[Rick Marken (920328 11:00)]
I want to clarify the points I made on friday in response
to Greg Williams suggestion that we direct our discussion to
hypotheses about the INTERNAL organization that produces the
observed behavior of living systems. As usual, Bill Powers
makes the point I wanted to make -- and far more clearly and
concisely -- in his 1978 Psych Review article (Quantitative
analysis of purposive systems) that is reprinted in the
the Living Control Systems collection.
The crucial point is on p. 146 of the book. Two equations are
found at the top of the page:
q.o = 1/g[q.i* - h(q.d)] (1) and
q.o = f[h(q.d)] (2)
Both equations describe the functional relationship between
an environmental (disturbance) variable, q.d, and a
system output variable, q.o. In both equations, the function
h() is the physical law that maps the distal stimulus variable
to the proximal stimulus variable (q.i). If the proximal variable
is visual then h() can be thought of as a linear multipler.
Equation 1 is the relationship between distal stimulus and
output response for a system where there are strong negative
feedback effects (from q.o to q.i -- the latter being the
proximal stimulus). The functional relationship between stimulus,
q.d, and response, q.o, is the inverse of the feedback function,
g(), that relates output to proximal input (q.i = g(q.o)).
This means that the observed relationship between input and
output has nothing to do with characterisatics of the
organism (the INTERNAL organization that we are trying to
understand, presumably). If you do an experiment with a
negative feedback system where you manipulate a stimulus
(q.d) and measure a response (q.o) and then plot q.o as a function
of q.d then the shape of that plot depends on the shape of the
feedback function (g()) and not on the properties of the organism!!!
Conventional psychologists do this kind of experiment to understand
the internal organization of organisms. Equation 2 shows that
they would be learning about the internal organization of the
organism IF they were dealing with an open loop system (what
Bill called a Z system -- one with zero negative feedback
effects of its outputs on its inputs). Equation 2 describes
the functional relationship between distal stimulus (q.d) and
output (q.o) for a Z system. This relationship depends on
the function f() which is the "organism function". f() is
a description of how the nervous system of the organism
transforms inputs into outputs. It is the function we must
know if we are going to develop a model of the internals
of the organism -- because it is the nature of these internals
that presumably determines the nature of f().
But f() does not even show up in the equations relating
inputs to outputs in a negative feedback system; it gets
"cancelled out" in a sense by the feedback effects.
So this is really the point I was trying to make on friday.
We will find input-output relationships when we study
organisms. But if the organism happens to be in a negative
feedback SITUATION with respect to the relevant inputs and
outputs, then observed relationships between
input and output tell us nothing about the organism, only
about it's environment. Models based on input-output studies
of negative feedback systems are, thus, models of the environment,
not of the organism (although the components are implemented
as internals to the organism part of the model; if the organism
is actually controlling a visual variable, for example, your
organism model -- which is a model of 1/g() -- is a neural
net model of the inverse of the laws of optics).
So, before building models of organisms, we should first
find out if the variables involved (paricularly q.i and q.o)
are part of a negative feedback SITUATION. This is done by
tesing for controlled variables.
Regards
Rick
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**************************************************************
Richard S. Marken USMail: 10459 Holman Ave
The Aerospace Corporation Los Angeles, CA 90024
Internet:marken@aerospace.aero.org
(310) 336-6214 (day)
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