History
The first suitable definition of a random sequence was given by Per Martin-Löf in 1966. Earlier researchers such as Richard von Mises had attempted to formalize the notion of a test for randomness in order to define a random sequence as one that passed all tests for randomness; however, the precise notion of a randomness test was left vague. Martin-Löf's key insight was to use the theory of computation to formally define the notion of a test for randomness. This contrasts with the idea of randomness in probability; in that theory, no particular element of a sample space can be said to be random.
Martin-Löf randomness has since been shown to admit many equivalent characterizations — in terms of compression, randomness tests, and gambling — that bear little outward resemblance to the original definition, but each of which satisfy our intuitive notion of properties that random sequences ought to have: random sequences should be incompressible, they should pass statistical tests for randomness, and it should be difficult to make money betting on them. The existence of these multiple definitions of Martin-Löf randomness, and the stability of these definitions under different models of computation, give evidence that Martin-Löf randomness is a fundamental property of mathematics and not an accident of Martin-Löf's particular model. The thesis that the definition of Martin-Löf randomness "correctly" captures the intuitive notion of randomness has been called the Martin-Löf–Chaitin Thesis; it is somewhat similar to the Church–Turing thesis.
Read more about this topic: Algorithmically Random Sequence
Famous quotes containing the word history:
“the future is simply nothing at all. Nothing has happened to the present by becoming past except that fresh slices of existence have been added to the total history of the world. The past is thus as real as the present.”
—Charlie Dunbar Broad (1887–1971)
“To a surprising extent the war-lords in shining armour, the apostles of the martial virtues, tend not to die fighting when the time comes. History is full of ignominious getaways by the great and famous.”
—George Orwell (1903–1950)
“History is the present. That’s why every generation writes it anew. But what most people think of as history is its end product, myth.”
—E.L. (Edgar Lawrence)