Re: Primes: Randomness and Prime Twin Proof

Martin Winer wrote:
Btw, have you realized yet that your response to Dave Rusin
amounts to an admission of defeat?
If you mean that for no n is Pat(n) absolutely random, then it's an
issue I'm not ready to deal with yet. If it's something else, please
fill me in, I've forgotten my secret decoder ring.

Dave Rusin' question was:

|>So why don't you answer your own question. I'll rig up a slot
machine
|>which at each pass gives you a real number between 0 and 1, and you
|>"win" if you get a rational number (with a power-of-2 denominator).
|>If you play this slot machine, is there a point where you never win
again?
|>1) yes
|>2) no
|>3) don't know
|>?

My answer... 3) don't know IFF the slot machine uses a pseduo random
generator and 2) No, IFF the machine uses a true random generator.

Rusin's original scenario was that of a timeless deity, who
of course uses a *true* random number generator for the
number-generating slot machine. Your answer "No" means
that means that eventually the deity must hit some rational
with power-of-2 denominator. And if you remember the
original scenario, that means some poor slob will be assigned
a slot machine that fails to win ever again after a certain point,
contrary to your claim. In other words, your own argument
works against itself, as Rusin said.

But probably, now that I think about it, you will just say that
the slob's machine wasn't "random". In other words, when the
true random number generator generates a number that doesn't
look random, you're allowed to throw it out?? Or that slot
machines predetermined by random numbers aren't random??
It's pretty hard to counter any claim that you *do* make when
your word "random" hasn't been precisely defined. Well, maybe
I'll retire from this discussion now; as I said, it was unwise for
me to wade in.

.

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