From: prim!dave@germany.eu.net (Dave Griffiths)
Subject: Re: Computability of the universe
Organization: Primitive Software Ltd.
Date: Fri, 11 Sep 1992 18:15:52 GMT

In article <18mgemINN34o@roundup.crhc.uiuc.edu> hougen@uirvld.csl.uiuc.edu (Darrell Roy Hougen) writes:
>lfoard@Turing.ORG (Lawrence C. Foard) writes:
>
>I'm afraid you are laboring under several mistaken or naive
>assumptions.  This is not meant as a flame, but one should be wary of
>thoughts that everything is simple and solved and knowable.
>
>) 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. 
>
>First of all, processes in the real world don't operate on numbers at
>all.  Numbers are just a mental abstraction of quantities that exist
>in the world.  Before dismissing irrational numbers, try to think of a
>process that operates on rational numbers. 
>
>If I give you a piece of metal and ask you how long it is, what will
>you answer?  If you measure it, you will undoubtedly arrive at a
>rational number, but that is only because rational numbers have finite
>representations in the usual representational scheme.  Therefore,
>measurements are always rounded to the nearest number of a given
>precision.  In reality, however, the length may not even be well
>defined in a mathematical sense.  As one magnifies the piece of metal,
>substructure will emerge showing not one length but many lengths and
>as the structure is magnified still further, fluctuating electron
>clouds will appear and the boundary will become fuzzy.  Thus, length
>is an abstraction and measurements of length are only meaningful at
>some scales.  The length of an object is neither a rational nor an
>irrational number, but it is convenient to represent it by the
>rational number that best approximates it.
>

I think you've missed the point. You assume that there is "reality" out
there that is infinitely subdivisible. You are thinking of a number or
a measurement as being an approximation to the "real" size. What the
original poster implied (I think :-) is that there is _no_ absolute reality
out there.

Question: how can you ever "know" that length in the real world is
a continuum if you're always limited in the accuracy of your measurements?
This is an act of faith on your part! It is a model of reality that so
far has worked pretty well. But it has problems. Infinities crop up all
over the place. And that doesn't make sense.

Now imagine if you could build a massive computer, bigger than the universe
and you ran a simulation of the "real" universe on it, and imagine if the
match between the simulation and "reality" was sufficiently good. Result:
intelligent life evolves in the simulation and from it's point of view the
world feels pretty "real", it's just that it starts to notice wierd things
like energy only being allowed in certain discrete quanta ;-).

Now _if_ this was possible, what use is your model of a "real" world? Apply
Occams Razor: there is no need for the infinite information content of a
real world.

Is the music on your compact disc somehow less than real? Would it continue
to be so if the sampling rate was far in excess of what your ear could
detect?

The discrete model _is_ reality.

:-)

Dave Griffiths