Re: True random numbers

From: Dr Chaos (mbkennelSPAMBEGONE_at_NOSPAMyahoo.com)
Date: 03/23/04 

Date: Tue, 23 Mar 2004 19:20:42 +0000 (UTC)

John C. Bollinger <jobollin@indiana.edu> wrote:
> Leslie Ballentine wrote:
>
>> There is an enormous amount of confusion about the meaning of the term
>> "random". Ask your friends for a definition, and consult a few books, and
>> you will discover a great variety of proposed meanings for the word.
>
> Indeed. A glimpse at Webster's New Universal was enlightening, mostly
> because it didn't include a statistical definition of the term.
> Consultation of my nearest statistics text then surprised me when I
> discovered that although it defined "random variable", "random number",
> "random process", and a few other related terms, it never defined
> "random" itself. Interesting.
>
>> I do
>> not have a pet definition to promote, but I would like to point out some
>> of the variety.
>>
>> 1. Random does not imply inteterministic. Indeed, dynamical chaos has
>> been aptly described (by the late Joe Ford) as "deterministic randomness".
>
> I find that one clever because it seems so oxymoronic (to me), yet as
> you say, it's very apt.

"random" is a mathematical description and mathematical concept, like
say, "continuously differentiable function".

Physical things have properties, which in some limits, are best describable
by mathematical laws, which humans have constructed to fulfill the axioms
of probability theory.

In that theory there are devices called 'random variables'.

Reality is as reality is.

> The fact that the value of each future output put bit is indeterministic
> does not guarantee absence of correlation, true. Nevertheless the
> underlying physical theory does not introduce such correlations, the
> equipment is designed to avoid introducing correlations as much as
> possible, and actual the self-correlation of the output has been
> examined and found to be quite small. I am not well enough versed in
> the theory or knowledgable enough about the experiment to determine
> whether the observed tiny self correlations were in fact within the
> range of the experiment's reasonable statistical error. Nevertheless, I
> certainly would assert that the reported degree of [non-]correlation
> should be at least as sufficient for statistical simulations as that of
> any pseudorandom number generation algorithm could be.

I would believe that any practical physical device would inevitably introduce
*more* correlation than a cryptographically strong, or even well-validated
statistical, PRNG.

It would be good to use a physical random number generator as a seed.

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