Did Church and Turing have a thesis about machines?by Andrew Hodgesfor Church's Thesis after 70 years, ed. Adam Olszewski (2006)This article is made available in .pdf form to be downloaded here. Copeland and Proudfoot's article in Scientific American, April 1999:
In April 1999 I read with amazement an article in the popular magazine Scientific American by the New Zealand philosophers B. J. Copeland and Diane Proudfoot, entitled 'Alan Turing's Forgotten Ideas in Computer Science,'
and advertised on the cover as 'The Lost Brainstorms of Alan Turing.'

This is the picture offered by Copeland and Proudfoot of the oracle, storing an infinite and uncomputable string of 0's and 1's. 
What do the authors mean by 'an exact amount of electricity?' If it means counting electric charges, then any measurement will give an integer, not an uncomputable number. If on the other hand they mean some classical measurement of a continuous variable, then they are ignoring the nature of matter. A macroscopic object like a capacitor is not even defined with much precision, let alone measurable to infinite precision. It is like asking for the exact width of a cloud. Even at zero temperature, its constituent particles are quantummechanical wavefunctions, involving superpositions of position, momentum and spin. A classical measurement cannot be related precisely to these. Further, general relativity tells us that the geometry of the space in which the object exists, is itself fluctuating in a way that depends on every particle in the universe, and this fluctuation affects all measurements. Standard physical theory would also imply that no measurement can be made to made to a precision involving distances below the Planck length, 10^{–33} cm., because spacetime geometry itself is in some kind of quantum fluctuation at this level. Far from being deterred by the Planck scale, Copeland and Proudfoot go on to illustrate making a measurement to an accuracy of one part in 2^{8735439}. Even this, however, is nothing compared with their demand for infinite precision. Note that the infinite precision is absolutely essential to their argument because any uncomputable number can be approximated as closely as desired by a computable number.
This kind of discussion would only be meaningful in a hypothetical or 'toy' universe, used for the sake of logical argument, where infiniteprecision measurements could be made. But even in such a fictional world, it is hard to see why any physical object should have a property which happens to agree precisely with the infinite slew of answers to the Halting problem as defined in one particular, arbitrary, conventional coding of Turing machines. And how could such a thing, even if true, ever be verified?
But Copeland and Proudfoot were not describing a 'toy' universe; they claimed that 'the search is under way' in the real world to find an oracle that could revolutionise computer science. Dear readers, I do not advise investing all your money on the basis of this prospectus.
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