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Path: cantaloupe.srv.cs.cmu.edu!rochester!udel!gatech!howland.reston.ans.net!ix.netcom.com!netcom.com!kovsky
From: kovsky@netcom.com (Bob Kovsky)
Subject: Re: Chaos
Message-ID: <kovskyD8A6GC.6zJ@netcom.com>
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References: <95128.175055S628602@vm.uni-bocconi.it>
Date: Mon, 8 May 1995 22:28:59 GMT
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In article <95128.175055S628602@vm.uni-bocconi.it>,
 <S628602@vm.uni-bocconi.it> wrote:
>What exactly is chaos (or Kaos or Caos;doese the spelling implicate different m
>eannings?) is it a mere synonym for anarchy or doese the word encompass a broad
>er reality? What is its relationship with existance and every day life? Any enl
>ighting answer are more than welcome
>                                         Best of wishes Lorenzo (lac)

	In common parlance, "chaos" refers to disorder, especially 
primordial disorder.

	Mathematicians have <borrowed> the term to describe various kinds
of mathematical objects (one description of "chaos" below).  When
mathematicians use the word "chaos," it is a <metaphor>.  Mathematicians
and their comrades in computers often borrow terms, use them as metaphors,
and then delude themselves that they are talking about the original
reference.  For example, some mathematicians specializing in computers
talk about <computer science>.  Now, "science" in its original form refers
to the study of naturally occurring phenomena.  Hence, while there might
be some forms of "computer science," such as psychological studies about
how human beings react when using computers, the term "science" does not
actually reference the activity of mathematicians using computers.  That
activity is mathematics. 

	Similarly, mathematicians specializing in computers like to talk 
about "artifical intelligence."  They talk about "what the computer 
does."  Of course, a computer "does" nothing in the sense that a human 
being "does" something, i.e., purposeful, conscious activity.  A computer 
is a machine whose operations can be organized by a human being.  All the 
"intelligence" is that of the human who programs the computer.  (Sly grin)

	As to "chaos":  There are mathematical objects called 
differential equations (the same principles apply to mathematical objects 
called difference equations).  A "solution" to a differential equation 
involves two mathematical objects.  One object is called "the initial 
conditions."  The other object is called the "orbit."  The latter term is 
borrowed from the motions of planets, which were the first natural 
phenomena splendidly described by mathematics.  The differential equation 
is the same no matter what the initial conditions.  

	Prior to modern times, the focus of attention was on differential
equations in which a small change in initial conditions was associated
with a small change in the orbit.  If you drop two balls to earth, even
from a distance as far away as the moon, they will stay close to each
other all the way down. 

	Recently, attention has focussed on differential equations where 
small differences in initial conditions yield big changes in the orbit.  
The favorite metaphor is that "a butterfly flapping its wings in China 
creates a thunderstorm in New York"  (or some such).  This is a metaphor 
because reality only rolls once and it is not possible to compare two 
scenarios, one where the butterfly and the other where the butterfly does 
not.  

	Enough flapping.

	

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    kovsky@netcom.com   |  Materials available by anonymous ftp
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