random

[Darren New]

Nick Perkins wrote:
> I thought I might try to pin down exactly what people here
> agree on, and what they dont.

sci.crypt is the usual place for such things.
 
> 0. 'Perfect Randomness' is a well-defined concept.

Yes, but there's more than one definition in use. Chaitin's and others.
 
> 1. 'Perfect Randomness' is attainable with a suitable physical RNG, eg. one
> that measures some quantum-level effect, such as radioactive decay.

Some would argue that 100% perfection isn't possible because you can't
eliminate all sources of bias. In theory, the decay is perfectly random.
In practice, you can't measure it perfectly.
 
> 2. There is a continuum of 'degrees of randomness', ranging from the
> trivially predictable to the very hard to predict. (and up to infinity?)

I would think "infinite randomness" would be "complete
unpredictability." I've never heard of "infinite randomness". Just
"infinite strings of random values."
 
> 3. For any useful, practical purpose, there is a degree of randomness that
> is sufficiently random, even if it is not 'perfectly random'.

One would think.
 
> 4. The result of rolling dice is determined not by any random behaviour of
> the cubes themselves, but by the unpredictability of the exact muscle
> movements of the thrower, which are determined by nerve impulses which are
> controlled by the brain.  Predicting the roll of a dice thus requires
> knowlege about the state of the throwers mind and body, which can be thought
> of as a huge program.( or perhaps, even unknowable?)

Nah. Cubes and nerves are both influenced by quantum effects, as well as
brownian motion of air molecules, etc.
 
> 5. Quantum random effects can be amplified to produce a 'macroscopic
> physical RNG' which exhibits 'perfect randomness'.

Agreed, with the restraints of (1)'s answer.
 
> 5 1/2. A multitude of random quantum effects tend to cancel each other out
> in a mocroscopic system, resulting in a very close approximation to
> Newtonian physics, and thereby losing the original randomness of each
> individual quantum effect.

No. All that happens is that the probability for something happening
becomes greater. Just like if you throw 2 dice, the probability of a 7
is much greater than a probability of a 2. You haven't lost the
randomness. It's just that the probabilities aren't equal any more. In a
macroscopic system, the probability of (say) an airplane suddenly
disappearing in Philadelpha and appearing in LA is there. It doesn't
cancel or get lost. It's just very small. Just like if you throw 10,000
dice, the chance of rolling "10,000" as the sum is exceedingly small.
But it'll happen just as often as you expect it to. You can very
reliably predict it won't happen, but if the dice are fair, you'll be
wrong just as often as chance says you'll be wrong.
 
> 6. 'Perfect Randomness' can not be produced by an algorithm, or..
> 
> 7. 'Perfect Randomness' can be produced by an algorithm, but the algorithm
> a) would have to be infinitely large
> b) would never halt

Depends on whether an infinitely large non-halting somethign is
considered an algorithm. It sounds like what you're really asking is
"can something 100% unpredictable be generated by something
deterministic about which we know everything." I think the answer is
trivially "no" there.

> 8. The phrase "state of sin" means beleiving that a RNG is perfect, when it
> is not, and says nothing about the usefullness of a RNG which is
> sufficiently random for one's purpose.

I interpret JVN's quote as "anyone expecting to get unpredictable
numbers from a fully disclosed deterministic system is fooling
themself."  Chaitin's work doesn't seem to contradict this.
 
-- 
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!