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MathGroup Archive 2004

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elements of cultural strength from the von Bertalanffy standpoint

  • To: mathgroup at smc.vnet.net
  • Subject: [mg49436] elements of cultural strength from the von Bertalanffy standpoint
  • From: Roger Bagula <tftn at earthlink.net>
  • Date: Tue, 20 Jul 2004 07:53:26 -0400 (EDT)
  • Reply-to: tftn at earthlink.net
  • Sender: owner-wri-mathgroup at wolfram.com

  From notes made in "General Systems Theory":

Elements of Cultural strength:
1) Mood ( economic climate/ Kondratieff-Mandelbrot cycles)
2) Resources ( Club of Rome "The Limits of Growth " simulations)
3) Population dynamics (Verhulst/ Lotka Volterra nonlinear differential 
equations)
4) Other elements ( cultural competition)
A nonlinear equation like:

Csf'=Csf+w1*P(mood)+w2*P(resources)+w3*P(population)+w4*P(competition)

{w1,w2,w3,w4} are observed weights from statistics like the stock market,
oil and rare metal prices, census and wars.
The map represents a multidimensional chaotic equation
that isn't easy to solve.
Isaac Asimov pointed out that the course of such events could be
changed by one man's invention or discovery of a new
technology ( his Mule).


Using a Jacobian with a social structure matrix Det[M(i,j)]<=1
J=log(N)+3*log(detM)+log(1-K*detM/N)-->1
which gives:
N-K--> Exp(1)
The social structure matrix assumption as being unitary or below
is that cultures have a convex hull structure:
that they live for a time then die.
This assumption is pretty much what history tells us.
That cultures have cycles like the stock market...
and sometimes just collapse in a catastrophe.
The Club of Rome results are pretty much the same projection the 
Petroleum  Geological predictions for future oil reserves
and were never a surprise to anybody.
What math says and what happens is usually different, but
many times because we heed the math.

This is an example Mathematica notebook showing a solution of a
  type of 4d system. x is taken as population like
and w as resource like: y,z are taken as mood and
competition variables.
I further added a cultural strength variable in another version
and it worked as well.
This set is not a "serious" model, but
one that I thought might calculate from my
previous 4d chaos work.
It is to show how such a model can be set up and solved using Mathematica.
Respectfully, Roger L. Bagula
tftn at earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 
619-5610814 :
URL : http://home.earthlink.net/~tftn
URL : http://victorian.fortunecity.com/carmelita/435/

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-- 
Respectfully, Roger L. Bagula
tftn at earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
URL :  http://home.earthlink.net/~tftn
URL :  http://victorian.fortunecity.com/carmelita/435/ 


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