Re: [asa] Results of Cameron's Survey

From: George Murphy <GMURPHY10@neo.rr.com>
Date: Mon Jun 29 2009 - 12:10:03 EDT

Iain -

This gets into the murky area of the interface between classical chaos theory & quantum mechanics, where I claim no great expertise. Since quantum mechanics is linear there's no "quantum chaos" in a straightforward sense. But in specifying the initial conditions more & more precisely for a classical system, as you suggest below, you'll eventually get to the limit specified by the uncertainty principle, & below that point you can't go. With a strong interpretation of QM even God can't because the uncertainty principle is not just about limits on what we can measure but is a statement that position-momentum pairs that violate it don't exist.

Shalom
George
http://home.roadrunner.com/~scitheologyglm

  ----- Original Message -----
  From: Iain Strachan
  To: George Murphy
  Cc: asa@calvin.edu
  Sent: Monday, June 29, 2009 11:13 AM
  Subject: Re: [asa] Results of Cameron's Survey

  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 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 12:10:41 2009

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