From: kurt@eskimo.celestial.com (Kurt Cockrum)
Subject: Re: Computability of the universe
Summary: Sorry about all the excess Platonism : )
Organization: >>> Eskimo North (206)-FOR-EVER <<<
Date: Fri, 11 Sep 1992 17:25:58 GMT

In article <1992Sep10.021939.10087@murdoch.acc.Virginia.EDU> lfoard@Turing.ORG (Lawrence C. Foard) writes:
>I've been arguing with several people over the "reality" of irrational
>numbers. By reality I mean a process in the real world that "operates"
>on irrational numbers. This is not to say that irrational numbers are
>meaningless since they represent the limiting case of many "real" things as
>the number of trials go to infinity. 
>
>My argument is that any given single expermental trial must be
>able to be >>exactly<< simulated by a finite turing machine in finite
>time. 

Yes, I agree.  Is this what you are calling "real"?  I would suggest that
what you have is a *representation* of an essentially *unspeakable* object.
A variety of these *representations* may exist (in each of our brains, if
nowhere else), not all identical to each
other, although they all "represent" the same, essentially unspeakable
object, because in the act of conceptualizing said unspeakable object, we
engage in unavoidable *representational* activity.  Don't forget that our
brains, which are our conceptual/representational organs, are finite, too.
Similar objects called streams exist in functional programming.  Any
unbounded loop or process might be said to represent *some* essentially
unspeakable object.  *Finite* computations are just a subset of the infinite
ones; a finite computation could be regarded as an infinite computation, the
last part of which is just a sequence of no-ops.  I suppose that
said unspeakable objects inhabit Platonic space.  Nice mind-candy.
Apologies if everybody in sci.math already knows all this... :)

One such object we give the name or representation "pi".
There's a Japanese fellow who's hobby is essentially trying to make large
representations of pi.  Actually, there are many "latent" objects in
Platonic space that never *will* be conceived or represented (by a conceiving
or representing thing), and so can be said to be "second-class citizens"
[ or members of a hyper-Platonic space :) ], because there just aren't
enough names to go around (most real numbers would seem to fall into this
category).  Guess I'd better stop now :) :).

Query:  is there any finite thing that *can't* be simulated
by a finite(-memory, I presume) Turing machine?

>If this is not the case we have to ask what we have left out of logic
>such that its not sufficient to explain the universe. In other words
>a world that cannot run on a finite turing machine is no better than
>assuming that some God above logic and reason pushs the particles
>around :-)

See below.

>I would like to go even further and say:
>The computing power available to us in 1 gram of matter in one cubic meter
>of space is exactly sufficient to simulate 1 gram of matter in one cubic
>meter of space.

Or, in other words, the identity simulation (the simulator simulates
itself, *not* something-that-is-not-the-simulator).  :)

>                In other words there is no inaccessable hidden
>reality/machinery. 

Perhaps it's hidden in one of those "compact" dimensions of the Kaluza-
Klein spatial theories :) [Which I don't even *pretend* to understand!]

>In the past problems an incompleteness in physical theories have always
>brought revolutions in physics. Maxwells equations not working in Newtonian
>relativity, etc.
>
>Who ever solves this puzzle (making finite computable quantum mechanics),
>will get Nobel prize, I just wish I knew where to start...  

Do I get it? :)

>If you do it remember where you heard it first :-)
>-- 
>------          Join the Pythagorean Reform Church!               .
>\    /        Repent of your evil irrational numbers             . .
> \  /   and bean eating ways. Accept 10 into your heart!        . . .
>  \/   Call the Pythagorean Reform Church BBS at 508-793-9568  . . . .
>    

Nay, nay, it is the lumpish Discretionists and Finiteers, with their
evil Integers and Rationals, which are like lumps in the Infinite Oatmeal
of the Continuum, who endanger all of our Platonic Selves, and indeed,
the very fabric of the universe.  Let us Transcend our finitude :) :)
-- 
kurt@grogatch.celestial.com (Kurt Cockrum)
 "People who sign their own .sig are just net.personality wanna-bees." --
 K. Cockrum