Re: [asa] Results of Cameron's Survey

From: Iain Strachan <igd.strachan@gmail.com>
Date: Mon Jun 29 2009 - 11:13:20 EDT

On Mon, Jun 29, 2009 at 3:52 PM, George Murphy<GMURPHY10@neo.rr.com> wrote:
> You can put me down with Terry's #4. (Or, if only the 3 answers given
> originally are allowed, as is usually the case with standardized tests,
I'll
> take #3 "under protest.")
>
> I would not absolutely rule out the idea of front-loading of design (#2)
but
> it seems to me that hardwiring the detailed outcome of any physical
process
> into its initial conditions billions of years in advance is just the sort
of
> thing that chaos theory - which is more precisely "sensitivity to initial
> conditions" - rules out for systems of any complexity (i.e.,
nonlinearity).

George:

Just a quick query here. Is it not the case that it's not ruled out so much
as non-computable

For example if I try to integrate the third order non-linear differential
equations for the Lorenz
Attractor<http://en.wikipedia.org/wiki/Lorenz_attractor>then I
experience that if a slight change is made to the initial values of
the state variables, then after a certain time, two runs that are otherwise
the same diverge and bear no resemblance to each other. But the smaller the
initial delta, the longer it will take to diverge. However, divergences can
be observed even at the machine precision level, for example if I change X0
to X0*(1+eps) where eps is the smallest constant so that in the machine
1+eps > eps. (In standard double precision arithmetic eps has the value
2.2204e-016).

But if one had a machine with billions of bits of precision for the
arithmetic, instead of 53 (double precision arithmetic has 53 bits for the
mantissa, 10 for the exponent and 1 for the sign, making 64 in total), then
it's clear that macroscopic changes in the outcome will only appear after an
immensely long time because the corresponding value of eps is so much
smaller.

So I wouldn't have said it was ruled out unless God only uses 64 bit
arithmetic!

Iain

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Received on Mon Jun 29 11:14:11 2009

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