random

[Tim Peters]

[Nick Perkins]
> ...
> The very idea of 'infinite randomness', in all it's unattainable
> glory, is somehow very pure and clear in everyone's mind.  It is, after
> all, the first concept of randomness that we all learned as children:
> that something is simply unpredictable, period.  Strange that it takes
> centuries of advanced math to try to pin down exactly what randomness
> means.

Knuth (in volume 2 of TAoCP) has entirely too good a time exploring this
question.  It's a miserable journey <wink>.  He picks a few plausible
definitions, persuasively argues they're too weak, then presents one that's
intuitively on the money.  But it turns out nothing can satisfy that
definition!  So it's on to page after page trying to recapture what was
"right" about that defn, but not so much that it's impossible to meet.

Here's a good roadmap to recent results on randomness and Chaitan's Omega
construction (note that these are research papers, not watered down):

    http://citeseer.nj.nec.com/calude00randomness.html

Over the last few years, lots of alternative constructions have been proved
equivalent, sometimes to the surprise of all concerned.  That usually means
there's a tedious grad-school course in the making, but for *most* Python
users random.random() is still good enough <wink>.