From: jhurst@amb4.ccalmr.ogi.edu (James Hurst)
Newsgroups: sci.environment
Subject: Catastrophe Theory in Enviromental Modeling?  NOT!
Summary: Provide a theoretical basis for it, will you?
Keywords: Stop the Catastrophe Theory Obfuscation
Date: 6 Oct 92 19:31:19 GMT
Article-I.D.: ogicse.43720
Distribution: world
Organization: Great White and the Buffalo Blues


[Because Gil's response to my last post was content-free, I chose to rephrase
my questions without the offensive political asides.]

>Gil Hardwick writes:

[regarding species protection versus ecosystem protection]
 
>We take a total systems approach here. 

Commendable.  I have argued at length here that biodiversity protection is 
best accomplished at the ecosystem level.

>Formal references can be made
>to Systems Theory and Strategic Management, which apply to any given
>endeavour, while in practice species mapping techniques deployed in
>context are the most useful.

Well, my BS detector went off when I read this.  To quote Rudy Kalman, "The
terms "system," "systems concepts," "systems approach," and "systems science"
are used so widely and so broadly as to connote fuzzy thinking.  [1]

Formal references to System Theory and $1.50 will get you a cup of coffee, but
neither will get you much respect in the hard sciences.  Coffee, by contrast,
is widely respected.  Sounds like marketing jargon to me, but perhaps in 
context it is respectable.

General Systems Theory was an attempt at a Grand Unification of the physical 
and social sciences, advanced by Bertalanffy, Laszlo, and Rappoport, among
others.  These gents attempted to apply the classical tradition of mathematical
systems theory to social systems [2].  Just to briefly note a few contrasts [3]:

			classical math. systems theory		social science

  1. Dynamics		Ordinary Differental Eqns.		Often unknown

  2. Dimensionality	Low (input/output)			Very, v. high

  3. Linearity		Linear					Nonlinear

  4. Coefficients	Constant				Variable

  5. Time dependence	Autonomous				Nonautomonous

  6. Domain		Frequency (complex)			Time (real)

  7. Mode of analysis	Laplace Transform, transfer fn.		Dependendent on
								problem struct.

  8. Parameters		Lumped					Distributed

  9. Regulation/control Output feedback/fixed plant		Adaptive control

  10. Typical problems	Stability, error, compensation design	Nature of the 
								system

  11. Nature of control	Regulator + I/O system			Feedback by 
								system of 
 							       simultaneous eqns

The field buried itself under a suffocating burden of Meaningless Jargon and 
Academic Pedantry rather quickly after a brief heyday.  A few groups, like
Jay Forrester's at MIT, hung on well into the 80's (They just lately briefly 
resurfaced).  Forrester modeled sets of difference equations using crude 
numerical techniques and feedback analysis.  Interesting, yes, and capable of
giving insight into system dynamics in limited cases, but for things much more 
complicated than inventory control, really pretty useless, IMHO.  Poor system
identification, dubious theoretical foundation, no numerical sophistication,
and frequent resort to throwing in parameters til the system works the way the 
modeler thinks it "ought" to. [4] (I trained w/ Forrester's group, btw).

>In my own work, spending so much time with Aboriginal people, I have
>also found Catastrophe Theory mapped onto the Social Sciences to be
>extremely effective in building complex analogues of the area under
>study. 

Well, the BS detector just went on Red Alert.  Perhaps you do build complex
analogues, and perhaps they even have some physical meaning.  But IMHO anything
to do with "Catastrophe Theory mapped onto the Social Sciences" and claiming to
be science has some serious credibility problems.

Rene Thom's Catastrophe Theory attempted to explain complex dynamical systems
in terms of a small set of simple 3-D manifolds.  The essential problem, 
relating observed behaviors to a theoretically or empirically defensible set
of governing equations, was never adequately addressed (see table 1, above).
But that didn't stop fans from inventing all sorts of flaky and fascinating
applications.  

Thom essentially insists on "structural stability," overall requiring that a
system of differential equations preserve its qualitative structure under
perturbation.  It makes sense to argue for structural stability only if one
believe that there are no interesting systems that MUST be modeled by 
struturally unstable equations.  (This is the quick version, this math is a
bit more tedious, but we can wade through it if Gil insists).  It was hoped 
that structural stability would be generic in all dimensions, but this is not
true for dimensions higher than 2.  [5]

All this occurred before the recognition that many or most natual complex 
dynamic systems exhibit the extreme sensitivity to initial conditions we now
know as chaos.  The notion that high dimensional systems of coupled partial 
differential equations would map onto smooth low-dimensional manifolds now seems
quaint at best.  The theoretical underpinning of Catastrophe Theory has been
kicked out.  For these reasons, and more, I am quite skeptical of anything 
*scientific* coming out of "Catastrophe Theory mapped onto the Social 
Sciences."   I don't doubt you do complex analogues, Gil, and they may well
be effective at advancing nonscientific goals.  However, I have serious 
doubts that such analogs bear significant resemblance to the physical processes 
of the environment.  The burden of proof rests with the proponents.

Of course, I may be wrong, and the ethnological community in Perth may have 
overcome these obstacles to create serious and impressive applications.  I
would be delighted to be so misinformed.  Please correct my misapprehensions, 
Gil.  We look forward to your lucid explanation of Catastrophe Theory as a 
legitimate tool in the Social Sciences.  Don't spare the references.  

Go ahead, Make My Day.  ;^)

Remember, Gil, this is SCI.environment.  If you're having trouble following 
the discussion, or just want to chat about dated, outlandish, and discredited 
theories, may I suggest talk.environment or alt.conspiracy?  

>Environmental stress levels and trigger events can be followed
>closely then by field assistants, often local people, and their data
>can be gathered later for processing.

This seems logical.  Environmental monitoring is commendable.  Why on earth 
dress threshold effects and statistically tractable occurrences in such dubious 
pseudoscience as Catastrophe Theory?  It certainly damages your credibility.  
Pretending nonexistent rigor is intellectually dishonest.

					Cheers,

					Jim

"There are, generally speaking, two circumstances in which it is difficult to
analyze mathematically a social system:  the first is when it is not linear;
the second is when it is."   B. Hendricks, "Some Confusions in the Qualitative
Analysis of the Social Sciences."  

[1]  R. Kalman, et. al, Topics in Mathematical Systems Theory.  McGraw-Hill,
New York.  1969

[2]  Ludwig Von Bertalanffy.  General Systems Theory.  George Braziller, New
York.  1968

[3]  David Berlinski.  On Systems Analysis:  An Essay Concerning the Limitaions
of Some Mathematical Methods in the Social, Political, and Biological Sciences.
MIT Press, Cambrige MA.  1976.

[4] Jay Forrester.  Industrial Dynamics.  MIT Press, Cambridge MA   ? date ?

[5] S. Smale.  "Structurally Stable Systems Are Not Dense."  Am. J. of 
Mathematics, V. 86, pp 491-496.  1966.

Disclaimer:  As usual, I speak for myself.
Newsgroups: sci.environment