[trekker7]

Is there really anything that is truly random? I've always wondered about this. If you define random as meaning "when rand() is called many times in a row, you will most probably get a different number each time" then both the Perl function and random.org are random, but to different extents.

But if you define random to mean something like "caused by unexplained or mysterious forces" or "non-deterministic", then how can anything in the universe be truly random? Even atmospheric noise is created by a sequence of deterministic events, right?

A dice roll is too (brain fires synapse, I move my hand forward and release the dice, dice interact with air in certain way, dice hit table and F=ma predicts their movements, etc...). Maybe since we don't have the facilities yet to watch a person throw some dice and predict what the outcome will be, this process is non-deterministic simply because we lack the technology to sketch it out. But with sufficient technology to scan the situation and chart the end result of the dice roll based on the initial conditions, doesn't the process become completely deterministic, and not random?

But maybe I'm just stretching the definition of random to mean something that it was never meant to mean.

[vitaminj]

Statistical randomness is pretty well defined. Say you have a set of independent and identically distributed (iid) random numbers, then if you plot a long run histogram it should resemble the probability density function of the distribution. Irrespective of whether it was generated by a pseudo-random algorithm or by quantum disturbances, your set of numbers is statistically random in a practical sense.

Your question seems more philosophical, though I think at the quantum level things become more or less random whichever way you think about it. Furthermore, Heisenberg's uncertainty principle suggests that we'll never have sufficient technology to measure both the position and momentum of a particle, which I would say is a pre-condition to observing a deterministic process at work on the quantum scale.

[cousin_it]

You are in a state of sin :-) Don't talk about random sequences, talk about random generators. There's an unambiguous definition of "true random number generator" in terms of probabilities, joint probabilities etc., but there's no way to determine if a given string of numbers is random, and in fact no definition of a "random string of numbers" other than "the output of a random number generator".

[anonym]

I am reminded of Borges's "Pierre Menard, Author of the Quixote" (http://www.coldbacon.com/writing/borges-quixote.html) (and what do you know, Borges even slips George Boole into it).

"He did not want to compose another Quixote —which is easy— but the Quixote itself. Needless to say, he never contemplated a mechanical transcription of the original; he did not propose to copy it. His admirable intention was to produce a few pages which would coincide—word for word and line for line—with those of Miguel de Cervantes."