Some paradoxes of randomness

Randomness is a surprisingly elusive concept to pin down. Thus, seeking ways of reliably generating sequences of random numbers leads to many paradoxes. A random sequence should contain no patterns and each number should be unpredictable from the previous ones. Surprisingly, perhaps, these definitional properties are of little practical help in generating such a sequence. By trial and error, a number of ‘physical’ methods have been found that serve successfully for the purpose. The most computationally efficient method, however, turns out to use a deterministic formula. The resulting sequences have all the required properties of random numbers except one – they are not actually random! Instead, they are termed ‘pseudorandom’. In a small number of applications (e.g. drawing lottery prizes), pseudorandom numbers will not do, but otherwise their use is unproblematic.