[From Bill Powers (930927.1315 MDT)]
Hans Blom (930927) --
Put an identical I-box in the path of r. If I is one-to-one,
this is allowed. Neither physically, physiologically,
psychologically, mathematically nor philosophically this seems
disallowed. In practice, it has the great advantage of putting
r' onto the same scale as the observable p'. Only in this
(observable) sense is it meaningful to talk about or design
tests for a "controlled variable".
This is valid only if you have previously defined the external
controlled variable in terms of the perceptual signal. In that
case, "I" is simply a multiplier of 1, with the appropriate
change of units from physical units to neural units. Putting the
same I in the reference signal path is fine as far as magnitudes
are concerned (multiplying by 1 doesn't change the magnitude of
the reference signal), but not as far as the units are concerned.
No conversion is necessary for the reference signal, as it is
already a neural signal. So the two "I"s are not the same: one
involves a conversion of units but the other cannot. The "I" in
the reference signal path is unnecessary, and for nit-pickers,
results in a signal with the wrong units.
···
---------------------------------
>p' |
> ----- p ----- ----- |
-->| I |--->|- | qo | | |
r' ----- r | CO|------>| W |->--
--->| I |--->|+ | | |
----- ----- -----
.....
So a better representation would be:
---------------------------------
>p' |
> ----- ----- |
> > > qo | | |
----------->|ICO|------>| W |->--
>(r)| | |
----- -----
Actually, I've used a shorthand much like this, but arranged to
show the same relationships that we show in the full diagram:
> r
--- ICO ---
> >
qi or p' qo
> >
<-- "W"<--
>
--- disturbance
The only difference from your diagram is the physical
arrangement, and the inclusion of an explicit disturbance.
One detail that I keep having a difference of opinion about
with Bill Powers is whether there is a "direct" path from
"action" to "perception":
r
+ \|/
- -------
---------->| C |-----------
> p ------- e \|/
------- -------
I | | O |
------- -------
/|\ /|\ | |
> ------------------------- |
> ------- |
-------------| W |<------------
-------
But this, too, may be a matter of semantics: where is the
border between "inside" and "outside"? Is my skin inside or
outside? How about the tissues between muscle fibers and skin?
I'm not sure what our difference is here -- I would route all
connections from O to I through the "W" (world) box. But this is,
indeed, a matter of where you draw the boundary. I draw it with
the nervous system above I and O, and the environment below them,
with I and O themselves being transducers in (and defining) the
boundary. From the viewpoint of the nervous system, the
environment is all that is not nervous system. So in a spinal
reflex, the input boundary is the set of sensors that detect
tension and stretch, and the output boundary is the set of motor
end-plates where the efferent signal from a spinal motor neuron
arrives at a muscle fiber. The muscle itself is part of "W",
transforming the outgoing neural signal into a contraction, and
the contraction into the stretch of the elastic elements of the
muscle and thus into a force applied to the tendons. The laws
here are those of the physical environment, not the nervous
system. In the PCT model, the loop is ALWAYS closed through the
environment by a path called, usually, the "environmental
feedback function." Thus all systems at all levels can be modeled
in the same way in relation to the environment.
When I act AS IF I catch a ball, my actions are hard to
distinguish from those actually employed when I play ball.
Well, yes, provided that you imagine a ball arriving from a
certain direction at a certain speed at a certain time. There is
no one set of _actions_ you can produce that would actually catch
any old ball: the actions have to vary with every instance of
catching a ball, or you won't catch it.
If you simply mean that you can produce arm and hand
configurations like those that are used when catching a ball,
this is true. But in PCT that is simply kinesthetic configuration
control, which may or may not have anything to do with catching a
ball. Those configuration-control systems are used by a visual
system in actually catching a ball, the reference-configurations
being adjusted to control the visual relationship between the
oncoming ball and the hands.
So it seems that no physical outside is required in order to
have a functional feedback system.
It's always required in the PCT model, because all levels of
control are defined so that the feedback loop is outside the
control system. In PCT the behaving system is the nervous system.
It is easy to add an internal "general model" (correlator +
memory + adaptation mechanism), such as the one that I propose
must exist, to the last diagram:
I remind you that in a real environment, there are independent
variables acting to alter the input. Your next diagram should be
drawn like this:
r
+ \|/
- -------
---------->| C |-----------
> p ------- e \|/
> ------- |
>--------->| M |<---------|
------- ------- -------
> I | |--------->| O |
------- adjust -------
/|\ /|\ | |
> ----------------------- |
> ------- |
----------| W |<------------
-------
/|\
>
----- independent disturbances
If the system is to be able to control p in spite of the presence
of independent disturbances (which is the general case), and if
most of these independent disturbances can't be perceived at the
source and are unpredictable (which is also the general case),
then the model M you propose is useful only for adjusting the
average system characteristics. It can't handle present-time
disturbances. A control-system model is not complete without
specific introduction of independent disturbances: they must be
explicitly represented in the system equations.
I have no objection to M as a method for stabilizing the control
system. We use something similar, although in a different place
in the diagram, to handle such adaptations. There are probably
several schemes that will work -- the only question is which one,
if any, the real system uses.
--------------------------------------------------------
Stefan Zadel (response to direct message) --
A disk with the arm models (and source code) is on the way. $20
plus -- don't forget -- $5 for your student membership in the CSG
for 1993-1994. I'm afraid that Arm Version 1 is in Turbo Pascal;
I never converted it to C.
------------------------------------------------------------
Best to all,
Bill P.