"To each computable sequence there corresponds at least one description number, while to no description number does there correspond more than one computable sequence. The computable sequences and numbers are therefore enumerable."
Alan Mathison Turing was an English mathematician, computer scientist, logician, cryptanalyst, philosopher and theoretical biologist. He was highly influential in the development of theoretical computer science, providing a formalisation of the concepts of algorithm and computation with the Turing machine, which can be considered a model of a general-purpose computer. Turing is widely considered t
"I am not very impressed with theological arguments whatever they may be used to support. Such arguments have often been found unsatisfactory in the past. In the time of Galileo it was argued that the texts, "And the sun stood still... and hasted not to go down about a whole day" (Joshua x. 13) and "He laid the foundations of the earth, that it should not move at any time" (Psalm cv. 5) were an adequate refutation of the Copernican theory."
"In some of the configurations in which the scanned square is blank... the machine writes down a new symbol on the scanned square: in other configurations it erases the scanned symbol."
"There is a remarkably close parallel between the problems of the physicist and those of the cryptographer. The system on which a message is enciphered corresponds to the laws of the universe, the intercepted messages to the evidence available, the keys for a day or a message to important constants which have to be determined. The correspondence is very close, but the subject matter of cryptography is very easily dealt with by discrete machinery, physics not so easily."
"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 "."
"This is only a foretaste of what is to come, and only the shadow of what is going to be. We have to have some experience with the machine before we really know its capabilities. It may take years before we settle down to the new possibilities, but I do not see why it should not enter any one of the fields normally covered by the human intellect, and eventually compete on equal terms."
"It is possible to invent a single machine which can be used to compute any computable sequence. If this machine \mathcal{U} is supplied with a tape on the beginning of which is written the S.D of some computing machine \mathcal{M}, then \mathcal{U} will compute the same sequence as \mathcal{M}."