How can randomness be defined?

[khanster]

I will give it a try:

Randomness appears to be the descriptive complexity of a data structure such, that description of the structure takes more bits of information than what appears to be contained in the structure itself.

In that respect, we live in a random world due to the inability for humans to create a description of reality that is perfectly isomorphic with reality.


An interesting way to generate random numbers?

http://www.random.org/integers/

This form allows you to generate random integers. The randomness comes from atmospheric noise, which for many purposes is better than the pseudo-random number algorithms typically used in computer programs.

 

[phoenixthoth]

In that respect, we live in a random world due to the inability for humans to create a description of reality that is perfectly isomorphic with reality.

Not yet anyway.

 

[Pythagorean]

I like the first sentence of wolfram's definiion of random number.

"as if by chance" is sloppy, but I think it means no a priori knowledge of cause and effect.

 

[phoenixthoth]

Pick the conjunction of all axioms ever to be employed. This set can be broken down into finitely many groups of axioms where two axioms/statements are in the same group if they imply each other.

Take the consequence hull (or closure) of that set of statements. (The smallest set of all consequences of those statements, say)

That is all of mathematics.

Thus mathematics is holographic in nature.