# Understanding control (was Re: Cooperation)

[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
model works and how it applies to behavior.

``````  One thing Bill said from
``````

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.

``````Demonstrations and parametric model comparisons with observable
``````

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.

``````Even using the "neural current on a wire" simplification used in all
``````

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?

``````Then let's ask about the output function. In most demo studies the
``````

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.

``````The environmental feedback function has its own dynamics. Bill
``````

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?

``````I am deliberately expressing a little of the detail we don't know
``````

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.

``````There are general things one can say about control systems. For
``````

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.

``````One can say that if there is some kind of filter that smooths out
``````

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.

``````So, yes, I agree with Rick that one should at least work through the
``````

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
``````

[From Rick Marken (2014.12.10.1012)]

···

Martin Taylor (2014.12.09.23.05)–

``````  MT: One thing Bill said from
``````

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.

RM: I think algebra is one of the languages one has to be able to speak in order to understand the fundamentals of PCT. You do need calculus (or digital simulations) to understand the dynamics of control. But you can certainly understand the most important, fundamental aspects of PCT with little more than basic algebra (indeed, there was no more than basic algebra used in the presentation of PCT in B:CP).

RM But while I do think that algebra is essential for understanding basic PCT, it doesn’t doesn’t guarantee such understanding. Nor does a knowledge of more complex mathematics. The proof of this is in some recent papers I’ve seen, written by people who clearly are very skilled at dynamic analysis of control systems (using calculus) who get the mapping of the control model to the behavior being modeled all wrong – basically by putting the reference signal outside the system. So some math skill is necessary but not sufficient for understanding PCT. You still have to be able to understand how the math relates to the behavior under study.

``````MT: Even using the "neural current on a wire" simplification used in all
``````

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?

RM: I think you already answered this yourself: by doing high-precision experimentation. That’s what PCT research should be about. But I believe non-researchers can understand the essentials of PCT with little more than a basic knowledge of algebra.

Best

Rick

``````Then let's ask about the output function. In most demo studies the
``````

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.

``````The environmental feedback function has its own dynamics. Bill
``````

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?

``````I am deliberately expressing a little of the detail we don't know
``````

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.

``````There are general things one can say about control systems. For
``````

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.

``````One can say that if there is some kind of filter that smooths out
``````

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.

``````So, yes, I agree with Rick that one should at least work through the
``````

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
``````

Richard S. Marken, Ph.D.
Author of Doing Research on Purpose.
Now available from Amazon or Barnes & Noble

In nature there’s no blemish but the mind

None can be called deformed but the unkind.

Shakespeare, Twelfth Night

[Martin Taylor 2014.12 10.13.25]

``````There is a whole spectrum of levels and kinds of understanding of
``````

PCT. One can get a basic understanding without even algebra, a
better understanding of at least tracking in a continuum with
algebra, and can compute the dynamic tracking behaviour of simple
linear complexes of control systems with no more than Laplace
Transforms. But, as Bill often said, nobody – not even he – can
look at a complicated control structure in a complex environment and
say what it will do. And as soon as you introduce non-linearities it
gets even harder to be correct in detail. For example, in a linear
system, conflict can lead to an exponential escalation, but with
non-linear error functions it might stabilize at a high level of
tension, oscillate, follow a chaotic trajectory, or even, if there
are tolerance zones, perhaps subside to zero. And we are talking
here only about simple tracking studies in one dimension. When you
deal in two dimensions being tracked simultaneously, things get more
hairy.
One of the hazards of detailed modelling is that one tends to become
wedded to a particular form of model. When I was trying to find a
good model to fit the massive dataset from the 1994 sleep study with
over 1000 different tracks, to see which parameters were affected by
sleep loss, I found two differently organized five-parameter models
that fitted better than the “standard model”, but were hardly
distinguishable from each other. (If you are interested, I reported
on this as CSG-2005, and the Powerpoint is at
.
I tried using non-linear functions, but I could not tell the
difference in fit unless I made the non-linearity extreme. In that
same study, we did some two-dimensional tracking runs at Tom
Bourbon’s suggestion, but Bill, who was helping me with the
analysis, did not know how to model it, so we excluded those tracks
from further consideration when reporting the work.
If one were to model systems with Bill’s Artificial Cerebellum as
the output function, I would expect the fit to be very good, because
the AC can incorporate many different possibilities using its large
number of degrees of freedom, but I would worry about whether this
meant that its structure was nearly right, or whether it was just
like any statistical “model” that “accounts for 75% of the variance”
in non-PCT experiments.
On the other hand, an intuition based on the idea of the control
hierarchy has been quite effective without algebra at the higher
perceptual levels. Quite so, though I’m not as convinced about the necessity of the
algebraic route to understanding. Different people learn in
different ways. Playing with demos might be enough for some people
that would get nothing but symbol dreams from working through the
algebra. But I do agree that it’s important to understand what one
loop does and what happens when you change gain and transport lag or
the dynamical characteristics of the environmental feedback path,
before trying to figure out the details of more complex structures.
Control is, at its most basic, a dynamic process, not a process in
which one awaits a stable, internally consistent, set of variable
values. So an intuition of how the bits move together is what one
has to achieve, and that’s something that simple algebra doesn’t
give you, no matter how useful it may be to many beginners.
Exactly so.
Martin

···

[From Rick Marken (2014.12.10.1012)]

``````            Martin Taylor
``````

(2014.12.09.23.05)–

``````              MT: One thing Bill said from
``````

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.

``````          RM: I think algebra is one of the languages one has to
``````

be able to speak in order to understand the fundamentals
of PCT. You do need calculus (or digital simulations) to
understand the dynamics of control. But you can certainly
understand the most important, fundamental aspects of PCT
with little more than basic algebra (indeed, there was no
more than basic algebra used in the presentation of PCT in
B:CP).

``````          RM But while I do think that algebra is essential for
``````

understanding basic PCT, it doesn’t doesn’t guarantee such
understanding. Nor does a knowledge of more complex
mathematics.

``````          The proof of this is in some recent papers I've seen,
``````

written by people who clearly are very skilled at dynamic
analysis of control systems (using calculus) who get the
mapping of the control model to the behavior being modeled
all wrong – basically by putting the reference signal
outside the system. So some math skill is necessary but
not sufficient for understanding PCT. You still have to be
able to understand how the math relates to the behavior
under study.