[From RIck Marken (930117.1000)]
Gary Cziko (930117.0125 GMT) --
I said
But there is still feedback -- closed loops --you just have a
higher level system that is setting a reference for the lower level
(finger movement) system that forces that lower level system to
operate beyond its ability to control.
Gary asks
Rick, I'm having trouble understanding the implications of this last
sentence. As I understand PCT, it is not the reference level which drives
behavior but rather the error signal.
I always use the term "behavior" to refer to controlled perceptual variables;
the reference signal (not the error) "drives" this behavior.
The same reference level can have
very different effects on behavior depending on the current perceptual
state.
Ah. You're talking about outputs as behavior. Your statement is
true of outputs -- you cannot predict output from reference signal
because output is also determined by disturbances to the controlled
perceptual input that is influenced by these outputs. Terminology
problem again.
So how can the reference level being sent down from on high have
any influence on behavior it is not first passed through a comparator and
turned into error? And the only way to have error is to compare the
reference level with the current perception, which means feedback must be
involved.
I'm sure Bill will be able to clarify this. Let me give it a first shot,
though the best way to explain it is to actually build the model; maybe
at the meeting; I can at least diagram it more easily there.
My mental model of "trill control" was a two level model. Level two
is a system that perceives "trill" -- the perecption is a rate of
change in frequency. So the reference input to this system specifies
the intended trill rate. This refernce signal can specify any rate of
trill -- from very slow to very fast. This system controls the
perception of trill rate by sending reference signals to lower level
systems that control the elevation of the pointing and middle
fingers above the key (the fingers that execute the trill); I don't
know how to build this circuit -- and more levels may be needed to
actually implement the thing -- but this was my mental model.
So somehow the trill frequency perception system is sending varying
references to the finger elevation systems as needed to produce
the required trill. If the required trill is slow then the varying
references to the finger elevation systems will be slow (if there are
no disturbances to finger elvation that variably slow or speed the
movememts of the fingers). Similarly, if the required trill is very fast
then the references to the elevation control systems will be very fast.
It was the "elevation control" systems that I imagined could be
driven "too fast" for control. These systems match their varying
references with varyingperceptions of finger elevation; and they
do it by sending efferents to the muscle systems to contract and relax
the muscles in just the way needed to produce these reference perceptions
(I'm skipping one necessry lower level that controls force but lets
try to keep this relatively simple). If the varying elevation reference
signals are not too fast or too slow then 1) Goldilocks would like
them and 2) they will be able to produce the elevation perceptions
exactly as specified -- even if there are variable disturbances
added to the fingers. If, however, the higher order system
has been given a reference for a trill rate that demands that it vary
the references to the elevation control systems too rapidly, then
the control (of the perception of finger elevation) exerted by these
system will be quite poor because there are physical limits on the speed
of the muscle-skeletal system -- you can request (via reference signal
variations) changes in finger elevation of 100/sec but you ain't gonna get
it. When you send references to a system that require it to produce
perceptual variations that it cannot produce, the system will still "try"
to match those references. It is possible to drive the elevation control
system at a rate where they can produce the requested changes in
elevation (say 15/sec for a concert pianist) but cannot CONTROL
elevation at that rate;if, for example, variable disturbances to elevation
were introduced during such a high frequency trill, they COULD NOT be
resisted (though the system would "try" to resist them -- they would
produce changes in error). So the disturbances would appear to have
their expected effect on the elevation of the finger's and it would look
(to an observer) like the elevation changes were being produced open loop
WHEN THEY ARE NOT.
The only way this makes sense to me is if "exagerrated" reference signals
are sent down which will have an effect on behavior regardless of what the
current perception of finger position is. Is this what you mean?
If you followed the above you can see that it is not.
The
perception is then effectively ignored, since things are happening so fast
the perceptions could not be used anyway.
The perception is not ignored; the nice thing about the above model
is that it requires no ad hoc assumptions about systems that would
somehow know when to ignore or not ignore a perception. The trill
control model I described is the same ol' PCT model we all know and
love; it produces APPARENTLY open loop behavior simply because a higher
level system is demanding perceptions from a lower level system too
rapidly; this creates no problems (due to chronic error) if there are no
disturbances; in the trill situation there typically are NOT disturbances
to elevation control and the higher order result of the basically uncontrolled
changes in finger elevation [the trill] is produced); if, however, the pianist
wanted to do this on an undulating keyboard s/he would find the
resulting trill quite irregular -- and there would be error in both
the high (trill) and lower (elevation) level control systems; the pianist
would eventually reorganize in that situation (find a new piano or settle
for slower trills).
Avery Andrews (930117.1426) --
My wild guess about trills would go as follows. They are too fast to
be produced by a feedback system tracking kinesthetic reference
levels (e.g. for a feedback system to solve (or better, evade) the
dynamics problem). So something else has to happen.
I don't like this proposal because it is not parsimonious. If you agree
that trills can be controlled if they occur slowly (I bet Gary could
come up with a portable demo to show that they ARE) then why should they
suddenly become open loop just because they get faster? ; the model
above predicts APPARENTLY OPEN LOOP behavior from a CLOSED LOOP system
that is being driven beyond its limits. No new assumpions are needed
about a mechanism that knows when to switch from a closed loop to an open
loop system.
Of course, parsimony alone does not a model recommend. My model (as
I suggested earlier) makes specific predictions about the effectiveness
of control of finger elevation (resistence to disturbance of finger
elevation changes) as the frequency of trill increases. I presume
that your model would predict that there would be a step function --
from closed loop control (and effective disturbance resistence) to
open loop control (and no disturbance resistence) as trill frequency
increases. Sounds like an experiment to me.
Best
Rick