random

[Darren New]

Alex Martelli wrote:
> So what does the "GIVEN _complete_ information" above
> is, if not a statement that you CAN be given complete
> information about

I interpreted it as meaning "given that you know everything about the
system that it's possible to know." If you have complete information,
then you know the exact probabilities that any particular item is in any
particular state. Just like if you have "perfect dice", it means that
all the probabilities are exactly 1/6. This doesn't tell you which
number a perfect die will roll next.

> And quips apart, what's "sinful" about dealing with
> randomness this way?  If the underlying maths are sound
> (and that, I surmise, IS what Chaitin has to do with it:
> showing the soundness of this finite-maths approach
> to randomness), why shouldn't RNG's be feasible and
> sin-less that are based on these techniques?

Well, it's not something you'd want to use to encrypt documents that the
bad guys will kill you over if they ever read them.

> I still haven't heard your definition of
> 'perfect' randomness, for example.

Generally, this is something along the lines of:
Given all available information about the mechanism used to generate the
bits, and an arbitrarily long sequence of generated bits, it's
impossible to predict with >50% accuracy what the next bit in the
sequence will be.

I'm not sure it always includes the first condition.

I don't think Chaitin's Omega meets this definition, since it is by
definition a single number than anyone can calculate equally well.

-- 
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!