random

[Nick Perkins]

...fascinating discussion gentlemen! (for the most part)

I thought I might try to pin down exactly what people here
agree on, and what they dont.

I suggest the following eleven statements, and invite
others to say whether each is True or False...
( phrased such that I beleive each is True )


0. 'Perfect Randomness' is a well-defined concept.

1. 'Perfect Randomness' is attainable with a suitable physical RNG, eg. one
that measures some quantum-level effect, such as radioactive decay.

2. There is a continuum of 'degrees of randomness', ranging from the
trivially predictable to the very hard to predict. (and up to infinity?)

3. For any useful, practical purpose, there is a degree of randomness that
is sufficiently random, even if it is not 'perfectly random'.

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?)

5. Quantum random effects can be amplified to produce a 'macroscopic
physical RNG' which exhibits 'perfect randomness'.

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.

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


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.

10. 'Perfect Randomness' is a mathematical curiosity which has no effect on
the lives of us mere mortals, for whom 'sufficient randomness' will always
be indistinguishable from 'perfect randomness' (hmmm....)


11. There is another point of disagreement, not listed here, which is:
_________________ (fill in the blank)