[From Bill Powers (950915.0925 MDT)]
Hans Blom (950914x) --
RE: challenge results
WOW! I am impressed! Your model controls better than mine! Now I have to
go off and figure out why.
With this start, do you think you could go on to create a model-based
control system of the same form as the Kalman Filter model? I don't mean
actually using the Kalman approach -- that probably wouldn't be
necessary in this simple case. I mean just put in a world-model between
u and an x' which is the modeled value of x, and then use your predicted
value of the disturbance to supply the necessary model of the
disturbance in the world-model in the same way you did before. We can
assume that the world-model has converged to the right value of k. So
you don't actually have to write the code that does the converging. If
this works, too, I think you will have solved the problem of dealing
with arbitrary independent disturbances while still allowing for the
output pattern to continue when the current perceptual input is
temporarily interrupted. That would be a very important result. Of
course we would then have to check to be sure that convergence would
still take place, using an actual adaptive model, but I don't forsee any
problem with that.
But then, I didn't forsee that your answer to the challenge would work,
either. 
Nice going.
···
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I used the term "slowing" to refer to the factor "slow" in
x2 := x2 + slow*(x1 - x2)
which is used in smoothing the disturbance and reference signal. The
input to this calculation is x1 and the output is x2. The calculated
change in x2 is the difference between x1 and x2. On any one iteration,
we allow only a fraction "slow" of this change actually to occur (that
is, we "slow" the change in x2). If x1 is a step function, x2 will
follow approximately an asymptotic exponential curve arriving eventually
at the value x1, from any starting value of x2. So this is just a
single-pole filter. I used a two-stage filter in creating the
disturbance and reference tables.
In general, if the nominal relationship is x2 = f(x1), the smoothing
process would be
x2 := x2 + slow*(f(x1) - x2)
You can condense the expression on the right, but this form makes its
logic clear.
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Avery Andrews (950915) --
There's an important subtlety which both my posting and rick's
reply overlooked, which is an ambiguity what it is for two
different people to `want the same thing'. Suppose I want for me
to eat, and also that you want for me to eat, so that we both have
reference levels of TRUE (or 1) for the proposition that ADA3 eats.
No conflict. On the other what if ADA3 and RM both want `to eat'.
This will not be a problem if there is enough food to go aroumd,
but will be if there isn't.
For conflict to exist, the _same physical variable_ must be involved in
both control processes, and the reference levels must be different.
Actually there is a potential for conflict in both cases, because in the
first case the question is left open as to WHAT and HOW MUCH both people
want ADA3 to eat. In the second case the conflict doesn't actually
become physical until you're down to the last available thing to eat
that both people want to eat.
The ambiguity you mention is a linguistic ambiguity -- the words as used
by the two people actually refer to different physical variables. When
Father says to Son, "I only want what's best for you," there will be
conflict only when the phrase "what's best for you" refers to different
states of the same variables (like how late Son is to stay out at night)
when used by the two people.
------------------------
But then there's another problem. High level perceptions are
produced by a reorganizable hierarchy from lower level ones. So
how could two different such reorganizable systems, having
different histories and different genetic makeups, come up with
high level perceptual functions that are in any sense the same?
That's often an unwarranted assumption. I think people solve this
problem in a practical way: if they seem to be in agreement with another
person, they let it go at that without really checking to see what
they're in agreement about.
She: Tomorrow's my birthday. What shall we do?
He: How about going bowling again at the Starlight Bowl?
She: Well, I'd like to do something different this year.
He: Sure, I know just the thing. Leave it to me. [Thinking, we'll go to
that new bowling alley that just opened].
She: Fine, just as long as we don't go to the Starlight again.
[Thinking, goodie, a nice dinner and movie]
He: That's settled, then.
There's another kind of answer, probably closer to your meaning, which
is that the brain may have evolved to contain the basic computing
functions needed to create perceptions of specific classes, while
leaving the particular instances of those classes that will be acquired
to reorganization in the current environment. So everyone will grow up
to perceive in terms of relationships or sequences or logical functions,
but not any _particular_ relationships or sequences or logical
functions. The fact that we all seem to have a natural ability to
perceive configurations would indicate that this ability is inherited,
although we may each end up perceiving the world in terms of different
configurations. But if we accept that the basic capacity is there, it's
very likely that through communication and other interactions we will
converge toward perceptions that are at least operationally
indistinguishable.
E.g. people seem to like to be with their friends, to have
harmonious social relationships, to make progress on things, all of
which seem to be references levels that are both high-level and
recurrent in the population.
There's a selection bias there, when you say "people seem to like..." .
You hang out with people like you, meaning people who do share something
like your perceptions and have similar reference levels for them.
Another person, whom you would be unlikely to meet, could also perceive
in terms of social relationships, but have a low reference level for
most of them, preferring solitude. So in your judgment of similarities
among people, you would not be including such people, and would get the
impression that most people are like you.
I think you'll find that on any social dimension you can find all
possible reference levels for any particular variable. Just consider the
range of reference levels there are for such variables as honesty, hard
work, pleasantness, competitiveness, conformity, community service,
leadership, communication, rationality, and power. You associate with
people who have somewhat similar goals in these regards, but there are
obviously other groups with very different goals (consider the Mafia or
the National Football League).
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Best,
Bill P.