From: paul@mtnmath.UUCP (Paul Budnik)
Newsgroups: sci.crypt

Subject: Re: Are there truly random phenomena?
Summary: Physicists have a bad record on this point.
Message-ID: <148@mtnmath.UUCP>
Date: 4 Aug 91 20:30:41 GMT
References: <> <>
Organization: Mountain Math Software, P. O. Box 2124, Saratoga, CA 95070
Lines: 26

In article <>, (Steven Bellovin) writes :
> In article <>, writes:
> > I think that trying
> > to create random-appearing signals in itself proves that things in nature
> > that by all criteria appear "random" are infact caused by something unknown. 
> Please study quantum mechanics before making statements like that.
> Here's a hint, though:  virtually all modern physicists think you're
> wrong.  And it's not because no one argued the point.

Physicists have a pretty bad record on this point. In the 1930s von Neuman
published a famous proof that claimed no more complete model could produce
predictions consistent with quantum mechanics. This was widely accepted
until the mid 60's when Bell published a refutation. There is no basis
for the widely accepted belief that randomness is fundamental to quantum

If you think about this as a problem in the theory of recursive functions
you can see how difficult it would be to come up with a theoretical argument
or experimental results that prove this. You are asking is there a recursively
enumerable set that includes all the predictions of quantum mechanics (a
recursively enumerable set) and all the observed results of experiments
(a finite set). Since the union of a finite and recursively enumerable set
is a recursively enumerable set the answer is yes.

Paul Budnik