(np) Reich + French theory - does it get any better than this?

[Monte Davis]

Mike Bailey:

> But seriously, Monte, what the heck is catastrophe theory, 
> and why isn't it compatible with orgonomics?  (if I may inquire?)

The name "catastrophe theory' was applied to both (1) a cluster of proven,
uncontroversial theorems in algebraic topology and (2) a very controversial
philosophical argument that the results of those theorems tell us something
deep (and sometimes useful) about how all sorts of processes are organized.

Think of any situation that that can be modeled with a 3D graph, where the
"z" value (height) is quantitatively dependent on the x and y values. For
example, the three axes could be the pressure (x), temperature (y) and
volume (z) of a gas. Any given combination of P, T, and V represents a point
in that space. All the possible V's -- the values for all combinations of P
and T -- form a curved, continuous surface. But what if the surface is
folded over itself so that there are two (or more) possible V values for a
given P and T? That would mean the volume could "jump" from a high to a low
value or vice versa while temperature and pressure stay the same. Which
would be crazy -- if you'd never seen H2O as ice, water and vapor. A
catastrophe is any such discontinuous jump in an otherwise continuously
varying system.

The mathematical part of catastrophe theory was the proof that for three and
four dimensions, there are only seven  possible *kinds* of fold in such a
"behavior surface" that are both topologically distinct (i.e. one can't be
smoothly transformed into another) and structurally stable. That last
criterion needs a book to explain it, but in very crude terms it means that
while you could in principle imagine an unlimited variety of folds and
wrinkles, any tiny perturbation causes all of them to collapse into one of
the seven -- so those are what we should expect to encounter.

Think of those seven types of fold (which Rene Thom dubbed the "elementary
catastrophes") as like the 3 (and ONLY 3) regular polygons that will tile
the plane (triangle, square, hexagon) or the 14 (and ONLY 14) Bravais
lattices that can be repeated indefinitely in a 3D crystal structure. (
http://en.wikipedia.org/wiki/Crystal_structure ) All are statements about
the constraints of 2D and 3D space: not "just anything" can happen, and we
can expect any surface tiled with regular polygons... any perfect crystal...
or any behavior controlled by two or three independent variables... to be in
accord.

Thom argued that nearly all science's mathematical models for natural
processes -- and a great many of our mental models of "that effect depends
entirely or primarily on the interaction of these two or three causes, and
once in a while the effect jumps from one level to another" -- fall into
that last category. Therefore, he said, the elementary catastrophes are
ubiquitous in nature and in our modes of thought: natural starting points
for an effort to recognize, classify, and sometimes predict "jumpy,"
discontinuous behavior of all kinds.