Alan Turing: Call

Alan Turing was British mathematician, logician, cryptanalyst, and computer scientist. Explore interesting quotes on call.
Alan Turing: 66   quotes 51   likes

“Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity.”

Alan Turing Systems of Logic Based on Ordinals

"Systems of Logic Based on Ordinals," section 11: The purpose of ordinal logics (1938), published in Proceedings of the London Mathematical Society, series 2, vol. 45 (1939)
In a footnote to the first sentence, Turing added: "We are leaving out of account that most important faculty which distinguishes topics of interest from others; in fact, we are regarding the function of the mathematician as simply to determine the truth or falsity of propositions."
Context: Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity. The activity of the intuition consists in making spontaneous judgements which are not the result of conscious trains of reasoning... The exercise of ingenuity in mathematics consists in aiding the intuition through suitable arrangements of propositions, and perhaps geometrical figures or drawings.

Exercises , Mathematics

“Suppose Mother wants Tommy to call at the cobbler's every morning on his way to school to see if her shoes are done, she can ask him afresh every morning. Alternatively she can stick up a notice once and for all in the hall which he will see when he leaves for school and which tells him to call for the shoes, and also to destroy the notice when he comes back if he has the shoes with him.”

Alan Turing Computing Machinery and Intelligence

Computing Machinery and Intelligence (1950)

School , Shoe , Way

“If an ɑ-machine prints two kinds of symbols, of which the first kind (called figures) consists entirely of 0 and 1 (the others being called symbols of the second kind), then the machine will be called a computing machine.”

Alan Turing Computable Numbers

On Computable Numbers, with an Application to the Entscheidungsproblem (1936)

“The machine is supplied with a "tape" (the analogue of paper) running through it, and divided into sections (called "squares") each capable of bearing a "symbol."”

Alan Turing Computable Numbers

On Computable Numbers, with an Application to the Entscheidungsproblem (1936)

“We may compare a man in the process of computing a real number to a machine which is only capable of a finite number of conditions q1, q2, ..., qK which will be called " m-configurations ."”

Alan Turing Computable Numbers

On Computable Numbers, with an Application to the Entscheidungsproblem (1936)