random

David C. Ullrich ullrich at math.okstate.edu
Mon Jun 4 16:22:11 CEST 2001


On Mon, 04 Jun 2001 01:12:32 GMT, Darren New <dnew at san.rr.com> wrote:

[...]
>
>Sure. *I* can write an algorithm to calculate the bits of Omega.

If I have the "definition" of Omega straight actually you can't.
(If an "algorithm" is required to halt, which is part of "my"
definition...)

> Then I
>run my algorithm, see that the first N bits of its output matches the
>first N bits of your sequence, and predict with very high probability
>what the next bit is, right? If you calculate the first 100,000 bits of
>Omega and give it to me, and you don't tell me that it's the first
>100,000 bits of Omega, and I think to try calculating the first 100,000
>bits of Omega and they match, then I guess the 100,001'st bit of Omega,
>then I have a >50% chance of getting the next bit right.
>
>If, on the other hand, you run a random number generator based on
>quantum radioactive decay, or you flip a coin 100,000 times, and it just
>*happens* to match the first 100,000 bits of Omega, and I notice that,
>and I guess the 100,001'st bit of Omega, then I have still only a 50%
>probability of being right.
>
>This is why some people say that any given finite string cannot be
>considered random or non-random by itself, without knowing how it's
>generated.
>
>-- 
>Darren New / Senior MTS & Free Radical / Invisible Worlds Inc.
>       San Diego, CA, USA (PST).  Cryptokeys on demand.
>     This is top-quality raw fish, the Rolls-Rice of Sushi!



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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