Chaos & Control

CSGnet Archive CSG1994
1

[Paul George 940727 1630]
A post I pulled from sci.econ thread that I thought might be interesting or
provoke discussion:

···

Subject: Re: Chaos and econ
From: Oliver Sparrow, ohgs@chatham.demon.co.uk
Date: Tue, 26 Jul 1994 08:17:03 +0000
In article <775210623snz@chatham.demon.co.uk> Oliver Sparrow,
ohgs@chatham.demon.co.uk writes:

The striking thing about economics is that it works at all: that regularities
emerge from a myriad of transactions, as pressure emerges as an active variable
from the thermodynamic rattling about of an equal myriad of molecules. We
adduce "rules" and try to capture these in equations. The equations
(abstractions of abstractions) are nonlinear and serially dependent, for the
most part; and can show chaotic behaviour. Actual time series in actual markets
show quasiperiodic chaotic structures from the deconvolution of which one can
make (used to be able to make) a great deal of money. All is fractal froth? Can
we know nothing?

Wrong, fortunately. Our dear old and forgotten friend, feedback, comes to the
rescue. One can see this - variously - as attractor basins, negative feedback,
learned or evolved adaptive homeostasis: but in many high level systems, there
are portions of the space which are, for their innate dynamics,
self-stabilizing. It is notable that highly stable self-governing engineering
systems are increasingly being written "at the edge of chaos", as dynamic
equilibria which are stable because of their self-correcting flexibility. What
we know of the control exerted on our own musculature suggests that the results
are obtained by a multi-perspective process of "voting" upon how to modify the
dynamics of a chaotic syste. One does not stand bolt upright: one sways,
imperceptibly, and your nervous system tweaks the dynamics such that the orbit
of your swaying stays within acceptable bounds. Many different bits of the
nervous system simultaneously do different (and sometimes antithetical) things
to bring this about, with no real co-ordination.

We learn economics on the basis that these feedback systems (supply, demand,
price) are givens, always true and always there. This is post hoc description
of the phenomena which we see about us and we tend to project this backward
onto the primitive markets which must once have existed. Cursory glances at how
the Eighteenth Century actually did commerce - or how the Mediterranean under
Rome was managed - suggest that quite different dynamics were at play,
including price clearing but a lot of odds and sods, chunks and lumps as well.
To call these imperfections is ex cathedra: what we have now *sees* them as
such, but who can say without a time machine? How, then, do "pure" but human
mediated feedback systems evolve and come to be?

Those who have written themselves a Mandelbrot dwell-time programme will recall
that one iterates a simple equation and counts how long it takes the numbers to
explode towards infinity. One colours that point in space with the
corresponding number of iterations, as a measure of its innate stability. Some
parts of the space (within the pseudocardiod) are usually coloured black, as
completely stable. One can iterate for ever. There is a fringe region, where
stability has a finite life time and there is outer colourfulness, where the
system shoots off to infinity almost immediately.

Consider: those social systems which are in the innner portion of what would,
for society at any one time, be the equivalent of the Mandelbrot set show
stability. Social systems which are at the fringe explode into instability. Run
the human condition (which is necessary for economies but not ecologies, to
which the same thoughts apply) and see what is left after a time has passed. If
societies remember and learn from each other, then the rules which keep us out
of the assymptotic regions will have been learned: they will be embedded as
natural truths, as they are embedded in the genes from which ecologies emerge.

Social systems are, therefore, the outcome of something like a genetic
algortihm and they carry "genes" - implicit ways of organising things
(ownership, value, contract, arbitration, law) - which keep them within stable
bounds. (Dawkins ideas of 'memes' have something in common with this.)
Occasionally, societies move outside of the stable region and we get Ruanda:
assymptotic change. The genes have learned to keep chaotic dynamics
under control and we live thereby. What we call "economics" is a small zone in
a huge and unfriendly space: it works, but only - and self-referentially -
because it works.
_________________________________________________

  Oliver Sparrow
  ohgs@chatham.demon.co.uk

-----------
As a note, Dawkinns mneme theory might have some implications as to how control
systems reorganize as a result of perceptions (at levels 7-8), particularly
those 'caused' by another organizm's perceptions. Chaos theory might also
provide some mechanisms for the 'randomness' yet success of the reorganization
process. I really don't have the math to evaluate this in detail.

{More meat for the pirannahs, sharks, or wolves :-)}

2

[Martin Taylor 940728 17:30]

Paul George 940727 1630

Chaos theory might also
provide some mechanisms for the 'randomness' yet success of the reorganization
process.

This isn't about chaos theory, but it is related. In chaos theory there
is a concept of "self-organized criticality" which in systems of special
kinds describes the result of a mechanism that maintains the system between
stability and chaos. I think that a living control hierarchy is such
a special kind of system.

There is a construct that I have called "The Bomb in the hierarchy" that
suggests that reorganization almost always (in the mathematical sense)
leads to a self-organized critical structure. It was discussed on the
net a year or more ago.

The Bomb works like this. Most, if not all, Elementary Control Units (ECUs,
a term we at DCIEM have come to prefer over ECSs) receive signals at their
perceptual inputs (i.e. sensory signals) from several sources, and their
outputs are distributed to contribute to the reference signals of several
lower ECUs.

The sources of the sensory signals are the perceptual signals of lower ECUs,
quite probably the same ones to which the outputs are distributed. In effect,
the link between an ECU and its correponding CEV goes through several parallel
paths whose effects combine (on output) at the CEV and (on input) at the
Perceptual Input Function.

Reorganization ensures that the overall control loop does not have a positive
gain, but it does not ensure that the same holds for each of the parallel
paths. Some might be having effects on the CEV that would push the
controlled perception in a direction to increase the error, but those are
weaker than the effects of the paths that decrease the error, so overall,
the gain is always negative for each loop in a properly reorganized hierarchy.

But the world changes. A door that was always previously open may be locked.
A road may become icy. And when some path that contributed to the negative
going effects is blocked, a hitherto suppressed path that has the opposite
effect might become dominant, turning the whole control loop into a positive
feedback condition. Bad stuff!!

Control loops, even ones that saturate, can't stay in a positive feedback
condition for long. Reorganization tends to step in and change either
what is perceived or the signs or connections of the output linkages. This
continues until the control loop again is stable, exhibiting negative
feedback under the new environmental conditions.

But consider what might be happening at higher levels while the control loop
we are considering has shifted from negative feedback (control) to positive
feedback (runaway). It is a contributor to control at higher levels, and
they have lost the benefit of its control in the part of their control loops
to which it contributes. One or more of those higher-level loops might as
a consequence go into a positive feedback state, also inducing reorganization.

This "triggering" effect of low-level runaway on higher-level control could
avalanche, or it might stop with the first runaway control system.
Reorganization will act only until the hierarchy is stable under the new
environmental conditions. It doesn't optimize. It just ensures that
all the control loops are stable NOW. When the environment changes again,
some other control loop might become unstable, leading to another possible
avalanche. Reorganization stops when the avalanche stops, just as the
sand-dune becomes stable after one or a billion grains of sand has moved
downslope enough for the slope to become just shallow enough for the
movement to stop.

As with a sand-dune avalanche, the head of the avalanche can also move
upstream (i.e. down to lower levels of the hierarchy), as the original
loop that went into positive feedback might send the reference levels for
lower systems out of the range that they can attain for their perceptual
signals. They are less likely to go into a regime of positive feedback,
but since they are nonlinear systems, it is possible. On the whole, though,
I think that for a mature hierarchy, this movement of the avalanche-head
is probably not something to worry about.

The Bomb is manifest in temporary bursts of maladaptive behaviour, such as
temper tantrums when something that "should" happen doesn't. It may be
manifest more strongly when a hierarchy that has not been severely disturbed
in its growing period is put under stress.

I think that the Bomb is the main factor that affects the development of a
living control hierarchy.

Martin

3

<[Bill Leach 940730.08:16 EST(EDT)]

[Paul George 940729 10:30]

... If the canonical HPC model does not permit the perception of error
signals or of output by 'parent' or 'sibling' nodes, how
does the system detect a reunaway or positive feedback situation? ...

First, the 'sibling' nodes definately do receive error signals or outputs
from higherly level nodes as that is where their references come from.

I don't believe that much has been done with the mechanics of the
"reorganizing system's" mechanics. I think that it is safe to say that
the PCT view is that somehow the reorganizing system does sense the error
signals. I believe that it is doubtful that the reorganizing system
senses the errors in a very direct way.

For example, sustained errors may result in some portion of the loop
releasing certain chemicals, the presence of which are indicative of the
condition (and possibly the general physical location of the loop having
the error).

This may relate to the thread on information theory. ...
..., the system must be able to at least deduce the 'effect' of actions
on perceptions, as well as deduce thing and interactions in the
environment not currently perceived. ...

In the first part of this statement, exactly what you mean could be
critical. In the sense that I think you mean, I take exception to your
assertion.

That is, the system does not "deduce the effect" of its own actions to
effect control. We as rather high level controls systems attempt such a
thing all the time but ALL of the perceptions concerning such a
'deduction' come from somewhere besides the control loop that is
effecting control.

A major part of the IT discussion centers (I think) upon the idea that
the organism can sense anything about a disturbance to an environmental
parameter that is perceived and in a state of good control.

I maintain (and I believe that Bill and Rick agree) that the organism
DOES NOT sense anything about the disturbance from the perceptual signal
of the control loop as long as control is good. (I also believe that
Martin agrees with this idea too).

Now where I do agree with Martin (at least in part) is that AN OUTSIDE
OBSERVER with access to the perceptual signal from within another
organism's control loop could determine some effects caused by the
disturbance WITH some additional information beyond the perceptual signal
itself.

Where I think that I disagree with Martin is 1) what constitutes
additional information and 2) whether this idea is currently of any value
to PCT.

I think that you identify an important idea in this whole discussion
with:

The relationships between A, B, & C are deduced by observation of their
'behavior' over time and generalization.

This is certainly true but takes place independently of the control loop
that did or is controlling "A".

Often this may require perception of a number of other variables.

And this is most definately true and is important because we often think
that we are correctly analyzing "what is going on" without necessarily
realizing that the perceptions that we are using for such an analysis are
not the perceptions that we are controlling. That is if I understand PCT
and indeed control theory itself, you can not determine the state or
condition of a disturbance using the perception of the environmental
parameter that is being disturbed if you are also controlling that
perception.

A difficulty (I think) concerning this whole issue stems from "common
sense" perceptions in ordinary experience of us all. In any control
situation in which we are conscious of our own control actions, we have
many uncontrolled perceptions available for input including various means
of observing physical movements of our own bodies. It is easy to
"conclude" that we do "perceive" the effects of a disturbance from the
control loop. I would say that it goes something like this:

We know that we are controlling something. Via uncontrolled perceptions
we observe the effects of disturbances upon the environment as well as
our own "counter actions". Thus, we can "perceive" effects of a
disturbance from our controlled perception.

It is that last step that is incorrect. We most definately can sometimes
perceive things about our control and about interference with that
control but as long as the control loop is actually controlling, such
'conclusions' are based upon other perceptions.

Most engineered control systems have perceptions associated directly with
system output that are used for additional control decisions. I don't
think that PCT exactly excludes such connections but the situation is
more of one that maintains that assuming such connections should be based
upon demonstration that either the connections physically exist or model
behavioural compliance requires such.

Since at this point in the infant science, no behaviour has been
demonstrated that would require the additional connection nor has the
model needed such a connection then why add it?

This idea rides right in there with Martin's Alerting phenomenon.
Discussion of such ideas and even trying to challenge the canonical model
is very worthwhile. These concepts are "important" to PCT if only
because there is such a strong belief that they do require "something
beyond" the current PCT model.

Whether Martin ever convinces any of the other PCTers or they him is in
many ways not too important to PCT itself. The theory gains by the
attempting no matter "who wins" as long as rational scientific
methodology is maintained. If Martin demonstrates that the behaviour
tagged as "Alerting" phenomenon is such that the model actually can not
encompass the behaviour then the model will be forced to evolve (and thus
improve). The operative phrase there however is "demonstrate" and in an
exacting science that is anything but easy.

-bill

4

[Martin Taylor 940730 11:40]

Paul George 940729 10:30

[Martin Taylor 940728 17:30]
Control loops, even ones that saturate, can't stay in a positive feedback
condition for long. Reorganization tends to step in and change either
what is perceived or the signs or connections of the output linkages. This
continues until the control loop again is stable, exhibiting negative
feedback under the new environmental conditions.

A question about the mechanism (forgive if it is covered in the basic
liturature, I've been working). If the canonical HPC model does not permit the
perception of error signals or of outputs by 'parent' or 'sibling' nodes, how
does the system detect a runaway or positive feedback situation?

When you get to the parts about reorganization, you will see that the
reorganization mechanism is separate from the main control hierarchy. It
affects the structure of the hierarchy directly, and in some respects
randomly. It acts with a probability that depends on the control of
"intrinsic variables" that are not accessible to the sensors of the main
control hierarchy. "Intrinsic variables" are presumed to be genetically
determined and have genetically determined reference levels. Many of them
are chemical states, rates, or levels, but one thing often taken to be
an intrinsic variable is a kind of globalized estimator of error in the
perceptual control hierarchy. We are using in our simulation a weighted
sum of the squared error and the derivative of the squared error over
one or more ECUs (the "one or more" qualifier means that the sum might
be taken over as much as the whole network, or it might be separately
performed over overlapping or separated modules as small as one ECU).

This sum is high for as long as the error is large and not decreasing,
or when it is increasing rapidly though possibly not (yet) large. It
handles situations in which the action of the control loop is resisted
by the environment (as in cases of conflict--try something different) and
cases in which the feedback loop has a positive gain (whoops! don't do that!).

The perceptual control hierarchy is not thought to have access directly
to the error signals, but the reorganizing control hierarchy does.

Martin

5

[Paul George 940801 10:00]

[Bill Leach 940730.08:16 EST(EDT)]

First, the 'sibling' nodes definately do receive error signals or outputs
from higherly level nodes as that is where their references come from.

I meant sibling to sibling or sibling to parent. Parents clearly send error
signals, or more accurately output signals, to affect the child's reference
values.

That is, the system does not "deduce the effect" of its own actions to
effect control. We as rather high level controls systems attempt such a
thing all the time but ALL of the perceptions concerning such a
'deduction' come from somewhere besides the control loop that is
effecting control.....
We most definately can sometimes perceive things about our control and about
interference with that control but as long as the control loop is actually
controlling, such 'conclusions' are based upon other perceptions

Granted. In reading your latest posts of the info theory thread I see I
misinterpreted your thrust. A given control loop does not detect output or
error, but 'higher' or possibly lateral(sibling) nodes may.

The canonical model I was referring to was a HPC system composed of the
canonical loops. By 'system' I meant the organism or a set of loops at levels
6-8+. Clearly we can have internal associations between actions (i.e. sets of
control loops which may be activated) and some delta to perceptions (controlled
or otherwise). Otherwise we could not define the level 7 sequences or change
the active loops when one 'method' of control was ineffective (i.e. changing
the gain of the loops)

I think the real point, judgeing from the B:CP discussion, is that we don't
know how reorginization works, but we know that it apparently does occur and is
needed for adaptive behavior and learning. Further, anthing above level 3 or 4
is basically speculation. To date PCT has focused on modeling the lower levels
to make sure the underpinning is sound.

Paul

6

[Paul George 940801 10:00]

[Bill Leach 940730.08:16 EST(EDT)]

First, the 'sibling' nodes definately do receive error signals or outputs
from higherly level nodes as that is where their references come from.

I meant sibling to sibling or sibling to parent. Parents clearly send error
signals, or more accurately output signals, to affect the child's reference
values.

That is, the system does not "deduce the effect" of its own actions to
effect control. We as rather high level controls systems attempt such a
thing all the time but ALL of the perceptions concerning such a
'deduction' come from somewhere besides the control loop that is
effecting control.....
We most definately can sometimes perceive things about our control and about
interference with that control but as long as the control loop is actually
controlling, such 'conclusions' are based upon other perceptions

Granted. In reading your latest posts of the info theory thread I see I
misinterpreted your thrust. A given control loop does not detect output or
error, but 'higher' or possibly lateral(sibling) nodes may.

The canonical model I was referring to was a HPC system composed of the
canonical loops. By 'system' I meant the organism or a set of loops at levels
6-8+. Clearly we can have internal associations between actions (i.e. sets of
control loops which may be activated) and some delta to perceptions (controlled
or otherwise). Otherwise we could not define the level 7 sequences or change
the active loops when one 'method' of control was ineffective (i.e. changing
the gain of the loops)

I think the real point, judgeing from the B:CP discussion, is that we don't
know how reorginization works, but we know that it apparently does occur and is
needed for adaptive behavior and learning. Further, anthing above level 3 or 4
is basically speculation. To date PCT has focused on modeling the lower levels
to make sure the underpinning is sound.

When you get to the parts about reorganization, you will see that the
reorganization mechanism is separate from the main control hierarchy. It
affects the structure of the hierarchy directly, and in some respects
randomly....
Many of them {intrinsic vars} are chemical states, rates, or levels, but one
thing often taken to be an intrinsic variable is a kind of globalized
estimator of error in the perceptual control hierarchy...
The perceptual control hierarchy is not thought to have access directly to the
error signals, but the reorganizing control hierarchy does....

I had read that part of B:CP, but thanks for the additional clarification on
the mechanism.
I guess I intellectually have a little problem with totally seperating (and
apparently ignoring most of the time) the meta-control system from the rest of
the control system. From my (ignorant) point of view they merely represent a
division of labor or an orthagonal control hierarchy (y=perceptual, x='span of
control', z=meta-control). Of course that may because I find adaptation,
learning, and the level 6-8 functions personally the most interesting.

Paul

7

Tom Bourbon [940802.1356]

[Paul George 940727 1630]
A post I pulled from sci.econ thread that I thought might be interesting or
provoke discussion:

Subject: Re: Chaos and econ
From: Oliver Sparrow, ohgs@chatham.demon.co.uk
Date: Tue, 26 Jul 1994 08:17:03 +0000
In article <775210623snz@chatham.demon.co.uk> Oliver Sparrow,
ohgs@chatham.demon.co.uk writes:

There followed a semi-coherent piece about economics, chaos, a "Mandelbrot
dwell-time programme," some examples the author thought illustrated
feedback, and other more or less randomly associated ideas.

Back to Paul George:

{More meat for the pirannahs, sharks, or wolves :-)}

This pirannaha isn't biting, Paul. I have a reference level of zero for
sensing my own participation in chaos-babble. Some other net, maybe -- one
where dynamic nonlinear sharks hang around. :wink:

Later,

Tom