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, q<s… - Alan Turing

Sometimes it is the people no one can imagine anything of who do the things no one can imagine.

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).

May not machines carry out something which ought to be described as thinking but which is very different from what a man does?