Quotes from work
Computable Numbers

Alan Turing

“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 Turing Computable Numbers

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

“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)

“[T]he m-configuration may be changed.”

Alan Turing Computable Numbers

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

“The machine may also change the square which is being scanned, but only by shifting it one place to right or left.”

Alan Turing Computable Numbers

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

“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.”

Alan Turing Computable Numbers

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

“The "scanned symbol" is the only one of which the machine is... "directly aware."”

Alan Turing Computable Numbers

However, by altering its m-configuration the machine can effectively remember some of the symbols which it has "seen" (scanned) previously.
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)

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