[From Bill Powers (920709.2000)]
Bruce Nevin (920709.0913) --
I haven't responded to one of your (somewhat rare) posts recently. Mostly
just because I agree with you, so with no error signal ... but don't take
that for a blanket endorsement!
I am imagining such a distributed reorganization system. It seems to
parallel the perceptual control hierarchy by virtue of pervading it.
This is a good starting point. As we take off from it, I'd like to restate
a ground-rule that I try to adhere to in talking about reorganization.
It is that reorganization can't use any facility that develops out of
reorganization. By this I mean that the processes behind reorganization
themselves can't make use of knowledge about the outside world at any
level, from kinesthetic to cognitive. This may turn out to be too
restrictive a demand, but in my mind answers to the basic questions about
reorganization must apply from the beginning of an individual's life,
before the hierarchy has been significantly elaborated. And implicit in
this view is the idea that the reorganizing system operates in the same way
throughout an individual's life.
Suggestions of how this might work are in the discussion of the origins
of life. Feedback loops between molecules and between cells does not
go away with the advent of nervous systems implementing control systems
as we usually discuss them. It seems extremely likely that they are
ongoing in parallel with such higher "orders" (as distinct from
"levels") of control.
Agree. With respect to the genetic-level control systems, my favorite
example is the repair enzymes, a product of DNA that continually restores
DNA to conform with some built-in reference pattern. This is just one of
many mechanisms that renders the organism relatively immune to externally-
induced mutations. In my proposals about the origin of life, the same
organization in a much less elaborate form existed from the beginning --
and as you say, it is still here, working away at the most basic
biochemical level. It's a complex control system, perhaps even a
hierarchical one -- but it's not a reorganizing system.
In particular, the kinds of feedback relations
whereby cells take their "voluntary" places in colonies, or within
fungi, or within various orders of plants, or within animals of
increasing complexity, are probably the same kinds of feedback
relations whereby they do so in the embryology and development of
multicellular organisms, and persist in "vegetative" functions that
preserve systemic integrity--what we call intrinsic error.
Excellent thought. PCT, it seems, suggests a whole new approach to
philogeny, cladistics, or what have you. Control supplies a theme that runs
through evolution and in fact shows its direction (Stephen J. Gould would
be horrified). And the principle of reorganization may offer a parallel
theme: the emergence of systematic control from nonsystematic control.
Perhaps repeated at many levels (orders?).
More specifically, it seems likely to me that the cooperating cells
constitutine each ECS can reorganize themselves so as to reduce or
increase something in their environment, such as neuropeptides.
Please elaborate on neuropeptides -- is this a generic term, or a specific
substance? What do they do? What makes them? Are you speaking of
neurotransmitters in general? Are these proteins with specific functions?
That chronic error in an ECS might result in increased production >and/or
release of neuropeptides, with an influence on the cells of >neighboring
ECSs; might result in chemical or even neural signals that >influence the
number, location, or sensitivity of receptor sites >associated with ECSs
that are neurally connected but not physically >close enough to be
"neighboring" in the same sense. And so on.
I've proposed previously that cell differentiation and the "turning off" of
genes could be a simple control process in cells sharing a common
environment. Imagine a set of cells all of which contain a gene that
specifies a reference level for some substance in the shared environment.
Imagine that there is a spread in the natural reference signals. At first,
all cells experience a deficit of that substance, and all therefore begin
creating it. As more and more cells appear through continuing stages of
cell division, the controlled substance (no puns please) will eventually be
brought to the reference level by the action of all the tiny control
systems controlling for a specific concentration of that substance. No one
control system can maintain the required concentration, but many working
independently and in parallel can.
Eventually the concentration will reach the level specified by cells with
the lowest reference settings. As the number of cells increases, that
concentration will exceed those lowest reference settings, and those cells
will cease to produce a contribution to the total concentration.
Equilibrium will occur when there are just enough cells with the highest
reference settings to produce enough of the substance to shut down all
control systems with a lower reference level, and leave a steady-state
population of cells with the highest reference levels just maintaining a
steady concentration of the substance in question. These are one-way
control systems; errors represent only deficits. Therefore there is no
conflict.
Under the usual cause-effect interpretation, the genes responsible for
producing the substance are "programmed" to "turn off" in some cells. The
PCT version of this explanation is that the genes remain as "active" as
ever, but feedback effects from the general concentration of the substance
are higher than the reference level, making the error go negative. As a
negative output is not possible, these control systems are effectively
turned off. There probably isn't any serious difference between this
interpretation and observations -- "repressor" enzymes are known, for
example, which we would interpret simply as perceptual signals with a
negative feedback connection.
My point is that there can appear to be coordinated actions and even
appportionment of functions among systems of the same level without, in
fact, any superordinate coordinating system existing. Your comment above is
on the same track as my thinking.
The existence of non-neural inter-cellular communication and >cooperation
as a mechanism for reorganization does not preclude other >mechanisms for
reorganization operating in parallel.
I agree ... however, I would not call what I just described above
"reorganization." The reason is that it can be accounted for entirely in
terms of the normal operation of control systems of the normal type. At a
given level of organization, cells containing multiple copies of the same
control systems will automatically divide the labor between them: those
with the highest reference levels for a given substance will end up
maintaining a specific concentration of that substance for ALL the cells.
If you think there are parallels between this principle and the
organization of social systems, so do I.
I think we have to use the concept of reorganization sparingly; it can too
easily become a catch-all for unsolved problems of every kind. I would like
to see as much of the growth of the organism as possible, and as much of
the behavioral hierarchy as possible, accounted for by normal interactions
among normal control systems. So I'm not in favor of ...
For example, the input function I of an ECS may reject one candidate
signal i_1 (or reduce its value) because other signals are not present >to
complement i_1 and so the input requirement of I is not met.
This is similar to a suggestion of Martin Taylor's that I also rejected,
and for the same reason. You're proposing a very complex "E"CS, and I
believe we should resist complexities until observations force us into
accepting them because we can see no alternative. We haven't reached that
point yet; we haven't proven that the normal operation of the hierarchy,
and a SIMPLE principle of reorganization, won't solve the problem. And we
may not be ready for such a proof for a very long time (I have no doubt
that it will be forthcoming).
A serious problem is that the neural signals would somehow have to be
interpreted in terms of the meaning they will be given in the new ECS, so
"complementarity" could be detected despite the fact that all neural
signals are basically alike -- just magnitudes.
In order to model what you propose, we would have to show functions in the
model that could detect input signals and judge their complementarity
WITHOUT combining them in the normal way. Then other functions would have
to be provided that convert this judgment about the potential input signals
into a process you call "rejection," which itself might be difficult to
embody in a model.
Even if you could draw such an elaborated diagram of a CCS (complex control
system), you might have problems with stating what a model based on such a
diagram would actually do, using only the rules you have put into it. You
can't just point to the function you want accomplished as proof, until you
can show that the presented model will actually behave in the imagined way.
We understand quite well how an ECS works, given a black box to accomplish
its input function. We can simulate such systems and discover what such a
system will do, even if the input function is too complex to represent
analytically or in any detail. but we know little about more complex
systems.
Most of the basic rules of thumb of PCT and HPCT are based on known and
demonstrated properties of simple control systems. If we start elaborating
on the simplest organization, we must go very slowly and take small steps,
because at every step we have to re-analyze the whole control system to
find out how our changes and additions have changed its basic properties.
Even the most innocuous change could alter the properties we are familiar
with beyond recognition. The only way to handle this is to introduce small
changes and re-do the analysis and simulations each time to find out
whether we have actually made a qualitative change in the system -- whether
we have created something with radically different rules of behavior. This
isn't the sort of thing that can be done every day or every month --
perhaps not even every year.
... what I understand of reorganization is that it is probably not
control either, but rather influence, exerting (strong) selective
"pressure" as the cells of ECSs "in distress" try different changes in
various aspects of their structure and function that they can change >...
Reorganization IS control: it uses, however, a unique kind of primitive
output function, which acts at random but at variable intervals. The result
is to bring a controlled variable to a reference level, the same result we
get from any control system. The list of functions possibly subject to
these random effects,
Gain
Weights on various signals in input and output functions
Location, number, and activity of neuropeptide receptor sites
Input function "requesting" an imagined signal to complement
existing input signals--could lead to changed reference
signals higher up if error is reduced in imagination
Neural connections with other ECSs
... is a good one, subject to preceding quibbles. What we have yet to
demonstrate is that random variations in such parameters can actually
result in organized semi-permanent systematic control systems.
In fact, none of your concepts amounts to a model yet, but all of them are
good candidates for the primordial soup of concepts from which we will
eventually evolve a more competent model. These are all things we must try
out in simulation.
... can one cell truly control another (in
the same intra-cellular terms in which a cell controls itself)?
Control systems control variables, not things. Your question thus really
asks, can a control system in one cell control a variable inside another
cell? And I think that pretty much answers itself: not if the same variable
is already under control in the other cell. It doesn't seem likely that a
chemical messenger representing a variable inside one cell membrane could
flow freely out of that cell and into a different one to provide a
perception of the controlled variable, nor that an output signal from one
cell could travel equally freely in the other direction.
Does the specialization of cells for cooperating functions have a
parallel in human differences of temperament, talent, etc., as well as >in
educative specialization for social function?
See comment a couple of pages ago.
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RE: modeling reorganization
A preliminary report, especially to Martin Taylor who has begun making some
noises about actually doing some joint simulation research on this subject.
I have been playing with reorganization as a way of solving a system of
linear equations:
y[m] = SUM(a[m,n]*x[n]) where m = n in all cases.
I actually started with the inverse problem: given a set of inputs x1..xn,
and a set of outputs y1..ym, with m = n, find the matrix of coefficients
a[m,n] that will satisfy all m equations. So this is like perceptual
learning.
The basis for reorganization is the sum of squared errors between r[m] and
y[m], where r[m] is the desired set of values of the functions, and y[m] is
the actual set of values for any given set of coefficients a[m,n]. The
vector x[n] is a fixed list of n numbers.
To reproduce the E. coli method, it's necessary to define a direction in m-
dimensional space, using an auxiliary matrix delta[m,n]. The entries in the
delta matrix are changed independently and at random between positive and
negative limits, to create a "tumble." The matrix is normalized so the sum
of its entries, squared, is 1. This makes the entries into direction
cosines in m-dimensional space. A constant times delta[m,n] is added to the
coefficient matrix a[m,n] on each iteration. "Tumbles," however, occur at
intervals determined by the error signal. Between tumbles, the hyperspace
point a[m][n] moves at a constant velocity (actually, this works best if
this velocity depends on the magnitude of error).
Also, instead of using the error (squared) itself, it's necessary to use
the time rate of change of error as the controlled variable. The interval
between reorganizations of the delta matrix is proportional to the negative
time rate of change of the squared error: the more rapidly the error is
decreasing, the greater is the number of iterations before the next
"tumble." When the error increases, there is a "tumble" on every iteration.
So the loop gain is set quite high -- maybe too high.
With 10 equations in 10 variables, the required matrix emerges after
somewhere between 2500 and 10000 iterations, and perhaps 1/10 that many
reorganizations. The RMS error between the target vector r[m] and the
actual-value vector y[m] is then about 0.001 of the initial error; the
numbers r[m] and y[m] agree to one part in 1000 of the maximum or better.
With m and n equal to 50, convergence occurs, but I haven't run it to
completion -- doing so would take days. This is NOT a parallel computer.
Interestingly, the rate of convergence per iteration with 50 dimensions is
not dramatically slower than that with 10 dimensions, given adjustment of
parameters for best performance. It's just that each iteration takes a LOT
longer with 50 than with 10 equations (with 50 equations, the delta[m,n]
matrix involves 2500 random changes per iteration).
I've already learned some things about this method of reorganization. The
best indicator for triggering tumbles is time rate of change of the error.
The variables being randomly altered must be changed not directly, but by
randomly choosing the rate at which they are altered on each iteration. The
delta matrix effectively creates movement in hyperspace at a constant
velocity or a velocity that decreases systematically with error, with only
the direction being altered at random when there is a reorganization event.
I think I can see now that directly varying the output values (in the
a[m,n] matrix) at random would not lead to systematic approach to a
solution, nor would simply using the magnitude of the error rather than its
rate of change. I don't know that for certain, but it seems likely.
I've tried using the squared error, the RMS error, and the mean error as
the basic error measure, and a constant velocity or a velocity that depends
on linear or squared error. Everything tried works, although convergence
rate is affected. Testing is so slow that I haven't really compared the
different possibilities in any useful way, nor have I found any way of
optimizing things like gain and step size. I'm sure that someone with a
better grasp of n-dimensional mathematics and probability than I have could
derive the optimum settings without all this experimentation.
I've also done one test in which complete control systems were used for
each of 10 dimensions. The result converges. But I haven't tested yet with
randomly varying reference signals. Neither have I set up any intrinsic
variables (other than the error signal itself) which are affected variously
by the controlled variables x[n], so that reorganization is based on an
indirect effect of the controlled variables. It turns out that there is an
enormous number of possibilities and variants to investigate; getting to
them all will take some time.
I hope to make a little more progress on this before the meeting. I have to
go to Boulder and Denver next week (a talk on What is Information, a panel
at the meeting of the International Society for Systems Science, into which
I was sweet-talked by Peter Corning -- I'll have a copy of my remarks for
distribution at the meeting and will put it on the net, too, afterward,
with permission from the ISSS). So I won't have a lot of time for this
until later in the summer, after the meeting.
One thing's sure: there's still a lot to learn about this process of
reorganization, even with simple linear systems. And it looks just as
powerful as I thought it would be.
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Best to all,
Bill P.