[PD] Random without repeating numbers

[Lawrence Joseph]

> > > But that's not random!!
>
> ( 02.11.29 11:14 -0500 ) Mathieu Bouchard:
> > It's a Markov chain with a probability matrix of:
>
> Then that's not random!
>
> "Almost always, such numbers are also required to be independent, so that
> there are no correlations between successive numbers."
> http://mathworld.wolfram.com/RandomNumber.html

This page does NOT give a general mathematical or statistical definition of
randomness, but rather discusses a specific type of randomness, often
associated with generating pseudo random numbers (uniform or other
distribution such as normal) on a computer.  It is perfectly legitimate to
have correlations among successive items in random number sequences, and to
still call this a random sequence.  There are many cases in science (for
example, Markov Chain Monte Carlo algorithms) where this is used to great
effect, and in music, it is very easy to imagine where correlated sequences
can produce musical effects that are more interesting than purely random
sequences.  Also, notice that the definition says "Almost always", NOT
"always"!

Lawrence