The paper also included a short calculation which bridged the two descriptions of a machine such as a computer, the logical description and the physical description.
He showed that in a job taking more than 1010 steps, a physical storage mechanism would be virtually certain to jump into the 'wrong' discrete state, because of the ever-present effects of random thermal noise. This was hardly a practical constraint.
He might have made a similar calculation regarding the effect of quantum indeterminacy, and the upshot would have been the same.
The determinism of the logical machine, although it could never be rendered with absolute perfection, was still effectively independent of all the 'Jabberwocky' of physics.
This part of the paper integrated his several interests in logic and physics, mapped out where his own work stood within a wider framework, and summed up a long chapter of unfulfilled ambitions.
A final section suggested approaches to 'intelligent machinery' which were not based on this crude 'teaching', but upon his real experience as a pure mathematician.
He considered the process of transforming problems from one formulation into another, solving a problem by proving a theorem in some other logical system, and translating the result back into the original form.
This corresponded closely with the real work of mathematics, that of detecting analogies, and searching for openings towards a proof within some framework of ideas.
'Further research into intelligence of machinery will probably be very greatly concerned with "searches" of this kind,' he wrote. 'We may perhaps call such searches "intellectual searches".
They might very briefly be defined as "searches carried out by brains for combinations with particular properties".'
Of course, this was not exactly unrelated to the task of cryptanalysis, that of finding patterns in the apparently patternless.