Turing machines

Turing machines are abstract computing devices, named after Alan Mathison Turing. A Turing machine operates on a potentially infinite tape uniformly divided into squares, and is capable of entering only a finite number of distinct internal configurations. Each square may contain a symbol from a finite alphabet. The machine can scan one square at a time and perform, depending on the content of the scanned square and its own internal configuration, one of the following operations: print or erase a symbol on the scanned square or move on to scan either one of the immediately adjacent squares. These elementary operations are possibly accompanied by a change of internal configuration. Turing argued that the class of functions calculable by means of an algorithmic procedure (a mechanical, stepwise, deterministic procedure) is to be identified with the class of functions computable by Turing machines. The epistemological significance of Turing machines and related mathematical results hinges upon this identification, which later became known as Turing’s thesis; an equivalent claim, Church’s thesis, had been advanced independently by Alonzo Church. Most crucially, mathematical results stating that certain functions cannot be computed by any Turing machine are interpreted, by Turing’s thesis, as establishing absolute limitations of computing agents.

Alan Mathison Turing, 1912-1954

The sudden death of Alan Turing on 7 June 1954 deprived mathematics and science of a great original mind at the height of its power. After some years of scientific indecision, since the end of the war, Turing had found, in his chemical theory of growth and form, a theme that gave the fullest scope for his rare combination of abilities, as a mathematical analyst with a flair for machine computing, and a natural philosopher full of bold original ideas. The preliminary report of 1952, and the account that will appear posthumously, describe only his first rough sketch of this theory, and the unfulfilled design must remain a painful reminder of the loss that his early death has caused to science. Alan Mathison Turing was born in London on 23 June 1912, the son of Julius Mathison Turing, of the Indian Civil Service, and of Ethel Sara Turing ( née Stoney). The name ‘Turing’ is of Scottish, perhaps ultimately of Norman origin, the final g being an addition made by Sir William Turing, of Aberdeenshire, in the reign of James VI and I. The Stoneys, an English-Irish family of Yorkshire origin, produced some distinguished physicists and engineers in the nineteenth century, three of whom became Fellows of the Society; and Edith A. Stoney was one of the early women equal-to-wranglers at Cambridge (bracketed with 17th Wrangler, 1893). Alan Turing’s interest in science began early and never wavered. Both at his preparatory schools and later at Sherborne, which he entered in 1926, the contrast between his absorbed interest in science and mathematics, and his indifference to Latin and ‘English subjects’ perplexed and distressed his teachers, bent on giving him a well-balanced education.