random

[Darren New]

> The quote above contains the premise "even given _complete_
> information". 

Except you snipped the end of the sentence, which is 
"complete information about how they're being generated."

I can have complete information about exactly how many atoms of uranium
I have in my sample, and still not be able to predict when the next atom
will pop. I have complete information about how the numbers are being
generated (watching a radioactive sample) without any information about
what the next number will be.

> I assume that is your definition of "an algorithm"?  That
> its state be finite? 

That's generally what it means. :-) That it's finite and deterministic.

> While you are absolutely certain that
> NO physical system can be described in finite terms,
> EVER?

That's what quantum physics says, and it's pretty much the best
supported physical theory we have.

> > >A physical system that is macroscopic enough to escape
> > >Heisenbergian conumdrums
> >
> > There is no such system.
> 
> In this case, no physical computer is predictable, and all
> we study about algorithms are abstractions -- since a
> computer system IS a physical system, then ALL bits
> coming out from it must be random in your sense of
> the word. 

Nope. Because you have an infinite number of possible states, and you
collapse some of those into a 0 bit and some into a 1 bit. It's because
you're *classifying* states in your brain as 1 or 0, ignoring the
reality that there's an infinite number of voltages that represent 0.

> If, on the other hand, you maintain that the output
> from a physical system CAN be predictable if that
> system is a computer running your program, then
> what makes you SO certain that NO other physical
> systems can also be predictable in the same sense?-)

Again, you're talking two diferent things. In the first, you're talking
about "the output will be somewhere between 4.5v and 5.5v on this
wire."  The other you're talking about an exact number.
 
> A couple centuries ago all scientists were certain of
> one thing, now they're all becoming certain of another,
> and I won't be around in a couple more centuries to
> laugh at the likely-different certainties they'll have
> then.  Meanwhile, mathematics is far from exempt
> from paradigm shifts, of course, but those never do
> 'contradict' the previous certainties (META-maths is
> different that way of course -- cfr. Russel's well
> known demolition of Frege's lifework:-), rather
> extend and generalize on them.

This is generally true of physics, too.

> quote talks generically about "random", without using
> the word "perfect" you now insert, and without any
> specification of infiniteness as a prerequisite, and, as
> such and without the needed qualifications, it is not
> correct.  _with_ the qualifications you want to place,
> it seems to become tautological ("I define X as being
> something that requires infinities: no finite system can
> reach X, it can only approach it") and therefore sterile
> and uninteresting, unless there are hidden layers of
> exoteric meaning nesting in it, I guess.

I think "random" here means "unpredictable". Tossing dice will lead to
random/unpredictable results, even if you know everything there is to
know about the dice and the table. Generating numbers between 1 and 6
will not be unpredictable if you know the seed and algorithm.


-- 
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!