Norman Samish wrote:

> Suppose an ideal random number generator produces, every microsecond, either
> a zero or a one and records it on a tape.  After a long time interval one
> would expect the tape to contain a random mix of zeroes and ones with the
> number of zeroes equal to the number of ones.  Is this necessarily true?  Is
> it possible that, even after an infinite time had passed, that the tape could
> contain all zeroes or all ones?  Or MUST the tape contain an equal number of
> zeroes and ones?  Why?  If you have a reference dealing with this topic,
> please let me know.  Thanks,
> Norm Samish

I don't think we can view time in terms of time passed and infinite. I think we
can
look at the problem in terms of a set of numbers over all time, or we can look
at
a set of numbers issued as a stream sampled over finite time.

I think a set of numbers can only be defined as infinite over all time, not
tested as such.
To be able to say that a process will be random at infinite time would seem to
imply
a deterministic process that can generate non determinism. :)

As for the ideal random number generator, if it's truly ideal, you could easily
never
see it produce anything buts all ones or all zeros for your lifetime, then
promptly after
you're dead, it starts producing something that appears random to a temporally
constrained
observer. An ideal random number generator could only be proved to be ideal over
all time
since any finite sampling of the stream would necessarily introduce order into
the evaluation,
lowering entropy and reducing randomness. IMO

Robert W.


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