[From Bill Powers (920824.1100)]
Avery Andrews (920823) --
First, I am very sceptical that people normally perceive the wheel
angle.
In HPCT, all that is required in order to say that a perception exists
is that a neural signal exists in a perceptual pathway. This has
nothing to do with consciousness. In a spinal control system, the
signals standing for muscle stretch and tendon tension are present at
all times, at some magnitude. Copies of those signals rise to the
brainstem, the cerebellum, the midbrain, and (by some direct pathways)
to the motor cortex. The control systems involving those perceptions
are always active. But we are seldom conscious of those signals unless
we deliberately attend to them, or something goes wrong that draws our
attention to those levels of organization.
Second, while taking a long drive yesterday I noticed something that
doesn't fit into my story as told, which is that on long distance
drives at least, most of my (and my wife's, as far as I could see)
steering movements were quick & small adjustments, whereby the wheel
was turned various distances, but at what seemed subjectively to be a
pretty uniform rate. These motions seemed to be completed before
there >was any noticeable change in the heading of the car. I don't
yet have >a real story about what's going on here, but I think it
involves >perceiving the car-heading to be wrong, ordering up more-or-
less enough >path-curvature to change it quickly enough, and then
repeating this to >straighten the car out again.
There are other controlled variables at lower levels, important ones
being the senses of sideward and rotational acceleration that indicate
the start of a movement of the car. If something accelerates the car
to the left (a bump), you feel an acceleration to the left as the car
presses sideways against you, accelerating your body toward the left.
You immediately turn the wheel to the right, reducing your body's
sideward acceleration (which you feel as a force). This doesn't
completely prevent the car's direction from changing, but the higher-
level systems based on vision can correct the residual error. So one
of the lower-level reference signals that is set by the higher-level
driving system is "zero lateral acceleration."
An interesting demonstration of this sort of effect shows up when you
accelerate the car with the foot-pedal. At the same time that the
speed-control system increases the reference level for visually-
detected speed, it raises the reference signal for forward
acceleration, which you feel as your stomach muscles tighten to force
your trunk forward and thus keep it stationary relative to the seat
and steering wheel. If the transmission happens accidentally to be in
neutral, the reference signal for greater forward force causes your
body to pitch forward, as if someone had slammed on the brakes.
Normally we are conscious as though from the viewpoint of a higher-
level system -- which level depends a lot on the level you habitually
adopt as a point of view. People like us spend a lot of time doing
logic and verbal manipulation, so very often we are unaware of the
workings of the lower level control systems. They operate, however,
just as well without awareness, and possibly better.
So you're right in being skeptical about people perceiving wheel
angle. If, however, you asked them what the wheel angle was, they
could tell you by paying attention to the positions of their hands or
by attending to the part of the visual field where the steering wheel
is. This doesn't mean that wheel angle isn't being controlled even
when they're not attending. If you're the passenger, just reach out
and tug at the wheel -- you'll feel resistance from the driver even
before the car has begun to deviate, and before the driver yells at
you. If you keep your disturbance small, in the range of normal
disturbances that arise from little irregularities in the road, the
driver might not even notice -- but the disturbances will still be
resisted. That tells you that wheel angle or at least angular velocity
is under active control by a system that's currently not in awareness,
but is still a necessary level in the steering hierarchy.
I'm delighted that you're thinking about control theory while you
drive. You'll learn a lot more about it by sorting out real control
experiences than you will writing model programs. Just don't forget to
attend to the higher levels every second or so!
You'll notice an implication that we can attend to perceptual signals
that are not at the highest levels in the brain. I'm not sure that's
true, but it seems to be true.
···
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Gary Cziko (920824.0010) --
This one seems to have kept you up pretty late.
I get especially nervous when I don't understand something which
you preface with "clearly."
Roger. I get the same feeling in reading philosophy when I run across
italicized words. Invariably, these are the words most in need of
definition and most lacking in it. Example: intention is a sense of
_aboutness_.
With nine intensity signals, why does "nine independent sensations
signals at a given time" mean? Do you mean nine sensation signals at
the same time? With nine intensity signals ranging from zero to some
maximum neural frequency it seems to me that there would be a lot
more >than just nine sensations possible just using weighted sums.
Yes, there could be jillions of different sensation signals. But only
nine AT A TIME can be controlled with respect to independently-set
reference levels without creating conflict. This is because
independent control amounts to solving simultaneous equations. You
have nine (perceptual) functions of the nine intensity signals that
must have specified values at the same moment. With nine equations in
nine unknowns, a solution is possible if the perceptual functions are
linearly independent. If you try to control 10 or more functions of 9
variables, you won't find a solution.
More than nine sensation-signals can be present at the same time, even
with only nine different intensity signals at the level below. But
only nine of them at a time can be controlled relative to specific
referenc levels.
Consider at all the colors we perceive with only three (I think)
intensity signals related to color. What am I missing here?
This has worried me, too. If we just look around at the environment,
we see an incredible number of hues of color. Is there a control
system for every hue? Part of the answer is in the fact that when we
ADJUST color (for example, with a TV set's color controls), we attend
to only one place in the visual field, around the center of vision.
It's as if we can exert active control only for what is in the center
of attention. All the other perceptual variables at the same level
just sit there in whatever state we left them (if they'll stay that
way -- otherwise they drift). When a lot of variables of the same type
need controlling simultaneously, you get the one-armed paper hanger
effect (OAPHE). Our attention jumps around among the variables, and we
have to switch our outputs from one reference signal to another,
trying to keep them all appropriately set as multiple disturbances
upset all the variables.
This is clearly an important part of an HPCT model that doesn't exist
in the present form. In a way it makes the modeling job easier -- it
says that we don't need a separate control system for each parallel
instance of a given type of perception. We seem to be able to keep
some small number -- 7 plus or mine 2? of control processes running in
parallel at the higher levels, at least within consciousness, but not
more. At the lower levels, we can apparently run far larger numbers at
the same time, but mostly because we don't need to be aware of them.
At or above some level, it seems that we can set up control processes
to run at the same time, but without attention they tend to decay and
drift. It seems to me that this is an area where we need a lot of
experimental data. We can measure control parameters rather easily and
quickly. Wouldn't some research group like to investigate how control
varies with attention? There are gobs and gobs of vital information to
be obtained here. This is a high-priority subject. Before we try to
construct models that can do this sort of "scanning" process, we have
to know what phenomena need modeling.
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Mark Olsen (920824) --
RE: unhappy past.
The past doesn't have any effect on the present, any more than the
future does. The past is gone, the future isn't happening yet. If an
unhappy childhood has any effect on an adult person, it's because of
attitudes, beliefs, opinions, and ways of doing things that exist
RIGHT NOW.
Memories, of course, are part of present time. Whether the content of
a memory is a true recording of past experiences is irrelevant; what
remains now is what constitutes the pool from which reference signals
can be drawn. Ed Ford says to replace the unhappy memories with happy
ones. Enlarge the pool and add to it memories that will be useful now,
in the present world, in relation to the people with whom you now
interact.
As you say, psychoanalysis does dwell extensively on the past, at
least in theory. but psychoanalysis is an incredibly inefficient mode
of therapy, and in many cases I know about the chief accomplishment is
to teach a client to describe his or her problems in a specialized
language, while becoming reconciled to having them go on forever.
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Martin Taylor (920824) --
Yes, it seems best to go public on this debate, as it pertains to
what's happening on the net.
I think that when you shift types as you go up levels, the degrees-of-
freedom problem takes on some new aspects. You already showed how you
could get 18 degrees of freedom out of 9, just by adding first
derivatives. Couldn't we get 9 more by adding second derivatives, and
so on? The question now is, what ELSE can be added that takes us out
of the domain defined by our original concept of intensities ->
sensations -> configurations?
Bandwidth really isn't the problem here -- we could keep all
variations well within the available bandwidth and still have a
problem to solve.
Consider this. We start with nine functions of nine variables, the
value of each function being adjustable to any reference level, and
each reference level now being adjustable with any time rate of
change, independently (well within the maximum bandwidth, remember).
So we could have r1 varying as sin(t), r2 varying as sin(2.7*t), and
so on. All nine reference levels can thus vary independently with
respect to oscillation frequency.
In addition, the amplitude of oscillation can be varied independently
for all nine systems. There's an outer envelope set by bandwidth; the
bandwidth and momentary frequency sets the maximum rate of variation
in amplitude, but within that envelope, there is complete freedom. Now
we have nine more dimensions.
At the event level, we can now have System 1 execute one complete
oscillation with a given amplitude, System 2 execute one, and so on,
to construct an event like a wave traveling one time across the
systems. Or we could divide the nine reference signals into three
groups and have a wave pass through groups 1,2, and 3 independently,
choosing an arbitrary pattern for each one. So the same nine systems
can be used to construct an infinity of different patterns of
variation at the event level. We now have not only nine derivatives
(at least) at an instant, but a time-spanning characteristic called
amplitude, and a time-spanning pattern characteristic that can extend
indefinitely through time.
I think it gets very difficult to define what we mean by degrees of
freedom when we get beyond the first four levels. In one sense, we
could say that the event level introduces just one new degree of
freedom, because we can execute only one pattern at a time using the
lower nine-component system. But suppose that at the event level, the
complex event is a one-bar phrase of eight notes -- a little fragment
of melody. At any time, only one phrase can be generated. But we can
then generate a number of other phrases holding the first note
constant, another set holding the second constant, and so on. Since
we're talking about time-spanning perceptions now, we can compare a
phrase emitted at one time with a phrase emitted at another time. We
can differentiate one song made of one set of phrases from another
song made with a different set of phrases -- even though they don't
coexist. We've now created a conceptual space in which various
components of a perception can change while holding other components
the same. We can define axes arbitrarily in such spaces, can't we?
Behind the strict degrees-of-freedom problem as we originally
conceived it, I think there are some level-specific assumptions that
aren't obvious. One is the concept of simultaneity -- we say that the
nine systems must in effect solve _simultaneous_ equations. When we
think of levels of perception in which temporal patterns are the
variable, the idea of simultaneity no longer applies. We can solve a
control problem that requires the nine systems to achieve their
reference states ONE AT A TIME or IN A CERTAIN PATTERN or IN CERTAIN
SPACE-TIME RELATIONSHIPS and so on. These are actually solutions to
conflicts that would arise if we demanded that all nine systems reach
zero error at once. These solutions may explain why higher levels
exist.
Even if we think of only nine letters on a keyboard with one finger
for each letter, typing the word "keyboards" is impossible to do with
a linear combination of finger-presses. We can clearly control each
finger simultaneously and independently with nine control systems, but
when we try to do so, the keyboard won't respond and we won't see the
word "keyboards" on the screen. We'll see whichever letter was hit
ahead of the others by a millisecond. The only way to solve this
problem is by introducing a time-spanning event in which the reference
signals for each finger are specified one at a time. A good typist can
learn to do this at the event level; a beginner does it at the
sequence level, and much more slowly.
And with only the nine fingers plus two more degrees of freedom (x and
y), we can type everything that it is possible to type. How many
degrees of freedom have I used in saying all this so far?
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