[From Rick Marken (940809.0845)}
Peter Cariani (940808) --
Rick, I think it's not a tall order to come up with a system that uses
intervals.
Agreed. But you often discover interesting things when you actually set up
the simulation; look at what Martin Taylor could have learned if he had set
up the one-way opposing control systems desscribed by Bill Powers
(940808.1845 MDT). I have no doubt that a model based on inter- spike
interval can be set up; it would be operating at a level of detail that is
somewhat lower than that at which we operate in our models -- that is, it
would operate at the level of spikes occurring over time; we assume that we
are dealing with numbers representing instantaneous spike rates (neural
currents). Bill Powers' version of an inter-spike interval based pitch
control model would be equivalent to a neural current based model. Yours
(based on coincidence detection) might behave a bit differently than the
neural current based model. It may be possible that these differences could
be picked up in behavioral or neurophysiological experiments. It would be
nice to start studying neurophysiology from a PCT perspective.
Darlene Dermil (940808) --
i'd like to know more about nonlinear control systems
In living control systems, nonlinearities exist wherever variables or
signals are transformed into other variables or signals. The function
transforming a controlled variable into a perceptual signal is surely
nonlinear (for intensity perceptions it may be a log or power function). The
neural comparator function is probably nonlinear (rather than a perfect
difference as we write it; r-p). The function transforming neural signals
into physical effects on the controlled variable is surely nonlinear.
These nonlinearities pose almost no problem for a living control system.
Stability can usually be achieved by adjustmenting the amplification and/or
the slowing that occurs in the loop. Because people are organized as a
hierarchy of control systems, they can even deal with nonlinearities that
are somewhat non-monotonic. This was illustrated experimentally in Powers'
Psych Review paper (1978) where he showed how people could deal with a cubic
relationship between their oun output and its effect on controlled variable.
For some values of output, the relationship between output and controlled
variable actually reverses, changing the net sign of the feedback from
negative to positive (bad). Other systems in the person seem to notice the
problem and reduce the gain in the positive feedback system to almost zero
until it is noticed that negative feedback has returned (the output has moved
back into the negative feedback range).
Best
Rick