> In studying the functioning of automata, it is clearly necessary to pay attention to a circumstance which has never before made its appearance in formal logic

> In studying the functioning of automata, it is clearly necessary to pay attention to a circumstance which has never before made its appearance in formal logic. Throughout all modern logic, the only thing that is important is whether a result can be achieved in a finite number of elementary steps or not. The size of the number of steps which are required, on the other hand, is hardly ever a concern of formal logic. Any finite sequence of correct steps is, as a matter of principle, as good as any other. [...] Thus the logic of automata will differ from the present system of formal logic in two relevant respects. 1. The actual length of “chains of reasoning,” that is, of the chains of operations, will have to be considered. Interestingly, according the Wikipedia [0], Gabriel Lamé published a running time analysis of Euclid's Algorithm [1] in 1844, more than a century before von Neumann suggested this. [0] https://en.wikipedia.org/wiki/Computational_complexity_theory#History https://en.wikipedia.org/wiki/Computational_complexity_theor... [1] http://archive.lib.msu.edu/crcmath/math/math/l/l064.htm http://archive.lib.msu.edu/crcmath/math/math/l/l064.htm