From Bill Powers (920825.0800)]
Avery Andrews (920824) --
I'd like to see if I can get your C code to compile and run on my
machine. Could you send it to me?
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Martin Taylor (920824.1540) --
You can get as many degrees of freedom as you want by taking
sufficiently many independent time samples.
I think we agree. The key to what I'm trying to say is probably in
that fact.
In a neural pathway, where redundant signals travel in parallel,
there's no coherence between various partitions of the signal, so it
must be difficult to compute the equivalent number of time samples per
second. But in the middle of the frequency range of a neural signal,
the number must be rather large. For example, in perceiving a shape
like a filled square, the number of parallel signals contributing to
the sense of squareness must be quite large (depending on the size of
the square). If the square is shrinking or expanding, the derivatives
could be computed over a pretty short time, I should think. Also, as
Rick showed experimentally, the best definition for the "size" of a
square is its area, so shrinking and expanding size at a uniform rate
would mean increasing and decreasing the number of contributing
channels at the square of the rate. What I'm getting at is that what
we casually label "a" signal contains a lot of detail that isn't
necessarily evident when we speak of something like "a sensation
signal." These details can change greatly without altering the meaning
of the signal at the sensation level.
Now we have nine more dimensions. [adding frequency and amplitude
for >>each of the nine reference signals]
No you don't, if I understand your layout. You only have the
selection >of values within the original nine dimensions.
I'm not really arguing here, just trying to get my thoughts straight
on this subject. Let me try to illustrate the point I'm stuck on
without getting formal about levels. I'll go along with your ten
variables instead of my nine, which number was picked because I had in
mind an example with three groups of three.
Suppose the 10 variables (which we agree are controlled at the
sensation level) are 10 notes on a piano, controlled by striking the
keys with 10 fingers. There are certainly 10 degrees of freedom for
controlling the loudness of these notes. Plotting a point in 10-
dimensional loudness space specifies a loudness for all of the 10
notes. So this should use up all the degrees of freedom available.
Now we can add one more dimension: repetition rate of each note. And
another: rate of increase of repetition rate. And another: rate of
increase of loudness as the repetition proceeds. (This does not add 10
more dimensions for each, as I said in my last post -- only one for
each). It's not likely that any real person could exert independent
control of all ten variables, let alone of all 13 (!) dimensions, but
we're talking "in principle" here.
Now where did these three extra dimensions come from? We both know
that you can't control 13 functions of 10 variables independently, yet
here we are doing that. The answer is that we didn't start with 10
variables: we started with 13. It's just that the sensation level of
perception doesn't register three of the aspects of the lower-level
signals _as independent aspects of the signals_. For a sensation-
control system, all that matters is the instantaneous amplitude of the
signal averaged over all redundant pathways. What makes the difference
between one sensation signal and another is the weighted-sum function
that creates different signals using weighting schemes that are not
linearly dependent. There is no scheme at this level that
differentiates signals on the basis of their time characteristics,
patterns of change, and so on.
Nevertheless, a system that DOES differentiate signals on these bases
will see that such variations are present in the original information
-- that there are, in fact, more degrees of freedom in the sensation
signals than the sensation-level systems can discriminate or control.
You handle this by speaking of time-sampling. A sensation-level
system, however, can't appreciate or control the variations in its own
perceptual signals that a time-sampling would reveal. In your way of
handling time, you speak from the objective viewpoint. For the system
itself to make any use of the temporal information, however, it must
contain perceptual functions that are sensitive to temporal aspects of
the sensation signals. These aspects are passed through the sensation
level without making any difference to the sensation-level control
systems. And the sensation reference signals can be varied in ways
that have no meaning to a sensation-controlling system.
Somewhere around 1956 or 1957, Kirk Sattley (hello, Silent One)
suggested to me that what I was calling levels of perception might
actually be dimensions of perception, not arranged in strict levels
but constituting a space in which perceptions are controlled. I have
opted to stick with the levels concept, in large part because of the
physical arrangement of the nervous system and considerable
information about identifications of types of perceptions with
locations lower or higher in the brain. But I haven't forgot Kirk's
proposal. In some cases it seems a better one than mine, especially
those where we seem to use a high-level control process to achieve a
low-level end (although that's often just a manner of speaking). I'm
not ready to adopt it, however, because of the clear dependence of
some kinds of perceptions on the existence of others, which seems to
imply the necessity of hierarchical control.
It's profitable to think of the levels as being dimensions of the
perceived world, because that's how we experience it. We don't
experience the world in layers; all the levels exist in it at the same
time, all mixed together, all in the same space. What I'm getting at
is that these levels may (to make an epistemological guess) reflect
more and more subtle aspects of what Wayne Hershberger called the
"immanent order." If that's the case, then in 10 sensation signals we
have actually 10 little packages of representations of the world, each
package capable of far more subtle variations than can be appreciated
by a perceptual function that responds only to weighted sums and acts
only to control that one aspect of the world.
As I said, perhaps your idea of temporal sampling is the key to the
added dimensions of experience that show up in the higher levels.
Practically all of the higher-order perceptions are time-spanning, or
time-irrelevant. At the sequence level, as long as the same sequence
is progressing as it should (m-i-s-s-i-s-s-i-i-p-i) we experience a
single thing, that particular sequence, with no error except where
there's a mistake. As you prove that (x + y)**2 equals x**2 + 2xy +
y**2 (Fortran), you're engaged in a single recognizeable rule-driven
or logical procedure that remains the same until the job's done.
Temporal sampling at the lower levels (fourth) is probably done by
hardware -- rapid-adapting neurons, local integral negative feedback,
and so on. At higher levels, however, memory gets into the act, so
that the time dimension can be exploited over very long spans of time.
This allows introduction of a dimension such as "familiarity."
Something is "familiar" if there's something like it already stored,
regardless of how long ago it was recorded. You can say of a melody
played on ten notes that it's like another melody, or that it's part
of a longer piece, or that it was written in 1846, or that it's trite,
and so on. A given melody can, independently, be all these things and
many other things besides, all at the same time. So as you say, the
dimensionality becomes unlimited -- even though everything has to
filter through the ten note-perceivers.
As to the "bottleneck" effect, it certainly exists, but we have ways
of getting around it to some extent. Pianos actually have 88 keys,
while nearly all pianists have 10 fingers. Yet as my friend Sam says,
there are always enough fingers to play the piece. This is reminiscent
of my comments yesterday about the OAPHE (one-armed paper hanger
effect). Because of the time dimension, we can multiplex (your term in
the Paris paper) our outputs and make them look like many more than
actually exist. A juggler can keep five balls in the air with two
hands, because physical processes don't begin and end instantaneously.
I'm beginning strongly to suspect that something similar happens in
the brain: a control system of limited capability switches back and
forth between multiple sets of lower-level systems, tweaking their
reference signals (which persist for a while between tweaks) and going
on to the next set, so a single system can behave like multiple
systems controlling the same variable at the same time, only in
different contexts at lower levels. A relatively small set of higher-
level systems, therefore, can act like a much larger set. Again I
plead for experimentation.
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RE: monkey cortex (920824.1630) --
I saw the article, but I've given up on saving articles having
something to do with control theory. There are too many. And it's just
too much work to sort out the wild interpretations put on the data, as
in
" ... motor neurons in the monkey cortex encode not the force being
applied by the muscles, but the force needed to counter the (visual)
disturbance added to the location of a target on which a cursor was
maintained in the presence of a constant bias force that was already
being compensated. "
Motor neurons don't encode forces needed to do something else. They
just produce forces by using muscles. This quote is an example of the
tunnel vision that pervades medical-style research: label everything
by its effects, and attribute the cause arbitrarily in the middle of
the loop. To explain to Georgeopolis why the above statement is
nonsense would require re-educating him from High School onward. Of
course he's looking at part of a control system. But how could we ever
explain that?
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Chris Malcom (920824) --
I've also made this observation about bicycle riding -- the first
thing you do when you turn left has to be to turn the front wheel
right, to get the bicycle out from under you and initiate a bank.
Your main point is important. The hierarchy does not learn to control
perceptions by describing them and reasoning about them. Describing
and reasoning are the RESULT of learning to control, not the cause. A
lot of people try to understand control theory strictly in terms of
verbal descriptions of how they work -- and as you know, that's not
good enough. The descriptions can be pertinent only after the right
perceptions have been acquired. The way people describe their actions
often has nothing to do with what's actually going on. Just think of
people saying "You make me mad!" This is the main reason why people
can't just read a book about PCT and understand it. They have to apply
the words to real experiences; only then do they realize what the
words actually mean.
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Best to all,
Bill P.