From: julian@fraser.sfu.ca (Julian Shillcock)
Subject: Re: behavior and evolution
Organization: Simon Fraser University, Burnaby, B.C., Canada
Date: Sun, 16 Aug 1992 22:26:00 GMT

maoh@phyast.nhn.uoknor.edu (Maureen O'Halloran) writes:


>We also can't solve any problem analytically (ie, write down an exact
>equation that is the solution) for more than two particles!  You may
>have heard some one say that the "three-body problem" has not been
>solved.  However given a big enough computer and enough time, we can
>solve problems numerically to arbitrary accuracy.

Not if it is in a chaotic part of its phase space we can't. Any initial 
error wil be exponentially magnified until we lose all accuracy. 

>When the number of particles in the system we're interested in gets
>large, things become so complicated they get simple again.
>Probabilities take over and statistical mechanics can be used to
>describe the average macroscopic properties of the system while
>ignoring microscopic motions of individual particles. If you use
>statmech and quantum at the same time you call it Many Body Quantum
>Theory. Thus the hardest problems to solve are "few-body problems",
>where the number of particles is too large to solve on present day
>computers, but too small for statistics to predict anything.
>  
>So the answer to "how many theories" depends on what you mean by a
>theory. Is F=ma a theory and F= GMm/r^2 = gravitational force 
>a separate theory?
>Or do you include gravity in classical mechanics when calculating
>trajectories and call them part of the same theory?

No, they are predictions of theories. Ideally there would be one theory
that predicted everything. But it would be rather incomprehensible.
I simply wanted to see what people thought theories were, as I have
heard some pretty daft "theories" on theories.
>> .... Then in stat. mech. one makes massive  assumptions
>>that allow predictions to be made but at the expense of knowing exactly what
>>the system is doing.

>Massive assumptions may be made in APPLYING stat mech, but the basic
>theory has very few assumptions.  The only one I can think of off-hand
>is that the probability of a certain macrostate is proportional to the
>number of microstates.

I was thinking of the ergodicity assumption, and the probabilistic way
we assume energy is shared out among all the particles in a system.

My idea of a theory is to take a set of initial assumptions and "givens"
then calculate the predictions/results of the theory and compare them with 
the experiements. There should not be more initial assumptions than
are demanded by the consistency o the theory, and Occam's razor applies.

But now in order to discuss science and God we cannot start from
assumptions that explicitly rule out a supernatural being: and,
of course, we must not simply assume such a being exists; we should
be open to evidence in the world and history and assess it.
The theories of physics patently do not include God but that is no
reason for disbelieving in God, in fact the fact that we can understand
some of the workings of the universe might lead us to consider a
rational creator who has imprinted the universe with a reflection of
this rationality. The obvious fact that we can DO science makes me more
sympathetic to a rational creator than, say, Descartes Evil Demon
who might be tricking him, or the New Age's quasi-mystical, pseudo-
scientific occultism. It might even allow us to distinguish between
deities (or philosophies) that postulate a chaotic universe or
a 19th century mechanical one.

I notice that no creationists have taken up my postings, I am 
disappointed.

julian