[From Bill Powers (920822.0800)]
Rick Marken (920821.2100) --
"Republicans" is, of course, a category, as is "Democrats" and "Jews."
According to TV reporters, many people who claim to be instances of
the Republican category were angry at Pat Buchanan's speech and
embarrassed at much of the rest of the proceedings. I expect there
were some Democrats who were embarrassed at the proceedings at the
other convention. As with most perceptions based on class membership
and other superficial "population sampling" methods and labels, it's
not likely that anything you say about either Democrats or Republicans
is true of any individual Democrat or Republican you happen to meet,
or any Jew, either.
System concepts tend to be unarticulated and largely unaware. I
suspect that everybody believes in "family values," even the Mafia.
But it's hard to say what a family value is, and more to the point,
what's good about it. What most people mean, I suspect, is "people
like us." As Bush said, people are raised to believe as their parents
believed, and as their parents before them. Apparently, to many
people, being raised to believe in something is a better reason to
believe it than reasons grounded in knowledge or understanding. The
difficulty is that not everyone is raised to believe in the same
things, so to argue for a belief on the grounds that one was raised
that way is to admit equal justification for contrary beliefs held by
people raised a different way. One would think that this principle
would lead to great tolerance of others and the realization that a
belief is, after all, only a belief, not knowledge. Apparently,
however, it leads in the opposite direction. The assumption is often
that the way I was raised is the right way, and everyone else is
misguided, perverted, ignorant, or evil.
This analysis cuts both ways in any politico-social confrontation. As
long as people act out of ill-formed and self-contradictory system
concepts, they will not understand what is good about some principles
and bad about others, save for the way one happens, by accident of
birth, to feel about them. People will simply be vehicles in which
other people's ideas from long ago replay themselves like recordings
-- and, of course, they are recordings, reference signals being, I
think, derived in large part from remembered experiences. At the
highest level there's not much room for other ways of picking them.
Politics is fertile ground for a control theorist. What's needed is a
study in depth of many individuals who call themselves by some party
label. What are they controlling for? What principles do they uphold,
and what methods do these principles justify? What kinds of errors do
they perceive in various social situations, and how do they see their
proposed actions as correcting those errors? What do they think of as
the good life? As being a good person? How do they think people work,
with respect to rewards and punishments, self-interest, social
interest, and so on? Each person's structure of perceptions and goals
at the higher levels explains how that person acts and what that
person strives for. A study that investigates these structures in many
individuals of different avowed political views could come up with
many of the reasons for our social difficulties, in the form of
contradictory goals, misperceptions, and methods of control that don't
actually work. Once the real reasons for failure of our social systems
were brought out, perhaps the way to a better solution to our problems
would become more apparent. It isn't that social problems are so
difficult. It's that our approach to them is confused and self-
defeating.
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Avery Andrews (920822) --
Making a computer model of a car for use by proposed steering control
systems shouldn't be too difficult. The steering wheel input to the
car can be make fairly realistic. A torque applied to the steering
wheel will cause the wheel to rotate until the restoring force equals
the applied torque. The restoring force will be proportional to the
centrifugal force, which is m*r^2/v, r being the radius of the turn
(computed from the steering wheel angle) and v being the tangential
velocity of the car. The radius of the turn is computed from the
distance between front and rear wheels and the angle of the front
wheels: where lines perpendicular to the rear and front wheels
intersect is the momentary center of curvature. This ignores factors
like tire slip and so on, but will be plenty close for the purpose.
You could probably just say that the radius of curvature is inversely
proportional to the steering wheel angle and be plenty close.
Empirically adjusted constants will make the behavior of the car
realistic enough.
At a low level, the human control system can sense and control either
the force applied to the steering wheel, or the steering wheel angle.
Different control properties will result, and I'm sure do result in
different drivers who solve the problem in different ways. Controlling
applied torque will result in a wheel angle that depends on speed,
whereas controlling wheel angle directly, rather than torque, will
make the wheel angle independent of speed. I think the former will
probably work better. A kinesthetic variable may prove important: the
feeling of lateral acceleration that you get in a turn.
The rate of drift of the car sideways is, as you say, obtainable from
dp/dt. Unless you want to make a whole visual model, the easiest way
to handle this is just to say that there's a perceptual signal equal
to dp/dt and not worry about how it's derived.
Hence there is a three-level hierarchy of controlled perceptions:
relative position, rate-of-change of position, and rate-of-rotation
of >the steering wheel.
Sounds workable to me. The easiest way to get the reference rate of
rotation of the steering wheel is to integrate the output of the rate-
of-change-of-position system. In other words, make the steering wheel
system control the angle of the wheel, which is easy, rather than the
rate of change of angle. By integrating the output of the higher
system, you'll get a reference signal that keeps changing as long as
there's an error in rate of turning -- which is just what you want,
because a fixed wheel angle corresponds to a particular rate of
turning of the car. When the rate of turning error is zero, the
integral of the output will be constant, holding the wheel at a
constant angle.
I think there's one missing step in here. If there's a position error
(relationship level), the car has to be moved sideways by a fixed
amount, ending up going in the same direction as before. To get there,
its direction has to be changed. Any change in direction will cause
sideward drift rate. So the next level down should control drift rate,
not direction. The drift rate is varied by varying the car's angle, so
car angle should be the next lower variable. And car angle is varied
by varying rate of change of car angle, which is varied by controlling
steering wheel angle. You'll end up with two derivative-perceiving
systems, because position involves two time-integrals of steering
wheel angle.
Of course the system could be designed more compactly with derivative
and integral calculations inside one system, but the point is to get
an arrangement that works before finding one that works the right way.
With regard to assessing curvatures of the road ahead, I finally
figured out the simplest way to anticipate curves. It's to perceive
the position of the car's hood relative to the road, but not the road
right under the hood of the car. If you simply look at the road 30 or
40 feet ahead of the car, at a place in line with the body of the car,
the curvature will be perceived automatically a little in advance of
the time when the wheel has to begin turning. When you're going
faster, you look farther ahead. From experience you learn how far
ahead to set your perception point at various speeds. This eliminates
the need for complicated perceptual calculations.
Have fun.
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Best to all,
Bill P.