificial Cerebellum, which could serve as a general

purpose output function that would adapt to a non-white

environmental feedback spectrum and quasi-periodic disturbances. Are

all output functions of this type? Do biological systems adapt to

ringing environmental feedback and periodical disturbances by using

some component of that kind? If so, how would we discover its

properties? By analyzing neuron maps, by modelling learning

behaviour in systems with non-white environmental feedback

functions? How would such a system interact with the non-linearity

of the error function, if it is nonlinear?

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I am deliberately expressing a little of the detail we don't know
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about biological control systems, and what basic models of even a

single simple control loop actually should be used in modelling, in

order to go to the opposite extreme, to say that all this might

matter in the end, but one can do a lot working with less precise

approaches, just as one can do high-school chemistry without being

able to solve the Schroedinger equation for a system.

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There are general things one can say about control systems. For
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example, loop transport lag determines how wide a bandwidth of

disturbance can be countered. No matter what happens in the

structure of the control loop, if adding the output to the

disturbance doesn’t reduce the variability of the perception,

control fails. If the transport lag is too long and the disturbance

changes unpredictably over that time span, the disturbance will have

changed too much for the output to counter. So, one expects evolved

control systems to be structured to minimize transport lags when

they are concerned with countering fast disturbances.

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One can say that if there is some kind of filter that smooths out
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fast disturbances before they influence the CEV that corresponds to

the controlled perception, control will be better than if the

disturbance comes through unfiltered. One can say that providing

more accurate perception (e.g. by using a microscope) one can

control more finely. There’s a lot one can say if one understands

the *principles* of control. Rick and others have designed

interfaces to equipment using these principles, but AFAIK not using

detailed mathematics. Kent has used both simple demonstrations and

the principles of control to theorize about the structures and

problems of society, which mathematically lie far outside the

legitimate range of extrapolation of the demos. The demos do,

however, suggest principles that seem as though they should apply,

and when they are applied, they seem to predict phenomena seen in

real societies.

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So, yes, I agree with Rick that one should at least work through the
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equations in their algebraic form, and if possible go further to see

how the dynamics of at least linear systems function. One should

study all of Bill’s and Rick’s (and anyone else’s) demonstrations.

One can get to understand control pretty well without doing those

things, I guess, but it’s an easy way to get into a position in

which one can reason in one’s own mind about what control might do

in different situations.

`Martin`