Chaos Theory; a place in biology?

John Reinitz reinitz-john at CS.YALE.EDU
Tue Sep 22 10:25:25 EST 1992

In article <133nmpp at> mwfolsom at (Mike Folsom) writes:
>In article <92256.194837MMF106 at> <MMF106 at> writes:
>>Hi there.  I'd like to pose a question that's been gnawing away at me:
>>can the principles of Chaos Theory be practically applied in
> (((stuff deleted)))
>>.........................................................Is Chaos Theory
>>the new paradigm shift, or just a castle in the sky?  What do ya'll think?
>>                                             Michelle M. Fink
>>                                             MMF106 at PSUVM.PSU.EDU
>I've been wondering about this to.  It may be that we are witness
>to the end of period when science has viewed the world in a highly 
>mechanical way.  I don't know much about nonlinear dynamics and 
>Chaos Theory but I'd like to know more. 
>Recently I ran across a new (1990) book in our library entitled
>__ Complexity, Chaos, and Biological Evolution __, edited by 
>Erik Mosekilde & Lis Mosekilde.  Pub. by Phlenum Press - its 
>volume 270 of the NATO ASI Series B.  I include the section  
>headings and statements from section heading pages for comment:

Nonlinear dynamics is clearly very important for biology. Life
is a process, dynamics is how you [precisely] describe a process,
and linear dynamics is already well-understood. Non-linear dynamics
is clearly important, but its name is rather uninforative, saying
what it isn't rather than what it is.

Chaotic dynamics has gotten a lot of attention recently, and it is
clear that chaotic phenomena occur in biology. One clinically
important example is ventricular fibrillation. 

I don't think it's of key importance right now, and here's why.
If you talk to physicists who work in chaos theory, they'll tell
you how there were plenty of dynamical systems around in the 19th
century that showed chaotic behavior, but people studied them in
parametric regimes where their behavior was quite regular. The situation
is similar in biology now. We don't understand the regular, predictable
dynamics of nearly all biological systems, and those are the dynamics
of key biological importance.

For example, from your book:
>Section V, Biological Structures and Morphogenesis -
>"Spontaneous form formation by self-organization in open thermodynamic 
>systems can form the basis for a whole new discipline of theoretical 
>study of developing organisms."

(At least some of us hope so :-) )

But of course development, overall, is not a chaotic process.
We all are born with the same number of fingers, toes, eyes,
and in the right place too! The theoretical problem is separating
the regularities from the noise.

In fact, your book had only the one chapter on chaos:

>Section VI, Chaos and Hyperchaos - 
>"With increasing number of state variables, new types of complex time
>evolution are realised, including various forms of higher order chaos."

>Right now I'd just like to know more about the whole area.

Chaos is well worth knowing about--- if only to understand the
limitations of current theory.  And *do* find some
of Shaws drawings of strange attractors :-)

John Reinitz

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