true randomness

[Clay Spence x3039]

Alexis and Mike,

Mike said:
> Adding a geiger counter to a Turing Machine may seem to make a machine
> more powerful, but ...

I did not mean to imply that adding a true-random generator would make
a Turing Machine much more powerful, although for certain applications
it would be helpful.  I read recently of a physicist who wanted to
simulate the three-dimensional Ising model, and used a newer
pseudo-random number generator which was supposed to be better than
some others.  To test his program he tried it on the two-dimensional
Ising model, for which the exact statistics are known.  The simulation
gave the wrong answers.  After searching for bugs, he switched to an
older pseudo-random number generator and the simulations produced
answers consistent with the exact statistics.  Of course, it is always
possible that he missed a bug in the code which implemented the newer
generator.

> ...it seems possible to me that there could exist a deterministic
> universe in which there could exist measurers (i.e. scientists) who
> would be confused into believing (for a time) that their universe
> must be probabilistic ...

As Paul Gleichauf pointed out, the non-local effects in quantum
mechanics forbid local hidden variables, so a deterministic
interpretation of quantum mechanics must be somewhat odd.  David Bohm
(I think that's the right Bohm) invented one which few people like, but
it's fairly simple and as far as I know makes predictions which are
identical to those of quantum mechanics.  The people who prefer more or
less conventional interpretations which involve randomness do so
because this seems simpler, and so Occam's razor favors it as the
preferable hypothesis.  You are always free to ignore Occam, he
frequently picks the wrong hypothesis, but it isn't clear that anyone
is confused.

And Alexis said:
> Since the direction that water spins down a drain thats located on the
> equator should also be truely random (presumably the initial perturbation 
> from the unstable equilibruim would come from Brownian motion in the
> fluid), it would seem more artistic, if less pragmatic, for an "intel-
> ligent" computer to periodically flush a line of toilets so situated.  
> (Yeah, I'm a computer scientist, but I don't do hardware :-)

It is true that one can get true randomness from a chaotic
deterministic system with infinite state, unlike a pseudo-random number
generator.  Rolling dice should work ok if done carefully.  (I gather
Turing machines don't have infinite state information?) As for toilets
flushing, which way the water spins depends more on the structure of
the toilet.  Even in New Jersy at about 40 degrees north, in
non-rigorous experiments I can get the water in my bathtub to go either
way.  I could do it even farther north in Goettingen, Germany.

About Alexis' summary of Mike's point:
>  b) it is far from clear that functionally equivalent computational
>	effects can not be generated by a Turing machine

I don't think this is relevant.  Neural nets can be simulated on a
Turing machine, and most people (or at least some people) don't think
it's a waste of time to study them.  The problem is assertion a), or
some modification of it.  I haven't yet heard an argument for quantum
computers that I found convincing.

Clay