[From Bill Powers (920821.0800)]
Avery Andrews (920820) --
As to `how many' regularities there are in nature, I doubt that this
is >a
question that can be profitably argued about. At a very minimum, PCT
depends on there being consistent correlations between the direction
of >gross effort and the direction of change of net result, & a
continuous >function relating the magnitudes of these two quantities.
We fall easily into treating nature as an abstract aspect of our
models, as if it were so hard to find any natural phenomenon that we
have to guess what nature would really look like if we could find
some. You're right: we depend for control on consistencies in nature.
I'd go farther -- we don't really expect natural laws to be
statistical. If there are disturbances, we expect to find
explanations for them and we expect that there will be some
systematic way of opposing them. Disturbances don't happen on a time-
scale or a scale of magnitude that prevents us from opposing most of
their effects instead of just cleaning up after them. I suppose that
defines our niche -- we perceive the world in such a way that we can
handle its vagaries.
But all is not quite as obvious and regular as you imply. The
correlation between gross effort and the direction of change of net
result is not always as we assume it to be, nor is it the same from
one circumstance to another. In BCP I brought up the example of a
horse pulling a cart up a hill, crossing the top, and pulling it down
the other side. When it's going down the other side, all its muscle
forces are pushing in a direction opposite to their direction when
going up the hill: the horse is moving forward by pushing backward.
When you lower a bucket into a well, the forces produced by your
muscles never push the bucket downward. When you slowly raise an
outstretched arm from your side to the overhead position and slowly
lower it again, the torques created by the muscles at the shoulder
joint are always in the upward direction; when the arm is moving
either up or down at a constant angular velocity, the torques are
identical at a given position. When you stretch your arm out to point
to something, the gross effect is in the direction of "reach" -- you
can just FEEL that "reaching effort." But there is no vector force in
the direction of pointing -- the net force is upward, counteracting
gravity. The main sensation of reaching comes from trying to bend the
elbow joint past its limit. There are no muscles in your arm that can
cause it, when already outstretched, to lengthen, even though
pointing "hard" feels that way.
When you swing that outstretched arm laterally, pointing first at one
object and then at another, the sideward forces rise to accelerate the
arm, drop to zero as the arm coasts toward the new direction
supported upward torques at the joint, and then reverse to decelerate
the arm to a stop -- all while the arm is swinging in the same
direction.
When you use the steering wheel of a car to control a car's position
on the road, there is no relationship between the steering wheel
angle and the lateral position. The relationship is between wheel
angle and the rate of change of sideward velocity -- the second time
derivative of position. You might have to turn the wheel to the left
in order to negotiate a right turn, if you're turning from a
direction into the wind. The steering wheel turns in the direction of
the curve at first. Then as the headwind becomes a crosswind, the
angle of the wheel lessens more and more, until it actually opposes
the turn (the crosswind alone is more than enough to make the car
follow the turn of the road). The same thing can happen on entering a
steeply banked turn when you're going around it at less than the
design speed.
When Astro is making a final approach to Mother in more thabn one
dimension, its jets are firing opposite to the direction of travel.
When its path is curving and its velocity is changing, its jets could
firing at any angle to the direction of travel.
Driving a screw into a piece of wood (after it is started) is done not
by pushing it into the wood but by twisting it. Hammering a nail in
requires, at the moment that the hammer head is about to strike the
nail, pulling the handle toward you to counteract centrifugal force.
The same is true of a golf swing -- just as the head of the club
strikes the ball, you're pulling strongly on the grip to keep the
head from continuing in a straight line into the ground. When you
throw a baseball, you release it at the moment its path is toward the
target, which is not when your arm is pointing at the target but when
it is at a large angle to the direction to the target. The follow-
through has no effect on the ball at all. When you go from a standing
position to a squat, it is gravity that moves your body downward
while your muscles exert efforts as if to stand up. When you press
lightly downward on a tabletop with one finger, the main force in
your arms is upward, supporting the arm and keeping the touch from
becoming heavier. Just at the point where you're pressing down with a
force equal to the weight of the arm times its average radius from
the body, a force of several kilograms at the fingertip, the upper-
arm muscles are mainly keeping the elbow from bending and the
shoulder muscles are doing nothing. There is another force at the
fingertip at which the shoulder muscles are supporting the upper arm
and one end of the forearm, while the biceps and triceps are doing
nothing but oppose each other.
The only way it can seem that gross effort corresponds to gross result
is by confusing the effort with the result. We simply assume that if
an effect is going in a given direction, the efforts we feel must be
aimed in that direction, too. This is what I mean when I say we name
behaviors after their controlled results, not after the efforts
required to keep them controlled. We not only name them that way, but
we interpret our experiences that way even without words. When you
unlatch the door on a car that is parked so it's tilted toward you,
you use the same term, "opening the door," for the action you take,
even though you have to push on the door to keep it from opening too
fast. We pay attention not to what we're doing, but to the effects of
what we're doing. Because we control so well, we don't pay any
attention to all the little disturbances that are present, even if
counteracting their effects requires reversing our normal action to
keep the same outcome going. Unless someone calls attention to them,
the disturbances won't even be noticed. Because they're not noticed,
the rather radical changes in action needed to cancel their effects
are also not noticed. We end up with an unrealistic sense of how
simple and straightforward behavior is. It's simple and
straightforward only because we're excellent control systems.
ยทยทยท
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I have on the page before me a diagram of a circuit that ought to
work, >and is supposedly based on the actual wiring of a real critter,
and which I believe I described accurately.
If I showed you only the connections in an electronic circuit, without
identifying the components or giving their values, neither you nor
anyone else could say what that circuit does. It makes a great deal of
difference, for example, whether the elements are flip-flops or
continuous amplifiers. It makes a lot of difference whether a given
synapse has 1 unit of effect on the following neuron or 1000 units,
and whether the effect is proportional, rate-sensitive, or time-
integrated. When closed loops can be traced out, it makes a lot of
difference if the net sign around the loop is positive or negative; if
positive, whether the gain is greater or less than 1, and if negative,
whether it is only -1 or -2 or more like -100. When signals from
different sources converge on a given neuron, it makes a difference
whether their effects are both excitatory, or opposite in sign. Do we
have an amplifying adder here, or a comparator, or a multiplier, or a
gate? You can't see the function of any connection just by looking at
its geometry.
None of these critical details can be derived simply from a drawing of
the network of neural connections in Aplysia.
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Best,
Bill P.