From: maoh@phyast.nhn.uoknor.edu (Maureen O'Halloran)
Subject: Re: behavior and evolution
Organization: Engineering Computer Network, University of Oklahoma, Norman, OK, USA
Date: Mon, 17 Aug 1992 01:33:25 GMT

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

Sorry, I should have said some problems.  Didn't mean to imply we
would understand everything if only we had big enough computers.

>>> .... 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.

I still wouldn't call that massive assumptions. I just didn't want to
leave the impression that statmech is on shaky grounds.

>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.
> ....

Sure.  It's hard to discuss God without a lot of cultural bias though.
Medieval theologians were often no dummies and thought they were being
perfectly logical but were working with certain unchallenged
assumptions.  Some of the results were pretty screwy though!
Of course we're _perfectly_ logical now ....

I tend to take a reductionist view of the definition of science.  I.e,
that you can't do "science" without being able to make reproducible
observations or experiments. This doesn't mean that you can't have
logical discussion about things that are not reproducible or that
nothing exists outside the realm of science.  It's just
hard to know if you're on the right track without the "reality check"
of experiment. Descartes started with "I think therefore I am" and
went on to derive God.  I haven't seen his argument but I can't get
past "I think I think therefore I think I am".  

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

>julian
> 

Sorry to break into your discussion then, but is it kind to
tease them that way?

--

Your original example of a sphere of visible universe was confusing
because in a _way_ the universe is "finite".  If it started out as a
point at t=0 (a.k.a. the big bang) then it has expanded to a "sphere"
of a "finite" size. Why do we say its infinite then?  Because of the
curvature of space-time you can never reach the "edge" of the
universe.  I can't think in non-Euclidean geometry, but the analogy I
heard was that the two dimensional surface of a sphere is finite 
but because its curved through a third dimension it has
no edges.  Similarly we are at the "center" of the universe, that is
its expanding isotropically around us, because its expanding like a
balloon and all points on the sphere expand equally and are symmetric
with respect to each other.  What's "outside" the universe?  Heaven
perhaps, but unfortunately we can't observe it.  Perhaps we're just a
bubble in someone else's universe.

Ain't physics confusing?

--- Maureen O'Halloran
 
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