David C. Ullrich ullrich at math.okstate.edu
Sun Jun 3 17:32:15 CEST 2001

On Sun, 3 Jun 2001 10:53:27 +0200, "Alex Martelli" <aleaxit at yahoo.com>

>But the method summarily given in the Sci.Am paper does show how
>to program the computation of any given bit of Omega

I was about to say "what??? No, that's impossible." I read on:

> but some would say the finite
>program is not "an algorithm" because it's not finite in time -- it
>may never halt 

Halting _is_ part of the standard definition of "algorithm";
this is not what "some" would say.

There's a _reason_ it's part of the definition. Elsewhere
you've claimed to be an engineer, seeming to imply you're
interested in practical matters. If you have a solution to
a problem but the "solution" takes infintely much time
does it really seem like a _useful_ solution in practical

Like say we want to use Omega to give a "perfect"
arithmetic RNG. We can do that. Except that when
we call x = rand() the call _never_ _returns_.
If you're really interested in RNG's that never
return then I take back everything I've said,
yes, JVN was wrong, there's no problem with
arithmetic RNGeneration.

>So where's the "state of sin" in this arithmetical and almost-algorithmical-
>except-for-the-little-detail-of-finiteness approach to randomness?

The quote from JVN was about someone _using_ arithmetic methods to
generate random numbers. If someone is "using" an RNG that _never_
_returns_ then he is _not_ generating random numbers. (A fortiori
he is not using arithmetic methods to generate random numbers.)


David C. Ullrich
"Sometimes you can have access violations all the 
time and the program still works." (Michael Caracena, 
comp.lang.pascal.delphi.misc 5/1/01)

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