The Turing Guide

402 | 36 INTRODUCING TURING’S mATHEmATICS and 2i (which equals 0 + 2i), and a real number such as 3 can be thought of as 3 + 0i. ...

wHITTy & wIlSON | 403 about the line x =^12 , and that as we progress vertically up and down the line x =^12 , many zeros do ...

404 | 36 INTRODUCING TURING’S mATHEmATICS Conclusion If the actual statement of the Riemann hypothesis seems an anticlimax after ...

CHAPTER 37 Decidability and the Entscheidungsproblem robin whitty I n 1936 Turing invented a mathematical model of computation, ...

406 | 37 DECIDABIlITy AND THE ENTSCHEIDUNGSPROBLEM 0 110 101 011 01 10 01 (= 27353) 0 (^0) A A A B B B C C C p q 1 1 1 0 0 00 0 ...

wHITTy | 407 problems’ covering most of mathematics as it was then known. The tenth problem, in post- Turing language, was to wr ...

408 | 37 DECIDABIlITy AND THE ENTSCHEIDUNGSPROBLEM produced this theory single-handedly at the age of 24. Although not alone in ...

wHITTy | 409 There are two technical themes that Turing, already by his early 20s an accomplished and widely read mathematician, ...

410 | 37 DECIDABIlITy AND THE ENTSCHEIDUNGSPROBLEM We shall certainly not attempt to describe how Turing’s universal machine wor ...

wHITTy | 411 which will in turn try to simulate H, and so on ad infinitum. The machine can never proceed to the point where it w ...

412 | 37 DECIDABIlITy AND THE ENTSCHEIDUNGSPROBLEM Turing’s prototype undecidable problem, the Entscheidungsproblem, so showing ...

wHITTy | 413 Moreover, every prime number can be obtained in this way, by making a suitable choice of whole numbers a, b, c, . . ...

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CHAPTER 38 Banburismus revisited: depths and Bayes edward simpson C hapter 13 covered all aspects of Banburismus, but without mu ...

416 | 38 BANBURISmUS REVISITED Where the same letter appears twice or more in a column (as N in position 182 or A in position 18 ...

SImPSON | 417 worth pursuing. Finding these was beyond the reach of manual methods, and the search was performed, starting afres ...

418 | 38 BANBURISmUS REVISITED We were not totally in the dark about what the work was for, as Mr Freeborn had told some staff a ...

SImPSON | 419 We now apply the same reasoning to a bulb’s passing the test. Out of a batch of 100 a true tester will pass 80. Fo ...

420 | 38 BANBURISmUS REVISITED In fact the 1 in 17 repeat rate is puzzlingly low. From a frequency count in Wikipedia we can der ...

SImPSON | 421 probably relied on his judgement, taking other considerations into account too, rather than on an automatic thresh ...