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20.
White and Gribbin, Op.
cit.,
pages 137–138.

21.
Ibid.,
pages 154–155.

22.
Feynman himself published several highly popular science/philosophy books. See for example:
The Meaning of It All,
London: Allen Lane The Penguin Press, 1998, especially chapter three, ‘This Unscientific Age’; see also White and Gribbin, Op.
cit.,
pages 176ff.

23.
White and Gribbin, Op.
cit.,
pages 179 and 182–183.

24.
Joel Davis, Alternate Realities: How Science Shapes Our View of the World, Op. cit., pages 159–162.

25.
White and Gribbin,
Op. cit.,
pages 208 and 274–
275.

26.
John Horgan,
The End of Science: Facing the Limits of Knowledge in the Twilight of the Scientific Age,
New York: Addison-Wesley, 1996; Broadway paperback, 1997, pages 7, 30–31, 126–127, 154. Some of these issues were first aired in what became a cult book published in 1979,
Godei, Escher, Bach: an eternal golden braid
(New York: Basic Books). Hofstadter started from a conceptual similarity he observed in the work of the mathematician, artist and musician for whom his book is named. This similarity arises, according to Hofstadter, because in certain fugues of Bach, and in paintings and drawings by Escher, where the rules of harmony or perspective, as the case may be, are followed, these works yet break out of the rules. In Escher’s art, for example, although no violence is done to perspective, water appears to flow up hill, and even in an impossible circle, or people going up and down the same stairs follow steps that bring them back together again, in other words they too are following
an impossible circle. For Hofstadter, the paradoxes in these formal systems (ie, ones that follow a set of rules) were important, conceptually linking mathematics, biology and philosophy in ways that, he believed, would one day help explain life and intelligence. He followed Monod in believing that we could only understand life by understanding how a phenomenon transcended the rules of its existence. One of Hofstadter’s aims was to argue that if artificial intelligence was ever to develop, this aspect of formal systems had to be clarified. Was Godei right in claiming that a formal system
cannot
provide grounds for proving that system? And did that imply we can never wholly understand ourselves? Or is there something fundamentally flawed about Gödel’s idea?
Godei, Escher, Bach
is an idiosyncratic book, to which no summary can do justice. It is full of drawings and visual illusions, by Escher, René Magritte and the author, mathematical puzzles with a serious intent, musical notation and chemical diagrams. Though rewarding, and despite its author’s relentlessly chatty tone, it is not an easy read. The book contains a marvellous annotated bibliography, introducing many important works in the field of artificial intelligence.

27.
White and Gribbin, Op.
cit.,
pages 292–301.

28.
See also: Martin Rees,
Just Six Numbers: The Deep Forces that Shape the Universe,
London: Weidenfeld & Nicolson, 1999; White and Gribbin,
Op.
cit., pages 216–217.

29.
David Deutsch,
The Fabric of Reality,
London: Allen Lane The Penguin Press, 1997; Penguin paperback, 1998, pages 1–29 for an introduction; see also: Horgan, Op.
cit.,
pages 222–223; and: P. C. W. Davies and J. Brown (editors),
Superstrings: A Theory of Everything?,
Cambridge: Cambridge University Press, 1988, pages 1–5.

30.
Brian Greene, The Elegant Universe: Superstrings, Hidden Dimensions and the Quest for the Ultimate Theory, London: Jonathan Cape, 1998, pages 174–176.

31.
Apart from the works already quoted, see: Richard Feynman,
The Meaning of It All,
New York: Addison Wesley Longman; London: Allen Lane, The Penguin Press, 1998; Paul Davies,
The Mind of God: Science and the Search for Ultimate Meaning,
New York and London: Simon & Schuster, 1992; Penguin paperback, 1993; Ian Stewart,
Does God Play Dice?,
Oxford: Blackwell, 1989; Penguin paperback, 1990; Timothy Ferris,
The Whole Shebang: A State-of-the-Universe(s) Report,
New York: Simon & Schuster, 1997. Note the somewhat ambitious flavour of the tides.

32.
Greene, Op. cit., passim.

33.
Ibid.,
pages 10–13. See also: Davies and Brown, Op.
cit.,
pages 26–29.

34.
Greene,
Op. cit.,
pages 136–137.

35.
Davies and Brown,
Op. cit.,
page 90, for an interview with Witten, and pages 170–191 for interviews with Abdus Salam and Sheldon Glashow. See also: Greene, Op
cit.,
pages 140–141.

36.
Greene,
Op. cit.,
pages 187ff.

37.
Ibid.,
pages 329–331.

38.
Ibid.,
page 362.

39.
Ibid.,
page 379.

40.
James Gleick,
Chaos: Making a New Science,
New York: Penguin, 1987.

41.
Horgan, Op.
cit.,
pages 193–194.

42.
George Johnson,
Strange Beauty,
London: Jonathan Cape, 1999. See also: Horgan, Op.
cit.,
pages 211–215.

43.
Horgan, Op.
cit.,
pages 203–206 and 208.

44.
Philip Anderson, ‘More is different,’
Science,
August 4, 1972, page 393. Quoted in Horgan, Op.
cit.,
pages 209–210.

45.
Ian Stewart,
Life’s Other Secret,
New York: Wiley, 1998; Penguin paperback, 1999.

46.
Stewart, Op.
cit.,
page xiii. A certain amount of revisionism has set in with regard to computers and mathematics. See, for example: P.J. R. Millican and A. Clark (editors),
Machines and Thought: The Legacy of Alan Turing,
volume 1, Oxford: Oxford University Press, 1999. Though David Deutsch, in
The Fabric of Reality, Op. cit.,
page 354, considers the Turing principle a fundamental of nature.

47.
Ibid.,
page 22.

48.
Ibid.,
page 66.

49.
Ibid.,
pages 89–90.

50.
See: Blay Whitby, ‘The Turing Test: AI’s Biggest Blind Alley?’, in Millican and Clark (editors). Op
cit.,
pages 53ff; See also: Stewart,
Op. cit.,
pages 95ff.

51.
Stewart,
Op. cit.,
pages 96ff.

52.
Ibid.
, page 162.

53.
Ibid.

54.
See: Joseph Ford, ‘Chaos: Past, Present, and Future’, in Millican and Clark (editors),
Op. cit.,
who takes the opposite view. ‘… order is totally dull; chaos is truly fascinating’ – page 259. ‘… in essence evolution is controlled chaos’ – page 260. In this book, Clark Glymour also considers whether there are ‘orders of order’ – page 278ff See also: Stewart, Op.
cit.,
page 245.

CONCLUSION: THE POSITIVE HOUR

1.
T. S. Eliot,
Collected Poems 1909–1935,
London: Faber, 1936, page 93.

2.
Jared Diamond,
Guns, Germs and Steel,
London: Jonathan Cape, 1997.

3.
Ibid.,
see map at page 177.

4.
Ibid.,
page 57.

5.
Ibid., page 58.

6.
Francis Fukuyama,
The End of History and the Last Man,
Glencoe: The Free Press, 1992.

7.
Ibid.,
page xi.

8.
Ibid.,
page xii.

9.
Ibid.,
page xiv.

10.
Ibid.,
page 196.

11.
David Landes,
The Wealth and Poverty of Nations,
New York: W. W. Norton, 1998; Abacus paperback, 1999

12.
Ibid.,
page 312.

13.
John Horgan, The End of Science: Facing the
Limits of Knowledge in the Twilight of the Scientific Age, Op. cit.

14.
Ibid.,
pages 9–10.

15.
Ibid.,
page 152.

16.
Ibid.

17.
Ibid.,
pages 152–153. Not dissimilar views were expressed by David Bohm, an American physicist-philosopher who left the United States at the height of the McCarthy era, settling in Britain. Bohm, like Fritjof Capra after him, in
The Tao of Physics
(London: Wildwood House, 1975), made links between Eastern religions and modern physics, which Bohm called the ‘implicate order’. In Bohm’s view, the current distinction between art and science is temporary. ‘It didn’t exist in the past, and there’s no reason why it should go on in the future.’ Science is not the mere accumulation of facts but the creation of ‘fresh modes of perception.’ A third scientist of like mind was Paul Feyerabend. He too had once taught at Berkeley but by the mid-nineties was living in retirement in Switzerland and Italy. In two books,
Against Method
(London: Verso, 1975) and
Farewell to Reason
(London: Verso, 1987), he argued that there is no logic to science and to scientific progress and that the ‘human compulsion to find absolute truths, however noble, too often culminates in tyranny’ (page 48). He conceived of science as a boring, homogenising influence on thought, stampeding other forms out of the way. So firmly did he hold this view that in his later book he went so far as to refuse to condemn fascism, his argument being that such an attitude had led to fascism in the first place. (For his critics it didn’t help that he had fought in the German army in World War II.)

18.
Maddox, Op.
cit.

19.
Ibid.,
page 122.

20.
Ibid.,
pages 56–57.

21.
Ibid.,
page 59.

22.
Ibid.,
page 88.

23.
In
Darwin Machines and the Nature of Knowledge
(Allen Lane, The Penguin Press, Penguin paperback, 1995),. Henry Plotkin, professor of psychology at University College, London, advanced the view that adaptations are themselves a form of knowledge, part of the history of an organism which determines how it is born and what it knows and is able to know. On this reasoning, the intelligence displayed by the ‘higher’ animals is clearly an evolved adaptation which is itself designed to help us adapt. According to Plotkin, there are several functions of intelligence, one of which is to aid social cohesion: man is a social animal who benefits from the cooperation of others. Language and culture may therefore be understood in that light.

24.
Claude Bonnefoy,
Conversations with Ioescu, Op. cit.,
pages 167–168. There is also, for example, the one-off (but not necessarily trivial) case of Oxford University Press which, in November 1998, discontinued its Poetry List, giving as its reason that poetry no longer earned its keep – there was in other words no longer a market for verse. This shocked the literary world in the anglophone countries, especially as Oxford’s list was the second biggest in Britain, dating back to 1918 when it published Gerard Manley Hopkins. In the wake of the fuss that followed it was revealed that only four London firms published poetry on a regular basis, releasing barely twenty-five new tides a year, each of which sells two- to three-thousand copies. This is scarcely a picture of robust health. In Peter Conrad’s book,
Modem Times, Modem Places
(Thames & Hudson, 1998), which was an examination of the arts in the last century, he says that he found far more of interest and importance to write about in the first fifty years than in the last and that, of the nearly thirty themes he identifies as important to the arts, well over half are responses to science (the next most important was a sense of place: Vienna, Berlin, Paris, America, Japan). Conrad’s view of the arts is not dissimilar from Lionel Trilling’s, updated. Music, literature, painting and theatre should help us keep our spirits up, help us ‘keep going’, in his words. An unexceptional view, perhaps, but a much-reduced aim compared, say, with a hundred years ago, when the likes of Wagner, Hofmannsthal and Bergson were alive. Even by Peter Conrad’s exacting standards, the role of the arts has contracted.

25.
Alvin Kernan,
The Death of Literature,
New Haven and London: Yale University Press, 1990, page 134.

26.
Ibid.,
page 135.

27.
Ibid.,
page 151.

28.
Ibid.,
page 210.

29.
John Barrow,
Impossibility: The Limits of Science and the Science of Limits,
Oxford and New York: Oxford University Press, 1998; Vintage paperback, 1999, page 94.

30.
Ibid.,
pages 94–95.

31.
Ibid.,
page 95.

32.
Robin Wright, The Moral Animal, Op. cit., page 325.

33.
P. B. Medawar,
The Hope of Progress,
London: Methuen, 1972, page 68.

34.
Judith Rich Harris: The Nurture Assumption: Why Children Turn Out the Way They Do, London: Bloomsbury, 1998.

35.
Wright,
Op. cit.,
page 315.

36.
Published as: Michael S. Roth (editor),
Freud: Conflict and Culture,
New York: Knopf, 1998.

37.
Paul Robinson, ‘Symbols at an Exhibition’,
New York Times,
12 November 1998, page 12.

38.
Ibid.,
page 12.

39.
Richard Noll, The Jung Cult, Princeton: Princeton University Press, 1994; and The Aryan Christ: The Seaet Life of Carl Gustav Jung, Op. cit.

40.
Russell Jacoby, The Last Intellectuals: American Culture in the Age of Academe, New York: Farrar, Straus & Giroux, 1987; Noonday paperback 1989. John Brockman (editor), The Third Culture, Op. cit.

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