"Let us now assume, for the sake of argument, that these machines are a genuine possibility, and look at the consequen…"

"The "scanned symbol" is the only one of which the machine is... "directly aware". However, by altering its m-configur…"

"Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which…"

"Instruction tables will have to be made up by mathematicians with computing experience and perhaps a certain puzzle-s…"

"A man provided with paper, pencil, and rubber, and subject to strict discipline, is in effect a universal machine."

"There is a remarkably close parallel between the problems of the physicist and those of the cryptographer. The system…"

"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 experie…"

"Science is a differential equation. Religion is a boundary condition."

"The Exclusion Principle is laid down purely for the benefit of the electrons themselves, who might be corrupted (and …"

"The "computable" numbers may be described briefly as the real numbers whose expressions as a decimal are calculable b…"