====== Random numbers ======

{{tag>Unknowable}}

>We can never decide for sure that a number is random, but what we can do is apply an increasing number of tests and treat our sequence of numbers as innocent until proved guilty."\\ \\ Source : [[https://www.st-andrews.ac.uk/mathematics-statistics/people/cmr1/|Prof. Colva Roney-Dougal,]] senior lecturer in Pure Mathematics at the University of St Andrews, speaking in [[http://www.bbc.co.uk/programmes/b00x9xjb|'Random and Pseudorandom', BBC 'In our time' ]] Jan. 2011.

Although the tests can show that a finite sequence of numbers //appears// to be random (i.e. it can't be mathematically represented in a shorter form) - there is currently no mathematical method to prove that if it continues, the next numbers in the sequence won't start to repeat.

>I can never prove that a sequence of numbers is random, I can only say that it looks and smells random given all the tests I've been able to apply so far."\\ \\ [Source as above]

That's to say it's unknowable if any particular sequence of numbers will //remain// random if its generation is continued.

A number of 'tests' have been developed to gauge //how// random a sequence of numbers might be. They include statistical tests, transforms, and measures of complexity - or a mixture of these.

//Note :// There is currently debate over whether it's possible to distinguish the output of high-quality modern-day pseudo-random number generators (computer algorithms commonly used in cryptography) and truly random sequences. This open question has crucial implications of the security of data encryption.

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Also see :[[content:mathematics:pi_normality]]

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