So, I was browsing wikipedia about Turing Machines, and - no! Wait! Come back!
...
Anyways, I was thinking about the way math and science have developed. in most - almost all - cases, the math required for a theory occurs well before the science catches up. Maxwell's equations are based on calculus that was well understood by the time he formulated them; quantum theory is based on all sorts of funky math - advanced calculus, matrices, etc - that were inventedwell before 1900. When you get things where the math doesn't exist, as with fractals and chaos, and the physical theories based thereon - the theory doesn't show up until after the math. It worked this way with computer science, as well: you have things like Hilbert's formallism, Church's Lambda Calculus, Turing machines - all setting up a strong conceptual foundation for computing long before the physical machines started appearing.
But.
Babbage came up with the Analytical engine - fully functional Turing machine, assuming it was ever built - way back in the first half of the 19th C. This is long before any of the developments above - Hilbert was 9 at Babbage's death, none of the others were even born yet - and there was almost literally none of the conceptual basis for computing then. Would this have stunted the development of the new field of mechanical computing? Prompted earlier and faster developments in information theory? None of the above? Any thoughts?