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From: tmoran@acm.org
Newsgroups: comp.lang.ada
Subject: Re: Generation of permutations
References: <3CD9505F.344C13EA@san.rr.com>
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> > If your random program generator will create all possible configurations
> 1) A random program generator will not necessarily create all possible
> configurations of RAM unless you run it an unbounded number of times.
  "If X then Y" is not disproved by "not X".  And you are thinking of
a mathematical random generator.  Randomness is not important for the
original argument - completeness is, as you note.  Try

  Seed : Big_Number_Type := 0;
  function Random return Big_Number_Type is
  begin
    Seed := Seed+1;
    return Seed-1;
  end Random;

It may not be statistically random, but it surely returns every
possible value of Big_Number_Type.

> 2) In trying to keep track of how many times you've done something, you
> wind up using memory that you might not have. For example, you can't
  Clearly you can't have the machine watch itself.  I'm sorry if that
wasn't clear.  But a finite machine can be watched by another (larger)
finite machine.

> 3) Finite computers are uninteresting to theoreticians. :-)
  And infinite computers are of only modest interest to [software]
engineers.  Like proving there is no largest prime.  Interesting,
educational, encouraging (or discouraging), but not a reason to
stop trying to make a better primality testing program.