[From Bill Powers (940803.0930 MDT)]
Dick Robertson (direct) -- yes, I got the post. Just busy.
···
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Chuck Tucker (direct) -- Roger on the video card. I'll wait to get the
info.
BTW how are the other demos with various type of reference signals
coming along.
Not very far, considering that this is the second day since the last
guest from the meeting left.
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Avery Andrews (940803.1149)--
Your approach sounds fine. I'm leaving this mostly in your hands, too
much to do.
As far as path-generation (note the careful avoidance of the word
`planning': paths can be generated as executed as well as perhaps
planned before execution), there actually is an empirical issue as to
whether the path is specified as a time-varying positions (`position
contour') on the one hand or a time-varying velocity on the other.
Does there have to be a choice? At one level the reference signals
specify position. At the next level they specify speed along a
particular path, or anyway some transition. The speed control systems
work by outputing a varying reference signal for position. Don't confuse
this with first-derivative damping at lower levels.
Bizzi did some experiments with fast, highly practiced movements which
seemed to support the positional view, but of course that doesn't mean
it's true for all movements.
"Fast" movements are right at the limits of control, aren't they? Maybe
it's just too obvious that if you're moving your hand slowly and
deliberately along a certain path, positional disturbances will be
corrected, even along the path. But the speed is still under control,
too.
If you set up two control systems, one for position and the next for
rate of change of position, and do just the right experiments, you can
get all sorts of phenomena. For example, if you're moving at the right
speed, a brief push displacing the finger in the direction of movement
will cause the finger to stop, then start up again, as if the finger
were waiting for the changing position reference signal to catch up with
it. It's just a matter of time constants and dynamics at the two levels.
You can read all sorts of complex logic into these details, but the
actual system is just behaving normally, the way it is designed. The
problem with the purely empirical approach is that you can never tell
whether you're seeing a new phenomenon or just the same old system under
somewhat unusual circumstances.
This is why it's important to play around with models. You discover all
sorts of unexpected behaviors that you didn't design into the model on
purpose. Without the model you'd treat all these behaviors as new
phenomena, each requiring its own explanation. But once you've explored
a model sufficiently, you can recognize such things as being nothing
special -- just what the same model does under the appropriate
circumstances. A good model always explains more than you designed it to
explain.
As for changing lo-level references slowly: in nu14 I imagine that
there is an implicit first level of control systems in charge of the
joint angles, so that there is a choice between summing up the error-
signals from the second order systems and then slowing that (what nu14
actually) does, or first slowing and then summing. Any thoughts?
Right, we don't need to bother with the arm dynamics and the muscle
systems. There doesn't seem to be any functional difference between
slowing the individual outputs before or after summing, so that's a
matter of convenience -- only evidence from the nervous system could
force us to select one over the other.
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Bill Leach (940731.22:00 EST) --
PCT simulation necessarily deals with small magnitude disturbance (as
compared to the dynamic control range) but many discussions DO deal
with "larger" variations.
In the tracking experiments, the peak-to-peak magnitude of the
disturbance is selected so that by itself it would move the cursor
almost from edge to edge of the screen (i.e., with the handle stationary
and centered). The movements of the handle that we observe would also,
if applied in the absence of the disturbance, move the cursor from edge
to edge of the screen. When both the handle and the disturbance are
active, both run through the same ranges, but in opposition to each
other, so the cursor actually moves left and right by only about 5% of
the edge-to-edge size of the screen.
The movements of the cursor are NOT "the disturbance." The disturbance
is the number that is added to the handle number to produce the cursor
position.
In the PCT simulations, the only limit on the size of the disturbance
(if we want to see normal control behavior) is whatever calls for the
maximum possible output from the control system needed to oppose the
effects of the disturbance. This maximum isn't usually specified in a
simulation -- the handle could move by 10E33 units if we supplied that
big a disturbance. In a real system there is a physical limit to the
amount of output possible, so the maximum usable disturbance is the
amount that would call for maximum physical output.
In other words, the disturbances we use correspond to the entire dynamic
range of the control system's output. The _effects_ of such disturbances
on the controlled variable, of course, remain small if control is good.
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Bill Leach (940802.23:53 EDT) --
(horning in)
Mary, are you postulating that the 'highest level' references establish
in a deterministic way the goals of the immediate level down...
Higher level reference signals determine only the higher level
perceptual signals. The reference signals actually sent to lower systems
depend on what disturbances are acting. To achieve a higher goal you
must VARY lower goals, not set them to fixed states.
Suppose you have the freely-chosen goal of holding a steering wheel
centered. This means that you must set reference signals for applied
force to WHATEVER LEVEL IS NEEDED to cancel any externally-originating
forces that also affect the position of the steering wheel. If the
external forces vary, you must vary the goal-setting for applied force
in exactly the opposite way, provided you still want to keep the
steering wheel centered. So the environment determines what forces you
will have to produce if you want to achieve the goal of a certain
steering wheel position.
Now, suppose you decide (freely) that instead of wanting to keep the
steering wheel centered, you want to keep the car on the road. This goal
now requires that you VARY the position of the steering wheel in any way
required to counteract crosswinds, tilts in the road, and curves in the
road. Now the physical properties of the world determine from moment to
moment the angle of the steering wheel that you must set as a subgoal in
order to achieve the higher goal of keeping the car on the road.
You can continue this: you must vary the position on the road in order
to turn off onto another road; you must vary your choice of roads in
order to get to your destination despite detour signs; you must vary
your destination if you want to close a deal with another person who has
moved to a different town; you must vary which person you close the deal
with if you want to get the best deal; and so forth. Each goal that
seems freely chosen at the moment becomes determined by external
circumstances when you take the next higher goal into consideration.
Even at the highest level, whatever it may be, you must VARY that
highest goal if you want to remain alive in the manner that best suits a
human being -- which is determined by your intrinsic reference signals,
which are inherited. The only thing you are truly free to do arbitrarily
is to be human -- and only the species, not you as an individual, can do
that, or choose to cease doing that.
So we have to conclude that free will does not consist of freedom to
choose goals arbitrarily. Arbitrary choice of goals would disable part
or all of the hierarchy of control above the level of the choice.
Where, then, could truly free will come into play? Obviously it must
come into play where it will not disrupt any higher control systems
(which will automatically resist the disruption). This suggests that it
will come into play where there are no higher control systems -- in
branches of the hierarchy that remain unfinished. But reorganization
will automatically come into play there, too, if intrinsic reference
levels are violated. So the range of free will is not completely
infinite, given the goal of staying alive.
However, for every control problem there are multiple solutions which
are equivalent in terms of their effects on intrinsic state. A person
can resolve certain problems either by becoming a mathematician or by
becoming a truck driver. Either way, the person will survive adequately
to prevent intrinsic error. So we can suspect that what is called free
will comes into play under "don't-care" conditions. Where there are
multiple routes to a successful organization, one can choose any route
freely, without constraint because of any knowable consequences at
higher or lower levels.
It is sometimes claimed that free will is evident in the fact that we
can volitionally produce any arbitrary action we please at any time, for
no reason. This is tantamount to saying that anything can be
reorganized. But that idea considers the volitional act only at the
microsecond of its execution. All acts have consequences, and we are not
free to like or dislike any particular consequence chosen at random. If
a volitional act, an act of reorganization, has consequences that cause
errors in existing control systems, or in the reorganizing system, there
will soon be a need for another volitional act, compensating for or
undoing the effects of the original one. In other words, if we do not
like the consequences of a volitional act, the only way we can correct
the problem is to nullify the volitional act: we have no choice, if we
want to go on experiencing what we like rather than what we dislike.
At bottom, what we like and what we dislike are built into us: pain
hurts, pleasure feels good. What we experience as pain and pleasure are
consequences of actions of control systems which exist beyond our
ability to be conscious of them: all we know is that certain
consequences seem in themselves to have a quality that is given, beyond
analysis. What we call feeling "good" or feeling "bad" is the criterion
against which we judge all experiences. Solving a difficult set of
equations feels good; failing feels bad. That is our built-in nature
speaking to us, through intrinsic error signals or diminution thereof.
So where does this leave "free will?" I think it leaves these words in
the same class as "intelligence" or "traits" or "phlogiston." These are
words that sound or once sounded, and were used, as though they must
have some profound meaning. This impression proved ultimately to be
mostly an illusion: there was no experience to go with the words.
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Your objection to Tom's remarks is valid:
Tom:
When you use them together, they do not explain .09 + .09 = .18; but
.09 * .09 = .008.
Variances are like probable errors squared. They add.
What Tom is saying applies to the truth-value of assertions. I suppose
there is a way of converting from "percent variance explained" to
"probability that the hypothesis is true." If you have two hypotheses,
each with a probability of truth of 0.6, then the probability that both
are true at the same time is 0.36. So if the hypotheses are each
"probably true", any conclusion that is drawn from assuming they are
both true is "probably false." This is what dooms a psychology built on
low-probability statistics to remaining a simple science, if it can be
called a science at all.
Of course any hypothesis that explains only 9% of the variance is
"probably false" to begin with.
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Peter Cariani (9403.0400) --
The presence of fine structure in a neural signal COULD be looked upon
as the multiplexing of several kinds of information, but it could also
be seen as the presence of high-frequency detail in a signal where the
basic measure is frequency. In the world of audition, this gets
confusing because the basic physical quantity being sensed is also a
frequency. I suspect, although I haven't worked this out, that there
must be some interesting relationships between the frequencies going in
and the frequencies coming out. Even if the output frequencies are
continuous variables, with no significance in any one spike, there can
be resonance or lock-in phenomena. For example, the perception of
octaves may indicate one system that is locking in to subharmonics of
the actual input frequency.
Alternately, there are other kinds of stimulus representations,
which in effect preserve harmonic structure by virtue of
a time domain encoding (such as interspike interval distributions)
Interspike intervals are just the reciprocal of instantaneous frequency;
I don't think that merely changing from a variable to its reciprocal can
make any fundamental difference in the process. Both are continuous
analog variables. The main difference is that while frequency goes
nicely to zero, interspike interval goes shooting up to infinity, which
is sort of inconvenient.
What you said above about preserving the harmonic structure is, I think,
significant. There are signals that carry information that isn't used
immediately, but which can be extracted by higher functions if the
waveforms are preserved. The one trap to avoid is assuming that just
because YOU can detect a structure in a signal, that structure is
significant to the system you're looking at. I would guess that if you
can see fine structure in a signal, that information hasn't been used
yet. "Using" it means converting the information into a signal that
represents it, one signal for each degree of freedom.
But that's just my peculiar way of looking at things.
I'm still hoping to get back to my SoundBlaster card before the end of
the summer.
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Best to all,
Bill P.