Proving the randomness of a random number generator?

[leichter_jerrold at emc.com]

| There's another definition of randomness I'm aware of, namely that the
| bits are derived from independent samples taken from some sample space
| based on some fixed probability distribution, but that doesn't seem
| relevant unless you're talking about a HWRNG.  As another poster
| pointed out, this definition is about a process, not an outcome, as
| all outcomes are equally likely.
That's not a definition of randomness except in terms of itself.  What does
"independent samples" mean?  For that matter, what's a "sample"?  It's an
element chosen at random from a sample space, no?

"All outcomes equally likely" is again simply a synonym:  "Equally likely"
comes down to "any of them could come out, and the one that does is chosen
at random".

Probability theory isn't going to help you here.  It takes the notion of
randomness as a starting point, not something to define - because you really
can't!  Randomness is defined by its properties within the theory; it
doesn't 
need anything else.

One can, in fact, argue plausibly that randomness doesn't "really" exist:  
It's simply a reflection of lack of knowledge.  Even if you get down to the 
level of quantum mechanics, it's not so much that when an atom decays is 
random, it's that we don't - and, in fact, perhaps *can't* - have the 
knowledge of when that decay will happen ahead of time.  Once the decay has 
occurred, all the apparent randomness disappears.  If it was "real", where
did 
it go?  (It's easy to see where our *ignorance* went....)

							-- Jerry

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