#### Ho-hum

I always had a problem with the idea that Turing provided a "blueprint" for computers. Even before him, general-purpose programmable state machines were conceived of and attempts to build them were made, as Babbage's unfinished Analytical Engine shows. What Turing did was, propose a concrete definition of "Mechanical Procedure" and anchor it to mathematics. This is what Hilbert was asking about -- whether there was a "definite method" to prove any given theorem -- leaving "definite method" undefined and an exercise for the reader. Turing came in and laid pipe between "definite" and "mechancial", and the rest is history. The Turing Machine is an eminently mathematical idea and it pays off big immediately, yielding the theorem that there is a "Universal Turing Machine" which can (be programmed to) emulate any other, that most mathematical functions are not computable, as in, deciding in a finite number of steps whether any given Turing Machine will ever stop is impossible and that Hilbert's question can be answered in the negative because of that. Moreover, as this mathematical idea is chained firmly to our physical world. Thus, in the same way that taking as given that motion is relative but not additive leads one to the conclusion that life is governed by an absolute maximum speed and that space and time are mixable quantities, taking as given that "mechanical procedures" are Turing Machines leads one to the conclusion we will have to slum it on a small "easily computable functions island" as most functions/problems are unsolvable while most solvable functions/problems are unreachable, costing exponentially many "mechanical steps" -- and life is short.

It helps that the idea of the Turing Machine can be shown to be equivalent to other ideas about what a "definite method" might be - among those, Alonzo Church's idea wherein "effectively calculable functions" were understood to be the set of general recursive functions. No better (in the sense of "more powerful") idea of "definite method" has ever been found. Hence, the Church/Turing thesis (NOT a theorem as it is not provable -- Special Relativity is not a theorem either) which just says that "effectively calculable" is equivalent to "calculable by Turing Machine" and that there is nothing beyond. This rapidly leads to the idea that human minds are indeed equivalent to some Turing Machine etc. etc. etc.

"Your learning is simply amazing Sir Bedivere..."