[lutusp]

> Real random numbers are useless because everything follow some distribution.

First, real random numbers are quite valuable. Second, yes, all numerical sequences follow a distribution, but one of those distributions is called the "normal distribution", and I think you may be able to guess what that refers to.

> Actually random generators in programming languages should be called pseudorandom to avoid confusions.

It would have been useful to explain the difference between the terms random and pseudorandom. "Pseudorandom" doesn't necessarily mean easily predictable or flawed, it means the sequence results from a deterministic algorithm and can be recreated exactly by restarting the generator with the same seed value.

[eru]

Why is the normal distribution important here? (In programming, people often start from the uniform distribution, don't they?)

[lutusp]

> Why is the normal distribution important here?

There may be a terminological confusion at work here. A normal or uniform number shows no internal pattern:

http://en.wikipedia.org/wiki/Normal_number

Quote: "In mathematics, a normal number is a real number whose infinite sequence of digits in every base b[1] is distributed uniformly in the sense that each of the b digit values has the same natural density 1/b, also all possible b^2 pairs of digits are equally likely with density b^−2, all b^3 triplets of digits equally likely with density b^−3, etc."

There are also pseudorandom generators whose purpose it is to generate results that agree with a normal or Gaussian distribution, for particular purposes.

http://www.design.caltech.edu/erik/Misc/Gaussian.html

Quote: "This note is about the topic of generating Gaussian pseudo-random numbers given a source of uniform pseudo-random numbers."

The problem here is that a normal number shows a uniform distribution of its digits among the possible values, and the term normal distribution is sometimes used to describe this outcome.

> In programming, people often start from the uniform distribution, don't they?

Yes, and as set out above, this starting point may be described in a confusing way.

[eru]

I have never seen the term normal distribution used in connection with anything but the Gaussian normal distribution. Especially not in connection with normal numbers. Can you point to some examples of people using this sense?