To each computable sequence there corresponds at least one description number, while to no description number does there correspond more than one com… - Alan Turing

It will be useful to put... tables into a... standard form. ...The lines of the table are... of form
m-config. | Symbol | Operations | Final m-config. In this way we obtain a complete description of the machine. ...This new description of the machine may be called the standard description (S.D). ...[W]e shall have a description of the machine in the form of an arabic numeral. The integer represented by this numeral may be called a description number (D.N) of the machine. The D.N determine the S.D and the structure of the machine uniquely. The machine whose D.N is n may be described as <math>\mathcal{M}</math>(n).

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

The "scanned symbol" is the only one of which the machine is... "directly aware". However, by altering its m-configuration the machine can effectively remember some of the symbols which it has "seen" (scanned) previously.