The Turing Guide

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CHAPTER 35 Radiolaria: validating the Turing theory bernard richards I n his 1952 paper ‘The chemical basis of morphogenesis’ Tu ...

384 | 35 RADIOlARIA: VAlIDATING THE TURING THEORy the three-dimensional version concerns the overall shape of an organism. In 19 ...

RICHARDS | 385 figure 35.2 Circopus sexfurcus with six spines, all set at 90° apart. Reproduced from Bernard Richards, ‘The morp ...

386 | 35 RADIOlARIA: VAlIDATING THE TURING THEORy figure 35.4 Circogonia icosahedra with twelve spines and twenty faces. Reprodu ...

RICHARDS | 387 figure 35.6 Cannocapsa stehoscopium with twenty spines. Reproduced from Bernard Richards, ‘The morphogenesis of R ...

388 | 35 RADIOlARIA: VAlIDATING THE TURING THEORy Conclusion At the end of May 1954 I showed my computer-generated contour maps ...

PART VII Mathematics ...

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CHAPTER 36 Introducing Turing’s mathematics robin whitty and robin wilson A lan Turing’s mathematical interests were deep and wi ...

392 | 36 INTRODUCING TURING’S mATHEmATICS his powers, and was certainly influential in his approach to codebreaking, so it makes ...

wHITTy & wIlSON | 393 6 7 8 9 5 4 3 2 1 0 6 7 5 4 3 2 1 0–40 40–8080–120120–160 160–200 >200^0 0–40 40–8080–120120–160 16 ...

394 | 36 INTRODUCING TURING’S mATHEmATICS that different types of customer have different spending patterns; there is a technica ...

wHITTy & wIlSON | 395 any technical mathematics. Over the course of these letters the salutation progressed from ‘Dear Mr Ha ...

396 | 36 INTRODUCING TURING’S mATHEmATICS What happens if we move to variables and ask about a corresponding multiplication in w ...

wHITTy & wIlSON | 397 apparently taken with the problem and, as he had with problems in the past, mastered it at breakneck s ...

398 | 36 INTRODUCING TURING’S mATHEmATICS regularity, that there are laws governing their behaviour, and that they obey these la ...

wHITTy & wIlSON | 399 Table 36.1 x, p(x), and their ratio x/p(x). x p(x) x/p(x) 10 4 2.5 100 25 4.0 1000 168 6.0 10,000 1229 ...

400 | 36 INTRODUCING TURING’S mATHEmATICS where each term is one-third of the previous one, converges to 1^12 , and that, for an ...

wHITTy & wIlSON | 401 define ζ(k) for other numbers k? For example, how might we define ζ(0) or ζ(−1)? We cannot define them ...