You picked a bad example with pi. Many mathematicians manipulate pi
with exact precision in their calculations. Many use computer programs
to do this also, eg Mathematica. The lack of any possible representation as a
rational number does not prove a barrier to this.
Your point would be better made with an object such as Omega, or
countless other numbers that defy description.
My point was that discrete grids omit many objects that are within the
domain of describability. You cannot map the set of rational numbers
onto a grid, whilst preserving the ordering property. You you can
describe them, and enumerate them. Whilst a continuum may not exist in
itself, discrete CA models do not capture everything that lies in the
domain of discrete describability. I've had a lengthy and exhausting
argument with Hal Ruhl over this issue - I don't really feel like
repeating it.
Cheers
Joel Dobrzelewski wrote:
>
> Russell and Brent:
>
> I understand this is an extreme position, but I state it this way on
> purpose: to bring the issue to the foreground and get to the heart of the
> problem of science today.
>
> As long as we insist that continuous objects really exist - we will always
> be fooling ourselves and forever chasing an unobtainable ghost.
>
> Descriptions of continuous structures are only that - descriptions. And
> they will *always* remain finite and discrete.
>
> The symbol "PI" is a finite description for an infinite *process*.
>
> No sheet of paper or gigabyte of RAM can contain PI.
>
> And thus, any theory we create or program we write MUST truncate PI at come
> point... otherwise we will forever be waiting for the theory to produce its
> first result.
>
> const PI = 3.1415926535
>
> These descriptions are entirely misleading - only approximations - never
> reality.
>
> It would be better to do this...
>
> const PI = 11101010000100010001111111100000111
>
> But even this is wrong. To truly illustrate the point, we must do the
> following...
>
> function PI () as string
> do
> 'calculate PI
> loop
> end function
>
> Does the function PI() ever return a value?
>
> No.
>
> It is not within our reach.
>
> This is not proof that there is no continuum.
>
> Only evidence that there can be no continuum FOR US.
>
> For us, there can only be one infinite process in the Universe - the
> universe itself.
>
> The one calculation that never ceases... but always remains FINITE in extent
> and always DISCRETE. Always calculating PI to ever more decimal places...
>
> Joel
>
>
>
----------------------------------------------------------------------------
Dr. Russell Standish Director
High Performance Computing Support Unit, Phone 9385 6967
UNSW SYDNEY 2052 Fax 9385 6965
Australia R.Standish.domain.name.hidden
Room 2075, Red Centre
http://parallel.hpc.unsw.edu.au/rks
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Received on Mon Jun 18 2001 - 17:10:19 PDT