回首頁

回第04期

涂林本事
不可計算的一生功業

全文閱

作        者 庫珀 S. Barry Cooper

作者簡介 庫珀是英國數學家與計算理論學家,現為英國里茲大學教授。他曾任2012 涂林年的顧問委員會主席。

譯        者 周樹靜

譯者簡介 周樹靜為臺灣數學科普譯者。

本文出處    Notices 59(2012)6, AMS。這是 Notices 在涂林百年誕辰的兩篇紀念文章之一。本文成於作者在英國牛頓數學科學研究院訪問期間。

延伸閱讀 
參考資料

Bibliography

1. S. Alexander, Space, Time, and Deity, Vol. 2, 1927.

2. L. Blum, F. Cucker, M. Shub, and S. Smale, Complexity and Real Computation, Springer, 1997.

3. C. D. Broad, The Mind and Its Place in Nature, Kegan-Paul, London, 1923.

4. R. Brooks, The case for embodied intelligence, in Alan Turing—His Work and Impact (S. B. Cooper and J. van Leeuwen, eds.), Elsevier, 2012.

5. S. B. Cooper, Computability Theory, Chapman & Hall/CRC Press, Boca Raton, FL, New York, London, 2004.

6. ________, Turing centenary: The incomputable reality, Nature, 482:465, 2012.

7. S. B. Cooper and J. van Leeuwen (eds.), Alan Turing—His Work and Impact, Elsevier, 2012.

8. A. R. Damasio, The Feeling of What Happens: Body and Emotion in the Making of Consciousness, Harcourt Brace, 1999.

9. M. Davis, The Universal Computer: The Road from Leibniz to Turing, A K Peters/CRC Press, 2011.

10. A. Einstein, Out of My Later Years, volume 48, Philosophical Library, 1950.

11. S. Feferman, Transfinite recursive progressions of axiomatic theories, J. Symbolic Logic, 27:259–316, 1962.

12. S. Feferman, Turing in the Land of O(z), in The Universal Turing Machine: A Half-Century Survey (R. Herken, ed.), Oxford University Press, New York, 1988, pp. 113–147.

13. R. P. Feynman, Simulating physics with computers, Int. J. Theoretical Physics, 21:467–488, 1981/82.

14. G. Gamow, One, Two, Three…Infinity (1947, revised 1961), Viking Press (copyright renewed by Barbara Gamow, 1974), Dover Publications.

15. R. O. Gandy, The confluence of ideas in 1936, in The Universal Turing Machine: A Half-Century Survey (R. Herken, ed.), Oxford University Press, New York, 1988, pp. 51–102.

16. J. Hadamard, The Psychology of Invention in the Mathematical Field, Princeton Univ. Press, Princeton, 1945.

17. W. Hasker, The Emergent Self, Cornell University Press, Ithaca, London, 1999.

18. A. Hodges, Alan Turing: The Enigma, Vintage, London, Melbourne, Johannesburg, 1992.

19. J. Kim, Physicalism, or Something Near Enough, Princeton University Press, Princeton, Oxford, 2005.

20. S. C. Kleene, Recursive functionals and quantifiers of finite types. I, Trans. Amer. Math. Soc., 91:1–52, 1959.

21. S. C. Kleene, Recursive functionals and quantifiers of finite types. II, Trans. Amer. Math. Soc., 108:106–142, 1963.

22. W. McCulloch and W. Pitts, A logical calculus of the ideas immanent in nervous activity, Bull. Math. Biophys., 5:115–133, 1943.

23 B. P. McLaughlin, The rise and fall of British emergentism, in Emergence or Reduction?—Essays on the Prospects of Nonreductive Physicalism (A. Beckermann, H. Flohr, J. Kim, eds.), de Gruyter, Berlin, 1992, pp. 49–93.

24. J. Myhill, Creative sets, Z. Math. Logik Grundlagen Math., 1:97–108, 1955.

25. P. Odifreddi, Classical Recursion Theory, North- Holland, Amsterdam, New York, Oxford, 1989.

26. R. Penrose, The Emperor’s New Mind: Concerning Computers, Minds, and the Laws of Physics, Oxford University Press, Oxford, New York, Melbourne, 2002.

27. E. L. Post, Degrees of recursive unsolvability: Preliminary report (abstract), Bull. Amer. Math. Soc., 54:641–642, 1948.

28. P. Smolensky, On the proper treatment of connectionism, Behavioral and Brain Sciences, 11:1–74, 1988.

29. R. I. Soare, Turing computability and information content, Philos. Trans. Royal Soc. London, Series A, to appear.

30. C. Teuscher, Turing’s Connectionism, An Investigation of Neural Network Architectures, Springer-Verlag, London, 2002.

31. ________, A modern perspective on Turing’s unorganized machines, in Alan Turing—His Work and Impact (S. B. Cooper and J. van Leeuwen, eds.), Elsevier, 2012.

32. A. M. Turing, On computable numbers with an application to the Entscheidungsproblem, Proc. London Math. Soc. (3), 42:230–265, 1936. A correction, 43:544–546, 1937.

33. ________, Systems of logic based on ordinals, Proc. London Math. Soc. (3), 45:161–228, 1939.

34 ________, Computing machinery and intelligence, Mind, 59:433–460, 1950.

35. ________, The chemical basis of morphogenesis, Philos. Trans. Royal Soc. London. Series B, Biological Sciences, 237(641):37–72, 1952.

36. ________, Intelligent machinery, in D. C. Ince, (ed.), Collected Works of A. M. Turing—Mechanical Intelligence, Elsevier Science Publishers, 1992.

37. J. von Neumann, The general and logical theory of automata, in: L. A. Jeffress (ed.), Cerebral Mechanisms in Behaviour: The Hixon Symposium, September 1948, Pasadena, Wiley & Sons, New York, 1951.

38. H. Wang, Reflections on Kurt Gödel, MIT Press, Cambridge, MA, 1987.

 

[補充]

39. L. Blum, Computing over the reals: Where Turing meets Newton, Notices, AMS, 51 no. 9, 2004.