[From Bill Powers (920704.1200)]
Martin Taylor (920704.1300) --
RE: Plausibility of random reorganization.
I like that "symmetry groups." Maybe some day I'll understand what it
means. But I get the idea.
The continuation of the story is based on there being far more sensory
DoF than action DoF (degrees of freedom). Under these conditions, it
is not possible for all percepts to be brought simultaneously to their
reference levels.
This reminds me of a problem that comes up in speaking of controlled
variables that are functions of sets of controlled variables. People have
asked me "What happens when disturbances come along that alter the inputs
without changing the perception?" One always tends to think of some
concrete situation, and unconsciously puts into it more than the
definitions require. If you're controlling Ax + By, then ONLY that quantity
is controlled. If a disturbance changes x and y in the right proportions to
leave Ax + By with the same value, then x and y simply change, with no
resistance from the control system. ONLY what is perceived is controlled.
It's true, as you say here and have said before, that there are far more
input variables than output variables, particularly at the lowest level
where the ratio is (if you say so) 20,000:1. So clearly, not each
individual input signal can come under independent control.
What happens is that BUNCHES of input signals are perceived as a single
signal, and THAT SIGNAL is brought under control. This leaves an enormous
number of ways in which individuals within the bunch can vary, but that's
irrelevant to any given control system. In those dimensions, the bunch is
simply not controlled.
This leaves, of course, many potential bunches that are never perceived,
and thus are never controlled. In the uncontrolled degrees of freedom,
those bunches simply change when they are disturbed.
Some people learn to perceive some functions of their inputs among all
those that are possible. This is why individuals are different -- they
perceive and control the same environment in slightly or greatly different
terms. They don't need to find THE way of perceiving and controlling; all
they need is A way that is sufficient to form a coherent hierarchy good
enough to sustain life.
Most potential percepts never become actual percepts.
One function of higher-level systems is to employ subsets of the available
lower-level systems in compatible suymmetry groups.
There is intrinsic conflict (I use the word advisedly, because I
link it conceptually to the physico-chemical intrinsic variables that
determine survival)...
Hmm .. coming closer to my concept. Goody.
The question can, in principle, be addressed by computational
experiments, but I think it would be hard in practice. To do the
experiment, one would have to design a model world with controllably >many
degrees of freedom, in which the model hierarchy could be >reorganized.
There would have to be some effect of its behaviour on >some simulated
intrinsic variables, and so forth.
This is exactly what has to be done, hard or not. Of course we don't have
to start with the most complex possible physical world model. I'd settle
for three environmental variables and three intrinsic variables variously
dependent on the environmental ones. I've wanted to get moving on this kind
of computer experiment for a long time but have always had some other
project that seemed more essential for teaching purposes. Maybe, after the
cockroach and the arm and the motion-illusion experiment and the formant
tracker ... I seem to think that happiness is a bunch of big error signals.
We really would be getting along much faster if there were more people
actually working at this sort of thing.
I'll leave for another day the complications that arise when the
behaviour of the world is discontinuous.
Not much of that in the physical world at the level where we experience it.
···
-----------------------------------------------------------------------
Best,
Bill P.