5 ms·
I think one of the most widely accepted definitions of randomness in mathematics was given by Martin-Löf. Basically it says that a process is random iff it doe
by pierrebouchet 14y ago
I think one of the most widely accepted definitions of randomness in mathematics was given by Martin-Löf.
Basically it says that a process is random iff it doesn't exhibit any atypical property that you can test with an algorithm.
In other words: if there is no computable way of proving that it's not random, then it is random.
- WiseWeasel 14y agoIn a practical sense, I'd say the definition is simply our inability to recognize a pattern at this point; it's completely subjective.
- jasomill 14y agoLehmer (1951), by way of Knuth Vol. 2, "A random sequence is a vague notion embodying the idea of a sequence in which each term is unpredictable to the uninitiated and whose digits pass a certain number of tests, traditional with statisticians and depending somewhat on the uses to which the sequence is to be put."
- jasomill 14y agoHow does this not trivially exclude everything (the first definition, not the circular restatement)? Considering that, say, a sequence of coin flips either has the property of "beginning with heads" or "beginning with tails," it certainly appears to.
- pierrebouchet 14y agoMy bad, I was being too vague - sorry for that. I meant "any atypical property" instead of "any property". An "atypical property" being a property that almost no sequence has, i.e the set of sequences which exhibit this propery is a measure-zero set.