[From Bill Powers (960910.1415 MDT)]
Hans Blom, 960910d--
The human controller has a built-in time delay of about 0.5 seconds, I
guess, the MCT controller doesn't. This can be tested: to a human, offer
the >feedback information at, say, 1 second intervals; this would make the delay
time negligible to the time within which a reaction is required.
In the best-fitting model of the human controller, we have an integral
output function and a transport lag (put into the perceptual function). The
best fitting transport lag for most people is about 0.16 seconds, or about
10 frames of the display at 60 frames per second. If you gave a human being
feedback information only once per second, tracking would be almost
impossible, using a disturbance with a bandwidth of about 0.25 Hz as we do.
When Rick did the reversal experiments, I believe the sampling rate (for
both human and model) was 25 per second -- the Mac has a slower frame rate
than a PC. The exponential runaway seen in both human and model, which
lasted about 0.4 seconds after the reversal, thus was sampled about 10
times, giving the opportunity for a good fit of an exponential to the data.
It was clear that the control system in the person did not reverse its sign
for 0.4 seconds, and that the consequence was the beginning of an
exponential runaway due to positive feedback.
Note that a transport lag of 0.16 sec does not mean that the behavior is a
series of corrections 0.16 sec apart. The output is continuously variable;
it is simply delayed by 160 milliseconds behind the continuous input
variations. In the past I tested the effect of sampling rate up to 1000 per
second, to make sure that a rate of 60 per second gave a true picture of the
input-output function. At 60 per second I got the same results as at 1000
per second. The 25 per second rate Rick used, forced by using a Mac, does
begin to show some differences from the data obtained at higher rates, but
they are small.
In armftau, the artificial cerebellum model using real dynamics, there are
time-ticks on the display showing tenths of a second. The value of dt, or
the time per iteration, is set, I believe, at 0.01 sec, and the physical
dynamics of the arm are computed accordingly. The mass, length, and moment
of inertia properties are those of my own left arm.
................
RE: Tom Bourbon's E. coli gain adaptation
I hope that this makes clear why I say that (in a certain sense) a
controller must be the inverse of the world in which it lives. Even a
PCT controller...
In fact the output function in the model in question was an integrator, and
the environmental feedback function was a proportional connection, but never
mind. A integral might be said to be the inverse of a constant of
proportionality in some cultures, although not, I suspect, among
mathematicians. When you say "in a certain sense" I hope what you mean is
"in an uncertain sense."
...............
Hans Blom, 960910g--
RE: perception
It is the level of relating a measurement y (of something that
presumably exists in the real world) to some thing x that exists
internally (in the model).
You should really be calling that variable x', shouldn't you, as it's the
output of the internal world-model? The one-to-one relationship I am talking
about is between y, the perceptual signal, and the variable x which exists
outside the sensors, in the environment. You treat y as if it is simply a
measurement of a corresponding variable in the external world. The question
I raised concerned perceptual signals y which are not direct functions of
single external variables (or vectors), but which are functions of multiple
external variables, with no one-to-one correspondence. For example, y might
stand for the retinal distance between two objects in the environment. This
distance must be computed from the relative positions of the two objects on
the retina; there isn't any "thing" out there that corresponds to a
distance. If p is a measure of position, then distance = p2 - p1. At least a
subtraction is necessary to compute the distance. Of course there are many
more complex examples of this.
"A before B" relates two events, i.e. two things that occur at a
certain moment in time. If an equation reads, e.g.
B (t) := f * A (t-6*dt)
and all other coefficients are zero, we can say that changes in B
follow changes in A after a time 6*dt and with a strength f.
Does this clarify things?
Not much. You're saying that perception of "before" requires that there be
someone who can look at the equation and interpret it to give a meaning of
"before" to the relations described by the equation. But we can't have
little people inside a model interpreting the equations; the model has to do
that interpreting by itself. So you still haven't said how the model
generates a perception of beforeness. You've only described the conditions
necessary for such a perception to be appropriate.
P.S. I am now receiving only single copies of your post, via CSG.
Congratulations.
ยทยทยท
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Bruce Abbott (960910.1400 EST) --
No, no, no, no, you miss the point. Simon is not making the Argument from
Design. Natural selection does not involve a Natural Selector, i.e., Mother
Nature or God, as you well know (and that fact necessitates the passive
voice -- there is no one doing the selecting).
Simon didn't _mean_ to be arguing from design, but that is the form his
argument took. Can you fix up Simon's argument so the parallel holds true?
If there is a purpose for Y, then Y is employed to realize that purpose. In
the case where there is no agent X, there is nothing employing Y, and
nothing to have a purpose regarding the use of Y. How can you make Simon's
argument NOT come out to be an argument from design?
Our problem here is that a pun is involved. The word "purpose" refers to a
reference signal in a control system. It also refers to the (or rather, a)
use to which something could be put. These two usages involve completely
different meanings, as in the sentences "I saw the book" and "I saw the
plank." The use to which something could be put is not the same thing as a
reference signal. To confuse these two meanings is to court chaos, as when
you hear me say "I saw the plank" and don't know whether I'm talking about
vision or carpentry.
If I say "the purpose of the robot is to weld the piece of metal in its claw
to the stationary workpiece," you can't know what I'm talking about aslong
as we confuse these two meanings. Do I mean that inside the robot there is a
reference condition defined as "this piece of metal welded to that
workpiece," or do I mean "this robot was constructed to weld the two pieces
together, to satisfy the intentions of the production manager?" In other
words, am I referring to a purpose held by the robot and concerned with
certain parts of its environment, or am I referring to something in the
designer's or owner's mind concerned with the use to which the robot could
be put?
I think that the reason purpose gets involved in so much verbal trickery is
that there hasn't been an adequate definition of it prior to PCT. We're
watching people trying to figure out what purpose is without any model to
give it a clear definition. Even a Nobel Laureate can't mount a convincing
argument under those conditions, except by employing puns.
The main purposes of a bird's wing are to provide the lift and thrust
necessary for powered flight (although they serve other purposes as well).
That's a good example of what I mean. I am quite sure, considering the
knowledge we share, that you do not mean that there is a reference signal in
the bird's wing that specifies a purpose to be achieved. What you mean is
that if the bird intends to fly, the wing can be put to that use. If the
bird wants to splash water on itself in a birdbath, the wing can be put to
that use, too.
I claim that there is no use inherent in any object, in the absence of
organisms. The idea that purpose inheres in objects is simply indefensible.
No matter what purpose you claim an object has, it is always possible to
find a different purpose for the same object. That is because purposes are
in the uses of objects, not in the objects. What is the purpose of the Moon?
To cause tides? I'm sure that you would reject that idea. But how is it
different from saying that the purpose of a wing is to power flight?
Best,
Bill P.
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