random

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>
wrote:

[...]
>
>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
terms?

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.)

>Alex
>
>
>



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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