His projected zeta-function machine would have well illustrated the point.
It was designed to calculate the zeta-function to within a certain accuracy of measurement.
If he had then found that this accuracy was insufficient for his purpose of investigating the Riemann Hypothesis, and needed another decimal place, then it would have meant a complete reengineering of the physical equipment—with much larger gear-wheels, or a much more delicate balance.
Every successive increase in accuracy would demand new equipment.
In contrast, if the values of the zeta-function were found by 'digital' methods—by pencil and paper and desk calculators—then an increase in accuracy might well entail a hundred times more work, but would not need any more physical apparatus.
This limitation in physical accuracy was the problem with the pre-war 'differential analysers', which existed to set up analogies (in terms of electrical amplitudes) for certain systems of differential equations.
It was this question which set up the great divide between 'analogue' and 'digital'.
Alan was naturally drawn towards the 'digital' machine, because the Turing machines of Computable Numbers were precisely the abstract versions of such machines.
His predisposition would have been reinforced by long experience with 'digital' problems in cryptanalysis—problems of which those working on numerical questions would be entirely ignorant, by virtue of the secrecy surrounding them.
He was certainly not ignorant of analogue approaches to problem-solving.
Apart from the zeta-function machine, the Delilah had an important 'analogue' aspect.
It depended crucially on accurate measurement and transmission of the amplitudes, in contrast to the X-system, which made them 'digital'.