random

[Darren New]

Alex Martelli wrote:
> _Complete_ information about how the numbers are generated
> requires complete information about the state of their generator.

Yep. The fun thing about quantum physics is that *complete* information
is available about the state of the generator, and you *still* don't
know when the atom will pop.

That's exactly what Einstein was complaining about.

> Position and velocity vector for each of these atoms are part of
> system's state.  So, if Heisenber Principle holds, how are you
> going to have complete information about this state?

Well, that's what quantum physics is all about, isn't it?
 
> If my physical system is designed and considered in ways
> that are macroscopic enough to escape uncertainty effects,

They can't be. But you can make the probability of something funky
happening arbitrarily small. It's still possible all the air in the room
will happen to bounce over to the same half at once, but very very
unlikely.

> Is your claim, then, that "randomness" MUST be used ONLY
> for systems which, at the level of observation under discussion,

No. The point I'm discussing is that an algorithm cannot generate
randomness. No matter how much complexity you add to a mathematical
formula, it's still 100% predictable if you know what the formula is.
This is untrue of physical random number generators.

> Chaotic effects may
> well ensure that the number of bits of information that would
> be needed to obtain prediction is higher than any practical
> measure.

In an algorithm, it's never going to be bigger than your seed.

> So what is so special, that distinguishes a computer system
> from a deck of cards -- considering both systems at a
> macroscopic enough level that quantum effects can be
> ignored, which is easier for the deck of cards I think but
> is commonly done for well-designed computers too:-) --
> so that I *could* get randomness from one and not the
> other? 

You don't get randomness from a deck of cards. You get randomness from
*shuffling* a deck of cards. The randomness comes from not knowing
exactly what the fingers were doing.

If you shuffled the cards algorithmically (e.g., with a mechanical card
shuffler that very reliably put them in the same order) then they
wouldn't be random at all, *if* you knew exactly how the mechanical card
shuffler worked. That's the equivalent of using an algorithm to generate
pseudo-random numbers.

> It seems more fruitful to me to consider the amount
> of information, i.e., a quantitative assessment of randomness,
> rather than claim that only if that amount is 'infinite' can
> the word 'randomness' be properly used.

It depends, again, on which meaning of "random" you want to use. For
some folks, "unpredictable" and "random" are two different things.

> Taking a set of states and deeming them equivalent can
> perfectly well be done -- who ever gets an "exact" number
> from physical measurement anyway?!  It applies just as
> well to the finite definition of randomness. 

Is fine. If you want to call "unpredictable" and "random" the same
thing, power to you. I thought you were trying to understand the Von
Neuman quote, not to argue that he's using words you don't like.

> > 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.
> 
> If you have COMPLETE information about the dice &c (taking
> a HUGE number of bits, no doubt) you can predict their
> trajectories, bounces (if allowed), rolls, AND final results.

No. Quantum effects will screw that up.

> Why should these macroscopic-physics effect be inherently
> unpredictable as you claim? 

If you start with a pooltable with perfect spheres for poolballs,
perfectly racked, you cannot sink all 15 balls with your eyes closed.
The probability cloud for the location of the last ball will be larger
than the pooltable.

> If you have complete information about the algorithm and
> the relevant part of the state of the computer where it
> runs, again you have predictability.

And that's why VN said calling it "random" is sinful.
 
-- 
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!