RE> quantum neural computer announcement

[aboulang@BBN.COM]

   To pick a nit:
   Since a correctly operating (pseudo) random number generator on a
   (conventional) computer *is* "produced by a chaotic, deterministic
   system", your assertion that you can use a computer to solve
   Schroedinger's equations and then select (pseudo) randomly based on
   the resulting probability distribution is equivalent to saying that
   you *can* produce this effect using a (chaotic) deterministic system.

Watch for them small brittle eggs ;-). The crux of the matter is that
computers (silicon or whatever) need to have access to the reals to
generate non-pseudo random numbers. The non-pseudo bit is important
here. There is a symbolic dynamics view of random number generates
that brings home the point that all these random number generators do
is chew on the bits that were originally input. You can't simulate
truly random choice with these. If you had access to a source of
infinite algorithmic-complexity numbers (most of reals), you would not
run out of bits. (Actually there was some interest by a fellow by the
name of Tom Erber to look at some NIST Penning-trap data to look for
recurrences in the "telegraphic" fluorescence of the trapped ion. He
did not see any.) There is a model of computation using real numbers
that some high-powered mathematicians have developed:
  
   "Blum L., M. Shub, and S. Smale, "On a Theory of Computation and
   Complexity Over the Real Numbers: NP Completeness, Recursive
   Functions and Universal Machines", Bull A.M.S. 21(1989): 1-49.

   It offers a model of computing using real numbers
   more powerful than a Turing Machine.

See also the following:

   "Neural Networks with Real Weights: Analog Computational Complexity"
    by Siegelmann and Sontag.
   This is available on neuroprose in (siegelmann.analog.ps.Z).

The problem with all of this is the plausibility of access to the
reals even with analog realizations. But this gets us off into another
topic.

I do however see the Blum, Shub, and Smale work as very foundational and
important.

Regards,
Albert Boulanger
aboulanger at bbn.com