[From Rick Marken (961023.0900)]
Bruce Gregory (961023.1015 EDT) --
Suppose I lay out a rectangle of land and measure two sides of the plot. I
now say, "I can tell you what the diagonal must be by applying the
Pythagorean theorem." Would you accuse me of Pythagorean mysticism because I
think that there is some natural principle that "governs" this relationship
in some trans-physical way?
No. You are simply describing a mathematical fact (a logic level perception)
that exists when a configuration perception is in a particular state
(rectangle). The discovery of the existence of this logic level perception
(the Pythagorean theorm) was a great achievment; and I celebrate Pythagorus'
logic (program?) level perceptual skills.
The "mysticism" I see in Martin's use of attractor theory is that he is using
mathematical facts about the behavior of oscillatory systems to _explain_ a
phenomenon (the convergence of individuals in a society to certain goals). I
think that what Martin is doing is equivalent to using mathematical facts
about the "behavior" of rectangles (such as the fact that the diagonal of a
rectangle = sqrt[x2+ y2]) to explain the rectangular shape of plots of
land.
The problem with Martin's mathematical approach to understanding phenomena
was described rather nicely by Bill Powers (961022.1830 MDT) this morning.
Martin had asked a question similar to yours above:
Does the fact that 3 + 3 > 4 "govern" the process of dividing my four cows,
three to each son, in a trans-physical way? Is that a natural principle?
Bill's reply is, I think, worth repeating:
This is an excellent example. It might seem to a mathematician that you have
difficulty dividing four cows among two sons, three to each son, BECAUSE
3+3 > 4. But I claim that the difficulty is in the actual process of
division, while "3 + 3 > 4" simply describes the difficulty.
There would be no difficulty if you were talking about family secrets. You
can divide four family secrets between two sons, three per son, quite
easily. That's because giving some things away doesn't mean they can't be
given away again. Behind this principle expressed as "3 + 3 > 4" there are
facts about the physical world; if those facts were different, the
mathematical representation of them would have to be different. It seems
that in this universe one whole physical object can't be in two places at
the same time. That's what the real difficulty with the cows is. If that
rule didn't exist, as it doesn't for family secrets, it wouldn't be relevant
that 3 + 3 > 4.
My view is that mathematics simply reflects the way the world seems to be.
It doesn't govern the world; it is designed to fit the world, in an
idealized way. It's always a simplification of the world and it depends on
assumptions which never cover all of the possibilities. Its main advantages
are that it doesn't change the definitions of variables in midstream and its
rules are completely explicit, so they can be used by anyone with the same
results. It's an aid to clear -- but not necessarily valid -- reasoning.
That last sentence hits particularly close to my heart. Mathematical models
are cool; but they don't give wisdom in themselves. They MUST be validated.
That means that the behavior of the model must be tested against actual
experience -- and that means doing EXPERIMENTS to test the model.
The "mysticism" of Martin's approach is that it is based on the idea that we
can learn something about the world by reason alone; that mathematical facts
in themselves reveal something about the causes of our experience. I find
this attitude somewhat frightening -- but completely consistent with what I
perceive to be a general societal move toward the "attractor" of mysticism; a
move that began big time in the 1960s and has continued unabated into the
present (I say this as a big fan of the 60's; the mysticism was, from my
perspective, an unfortunate adjunct to the good part -- drugs, sex and rock
and roll;-)). I think this trend toward mysticism has had a very unfortunate
influence in many areas of science -- particularly physics.
It's tough times for those of us (like me) who are interested in testing
math models by "looking through the telescope" -- especially when those of us
who are doing it (like me) are not all Galileo caliber thinkers. So I tend to
get a little touchy when the people who don't want to help me look through
the telescope tell me that their mathematical models explain the way things
"must be". Just another one of my many character flaws, I suppose;-)
Bruce Abbott (961023.0900 EST) --
RE: method of levels
Bill Powers, meet Carl Rogers. Rogers called this approach "person-centered
therapy." Not surprisingly, you find it listed under "humanistic therapies"
in most psychology texts.
I think you are correct. All PCT adds is a model that (I think) helps one
understand what one is doing in "person-centered therapy" ("method of levels")
and why such an approach might be helpful.
Best
Rick