[From Bill Powers (940810.0930 MDT)]
Paul George (940809.1730)--
You make some good points, again. Obviously we all could have done
better in communicating PCT, had we known what kind of response we would
get from the mainstream. I was pretty naive: I thought that just
describing the model as clearly as I could would be enough!
I strongly agree with you about evangelical overstatements of the
accomplishments of PCT. There are many areas in which we have no actual
data about the worth of PCT as a useful model of behavior. We're working
on that, but I truly wish we could all remember to limit our claims to
what we can back up with demonstrations and data. There's nothing wrong
with extrapolations, as long as they're labelled as such. But touting
PCT as the One True Faith is a certain turnoff for any intelligent
person. I'm especially disturbed by claims that PCT is a "proven theory"
in areas where it is no such thing. If asked, I will disavow such
claims.
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Bill Leach (940809.0532 EDT) --
A minor problem that I see is that if both tension and position are
considered, when "dropping" ones arm to ones side then the question
comes up, why would this be accomplished by setting tension to zero but
maintaining the position reference? Seems to me that to control in
such a manner would create an unnecessarily large position error.
As I understand the position control systems, their error outputs become
the reference inputs to the muscle-length and tension control systems
(it's a hierarchy of control). All these systems (considering the nature
of neurons) have to be constructed as balanced sets of one-way control
systems. This means that turning off the position control systems by
setting the reference signals on BOTH sides to zero results in zero
error outputs on both sides, which sets the opposing reference signals
at the lower levels to zero, also on both sides. So the whole system
simply ceases to control, and your arm turns into a pendulum.
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Gary Cziko (940810.0425 GMT) --
I'm not sure what the advantages would be for genetic algorithm (GA)
users who use GAs to find a solution that will work in an unchanging
environment and then just use the solution.
What I have nasty suspicions about is whether these algorithms are
really being used in a defensible way. I'm being told that pure mutation
is not used much; that sexual crossovers are the main tool. What are the
elements that are shuffled around? Are they things like "genes for
turning left" or "genes for moving toward food?" In other words, is
there any reason at all to think that the genes being recombined are
actually capable of producing the results they are supposed to produce?
If you just start with a list of capabilities and shuffle them, you're
skipping over the part of the model that connects the capabilities to
the genes, and that, in my opinion, is the weak point of the model. I
would like to hear more from you or anyone else about the actual
assumptions used in GA models.
I recall that the co-discoverer of natural selection, Charles Russell
Wallace, had much the same objection to Darwin's use of "natural
selection" and recommended instead "survival of the fittest" to get
away from the idea that something external to the organisms (God,
Mother Nature) was doing the selecting.
Even more to the point would have been "survival of the survivors." To
me the critical assumption is the relationship between so-called fitness
and survival. If you think of the usual assumptions about what leads to
fitness -- health, strength, prudence, altruism, etc. -- it would seem
on objective assessment of rates of population growth in various parts
of the world that these have an inverse relationship to reproductive
success. There are certainly positive instances of various informal
concepts of factors leading to fitness, but it seems to me that negative
instances are rather swept under the rug: well, evolution moves in
mysterious ways. Even the child-spewing starving sickly poor of Africa
are, in some way which mere mortals are not permitted to understand,
more "fit" than the inhabitants of wealthy countries with near-zero
population growth.
PCT says that there is no way in which "behavior" can be inherited --
that is, actions which have particular effects. At best, we inherit
control systems, and perhaps a few modes of perception and reference
signals. The overt behavior we produce has to be variable in order that
regular consequences be achieved. So unless GA models are cast in terms
of genes for controlled perceptions and reference signals, it's hard to
see how they could describe real genetic effects. The fact that they
seem to do so suggests to the PCTer that somebody is cheating.
While I appreciate the meaning of Plotkin's remarks -- that crossover is
building on what works, while mutation introduces new possibilities --
the question still remains whether changes in the constitution of DNA
(however achieved) have a sufficiently high probability of leading to
greater survival to account for the evolutionary adaptations we see, on
the time scale that we see. It's just not logical to point to the
results of assuming the sufficiency as a proof of the sufficiency. There
is a HUGE gap between the level at which crossovers and mutations occur
and the level at which we see behaviors that bear on survival. I get the
feeling of being sold a parrot by Michael Palin.
Martin Taylor (940809.1700) --
RE: stealing thunder
To reinvent something is to invent it as if it had not been invented
before. I hoped that I had been careful enough everywhere to credit
you. Sorry if not ...
That's not my problem. In the BYTE articles I presented a working
simulation which behaves as I claimed the model would behave. That is
the only backing for statements about how one-way systems will work in
combination, so far. You are offering a smorgasbord of new arrangments
of one-way systems, without any proof that the behavior of these new
arrangements would be anything like what you claim it will be. In fact,
when I did a simulation of a case you said wouldn't work, I got
perfectly normal control behavior, showing that your pencil-and-paper
approach did not lead you to a correct description of what such a system
would actually do. I have doubts about most of your other descriptions,
too -- which you could easily and permanently allay by writing a
simulation that behaves exactly as you predict, for each case.
You can download Simcon 4.5 from Bill Silvert's server; it is included
in Dag's demo programs. I highly recommend that you obtain it and use it
to test your claims before you use them as the basis for even further
hypothetical developments.
What I thought you had been approving was the extension to N
dimensions, and the demonstration that the effective virtual control
system's control law was related to the derivative of the control law
of the contributing one-way systems (the difference between the
derivatives, in the case of an opposed colinear pair). If I remember,
I had asked you whether that relation had been demonstrated. You said
that it was true, but did not provide the proof. That was one thing I
provided, and what I thought you were asking for a couple of days ago.
If I agreed, I quite possibly didn't fully understand what I was
agreeing to. My intuition about how complex control arrangements will
actually work is no better than yours, without a simulation to show what
really happens. As I recall, you concluded that the loop gain of a
combined linear opposing pair would be zero, and that is certainly not
true. It's not even true in the conflicted case, as Kent McClelland
demonstrated at the CSG meeting last year: a pair of conflicted systems
can maintain control until one or the other output runs into a limit.
That is actually what I saw when I forgot to include the cross-
connection between the control systems, in the first simulation
(mentioned yesterday) that I did. The outputs became very large, but
control continued.
... is the output in each side related to the square of the error, or
just the linear error?
Just the linear error.
In the Byte article, so far as I can see, it is the linear error, and
when you oppose two linear control systems, nothing happens to the CEV.
Forget that conclusion that you drew last December. It is wrong. The
systems in the BYTE article were linear, too.
Something seems to be happening different from the setup we discussed
in December.
No, it's just that the conclusions drawn last December, whether I agreed
to them or not, were wrong.
I forgot the
cross-connections between the halves of the system, and got just a
plain old conflict.
One would get that, and no control, with linear opposed systems.
No, forget that conclusion, it is wrong. I got conflict, but I also got
control because the outputs did not limit.
If the output integrator had a reasonably short time-constant, it seems
to me (without simulating it) that the outputs should stabilize at a
fixed level in maintaining their individual errors at the right
magnitude to bring the perception to the reference level that is the
average of the two individual reference levels.
The time-constant of the output integrator is irrelevant. In fact I used
an amplifier with a 1-second time constant (not a pure integrator) in
the outputs of the simulation. There's really no point in continuing to
try to guess what will happen; the simulation shows what DOES happen.
Since I can't run the Simcon program, maybe you could suggest when one
of the opposed outputs might not be "needed."
When both systems are active but a large disturbance is applied. The
system opposing that disturbance produces all the opposing output and
the other system shuts its output all the way off.
Surely the point of opposed square-law systems is that they are both
needed all the time?
The point is that we can use a linear spring model in the region where
both systems are active. Outside that region the system still works, but
the output function is nonlinear. That causes no great problem.
Do the feedback paths using cross-over error connections lead to a
situation in which only one of the outputs is active at any one moment?
Yes, given a large enough disturbance.
In the system you were contemplating ...
...would you expect all of the thousands of individual error signals to
be cross-connected to all of the other outputs? This seems an awfully
complicated structure, but maybe it is so.
I'm not a physiologist, and can't comment; it would be helpful if some
of our physiological readers could shed light on whether these millions
of cross connections among the individual spinal control loops exist,
and how the positive and negative signs relate (are they ALL
inhibitory, or are the connections among control systems whose ouputs
pull in much the same direction additive?).
I believe it is so, if not for all at least for most. There are
internucial Renshaw cells which connect signals for one spinal control
loop to opposing loops, the sign of the Renshaw cell's output being
uniformly negative. The reference signals, error signals, and perceptual
signals all can cross over, with a sign reversal. Stretching the biceps
causes the triceps to relax, through sign-reversed copies of the stretch
error signal.
Internuncials are needed, by the way, because there is apparently a law
that says all the branches of a given neural fiber are either
exclusively excitatory or exclusively inhibitory in their effects on any
destinations: no exceptions known. An internuncial neuron is required to
produce a sign reversal.
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Best to all,
Bill P.