This didn't seem to get distributed. Here we go again (slightly
edited); I apologize if it repeats. (I also apologize for using
1/f() to denote the inverse of f();-))
···
----------------
From Rick Marken (970128.0900)]
Me:
The nervous system controls perceptual inputs; it doesn't
calculate actions.
Scott Stirling (970127)--
So no mathematical calculations are involved, right?
Excellent questions in your post, Scott. Avery.Andrews (970128, Eastern
Australia), one of our other resident linguists, gave an excellent
answer. But I think this topic is so important that I will try to give
one myself.
Control theory is about how people produce intended results (such as
a caught ball). PCT says this is done by control of a hierarchy of
perceptual variables. Blom et al (the "Modern Control Theory" -- MCT
--crowd) say it is done by calculation of outputs based on a "model" of
the environment.
Here is a way to look at the MCT approach to the production of
intended results. MCT recognizes that intended results are produced
by the outputs of the system and that there is a functional
relationship between outputs and results. This functional relationship
is called "the environment function" or the "feedback function". Here
is an example of an environment function that relates a human output
(neural current) to a result of that output (distance of a ball from
the hand):
Result + |<---------------------------------*
(Hand/Ball | * |
Distance) | * |
> * |
(caught) 0|<----------------------- * |
> * | |
> f(o) * | |
> * | |
> * | |
- | * v v
-----------------------------------------
Output (neural current, spikes/sec)
The stars map out the "environment function", f(o), that relates
what your nervous system does (generates neural currents) to a result
of that neural activity (movement of your hand to a position relative
to the ball). Note that the function is VERY non-linear, though it
is monotonic.
According to MCT, if you intend to produce a particular result (such
as the result "ball zero distance from hand" which I call "caught" on
the graph) then you have to _compute_ the neural currents that you
have to generate to produce this result. In order to do this, you
have to have a model of f(o) in your brain (this is the "model" in
"model based control"). If you have a model of f(o), then you compute
the output required generate that result by "working back" from the
intended result (the value of f(o)) to the output (o) that produces
that value of f(o). That is, you find the inverse of f(o); this is the
value of output that produces the intended result f(o).
Computing the inverse of f(o) is like moving from the intended result
on the y axis above, along the horizontal line until you hit f(o). At
that point you move verticaly to the point on the output axis to find
that value of output that produces that value of f(o) (the intended
result).
If you intend to produce a different result (such as having the ball go
over your hand by a certain amount) then you start from this new result
(which is the value of f(o) at the + sign), move horizontally to the
f(o) curve and then move down to find the output value that produces
this result.
So MCT says that, in order to produce intended results, we have to
have a good "model" of f(o), the environmental function that relates
neural activity (the only output that is completely determined by the
control system itself) to the intended result. PCT questions this
model on two grounds: 1) it seems VERY unlikely that the brain can
do the computations required to estimate f(o) OR to compute it's
inverse and 2) this model fails to explain how we produce intended
results in the context of _unpredictable_ and _undetectable_
disturbances. The result on the y axis is not just a function of our
outputs; it also a function of forces that are independent of our
outputs -- such as gusts of wind -- that are completely unpredictable.
Despite such disturbances, we are able to reliably produce the results
we intend; we can, for example, catch a ball rather reliably on a windy
day.
The MCT approach to the production of intended results is based on
open-loop concepts of behavior that were (unfortunately) borrowed by
control theorists (who had been moving in the correct direction until
then) from psychologists.
A real closed loop control system doesn't doesn't compute outputs;
the outputs of a closed loop control system are always proportional
to r-p, the difference between the intended, r, and actual, p, results
of output. PCT explains the behavior that MCT says is computed output
in terms of controlled INPUT. A control system produces intended
results because it can PERCEIVE the state of those results (for
example, it can perceive the distance of the ball from the hand) and
it can vary its outputs appropriately (meaning, with the appropriate
SIGN and GAIN) to keep "pushing the perception of the result toward the
intended state, r.
The significant "computation" that goes on in a control system occurs
onn the INPUT (perceptual) side of the system and in the ORGANIZATION
of the relationship between control systems. In order to catch a ball
you have to design a control system that can _perceive_ the state of
the intended result; that can _continuously_ percieve the distance of
the ball from the hand, for example. You also have to design other
control systems that can control perceptions of acceleration and
velocity of the hand (to move the hand relative to the ball),
perceptions of convergence of the eyes (to keep the ball and hand
"centered" in vision), etc.
All of these aspects of the design of a hierarchical perceptual
control system, one that can produce intended results in a disturbance
pronce environment (and in an environment where even the environment
function, f(o) can change!), are embodied in Bill Powers' Little Man
demo that Avery mentioned. When you understand how the Little Man
works you will have gone a LONG way toward understanding how HPCT
works and (I believe) how humans work, too.
Best
Rick