The Eleven Pictures of Time

550 NOTES TO CHAPTER 10 22. No doubt the process suggested above involves what has come to be known as reductionism. But I presume that most anti-reduc- tionists chew their food, and don’t gulp it down whole. Currently, the reductionist’s real objection is to the mechanisation of life that results from reductionism (with instantaneity) and not to the mere reduction of a problem to a more manageable size. 23. E. Schrödinger, What is Life?, reprint Cambridge University Press, Cambridge, 1992. CHAPTER 10 1. E. P. Thompson, ‘Time, Work-Discipline and Industrial Capitalism’, Past and Present 38, 1967, pp. 56–97; Lewis Mumford, Technics and Civilization, Harcourt Brace, New York, 1934; Sebastian de Grazia ‘Time and Work’ in The Future of Time, ed. Henn Yakes, Garden City, New York, 1971. Georges Gurvitch, The Spectrum of Social Time, D. Reidel, Dordrecht, 1964. 2. John Hassard, ed., The Sociology of Time, Macmillan, London, 1990. 3. David S. Landes, Revolution in Time: Clocks and the Making of the Modern World, Harvard University Press, Cambridge, Mass., 1983, pp. 59–66. 4. These were the lauds, prime, tierce, sext, none, vespers, and compline; the night prayer was called the vigil, and later the matins. 5. See, e.g., Suzan Rose Benedict, A Comparative Study of the Early Treatises Introducing into Europe the Hindu Art of Reckoning (Ph.D. Thesis, University of Michigan), Rumford Press, 1914. ‘Algorismus’ is a Latinisation of al Khwarizmi, who translated into Arabic the mathematical texts of Brahmagupta. There was a protracted conflict between the algorismus texts and abacus texts. The eventual victory of algorismus over abacus was depicted by a smiling Boethius using Indian numerals, and a glum Pythagoras to whom the abacus technique was attributed. This picture first appeared in the Margarita Philosophica of Gregor Reisch, 1503, and is reproduced, for example, in Karl Menninger, Number Words and Number Symbols: A Cultural History of Numbers, trans. Paul Broneer, MIT Press, Cambridge, Mass., 1970, p. 350. According to the periodisation suggested by Menso Folkerts, the abacus period commenced by the 12th century, though the use of the abacus is obviously much older. Menso Folkerts, Lecture at the Second Meeting of the International Laboratory for the History of Science, Max Planck Institute for the History of Science, Berlin, 19–26 June 1999.

NOTES TO CHAPTER 10 551 6. E. C. Phillips, ‘The proposals of Father Christopher Clavius, S. J. for improving the Teaching of Mathematics’, Bulletin of the American Association of Jesuit Scientists (Eastern Section) vol. XVIII, May 1941, No. 4, pp. 203–6. The document was written before ca. 1575, when its recommendations were actually implemented in the Collegio Romano. 7. According to Whitrow, the ‘verge-and-folio’ escapement which made possible the mechanical clock was invented between 1280 and 1300. G. J. Whitrow, Time in History, Oxford University Press, Oxford, 1989, p. 103. This type of clock was inaccurate because the balance controlling the frequency of oscillations had no natural period of its own. Later this was linked to the oscillations of a pendulum, and then a cycloidal pendulum, which measured ‘equal intervals of time’ according to Newtonian mechanics. 8. G. J. Whitrow, Time in History, p. 102; emphasis mine. 9. Douglas Peck, ‘Columbus Used Dead Reckoning Navigation in His 1492 Voyage of Discovery to the new World’, Encounters: A Quin- centenary Review, 1990 (Summer), pp. 18–21. 10. C. K. Raju, ‘Kamâl or Râpalagai’, Paper presented at the Xth Indo-Portuguese Conference on History, Indian National Science Academy, New Delhi, 1998. To appear in Proc. 11. J. W. Norie, Norie’s Nautical Tables, London, 1864, pp. 59–60. 12. See, for example, K. S. Shukla, ed. and trans., Bhâskara I and his Works, Part III: Laghu Bhâskarîya, Department of Mathematics and Astronomy, Lucknow University, 1963. The Laghu Bhâskarîya was a widely used 6th or 7th century jyotiìa text. 13. The exact relation is sin δ = sin φ sin a, where δ is the declination, φ is the local latitude, and a is the solar altitude on the prime vertical. Laghu Bhâskarîya iii 22–23 et. seq., Maha Bhâskarîya, iii 37–38. Bhâskara I and His Works, Part III, and Part II respectively, ed. and trans. K. S. Shukla, Department of Mathematics and Astronomy, Lucknow University, 1963. Hence, to determine latitude, accurate sine tables were also needed, in addition to an accurate calendar, and Clavius, for example, produced these sine tables. 14. To reiterate, since the church retained the equinoctial cycle as the basis of the calendar, it did not intend to ignore natural cycles altogether. Thus, by continuing to ignore the natural cycle of the moon, and retaining the unequal months, the church was presumably demonstrating its commitment to the state, through its continuing reverence for the petty egos of Roman dictators, together, perhaps, with its commitment to inequity even with regard to the duration of months! Curiously, historians like Whitrow have called this ‘a uniform calendar corresponding to the

552 NOTES TO CHAPTER 10 needs of a universal society and based upon the Christian year.’ Whitrow, Time in History, p. 70. 15. ‘Com tudo não me parece que sera impossivel saberse, mas has de ser por via d‘algum mouro honorado ou brahmane muito intel- ligente que saiba as cronicas dos tiempos, dos quais eu procurarei saber tudo.’ Letter by Matteo Ricci to Petri Maffei on 1 December 1581, Goa 38 I, ff. 129r–130v, corrected and reproduced in Documenta Indica, XII, pp. 472–77. (The quote is from p. 474.) Also reproduced in Tacchi Venturi, Matteo Ricci S.I., Le Lettre Dalla Cina 1580–1610, vol. 2, Macerata, 1613. 16. Martin Bernal, Black Athena: The Afroasiatic Roots of Classical Civiliza- tion. Volume 1: The Fabrication of Ancient Greece 1785–1985, Vintage, London, 1987. Alexandria was located in Egypt, in the continent of Africa. Most early scientific discoveries today attributed to Greeks (Eratosthenes, ‘Euclid’, Archimedes, Ptolemy, etc.) relate to Alexandria, not Athens, and were earlier attributed to the knowledge of the Egyptians, accumulated in the Great Library of Alexandria. Present-day knowledge of most of the science and philosophy attributed to Greeks relates to medieval Latin transla- tions of Arabic works, or of Byzantine Greek texts which translated Arabic works. The story of ‘Greek’ origins is thus a racist appropria- tion carried out with the help of colonial historians. Likewise, the story of a purely European origin of ‘modern science’ involved numerous appropriations from India and China. 17. Otto Neugebauer, ‘On the Planetary Theory of Copernicus,’ Vistas in Astronomy, 10, 1968, pp. 89–103. George Saliba, ‘Arabic Astronomy and Copernicus’, chap. 15 in A History of Arabic Astronomy, New York University Press, New York, 1994, p. 291. The heliocentric theory was one of the competing theories in Indo- Arabic astronomy for several centuries prior to Copernicus, and references to it may be found even in the poetry of Amir Khusrau, a 14th century CE poet of Delhi. 18. C. K. Raju, ‘Computers, Mathematics Education, and the Alterna- tive Epistemology of the Calculus in the Yuktibhâìâ’, Philosophy East and West, 51(3), 2001, pp. 325–62; C. K. Raju and Dennis Almeida (Aryabhata Group) ‘The Transmission of the Calculus from Kerala to Europe, Part I: Motivation and Opportunity’, and ‘Part II: Documentary and Circumstantial Evidence’. Paper presented at the Aryabhata Conference, Trivandrum, January 2000. C. K. Raju ‘The Infinitesimal Calculus: How and Why it Was Imported into Europe’, paper presented at an International Semi- nar on East-West Transitions, National Institute of Advanced Study, Bangalore, December 2000 (submitted for publication).

NOTES TO CHAPTER 10 553 19. For detailed quotations, etc., see C. K. Raju, ‘Kamâl or Râpalagai’ cited earlier. Briefly, the Laghu Bhâskarîya II.8 gives a rule for determining the local longitude using a clepsydra. Bhaskara I and his works, Part II: Laghu-Bhâskarîya, ed. and trans., K. S. Shukla, Department of Mathematics and Astronomy, Lucknow University, 1963, p. 53. 20. E. S. Kennedy, A Commentary upon Bîrûni’s Kitab Tahdid al-Amakin: An 11th Century Treatise on Mathematical Geography, Beirut, 1973, p. 164. 21. For Fermat’s challenge problem see D. Struik, A Sourcebook of Mathematics 1200–1800, Harvard University Press, Cambridge, Mass., 1969, p. 29. For the Brahmagupta–Bhaskara equation, see T. S. Bhanu-Murthy, A Modern Introduction to Ancient Indian Mathematics, Wiley Eastern, New Delhi, 1992, Chapter 3, p. 121. For Fermat’s access to Jesuit sources, and for details on why it is unlikely that Fermat independently rediscovered this, see the paper by C. K. Raju and Dennis Almeida, cited earlier. For Fermat’s access to Bombelli’s preface to his translation of Diophantus, acknow- ledging Indian contributions, see C. K. Raju, ‘How and Why the Calculus was Imported into Europe’, cited earlier. 22. C. K. Raju, ‘Computers, Mathematics Education and the Alterna- tive Epistemology of the Calculus in the Yuktibhâìâ’, Philosophy East and West, 51 (3), 2001, pp. 325–62. 23. Cavalieri, a student of Galileo, waited for five years for his teacher to publish first on the calculus. Galileo’s access to the Collegio Romano is well documented. See William Wallace, Galileo and his Sources: The Heritage of the Collegio Romano in Galileo’s Science, Princeton University Press, 1984. 24. The navigational unit of zam incorporates exactly the Indian method of measuring the radius of the earth, as documented by al Bîrûnî. Al Bîrûnî’s accurate results agreed with Caliph al Mamun’s measurements (early 9th century), and the earlier Indian estimates of the radius of the earth, whose exact basis is not recorded. See C. K. Raju ‘Kamâl or Râpalagai’ cited earlier. 25. Whitrow, Time in History, p. 141. 26. Nigel Thrift, ‘The Making of a Capitalist Time-Consciousness’, in The Sociology of Time, ed. J. Hassard, cited earlier, pp. 105–29. 27. This was similar to the traditional Indian astronomical technique of using the meridian through Ujjain—another one of those little facts that Western historians of science have forgotten. 28. Bronislaw Malinowski, ‘Tie-reckoning in the Trobriands’, in The Sociology of Time, ed. J. Hassard, cited earlier, pp. 203–18. (Ex- tracted from ‘Lunar and seasonal calendar in the Trobriands’, J. Anthropological Institute of Great Britain and Ireland, 56–57, 1926–27.)

554 NOTES TO CHAPTER 10 29. Karl Marx, Capital, vol. I; reprint, Progress Publishers, Moscow, 1974, p. 392. 30. H. -J. Voth, ‘Time and Work in Eighteenth-Century London’, Journal of Economic History, 58, 1998, pp. 29–58. 31. In India, for example, this is calculated by fixing the minimum wage as the poverty line: the cost of purchasing enough food to maintain the basal metabolic rate (1800 KCal) + light physical activity (sitting or standing), to give a figure of 2400 Kcal (though the poor are typically involved in hard labour). The most well- known (though not the first) attempt to calculate it this way was by the economists V. M. Dandekar and N. Rath. The study, conducted on behalf of the Ford Foundation, did not take into this calculation the needs of the poor for clothes, or housing, or medicine etc., on the grounds that they spent very little on these things anyway! Even this miserable figure was found to be too high, and P. V. Sukhatme’s theory was used to bring this down. The theory relied on a malapropism: confusing autoregression with autoregulation to call stunted growth ‘homeostasis’. From the point of view of physics (conservation of energy) and statistics, Sukhatme’s theory was as befuddled as he was when I repeatedly asked him to show me even the data on the 5 persons on which he claimed to have based his theory. (He never did.) The theory was adopted by the Government of India, and internationally by the Food and Agricul- tural Organization, to bring down the poverty line, and reduce poverty estimates. The real point of these calculations by Dandekar et al. is not to ensure that the poor get a minimum wage: for the state does not devote resources to ensure that. The real point is that poverty is the capitalist substitute for slavery; without poverty, the capitalist cannot negotiate an unfair exchange. In the US, slaves sold ‘down the river’ died soon because they were over- worked and underfed; and the aristocracy found this to be the most profitable course since the cost of replacing slaves was lower than the cost of maintaining them. Thus, the work of Dandekar et al. served the hidden agenda of calculating how the poor can be most profitably starved. Now, perhaps, the only hope for the poor seems to be to rely on the process which broke the slave trade: the north of North America fought with the south because they produced goods cheaper in the south with slave labour. The first sign of this is the recent US concern for child labour in India. See Jaya Mehta, ‘Nutritional norms and the measurement of malnourishment and poverty’, Economic and Political Weekly, 14 August 1982; ‘Poverty data’, State of India’s Economy, Public Interest Research Group, New Delhi, 1995; ‘Concern for child labour’. In: My Name is Today,

NOTES TO CHAPTER 10 555 Butterflies Programme of Street and Working Children, excerpted in The Times of India, 30 March 1994. 32. Max Weber, The Protestant Ethic and the Spirit of Capitalism, [1930], George Allen and Unwin, London, 1968, pp. 60–61. 33. Nigel Thrift, in The Sociology of Time, ed. J. Hassard, cited earlier, p. 112. 34. Pierre Bourdieu, ‘The Attitude of the Algerian Peasant Towards Time’, Mediterranean Countryman, 6, 1963, pp. 55–72. However, they started working harder when their wages were tripled. 35. M. Adas, Machines as the Measure of Men. Science, Technology and Ideologies of Western Dominance, reprint, Oxford University Press, New Delhi, 1990, pp. 242–45. 36. Ibid., p. 225. 37. Ibid., p. 226. 38. A. Giddens, The Class Structure of Advanced Societies, Hutchinson, London, 1973. 39. The Times of India, December 94, op. ed. page. 40. As with the equation time=money, this temporal assumption was also a source of racist comment when the temporal beliefs of an industrial society collided with those of an agricultural society during colonialism. ‘By the late nineteenth century…lack of “prevoyance” or “ability to anticipate” was considered a clear sign of the primitive state of African societies…Edmund Ferry claimed that the peoples of Sudan had no verb forms to express the past tense and in fact made no distinction between past, present, and future…H. L. Duff compared Africans to “intelligent animals” because of their presentist orientations.’ See Adas, Machines as the Measure of Men, in the place cited earlier. 41. For a review, see, e.g., D. K. Wood, Men Against Time, University of Kansas Press, 1982. 42. A. & B. Bel, ‘Polychronie—une approache nouvelle du travail choregraphique et des interactions dans-musique’, Actes du Collo- que International pour la Danse et la Recherche Choregraphique Contemporaines (Paris: GERMS)(to appear). 43. David Wood, The Deconstruction of Time, Humanities Press Interna- tional, Atlantic Highlands, NJ, 1989. 44. Mircea Eliade, Cosmos and History: The Myth of the Eternal Return, trans. W. Trask, Harper, New York, 1959, p. 153. 45. T. S. Eliot, Essays Ancient and Modern, Harcourt Brace, New York, 1932, p. 138; ‘The idea of a Christian Society’, in The Idea of a Christian Society and Notes Towards the Definition of Culture, Harvest, New York, 1940, pp. 14–19.

556 NOTES TO CHAPTER 11 CHAPTER 11 1. See, e.g., Stephen E. Hanson, Time and Revolution, University of North Carolina Press, Chapel Hill, 1997, p. 15. Hanson cites Mircea Eliade’s Cosmos and History, cited in Chapter 10. 2. As recorded in the Sâmanna Phala Sutta of the Dîgha Nikâya. T. W. R. Rhys-Davids, trans., Dialogues of the Buddha (3 vols), London, 1899–1921, vol. I, pp. 68–69. Parallel records are available amongst the Jains. The term ‘recluse’ is not properly translated, since these six had not run away to the Himalaya. ‘Homeless wanderer’ is a more accurate if clumsier term, since they did not live the married life of an ordinary householder either. 3. This ‘natural’ inclination should be distinguished from the reflex or habitual inclination to survive. 4. In the Viìäu Purâäa, the reduction proceeds through equations of the type 1 year of mortals = 1 day of the gods and so on up to a day and night of Brahmâ. Perhaps this reduction is to be seen in terms of subjective time, as determined by the life span, say. But the justification offered is rather curious in places. For instance, see note 27 of Chapter 1. 5. The Brahmajâla Sutta of the Dîgha Nikâya of the Sutta Pitaka. See, e.g., T. W. Rhys Davids, trans., The Dialogues of the Buddha, vol. 1; or the more easily available, Maurice Walshe, trans., The Long Discourses of the Buddha: A Translation of the Dîgha Nikâya, Wisdom Publications, Boston, 1995. 6. The use of a quibble was, however, considered acceptable as a means of destroying those who had become too powerful and supported evil. For example, in the same battle, the venerable Bhishma, who had the boon that he could be killed neither by man nor by woman, was killed by a hermaphrodite, Shikhandin, against whom he refused to fight. 7. Like the Stoics, we hear of Lokâyata or Cârvâka only from their opponents, but the relation here is marked by mutual contempt and explicit abuse. There are two meanings of ‘Lokâyata’. The first is lokesu (people) + âyatah (prevalent) = people’s philosophy; the second, attributed to a 5th century CE Buddhist commentator Buddhaghosha, is loka ([this] world) + âyatana (basis) = this-world- ly philosophy or materialism. In all likelihood, both meanings apply—the people’s philosophy was materialistic—as supposed in D. P. Chattopadhyaya, cited earlier. There is a small probability, however, that the two meanings may be a bit like there being simultaneously two D. P. Chattopadhyaya-s (both Debi Prasad) in one philosophy department of the same university (Jâdavpur), both of whom are cited earlier in this book, it being assumed that the one referred to is clear from the context!

NOTES TO CHAPTER 11 557 8. T. W. Rhys-Davids, trans., Dialogues of the Buddha, cited earlier, vol. 1, pp. 73–74; quoted in D. P. Chattopadhyaya, Lokâyata: A Study in Ancient Indian Materialism, Peoples Publishing House, New Delhi, 1959, p. 510; cf. Dîgha Nikâya, trans. Maurice Walshe, cited above. 9. Debiprasad Chattopadhyaya and M. K. Gangopadhyaya, eds., Cârvâka/Lokâyata: An Anthology of Source Materials and Some Recent Studies, ICPR, New Delhi, 1990, pp. 246–54. Mâdhava and his brother Sâyana were ministers in the Vijayanagar empire which sent Vasco da Gama into ecstasies over the wealth in India. Sarva Darìana Sangraha of Madhavacarya, ed. K. L. Joshi, trans. E. B. Cowell and A. E. Gough, Parimal Publications, Delhi, 1986. 10. S. N. Dasgupta, A History of Indian Philosophy, vol. 3; reprint Orient Books, New Delhi, 1975, p. 533. 11. D. P. Chattopadhyaya, Lokâyata, cited earlier. He also examines in depth the related bias of patriarchy. 12. D. P. Chattopadhyaya, in Lokâyata, also argues at length that triangles used in the yantra-s of Tantra are esoteric symbols of female genitalia, and that similar esoteric symbols were used in Egypt. These fertility symbols were presumably related to agricul- ture. 13. D. R. Shastri, A Short History of Indian Materialism, Sensationalism and Hedonism, Calcutta, p. 36; cited in Chattopadhyaya, Lokâyata, p. 18. Reproduced inCârvâka/Lokâyata, ed. Debiprasad Chattopad- hyaya and M. K. Gangopadhyaya, pp. 394–431. 14. D. P. Chattopadhyaya, Lokâyata, p. 31. This is an old saying, attributed to the Cârvâka mentor Brhaspati by Madhava in his Sarva Darìana Samgraha; see Cârvâka/Lokâyata, ed. Debiprasad Chattopadhyaya and M. K. Gangopadhyaya, p. 254. 15. The ‘learned’ Western pundits who so facilely refer to Buddhism as Hindu heterodoxy, should first locate at least one heterodox Christian sect which rejects the Bible in toto or one heterodox Islamic sect which similarly rejects the Ku‘rân. 16. Quoted by S. N. Dasgupta in A History of Indian Philosophy, vol. 3, Cambridge, 1922–55, p. 539. 17. Manibhadra was a commentator on the 8th century Haribhadra’s Sat Darsìna Samuccaya. D. P. Chattopadhyaya, Lokâyata, pp. 29–30. Cârvâka/Lokâyata, ed. Debiprasad Chattopadhyaya and M. K. Gan- gopadhyaya, p. 260. 18. Dasgupta, Indian Philosophy, vol. 3, p. 536. 19. The elite hostility to Lokâyâta is well known. But even the Buddha rejected the teaching of Lokâyata doctrines as a dukkata offence; D. P. Chattopadhyaya, Lokâyâta, pp. 38–39; F. Max Mueller, ed., Sacred Books of the East, Oxford, 1859, vol. 20, pp. 151–52.

558 NOTES TO CHAPTER 11 20. Dhammapada, trans. E. W. Burlingame, Buddhist Legends, (Harvard Oriental Series, vol. 30), Harvard University Press, Cambridge, Mass., 1921. Reprinted by Pali Text Society, Routledge and Kegan Paul, London, 1977, p. 128. 21. B. M. Baruah, A History of Pre-Buddhistic Indian Philosophy, Calcutta, 1921; reprint Motilal Banarsidass, Delhi, 1970. 22. Yoga Bhâsya 3.52. J. H. Woods, trans., The Yoga System of Patañjali… (Harvard Oriental Series, vol. 17), Harvard University Press, Cambridge, Mass., 1927, pp. 287–88; here reproduced from the modified translation by C. K. Raju, ‘Time in Indian and Western Traditions and Time in Physics’, in Astronomy, Mathematics, and Biology in Indian Tradition (PHISPC Monographs, No. 3), ed. D. P. Chattopadhyaya and Ravinder Kumar, PHISPC, New Delhi, 1995, p. 68. 23. Th. Stcherbatsky, Buddhist Logic, vol. I, Dover, New York, 1962, p.106. 24. The Buddha’s answer involved graded pedagogy. At the zeroth level, he points out (through a counter-question) that if Ajâtasattu’s slave became a Buddhist monk, the king would treat him with respect. Seeing that the king understands, he proceeds to give him the answer. 25. Lewis Carroll, The Annotated Alice, with an introduction and notes by Martin Gardner, Penguin, 1984, p. 67. 26. Friedrich Nietzsche, The Anti-Christ, 20, in Twilight of the Idols and the Anti-Christ, trans. R. J. Hollingdale, Penguin Books, 1990, pp. 141–42. 27. In fact, since existence did not continue for more than an instant, one acts not out of self interest (for future rewards, etc.) but out of compassion for those (including oneself) coming later. 28. One cannot justify inter-temporal comparisons of utility on the grounds that there are only ‘slight’ changes over time, since the term ‘slight’ is a cardinal notion, and the very point in question is the existence of a cardinal utility function. 29. F. Max-Mueller, Sacred Books of the East, vol. 13, pp. 84–85. 30. Kaccâyanagotta-Sutta, Samyukta Nîkâya, 2.17. 31. We recall from Chapter 1 how Kassapa responded to Pâyâsi with the allegory of a pregnant woman who died with her child because she cut open her womb to check whether the child was a boy or a girl, to decide her share in the inheritance. 32. D. D. Kosambi, An Introduction to the Study of Indian History, Popular Prakashan, Bombay, 1956. 33. This association of monasteries with trade routes enabled Kosambi to uncover Buddhist sites in the mountains around the Karla caves. While Kosambi’s ideas are insightful, not all of them are quite

NOTES TO CHAPTER 11 559 convincing. Thus, it does make sense to say that beef-eating was prohibited because a shift from a pastoral to an agricultural economy made animals too valuable to be given up easily for sacrifice; but one wonders why a similar shift in other parts of the world failed to produce similar prohibitions against beef-eating. Similarly, this logic does not explain the sudden stress on animal rights (even Aíoka prohibited needless slaughter of cocks and hens in his kitchen) or the insistence of numerous wanderers to go about naked—these were not uniquely the Jain ascetic extremes against which the Buddha preached moderation. Similarly, the current association of Jainism with trade was surely not what Mahavira had preached. Likewise, what accounts for the sudden interest in animal rights in the West today? 34. D. P. Chattopadhyaya, Lokâyata, cited earlier. 35. The Reader’s Digest Great World Atlas, First Edition, Sixth Revise, Reader’s Digest Association, London and Cape Town, 1962, p. 131. 36. D. D. Kosambi, Indian History, for example, p. 136. 37. Vaiíeìika Sutra 2.10. K. H. Potter, ed., Encyclopaedia of Indian Philosophy, vol. 2, Motilal Banarsidass, Delhi 1987, p. 218. 38. Vaiíeáika Sutra 1.15. Potter, ed., Encyclopaedia of Indian Philosophy, vol. 2, p. 216. 39. The Nyâya Sûtra (IV.2.17) asserts that ‘atoms are not further divisible’, and then states the objection (pûrva pakìa) that this is impossible since ‘atoms are pervaded by aether’ (IV.2.18), ‘else aether would not be all-pervasive’ (IV.2.19). The Nyâya Sûtra of Gautama, trans. Ganganath Jha, vol. 4, reprint, Motilal Banar- sidass, Delhi, 1984, pp. 131–32. 40. Nyâya Sûtra, IV.2.20. Ibid. 41. Nyâya Sûtra, IV.2.24. Ibid. 42. Mary Hesse, Forces and Fields, pp. 160–67. 43. Udyotkara gave a linguistic resolution of the problem: ‘ “contact” qualifies the two atoms in contact; it is not a physical property’. Nyâya Varttika, trans. Ganganath Jha [1919], reproduced in En- cyclopaedia of Indian Philosophy, ed. Potter, vol. 2, pp. 334–35. For more details, in relation to fields and particles, see C. K. Raju, ‘The Electromagnetic Field’, chap. 5a in Time: Towards a Consistent Theory, Kluwer Academic, Dordrecht, 1994, pp. 102–15. 44. The African belief (Chapter 1, note 33) is that the dead are not quite dead, but retain their individuality till such time as there are people alive who personally knew them. Memories of the dead may sometimes arise in the minds of such people, and the dead surely are partly the cause these memories—the dead, though past, hence

560 NOTES TO CHAPTER 11 may be regarded as continuing to exist. John S. Mbiti, African Religions and Philosophy, Heinemann, London, 1969. 45. Hajime Nakamura, A History of Early Vedanta Philosophy, trans. Trevor Leggett et al., Motilal Banarsidass, Delhi, 1983, p. 237. 46. R. A. Nicholson, A Literary History of the Arabs, T. Fisher Unwin, London, 1907. Krishna Chaitanya, A History of Arabic Literature, Manohar Prakashan, New Delhi, 1983. 47. This was similar to the Neoplatonic intention of Proclus, the earliest actual source of the Elements; the term ‘equality’ was replaced by the term ‘congruence’ only by Hilbert and others, in the 20th century CE. 48. See, e.g., R. C. Taylor in Neoplatonism and Islamic Thought, ed. Parviz Morewedge, SUNY, Albany, 1992. 49. Krishna Chaitanya, History of Arabic Literature, pp. 98–99. This sort of thing has with facility been dubbed pantheism. 50. Maimonides, Guide of the Perplexed, part 1, chaps 73–76, trans. S. Pines, University of Chicago Press, Chicago, 1974. (Also, Maimonides, Guide for the Perplexed, trans. M. Friedlander, Dover, New York, 2000.) 51. Futuhat, II, p. 523; cited by Mahmoud al-Ghorah, in Muhyiddin Ibn ‘Arabî, ed. Stephen Hirtenstein and Michael Tiernan, Element, Shaftesbury, 1993, p. 208. 52. In Islam there is no institution like a church, and no scriptural recognition of a division between the temporal and the spiritual (‘Give unto God what is God’s and unto Caesar what is Caesar’s’). In India, the linkage between orthodoxy and the state started appearing very late, with the last effective Moghul emperor Auran- gazeb who slew his Sufi step-brother Dara Shûkoh. With the col- lapse of the Moghul empire, this tendency dissipated before it could take hold. 53. For example, Shaikh Ahmad Sirhindi, Maktûbât (Letters), ff. 52– 53b, in Sources of Indian Tradition, trans. Wm. Theodore de Bary et al.; reprint, Motilal Banarsidass, Delhi, 1972, p. 449. Sirhindi, who regarded Akbar as a thorn in the side of Islam, died in Jehangir’s time. 54. Farid al-din Attar, Muslim Saints and Mystics, trans. A. J. Arberry, Arkana, London, 1990, p. 119. 55. Max Weber, The Protestant Ethic and the Spirit of Capitalism [1930], George Allen and Unwin, London, 1968. A detailed critical ex- amination of his thesis would be out of place here. 56. To call as ‘capitalist’ one who rationally maximises profit with a religious zeal would reduce Weber’s thesis to an irrefutable cir- cularity.

NOTES TO CHAPTER 11 561 57. Statement attributed to Mother Teresa’s successor, Sister Nirmala, as reported in various newspapers. See the discussion on the editorial page of The Times of India, 17 September 1997. It should be observed that their concern is not with the removal of poverty— for which man-made condition they appeal to divine sanction—but with alleviating the suffering of the poor. Hope has always served as a means of control, as in the lotteries used to tax the poor. Therefore, offering hope to the poor, without wanting to remove poverty, is regarded as a socially laudable objective. 58. The technical difference is that class permits some individual mobility, while caste, except in very extraordinary cases, permits only group mobility. Hence caste loyalties are stronger than class loyalties, for the system ties the benefit of the individual to that of the group. 59. For some more details, see C. K. Raju, ‘Computers, Mathematics Education, and the Alternative Epistemology of the Calculus in the Yuktibhâìâ’, Philosophy East and West, 51(3), 2001, pp. 325–62; ‘Mathematics and Culture’, in History, Culture and Truth: Essays Presented to D. P. Chattopadhyaya, ed. Daya Krishna and K. Satchidananda Murthy, Kalki Prakash, New Delhi, 1999, pp. 179– 93. Reprinted in Philosophy of Mathematics Education 11. Available at www.ex.ac.uk/~PErnest/pome/art18.htm. 60. P. C. Mahalanobis, ‘The Foundations of Statistics (A Study in Jaina Logic)’, Dialectica 8, 1954, pp. 95–111; reproduced in Sankhya, Indian Journal of Statistics, 18, 1957, pp. 183–94; reproduced as Appendix IV B in Formation of the Theoretical Fundamentals of Natural Science vol. 2 of History of Science and Technology in Ancient India, by D. P. Chattopadhyaya, Firma KLM, Calcutta, 1991, pp. 417–32. 61. J. B. S. Haldane, ‘The Syadavada system of Predication’, Sankhya, Indian Journal of Statistics, 18, 1957, pp. 195–200; reproduced as Appendix IV C in Theoretical Fundamentals of Natural Science, by D. P. Chattopadhyaya, cited above, pp. 433–40. 62. D. S. Kothari, ‘Modern Physics and Syadavada’, Appendix IV D in Theoretical Fundamentals of Natural Science, by D. P. Chattopad- hyaya, cited above, pp. 441–48. 63. Sadly, Mahalanobis refers to the Buddhist doctrine of flux, in this context as ‘one well-known school of Buddhist philosophy which holds that reality consists of an infinite sequence of [atomistic] or completely independent [moments] which have no connexion with one another.’ Footnote 24 there actually relates to footnote 25 in the text, and the footnote 1 referred in it is actually footnote 22 in the text. Mahalanobis, cited above, pp. 424–25. 64. Rhys-Davids, trans., Dialogues of the Buddha, cited earlier, vol. 1, p. 75.

562 NOTES TO CHAPTER 11 65. Dîgha Nikâya, trans. Maurice Walshe, p. 97. 66. S. C. Vidyabhuìaä, A History of Indian Logic, Calcutta, 1921, reprint Munshiram Manoharlal, New Delhi, 1977. 67. That is, if Bhadrabâhu really was the brother of the astronomer Varâhamihîra, roughly a contemporary of Âryabhata, whose work on astronomy, cited in Chapter 1, note 27, is securely fixed at 498. 68. J. B. S. Haldane, cited earlier. 69. D. S. Kothari, cited earlier, and his advisors, strangely seem to have been unaware of the work of Reichenbach, done nearly forty years earlier. For details of Reichenbach’s work, and an exposition of three valued logic see C. K. Raju, ‘Philosophical Time’, chap. 1 in Time: Towards a Consistent Theory, Kluwer Academic, Dordrecht, 1994. In view of the unsuccessfulness of this approach, it seems to me that using a three valued logic as the foundation of statistics, as suggested by Mahalanobis, leads neither to classical nor to quantum statistics! 70. The Jaina units of time suggest that this time atom is linked to human perception of sound, which has a cutoff at 18KHz (or the next octave). 71. C. K. Raju, ‘Quantum-Mechanical Time’, chap. 6b and its appen- dix in Time: Towards a Consistent Theory, cited earlier. 72. B. M. Barua, D. Litt. Thesis, University of London, 1921, cited earlier. In Barua’s view this was modified to a five-fold negation by Sañjaya Belaààhaputta. 73. Dîgha Nikâya, trans., Maurice Walshe, p. 541, footnote 62 to Sutta 1. 74. Ibid. pp. 78–79. 75. Mulamâdhymakakârika 18.8. David J. Kalupahana, trans., Nagar- juna, SUNY, New York, 1986, p. 269. 76. Dîgha Nikâya, trans. Maurice Walshe, pp. 80–81 77. For this reason, I am doubtful of the translation of Nagarjuna’s prasang into reductio ad absurdum. Though it is Nagarjuna’s objec- tive to bring out the absurdity of certain beliefs, reductio has a specific meaning today (and in Euclid’s Elements) in the context of two-valued logic. 78. G. N. Ramachandran, Tech. Report, Dept. of Mathematical Biol- ogy, Indian Institute of Science, Bangalore (198?). 79. This means that we have eight truth values, the negation of the first being the second, the negation of the second being the third, and so on, with the negation of the last being the first. For more details on cyclic negation, see the text of N. Rescher, Many-Valued Logic, McGraw Hill, New York, 1969. 80. Hsueh-li Cheng, Empty Logic: Mâdhyamika Buddhism from Chinese Sources, Motilal Banarsidass, Delhi, 1991, p. 36. An interesting

NOTES TO CHAPTER 11 563 attempt to interpret dependent coorigination from the viewpoint of systems theory may be found in Joanna Macy, Mutual Causality in Buddhism and General Systems Theory, SUNY, Albany, 1991. 81. Trans. D. Chatterji, ‘Hetucakranirnaya’, Indian Historical Quarterly, 9, 1933, pp. 511–14. 82. Dignâga clearly has the last word in S. C. Vidyabhuíaä’s, Indian Logic, cited earlier, p. 299 and pull-out diagram annexed as the last page of the book! 83. R. S. Y. Chi, Buddhist Formal Logic, The Royal Asiatic Society, London, 1969; reprint Motilal Banarsidass, Delhi, 1984, p. 5. The claim is in the ellipsis which expand to read, ‘In fact, the so-called “similar” and “dissimilar” instances refer to the likeness to the major term but not to the middle term [reason, hetu]’. See, however, Vidyabhuíaä, Indian Logic, p. 291. In addition, there are some minor discrepancies which I am not competent to comment upon. 84. Nothing can possibly be redundant in a text as brief as the Hetucak- ra, and the Sanskrit formulae of the Nyâyavarttika clearly does not cover the last stanza of the Hetucakra, a point which Udyotkara also overlooks in his arguments against the Buddhist notion of instant of time. B. K. Matilal, Logic, Language, and Reality, Motilal Banar- sidass, Delhi, 1985, p. 146, expresses the same opinion, ‘My own feeling is that to make sense of the use of negation in Buddhist philosophy in general, one needs to venture outside the perspec- tive of the standard notion of negation.’ See also, H. Herzberger, ‘Double Negation in Buddhist Logic’, Journal of Indian Philosophy, 3, 1975, pp. 1–16. 85. See, e.g., A. N. Prior, Past, Present, and Future, Clarendon, Oxford, 1967. 86. See, e.g., E. Mendelson, Introduction to Mathematical Logic, Van Nostrand Reinhold, New York, 1964. 87. To the above points, one could add the following. (3) Udyotkara’s Nyâyavarttika is implicitly, explicitly, and polemically against Bud- dhist philosophy; so I see no reason to regard Udyotkara’s as the last word on Dignâga, especially since that last word is positioned at such a peculiar moment in the history of Buddhism in this country, when no Buddhist was left to respond to Udyotkara. (4) Dignâga’s logic, in his Pramânasamuccaya, cannot be instantly for- malised, because he explicitly rejected tautological inferences as trivial, while Western logic admits only such inferences. Thus, to infer fire from smoke was a trivial inference. Nor from a smoky hill should one infer a fire on the hill (for the connection between fire and hill could not be inferred—the apparent connection between smoke and hill may be only an illusion). Hence, from a smoky hill

564 NOTES TO CHAPTER 12 one inferred a fiery hill—from an apparently smoky hill one inferred an apparently fiery hill. CHAPTER 12 1. To be quite precise, the ‘is’ here refers to an existential ‘is’ and not a tensed ‘is’. Also, the ‘is’ is not a metaphysical ‘is’ as in the statement ‘God is’, which, though syntactically an existential state- ment, may be rejected as semantically void on the grounds that the claimed existent is inconsistent, irrefutable, and redundant. The statement asserting the existence of a moral law could, with some justification, be treated similarly to the statement ‘God is’. The difference arises from the undisputedly physical beliefs underlying values (irrespective of their validity). 2. A. Prior, Deontic Logic, Oxford University Press, Oxford, 1966. For a review of the is/ought dichotomy in Kant and Hegel, see, for example, R. P. Singh, Dialectic of Reason, Intellectual Publishing House, New Delhi, 1995. 3. Bertrand Russell, History of Western Philosophy, George Allen and Unwin, London, 1946, p. 164. 4. Ibid., p. 111. Russell continues by contrasting this with Western Christianity: ‘In Christian ethics, a pure heart is the essential, and is at least as likely to be found among the ignorant as among the learned. This difference between Greek and Christian ethics has persisted down to the present day.’ 5. This elaborates my earlier article, ‘Reconstruction of Values: The Role of Science’, in Cultural Reorientation in Modern India, ed. Indu Banga and Jaidev, Indian Institute of Advanced Study, Shimla, 1996, pp. 369–92. 6. To be sure, one could still say, for example, that from the fact that this man is drunk it does not follow that this man ought to be drunk. But this kind of quibbling is not germane to the point. 7. Konrad Lorenz, On Aggression, Methuen, London, 1968, p. 24. 8. In von Neumann’s formalistic tradition, one would say that the input–output matrix is irreducible (no non-trivial invariant sub- spaces). 9. The Dunkel Draft of Uruguay Round of GATT Negotiations, p. 73, and part III, p. 76 and sequel, and Sections S and T. 10. This term is used in the sense of Paul M. Sweezy, Post-Revolutionary Society, Monthly Review Press, New York, 1980. 11. Jaya Mehta, ‘Plan and Market’ (unpublished). 12. E. O. Wilson, Sociobiology The New Synthesis, Harvard University Press, Cambridge, Mass., 1975; E. O. Wilson, On Human Nature, Harvard University Press, Cambridge, Mass., 1978; C. Lumsden

NOTES TO CHAPTER 12 565 and E.O. Wilson, Genes, Mind, and Culture, Harvard University Press, Cambridge, Mass., 1981. R. Dawkins, The Selfish Gene, Ox- ford University Press, Oxford, 1976. P. Kitcher, Vaulting Ambition, MIT Press, Cambridge, Mass., 1985. M. Rose, Sociobiology: Sense or Nonsense?, D. Reidel, Dordrecht, 1979. A. Caplan, ed., The Sociobiol- ogy Debate, Harper and Row, New York, 1978. J. Maynard Smith, Evolution and the Theory of Genes, Cambridge University Press, Cambridge, 1982. Biology as a Social Weapon, ed. Sciences for the People Collective, Burgess, Minneapolis, 1977. R. S. Lewontin, S. Rose and L. Kamin, Not in Our Genes, Pantheon, New York, 1984. S. J. Gould, Ever Since Darwin, Norton, New York, 1977, pp. 251– 59, 13. H. Tetrode, Zeit. Phys. 10, 1922, p. 317, as quoted by J. A. Wheeler and R. P. Feynman, Rev. Mod. Phys., 17, 1945, p. 159. A more detailed quote reads: ‘The sun would not radiate if it were alone in space and no other bodies could absorb its radiation…If for example I observed through my telescope yesterday evening that star which let us say is 100 light years away, then not only did I know that the light which it allowed to reach my eye was emitted 100 years ago, but also the star or individual atoms of it knew already 100 years ago that I, who then did not even exist, would view it yesterday evening at such and such a time…’ In the sense in which this quote is used here, the references to knowledge, etc., are to be put down to bad expression. A similar idea is attributed by them to G. N. Lewis, Proc. US Nat. Acad. Sci., 12, 1926, p. 22. 14. N. Georgescu-Roegen, The Entropy Law and the Economic Process, Harvard University Press, Cambridge, Mass., 1971. J. Rifkin with T. Howard, Entropy: A New World View, Bantam, 1980.



Index Α impossibility theorem extended to rational choice, 372 Abu Yazîd, 390, 440 Advait Vedant and intertemporal comparisons of utility, 372–373 time beliefs in, 470 Aívatthâmâ, 359 utility an ordinal concept, 347 Ajâtasattu, 361, 397, 402 al-Ash‘arî, 139, 385 Buddha’s answer to his question, Ashoka, the Great, 70 370 Asimov, Isaac, 52, 90, 352 Buddha’s counter-question, 377 Athanasius, 130, 132–133 Lokâyata answer to his question ir- Augustine, 42, 95–96, 173, 180, relevant, 361 390, 405, 457, 466 Mahavira’s answer, 382 parricide, 355 appealed to natural inclinations like parricided, 356 advertisers, 414 question, 356 question unanswerable by or- argument revived by Hawking, 293 thodoxy, 361 chided Porphyry for learning from Ajit Keíakambali, 28, 45, 361 India, 325 Akìapad Gautam, 396 Alexander, 278 Christ repeatedly crucified, 42, 48 apocalyptic time, 288–289, 457 confused distinct pictures of ‘cyclic’ changed belief in life after death time, 457 from physical to moral belief, 44 ‘cyclic’ time contrary to free will, 457 changeover to superlinear time, 409 and doctrine of sin, 44, 408 definition of equal intervals of time, as variety of linear time, 289 173 Aquinas, Thomas, 388–389 Archimedean property, 105 doctrine of sin contrasted with Bud- Archimedes, 75 dhism, 371 Aristotle, 139, 278, 288, 299, 401 Arius, 131–132 free will necessary for culpability, 49 Arrow, Kenneth, 347, 418 good and bad sharply demarcated, impossibility of social choice, 347 impossibility theorem, 348 359 impossibility theorem and Pareto heaven and hell as permanent, 174, optimality, 348 360 heaven and hell as Tiplerian realities, 115 human choices not decided by God, 174 human freedom equals ignorance of the future, 254

568 INDEX idea of becoming incompatible with ridiculed Augustine’s notion of relativity, 176 time, 135 his ideas underlying intellectual royal dispensation for Newton, 130 property, 423 statement of temporal dichotomy, inconvenienced by temporary 136 heaven and hell, 41 time expressed by a line, 136 Barrow, J. D., 88 individual as cause, 172–173 Barua, B. M., 401 individual as recipient of credit and Bergson, Henri, 352 Besso, Michele, 146, 167, 257 blame, 172, 422 Bhadrabâhu, 397, 399–400, 436 invention of salamanders, 315 Bhagvad Gîtâ, 33, 392 knew his system reinforced status Bhâskara I, 330, 333–334, 336 used time difference to fix local lon- quo, 395 linguistic difficulty in his idea of gitude, 338 Bhâskara II, 334, 340 eternal return, 293 Al-Bîrûnî, 333–334, 336 his notion of identity compared black holes, 244 Bohr, Niels, 88, 400 with Buddhist, 405 Boltzmann, Ludwig, 193 notion of time, 173 notion of time ridiculed by Barrow, answer to Loschmidt’s paradox, 193 Einstein not acquainted with his 135 opinion on age of the world, 96 work, 167 past and future as non-existent, 173 entropy increase illusory, 193 past as non-existent, 299 objections to his account of entropy political implication of subjective fu- increase, 203 ture, 116 physics applies equally to animate quibble about fatalism and deter- matter, 182 minism, 49, 174, 252 reversibility objections to entropy rejection of ‘cyclic’ time, 48, 457 his religious environment, 40 law, 192 his solution officially approved, 44 suicide, 194 summary of his changed beliefs in Bon, Gustav le, 345 Borges, Louis, 352 afterlife, 44 Brahmagupta, 334 theology supported by Tipler, 50 Brahmajâla Sutta, 401–402 time as subjective, 45 Brewster, David, 125 ‘trite saying’ cited by Barrow, 135 A Brief History of Time, 88 use of force for conversion, 40 Brillouin, L., 262 Averroes broken time, 463–464 See Ibn Rushd Brown, Frederic, 255 Avicenna Brown, the botanist, 185 See Ibn Sînâ Bruno, Giordono, 430 Buchanan, John, 345 Β Buddha, 28, 278, 346, 361 answer to Ajâtasattu, 370 Bacon, Francis, 237, 254–255, 259 concern for human suffering, not spookiness of action at a distance, 300 God, 372 conditioned coorigination, 373 Bacon, Roger, 75 denial of the soul explained, 371 Barrow, Isaac, 132, 135–136, 158, denied existence of God, 57 461 and breeding of clerics, 129 even-tenor hypothesis, 135 formula for equal intervals of time, 136

INDEX 569 did not directly reject life after past does not cease to exist, 34 (n. death, 366 33) difference of logic made refutation rejection of creation, 57 difficult, 400 rejection of testimony, 364 values contrasted with industrial efforts at social reorganization, 377 capitalism, 372 influence of Sâókhya notion of varied notions of logic, 403 atomic time, 368 Χ instant as cosmos, 369 intention important, 383 Caesar, Julius, 21, 330 Middle Way, 381 calculus momentariness and fragmentation confusion about infinitesimals in of identity, 370 Europe, 211 no authoritative tradition of God in Dedekind’s invention of real num- his time, 372 bers, 211 no consciousness after death, 358 epistemological divide between non-belief in soul, 367 India and Europe, 335 summary, 469 and tribal values of classless society, imported from India during Gregorian calendar reform, 375 333 use of logic of 4-alternatives, 401 Indian approach used ‘indivisibles’, used a different logic, 278 like Cavalieri, 211 (n. 32), 334 Wriggling of the Eel, 402 Buddhism, 435, 470 needed to derive precise sine values for latitude determination, 333 accepts only manifest and in- ference, 58 calendar difficulty with Roman, 324 causal efficacy as criterion of exist- Gregorian reform, 324 ence, 299 Gregorian reform and import of cal- culus into Europe, 333 continuation of memory not same Gregorian reform motivated by as continuation of identity, 371 needs of navigation, 331 Gregorian reform rejected by deliverance available immediately, Protestants until 1752, 331 370 Gregorian reform used inputs from Arabs, 332 denial of soul and Augustine’s Indian calendar of 5th c. CE, 324 doctrine of sin, 371 inputs to Gregorian reform from India, 331 identity does not persist for two in- needed for determining latitude stants, 32 (n. 24), 367 from solar altitude at noon, 330 instants compared to cosmic cycles, Papal Bull of 1582, 333 370 reform required change in date of Easter, 331 Jâtaka tales, 42 logic of 4-alternatives, 401 Calvino, Italo, 352 Cantor, Georg, 105, 212 logic related to Jaina logic, 401 Capital, 340 logic related to notion of instant, capitalism 367 are its time beliefs physically valid?, logic related to structure of time in- 351 stant, 400 logic, Udyotkara’s act and Schrödinger’s cat, 400 momentariness and Alice in Wonderland, 370 momentariness and identity, 405 Nietzsche’s description, 372

570 INDEX can the future be rationally calcu- cause lated?, 351 can it be fixed in a social context?, 462 collapse of future look-ahead and collapse of values, 351 causal beliefs of dancing chief, 225 ‘causal’ description in physics and collapse of values, 344 commodification of leisure time, instantaneity, 298 343 causal inexplicability of anticipatory commodification of time, 323 phenomena, 261, 305 commodification of work-time, 341– causal inexplicability of initial cause 342 in a causal chain, 316 constraint on work-time drives tech- causal necessaity distinguished from nological advance in, 340 logical necessity by al-Ghazâlî, crisis of overproduction and shor- 223 tening of working hours, 341 closed causal chains, 254 culture to be globalised must suit it, ‘conspiracy’ of causes, 260 355 contact and chains of causes, 178 distribution of resources in, 462 difficulty of locating causes in the incompatibility with ontically past, 299 broken time, 350 key role of culture in globalisation, and existence of past in Buddhism, 299 346 mechanisation of production and future causes and spontaneity, 260 homogenisation of work time, impossibility of causal explanation 341 for Popper’s pond, 260 modifies human behaviour to con- trol the production process, is priority compatible with 345 relativity?, 463 its moral law, 343 its moral law related to time beliefs, located in individuals, 172 349 locating causes forcibly may lead to needs inequity, 346 roots of its harmony with Western closed causal chains, 306 Christianity, 390 may not be followed by effect, with time beliefs and values incom- patible with other cultures, 390 ontically broken time, 223 time beliefs contrasted with time beliefs in pre-capitalist multiplicity of causes with super- societies, 345 linear time, 316 time beliefs harmonise with See also mundane time Western Christianity, 355 time=money, 343 needed for mechanical replication, value of punctuality, 340, 343 307 values contrasted with pre-capitalist values, 344 neither contact nor disjunction be- values harmonise with Western tween cause and effect, 299 (n. Christianity, 354 2) and Western Christianity as the fu- ture universal church, 395 principle of ‘causality’ and Capra, Fritjof, 59 tachyons, 236 Casimir, Hendrik, 247–248 Cauchy, Augustin-Louis, 179 principle of causality as an assump- tion underlying paradoxes, 258 rejecting the hypothesis of causality leads to a tilt, 304 replaced by conditioned coorigina- tion, 469 used to fix credits and blame, 462 why not allow creative acts also at other moments of time?, 316

INDEX 571 why should all phenomena be as a shackle to the industrial work- mechanically replicable?, 307 place, 342 Cavalieri, (Francesco) Bonaventura, size of early mechanical clocks, 326 334 social standardisaton, railways, and Chandogya Upaniìad, 439 GMT, 339 chaos, 463 as source of ritual discipline, 326 Charlie Chaplin, 342 unreliability of mechanical clock in Chattopadhyaya, Debiprasad, 362, 1707, 338 375 closed time loops, 464 Chi, R. S. Y., 404 See also closed timelike curves chocolate–ice cream machine, 227, See also wormholes, time travel closed timelike curves, 47 463, 539 and chronology condition, 251 Christianity, Donatist, 40 and chronology protection conjec- Christianity, Early ture, 250 distinguished from closed timelike not persecuted by Roman Empire, geodesics and cosmic recur- since not known, 40 (n. 11) rence, 242 and exact recurrence, 48 belief in life after death in, 35, 456 in Gödel cosmos, 242 Colbert, Jean Baptiste, 335 Christianity, Eastern Orthodox, 62 Columbus, Christopher, 327–328 Christianity, Syrian, 58, 95 complexity, 463 Christianity, Western conditioned coorigination, 469 basis of Dhamma, 373 attack on providence in, 463 defined, 373 curse on cyclic time strengthened denies individual as cause, 377 distinguished from mundane hierarchy, 45 causality, 376 made soul metaphysical, 45 if applied to industrial capitalism, 377 moral dichotomy and linear-cyclic Constantine, 40, 131 dichotomy, 45 award of, 84 Contact, 244 rejected both manifest and in- Copernicus, 55 ference as means of proof, 45 translated, 332 cosmic recurrence rejection of Origen signified rejec- See also quasi-cyclic time tion of equity, 45 analogy to natural cycles, 33 deliverance as the goal, 35 chronology condition, 48, 457 difficulty in identifying an in- chronology protection conjecture, dividual across cycles of the cosmos, 31 464 distinguished from eternal recur- Chuang Tzu, 25 rence, 33–34 City of God, 41 explained, 31–32 and inability to remember past Clavius, Christoph, 331, 333–334 lives, 32 Cleopatra, 424–425 linked to early belief in life after clock death, 31 makes life after death refutable, 32 chronometer and longitude deter- mination, 336 clepsydra used for longitude deter- mination, 333 (n. 19) even tenor and equal motions, 136 mechanical vs gnomon, 326 needed for length measurement, 159 Newton’s rejection of solar motion, 136 Poincaré’s definition of a proper clock, 159

572 INDEX necessary under many circumstan- localising slows down rate of innova- ces, 32 tion, 424 requires many natural cycles, 33 located using counterfactuals, 424 symbolised by the butterfly, 25 nature of time underlying social dis- symbolised by the plumed serpent, tribution of, 146, 172, 406 34 reference to human agency rhetori- symbolised by the Wheel, 34 its time scale in early myth, 33 cal, 393 The Cosmological Anthropic Principle, theology of causation justifies dis- 88 tribution in proportion to creation political strength, 394 unequal distribution of, 45 beginning does not imply a Creator, Curie, Marie, 67, 151 89 the curse on cyclic time church and state during Justinian’s Biblical, 90 reign, 37 continuous creation in Islamic theol- compression of the time-scale, 43 confused quasi-cyclic time with su- ogy, 386 percyclic, 41 criticised in Buddhism, 57 creation of temporal dichotomy, 45 in Islamic theology, 92 its date, 37 in Úgveda, 90 its foundations in Augustinian theol- creationism, 53 ogy, 40 equal neglect and Kansas ruling, 54 helped to legitimise inequity, 45 equal time and Arkansas law, 54 Jerome’s denunciation of Origen, 40 in Australia, 55 Jerome’s real difficulty with equity, rejected in Buddhism, 382 41 Scopes trial, 54 Justinian’s anathemas, 39–40 quibble over fatalism and deter- credits minism, 49 in absence of cause, 176 its three disabilities summarised, 46 attributed to market, 422 Curzon, George, 345 cannot be localised within in- cyclic time, 455, 457, 464–465 dividuals with tilt, 317 and Newton’s error, 134, 136 cannot be localised within in- rejected by Newton, 461 dividuals, with history-depend- Cyril of Alexandria, 72, 131, 325 ent evolution, 317 and conditioned coorigination, 377 ∆ disputes resolved by convention, 394 Dali, Salvador, 25 distributed in science in the same Darwin, Charles, 219, 415–416 way as in society, 146 Davies, Paul, 88–89, 309, 459 distributed in society using cause, Dawkins, Richard, 426 317 Dedekind, Richard, 210–212 distribution on Day of Judgment, deliverance 172 eternal, 172 contrasted with eternal return, 33 in football, 316, 421 denied in Mahâbhârata, along with for ripple in Popper’s pond, 421 life after death, 28 individual as recipient of, 422–423 impossible with eternal return, 42 individual as sole recipient of, 421 and Islamic Philosophers, 29 link to causes ensures that disputes as natural value with quasi-cyclic are settled politically, 394 time, 357 localised to accumulate capital, 423

INDEX 573 its possibility and desirability in changed equations immediately myth and symbol, 34 after Hilbert’s communica- tion, 165 Descartes, René, 210, 334 aether and action by contact, 300 claimed to have independently rediscovered many reported Dîgha Nikâya, 401–402 results, 462 Dignâga, 364, 403, 405 Dirac, P. A. M., 107–108, 304, 308 credited with relativity on grounds Doppler shift, 94 that Poincaré ‘waffled’ about Droäâcârya, 359 aether, 466 Drude, Paul, 144 Duhem, Pierre, 199 cried over Yahuda’s theory, 125 Dukas, Helen, 160 did he know of Poincaré’s 1904 Dunne, J. W., 263–265 Duns Scotus, John, 139–140 paper?, 149, 152, 162 Duryodhana, 360 did he know of Poincaré’s 1905 Dyson, Freeman J., 108, 113 paper?, 149, 160 Ε did not obtain the solution used in Eco, Umberto, 352 calculations for the three cru- ecumenical council cial tests, 166 did not reject aether in the sense of fifth, 38, 44 action by contact, 163 first, 324, 331 and Drude, 144 Eddington, Arthur S., 282 erred about aether in the sense of The Egyptian Book of the Dead, 34 action by contact, 298, 303, Einstein, Albert, 94, 185, 224, 252, 466 family quarrel over Mileva, 143 298, 462 formula for success, 168 his 1905 paper and Poincaré’s 1905 ‘God created the donkey…’, 143 Grossman’s mathematical support paper, 149 inadequate, 165 acknowledged Poincaré for general Hawking’s praise, 164 Hilbert’s formulation of the equa- relativity, 164 tions of general relativity, 165 action at a distance as spooky, 164 Hoffman and Dukas on his against authority, 53 knowledge of Poincaré, 160 appointment in patent office, 145 ignorance of mathematics, 164–165 as an appraiser, 166 ignorance of mathematics linked to as an expositor of Poincaré’s views, discovery of special relativity, 165 160 impudence his guardian angel, 145 attributed credit for relativity by on the influence on him of the Michelson–Morley experi- Planck, 150 ment, 148 aware that ideas cannot be invited by Hilbert, 165 jobless phase, 143 patented, 167 knew French, 162 on Besso’s inability to take a quick knew of Poincaré’s 1902 book, 152 knowledge of Poincaré’s essay on decision, 167 time, 161 his biographers on his knowledge and Lieserl, 145–146 mathematical error from non-rejec- of Poincaré, 149 tion of aether, 303 blundered in attempting to alter not legally a plagiarist, 167 Hilbert’s formulation of the equations of general relativity, 166 can his public image be revised?, 169

574 INDEX then obscure relative to Poincaré, eternal recurrence 168 See also supercyclic time on existence after death, 257 distinguished from cosmic recur- opinion of women, 143 rence, 33 on origin of relativity, 146–147 other children, 146 Eudemus of Rhodes, 31 (n. 21) patch-up with Hilbert, 165–166 and the myth of Sisyphus, 34 Poincaré’s presentation of the Nietzsche’s demon, 35 eternal return decisive argument in his 1905 See eternal recurrence paper, 162 Euclid, the geometer, 106, 210– reactions to Poincaré’s 1902 book as recorded by Solovine, 161 211, 278 rediscovery of statistical mechanics, did he exist?, 210 166 equality of triangles and political rejection of tachyons, 235 study group, 161 equity, 38 summary of Whittaker’s case against and Proclus, 27, 210 him, 160 return to Europe via Islamic ration- took one step less than Poincaré, 462 tried to place Newton’s al theology, 210 manuscripts, 125 unaware of observations of Φ Brownian motion, 167 used the term ‘longitudinal mass’ in falsifiability Lorentz’s 1904 paper, 156 See refutability was he present when Poincaré’s 1904 paper was discussed in Faraday, Michael, 154 Berne?, 149 Fermat, Pierre de, 334 and Whittaker, 148 Feynman, R. P., 82, 308–309 Whittaker’s authority insufficient, Feynman diagram, 294 150 Fischer, Bobby, 114–115 Whittaker’s biography, 167 fission-fusion time, 294, 297 Wigner’s impression of the origin of general relativity, 164 and Schrödinger’s cat, 277 Einstein, Hermann, 143 Fitzgerald, G. F., 151 Einstein–de Sitter cosmological Forbes, 345 model, 309 Foucault’s Pendulum, 352 Elements, 211–212, 278 Foundation, 352 Eliade, Mircea, 353 free will Eliot, T. S., 353–354 and Toynbee, 353 compatibility with determinism of Ellis, G. F. R., 48, 109 physics, 463 The Emperor’s New Mind, 88 entropy, 465 needed to distribute rewards and epistemically broken time punishment, 457 classical chance distinguished from quantum chance, 221 needed to validate physics, 463 does not reconcile superlinear and Friedmann, A. A., 94, 100–101, mundane time, 224 and entropy increase with deter- 308–309 ministic mechanics, 198 fundamentalism, 54 future, 458, 463 Γ Galileo, 53, 55–56, 83, 252, 335– 336, 430 had pope’s permission, 55 Gallup, George, Jr, 22 Vasco da Gama, 327–328 Mahatma Gandhi, 382 Gandhi, Indira, 264

INDEX 575 al-Ghazâlî, 139, 223, 291, 385, 463, Η 469 Hadamard, Jacques, 198–199, 203 accepted continuous creation, 92 Haldane, J. B. S., 399–400, 403 broke time ontically to value ethics Haller, Friedrich, 145 Hamlet, 237, 255, 259 above knowledge, 386 Harrison, E. R., 97 Hartle, Jim, 111 causal necessity distinguished from Hawking, Stephen, 47, 56, 108, logical necessity, 139 164, 203 denied agency to inanimate things, asked about the meaning of sin- 140 gularities, 100 destruction of rationality meant to assumption of smoothness in sin- restore values, 386 gularity theory linked to han- distinguished logical necessity from dling of infinity, 104 causal, 223 attacked for introducing imaginary time, 111 God bound by logic but not causal chronology condition, 48, 250 necessity, 389 chronology condition and closed causal chains, 109 God not constrained by cause and chronology protection conjecture, effect, 222 250, 464 cited by Tipler, 114 granted that Allah bound by logic, correspondence of singularities 139 with creation and apocalypse, 88 Hand and Pen, 385 ‘cyclic’ time contrary to free will, 457 human creativity and immanent does a singularity involve creation God, 388 or destruction?, 102 false distinction between infinities inanimate objects cannot be agents, of singularity theory and those 386 of quantum gravity, 106–109 ‘free will’ equated to ignorance of is everything unpredictable?, 222 the future, 254 laws of physics ensure their own and occasionalism, 223 failure, 251 ontically broken time destroys no-boundary condition, 111 operational argument for ‘free will’, rationality, 223 252 reintroduced curse on ‘cyclic’ time, Paper, Ink, Pen, Hand, 386 457 revived Augustine’s argument, 293 position on agency misrepresented singularities and chronology protec- by Western theologians, 140 tion conjecture, 251 singularity compared with Fried- rationality limits Allah’s creativity, mann singularity, 101 386 singularity-God as God of gaps, 110 superlinear time confused with thought equity should not be mundane time, 457 revealed to the masses, 387 world evolves by continuous crea- tion, not rationally, 386 Gibbon, Edward, 70 Gibbs, Willard, 167 Giddens, 346 God and the New Physics, 88 Gödel, Kurt, 94, 212–214, 217, 242– 243, 257, 279 cosmos may not have a global no- tion of time, 242 Gregorios, Paulos Mar, 396 Gregory, James, 334 Grossman, Marcel, 143, 145, 164 Guäaratna, 362

576 INDEX his theory of time shaped by curse See also Abu Yazîd, al-Ash‘arî, al- on ‘cyclic’ time, 38 Ghazâlî, Ibn ‘Arabî, Ibn Sînâ, Ibn Rushd, al-Râzî, Rumî universe started rationally, 110 basic premises of rational theology, his work supports harmony of 384 continuous creation in, 29 science and religion, 459 number of souls need not be con- Heaviside, Oliver, 107–108, 149 stant, 29 Heidegger, Martin, 194 and ontically broken time, 384 Herodotus, 135 ontically broken time induces sur- Hetucakra, 403, 405 render to God, 386 Hilbert, David, 105, 164–166, 168, perceived in conflict with science, 458 211–212, 242 Philosophers, 29 diagrams irrelevant to mathemati- providence in, 463 rational theology in contrasted with cal proof, 212 Christian rational theology, disallowed the empirical in mathe- 388 rational theology retained matical proof, 211 Neoplatonic focus on equity, wanted to make mathematics 210 rationality and immanence vs mechanical, 212 transcendence, 388 Hilbert–Einstein equations, 242 three traditions about time in, 385 Hitler, Adolph, 76 Island of the Day Before, 352 Hoffmann, Banesh, 160 Hooke, Robert, 336 ϑ Hosius, of Cordoba, 131 Hoyle, Fred, 309 Jainism, 70, 470 Hoyle–Narlikar theory, 310 Jâtaka, 26, 42 Hubble, Edwin, 94–95 Jerome, 38, 40–41 Hubble’s law, 93 Joyce, James, 353 Huen Tsang, 403 Jung, C. G., 263 Hume, David, 55, 178 Justinian, 37, 39–40, 44, 390 Huntington, Sam P., 64 Huxley, Aldous, 352 closed Alexandrian school, 210 Huygens, 335 Hypatia, 72, 210 Κ Ι Kaäâda, 379 Kabir, 386 Ibn ‘Arabî, 386, 469 Kamalaíîla, 382 Ibn Rushd, 389 Kant, Immanuel, 55, 80, 278 Ibn Sînâ, 385 Karpov, Andrei, 114 Kasparov, Gary, 218 belief in quasi-cyclicity, 469 Kassapa, 28–29 If on a Winter’s Night a Traveller, 352 Kaàha Upaniìad, 21 individual Kautiliya, 344 Keíakambali, 361 See also credit Kepler, 138 as cause, 173, 316–317, 407–408, Keynes, John Maynard, 125, 426 Khameini, 58 421, 423 Khomeini, 58 not as sole cause with conditioned Kleiner, Alfred, 145 coorigination, 377 irreversible time and time-symmetry of physics, 289 as a type of ‘linear’ time, 289 Islam

INDEX 577 Kosambi, D. D., 374–375, 377 taboo on, benefits the priest, 22 three-fold classification, 23 Λ and time travel, 30 life after death just once Labyrinths, 352 See resurrection Landes, David, 323–324 Lindemann, Frederick, 145 Laplace, 174, 193, 202–203, 369, linear time, 455, 458 chosen by Newton, 461 409 Livingston, 345 Laplace’s demon, 470 logic is 2-valued logic compatible with The Large Scale Structure of empirical time?, 273 Spacetime, 48 2-valued logic need not be empiri- Larmor, Joseph, 161 Lavoisier, Antoine-Laurent, 156 cally valid, 405 Leibniz, G. W., 28, 334–335 2-valued logic not universal, 405 Lenard, Philipp, 144 3-valued logic used by Reichenbach Lieserl, 145–146 life after death, 455 for q.m., 400 Ajâtasattu’s appraisal of Sañjay’s bodily survival in post-Christian view, 43 logic, 397 Aristotelian logic fails in q.m., 297 caused by fear of death?, 21 as a priori, 278 deliverance from it considered as the basis of mathematical proof, desirable, 33 278, 396 doubts about, 21 Bhadrabâhu’s ten-limbed syllogism, effect of previous lives, 26 eternality of heaven and doctrine of 397 Buddhist logic and Buddhist in- sin, 41 Gallup poll on, 22 stant, 400 Ibn Fârid’s ridicule, 30 Buddhist logic as quasi truth-func- is fear of death cause or correla- tional, 401 tion?, 21 Buddhist logic related to Haldane’s is it important to remember past view, 400 lives?, 28 Buddhist logic related to Jaina, 403 Kassapa’s reply to Pâyâsi, 28 decided by culture, 278 learning as recollection, 26 deduction not infallible, 396 loss of bodily identity in pagan did Dinnâga ignore identity across thought, 39 time?, 405 McTaggart’s reconciliation with did Dinnâga start with 2-valued genetics, 30 logic?, 405 moral reasons for believing in, 45 does it precede empirical reality or moved from physical to moral con- follow it?, 278 text, 44 four alternatives, 401 Pâyâsi’s experiments with dying fourth alternative interpreted, 401 Haldane’s interpretation of people, 22 population increase and transmigra- syâdavâda, 399 Jaina logic of syâdavâda, 396 tion, 29 logical proof compared to irrational See also quasi-cyclic time refutable in the context of cosmic proof, 446 recurrence, 32 logical proof defined, 444–445 related to cosmic recurrence, 30 many-valued, 401 retention of bodily identity in Chris- modus ponens, 445 tian thought, 40 non-sequitur, 445 Shelley’s ridiculing of, 27

578 INDEX pre-Buddhist, 397 Markov, Andrey A., 186, 207, 311 predicate calculus of Dinnâga, 403 Marx, Karl, 61, 63, 82, 340–341, quantifiers introduced by Dinnâga, 376, 411 405 Maxwell, J. C., 154, 262 quasi truth-functional logic and Mazarin, 335 Mazdakism, 41 (n. 17) q.m., 297, 401 McTaggart, J. M. E., 371 relates to culture through picture of Michelson, Albert, 151, 154 Michelson–Morley experiment, 147– time, 279 Schrödinger’s cat and fission-fusion 148, 150–151, 461 Miller, D. C., 148 time, 277 Minkowski, Hermann, 143 Lorentz, H. A., 462 mokìa, 35, 357 cited by Poincaré, 154 See deliverance cited by Whittaker, 149 Moody, Raymond, 28 did Einstein know of his 1904 More, Henry, 133 mundane time, 288, 458, 465 paper?, 167 force law stated earlier by assumed by utilitarian principle, 349 its asymmetry does not refute cos- Heaviside, 149 forced to abandon constancy of mic recurrence, 32 and asymmetry of knowledge about mass, 156 Hoffman and Dukas on Poincaré’s one’s decision, 180 cannot be reconciled with super- use of his work, 161 life-sketch, 150 linear time through broken ‘local time’, 151 time, 224 ‘local time’ and Poincaré’s defini- and creation of the future by humans, 173 tion of a proper clock, 159 creation of future incompatible with ‘local time’ and time measurement, block universe of relativity, 176 difficulty in reconciling with super- 158 linear time, 180 nominated Poincaré for Nobel distinguished from superlinear time, 46 prize, 151 entropy increase does not reconcile physical explanation of length con- it with superlinear time, 198 future cannot be joined to past, un- traction, 150 like superlinear time, 49 Poincaré’s critical approval of his implicitly confused with superlinear time by Hawking, 48 theory, 155 as a type of ‘linear’ time, 46 Poincaré’s difficulty with his theory, The Myth of the Eternal Return, 353 155 Ν ‘waffled’, 150 Lorenz, Edward, 200, 291 Nabokov, Vladimir, 352 Lorenz, Konrad, 415–416 Nagarjuna, 381, 396, 401–402 Loschmidt, Joseph, 192–193 Nahin, Paul J., 233 Lymington, Lord, 125 The Name of the Rose, 352 Lysenko, T. D., 116 Narlikar, Jayant, 309 naturalistic ethic, 415 Μ makes moral dichotomy irrelevant, Maäibhadra, 365 420 Mâdhava, 362 Mahâbhârata, 41 Mahavira, 381–384 Maimonides, 386 Malebranche, 222 Mann, Thomas, 352 Maric, Mileva, 144–145

INDEX 579 resolution of ambiguities in, 420 Vasco da Gama’s abilities, 328 summary, 420 Vernier principle and kamâl, 329 and tilt, 420 Nestor, 131 navigation von Neumann, John, 82, 347 accurate calendar needed for Newbigin, Leslie, 59 Newton, Isaac, 123, 143, 252, 458, latitude determination, 330 appointment of Nunes, 329 460 British prize of 1711, 339 babyhood, 123 calendar reform solved latitude born on Christmas, 123 choice of linear time unnecessary problem, 333 clock and longitude determination, because of instantaneity, 137 chose linear time, 461 336 deposition in parliament, 338 Columbus’ ability, 327 as historian, 134 cross staff, 329 laws adapted to the solar system, dead reckoning, 327 determination of longitude on land, 312 do his laws fail for the galaxy?, 301 336 laws of motion as instantaneous, 300 difficulties with longitude calcula- laws of motion not physical, 137 are his laws universal?, 312 tion, 333 mechanical universe unintended, difficulty with the size of the globe, 409 335 in Pareto’s thought, 348 equinoxes and solstices, 330 physical content of his theory, 137 Europeans did not know celestial posthumous theological works, 124 rejected equal motion for time navigation, 328 forced calendar reform, 330 measurement, 136 and formation of British Royal his rejection of temporal dichotomy Society, 335 related to his apocalyptic view and formation of French Royal of history, 136 restatement of even tenor Academy, 335 hypothesis, 136 heaving the log, 328 retained room for Providence, 389 kamâl or râpalagai, 328 revision of Earth’s size, 335 as key to European prosperity, 327 thought Laws of God had been latitude calculation and solar revealed to him, 55 victim of temporal dichotomy, 84 declination, 330 victim of the curse on ‘cyclic’ time, limitations of using the pole star, 134, 461 viewed historical time as apocalyp- 329 tic, 135 longitude determination in Indian way of handling infinity, 104 what exactly did his laws achieve?, texts, 333 138 al-Mâmûn’s determination of size of why are Newton’s laws called laws?, 138 the Earth, 335 Newton, Hannah, 123 and mathematical geography of al- Newton, Isaac, the father, 123 Newton-Smith, W. H., 294 Birûnî, 333 Newton–Raphson method, 149 measurement of solar altitude at Newtonian physics noon, 329 Picard’s re-determination of the size of Earth, 336 prize offered by Philip II in 1567, 329 quadrant, 329 rewards offered by various govern- ments, 335

580 INDEX difficulty with time in, 461 Justinian closed his Alexandrian providence in, 470 school, 210 Nicene council See ecumenical council motivated by equity, 390 Nietzsche, Friedrich, 35 Plotinus’ teacher, 385 on Buddhism, 372 quasi-cyclic time problematic to the eternal return as a Markov process, church, 40 185 rejected to reject equity, 45 eternal return focal point of his Roman empire tolerant in his time, philosophy, 194 40 finiteness of total energy, 195 taught cyclic time, 38 on Biblical creation, 53 his teachings similar to doctrine of on religion and science, 84 proof of recurrence, 195 karma, 38 reference to heat death of the Orwell, George, 64 Ouspensky, P. D., 353 universe, 195 superman, 35 Π victim of temporal dichotomy, 84, Pais, Abraham, 161–163 353 paradox world as uncreated, 195 nirvâäa, 35, 42 Aristotle’s sea battle, 288 See deliverance autofanticide, 254 Nobel, Alfred, 151 barber, 213 North, Roger, 132 beginning of time, 284 Nunes, Pedro, 329, 331 bilking, 255 Nyâyavarttika, 405 Cantor’s, 212 closed causal-chain, 254 Ο dancing chief, 225 Einstein-Podolsky-Rosen, 302 Ockham, Wilhelm of, 140 grandfather, 253 Olbers’ paradox, 93, 104 Loschmidt’s, 192 ontically broken time matricide, 254 mystery novel, 226, 252 See also providence Popper’s pond, 259, 305 destroys causal necessity, 223 rocketship, 48 destroys voluntary action, 223 Schrödinger’s cat, 273 does not reconcile superlinear and Schrödinger’s dance, 226 of superlinear time, 290 mundane time, 224 tachyonic anti-telephone, 237 and al-Ghazâlî, 222 triplet, 232 and interest rate in a capitalist twin, 231 underlying assumptions, 258 economy, 350 underlying assumptions inconsis- and quantum chance, 220–221 Order out of Chaos, 89 tent, 272 Origen, 35, 69–70 Wheeler–Feynman, 256 heaven and hell temporary, 41 Zermelo’s, 193 held out hope of deliverance for all Pareto, Vilfredo, 348 Partridge, R. B., 309–310 humanity, 40 Pascal, Blaise, 334 Jerome used his notes to translate patent law, 462 Paul II, Pope John, 85 the Bible, 38 Pâyâsi, 22, 28–29 Jerome’s denunciation, 40 Penrose, Roger, 252, 254, 459 Jerome’s misrepresentation of his teaching, 41 Jerome’s praise, 38

INDEX 581 assumption of smoothness in sin- Einstein’s reaction to his Science and gularity theory linked to han- Hypothesis, 161 dling of infinity, 104 equal intervals of time and simul- books on mind, 88 taneity, 158 cited by Tipler, 114 singularities, 101–102 Hoffman and Dukas on, 161 and ‘uncomputability’ of parallel laid philosophical and mathemati- computers, 215 cal foundation of relativity, 151 Pernet, Jean, 143 life-sketch, 151 The Physics of Immortality, 88 new mechanics, 157, 160 Picard, 335–336 non-existence of absolute motion, Planck, Max, 150, 248 Plato, 27, 358 154 Plesch, Janos, 145 not awarded Nobel prize since he Plimer, Ian, 55 Plotinus, 385 was also a mathematician, 151 Poincaré, 137, 164–165, 224, 298, not credited by relativists today, 150 Pais’ statement that he needed the 302, 462 acknowledged by Einstein for aether, 162 on physical law as statistical, 185 general relativity, 164 priority in special relativity, 461 on aether, 162 prophetic denial of prophecy, 163 biographers on Einstein’s his reasoning leading up to the knowledge of his 1905 paper, Principle of Relativity, 152 149 recurrence compared with on chance and determinism, 183 on chance and determinism recon- Markovian recurrence, 204 ciled through Hadamard’s recurrence theorem, 35, 193 result, 200 recurrence time computed, 196 cited by Whittaker, 149 redefinition of equal intervals of contemporaneity as sign of his genius, 151 time, 158 on the crisis in physics, 155 rejection of absolute space, hence on the crisis in the physics of prin- ciples, 156 aether, 153 definition of equal intervals of time, rejection of Newtonian space and 461 definition of proper clock, 159 time, 153 definition of time measurement simplicity as a guiding principle, compared with Barrow’s and Augustine’s, 173 159 difficulty with Lorentz’s accumula- speed of light compared to absolute tion of hypothesis, 155 did Einstein know of his 1904 zero, 149 paper?, 152 St. Louis lecture, 148 did Einstein know of his 1904 talk subtlety in elevation of principle of and paper?, 149 had Einstein known of his 1905 relativity, 156 paper, 149 then-famous relative to Einstein, Einstein’s knowledge of, 461 Einstein’s knowledge of his 1904 lec- 168 ture and paper, 167 two revolutions, 163 unhappiness with Lorentz contrac- tion, 154 unpredictability of weather, 200 use of refutability, 162 ‘waffled’ in Thorne’s opinion, 150 why he earlier stated the principle of relative motion as a conjec- ture, 155 work on chaos and dynamical sys- tems, 198

582 INDEX Pope, Alexander, 139 See also life after death Popper, Karl, 252, 254 not a spiral that can be unrolled, converging ripple in a pond implies 293 order creation, 311 used by Origen to justify exorcism of Laplace’s demon, 202– deliverance to all, 40 203 as physical basis of ethical belief, impossibility of anticipation, 305 357 pond, 316, 421 its rejection elevated metaphysics pond as allegory, 310 pond paradox, 259, 303, 305 over physics, 45 pond paradox recalled, 425 its rejection in Western Christianity possibility of a convergent ripple in intended to benefit the state, a pond, 311 45 refutability anticipated by Poincaré, symbolised in Buddhist architec- ture, 34 162 as one type of ‘cyclic’ time, 293 resolution of pond paradox, 306– its unique partial rejection in Western Christianity, 45 307 values with, 35, 357 Priestley, J. B., 263 what if it were really the case?, 357 Prigogine, Ilya, 88, 194, 314, 459 Proclus Ρ admitted empirical at the begin- Ramachandran, G. N., 402 ning of geomet, 211 rationality and providence, 224, and origin of mathematical proof, 386, 469 210 al-Râzî, 34 recurrence geometric diagrams and learning as recollecti, 211 Nietzsche’s proof, 194 Poincaré’s theorem, 193 proof important for its effect on recurrence, cosmic human mind, 211 See cosmic recurrence recurrence, eternal sole reference to ‘Euclid’, 210 See eternal recurrence sought to persuade humans refutability, 22 defined, 449 through geometry, 212 empirical, 452 providence logical, 452 Pâyâsi’s experiments with life after See also ontically broken time dispute with rationality in Islam, death, 22 underlying assumptions contradict 139 like continuous creation, 139 current physical theory, 453 Purandara, 365 underlying temporal assumptions, Pygmalion, 206 452 Θ Regiomontanus, 333 Reichenbach, Hans, 400 Quasi-cyclic time, 31, 33 resurrection, 39–40, 44, 456 changed to apocalyptic time by Augustine, 44 See also apocalyptic time confused with eternal return by Úgveda, 90 Augustine, 457 Rhazes confused with supercyclic time, 42 confused with supercyclic time by See al-Râzî Augustine, 41 Ricci, Matteo, 331–333 distinguished from supercyclic, 35 Richelieu, 335 its unique partial rejection in Western Christianity, 45

INDEX 583 Riemann, Bernhard, 239 Whitehead on, 52 Roemer, 335 why did the church retract strictures Ruelle, David, 219 Rumi, Jalal u’D Din, 29, 385, 469 against Galileo now?, 53 Russell, Bertrand, 72, 75, 212 Scopes trial, 54 Scopes, John T., 54 Σ Seth, Vikram, 353 Shadows of the Mind, 88 Sagan, Carl, 244 Shah Jehan, 394 Salam, Abdus, 108 Shakespeare, 237, 254–255, 259 Sañjaya Belaààhaputta, 397, 402 Shelley, P. B., 27 Sarva Darían Samgraha, 362 singularities, 460 Schrödinger, Erwin, 226, 400 de Sitter, 94, 243 Adam Smith, 344 cat, 273, 293, 297, 470 Smith, Newton’s stepfather, 123 characterisation of life, 312 Socrates, 26 on ‘free will’, 226 Solovine, M., 161 opinion that life involves classical soul chance, 313 butterfly symbol for, 25 Schwarzschild, Karl, 166 Chuang Tzu’s dream, 25 Science and Hypothesis, 161 existence denied in Buddhism, 367 science and religion as irrefutable, 30 Pâyâsi’s experiments to see it, 22 ‘religion’ decides truth by authority, Socrates on learning as recollection, 53 26 as an instrument in the quarrel be- turned metaphysical by the curse, 45 tween Protestants and went to heaven and hell between Catholics, 55 lives, 41 Asimov on, 52 Spassky, Boris, 114 creationism vs uniformitarianism Speak, Memory, 352 Spencer, Herbert, 416 and evolution, 53 Spengler, Oswald, 60–61, 63–64, dichotomy erases distinction be- 77, 115–116 tween religions, 57 spontaneity, 465–466 different facets of the same truth?, and chance in evolution of life, 313 56 creates order, while chance usually Galileo’s retraction, 53 harmony agenda and scientists, 459 creates disorder, 314 harmony cannot be established by distinguished from chance, 311 and life, 312 creation, 58 linked to collectivity of causes, 317 Nietzsche on, 53 microphysical related to macro- not the same as reason vs faith, 58 one science, many religions, 56 physical, 313 Pope’s agenda for harmony, 459 and order creation in evolution of proofs of God’s existence contrary life, 314 to Buddhism, 57 and tilt, 306 religion as a private belief, 58 Stevin, Simon, 334 state authority now intervenes, 54 stoicism, 35 the new harmony, 56 structured time, 297 the three stages of harmony, truce See also conditioned coorigination and conflict, 55 See also logic what does religion mean in the and logic, 396 and Schrödinger’s cat, 277 phrase?, 58 which is the religion in the phrase, 458

584 INDEX A Study of History, 61, 79 Hawking’s confusion about ‘linear’ Sûfî-s, 470 time, 48 A Suitable Boy, 353 Summers, Lawrence, 348–349 its incoherence, 271 Sunni-s, 470 Newton as victim of, 84 supercyclic time, 284 Newton’s use of apocalyptic time, confused with quasi-cyclic, 42 136 likened to a stuck gramophone Nietzsche as victim of, 84 origin in confusion of quasi-cyclic record, 42 need for a four-place relation, 293 time with supercyclic, 41 as one type of ‘cyclic’ time, 292 its resolution by the eleven pictures superlinear time, 465 and Augustine’s theological difficul- of time, 271 Spengler vs Toynbee, 62 ty, 180 its three key disabilities, 46 cannot be reconciled with mundane used to explain harmony of time using broken time, 224 capitalism with Western Chris- difficulty of reconciling with mun- tianity, 355 Tertullian, 323 dane time, 180 Tetrode, H., 427 entropy increase does not reconcile Theodora, 37, 145 Theophilus of Alexandria, 325 it with mundane time, 198 Thorne, Kip, 150, 162, 243, 245, forced by relativity, 179 250 reconciled with mundane time tilt alternative logics and the formalism using Augustine’s quibble, 183 of q.m., 296 reconciling with mundane time causes cannot be located within in- dividuals, 317 needs stochastic physics, 205 and characterisation of living or- Ívetâsvatara Upaniìad, 34 ganisms, 313 Szilard, Leo, 262 collectivity of causes distinguished from a multiplicity, 421 Τ compared with mundane time, 315 and competing growth of entropy tachyons, 235 and order, 314 anti-telephone, 237 and conditioned coorigination, 435 experiments to detect them, 236 differs from stochastic evolution, reinterpretation principle, 236 311 rejected by Tolman, 237 do-able comparisons with other pic- tures of evolution, 312 Tantrasangraha, 334 and equations of physics, 466 Telling Lies for God , 55 equations solvable for biological temporal dichotomy macromolecules, 312 links present to past and future, 315 Augustine’s misrepresentation of living organisms as empirical Origen, 42 evidence for, 312 and long-term purposive activity, and Augustine’s moral dichotomy, 421, 425 45 may work where chance, chaos, and quantum collapse fail, 411 Barrow’s statement, 136 and microphysical loops in time, confusing mundane with super- 294 linear time, 46 and the ‘deconstruction’ of time, 353 and doctrine of sin, 41 and Mircea Eliade, 353 and T. S. Eliot, 353 and even tenor, 135

INDEX 585 and non-mechanistic physics, 311 speed of light cannot be measured, not an additional hypothesis, 304 159 order creation and cooperative be- time travel haviour in Popper’s pond, 316 assumptions underlying the as partial anticipation, 304 paradoxes, 258 and purposive explanations, 315 bilking argument, 255 bringing information to the body, and quasi-cyclic time, 421, 428 238 relates purpose to choice, 429 does a wormhole permit backward similarities and differences with time travel?, 249 dreaming the future, 262 mundane time, 420 in Gödel’s cosmos, 242 and spontaneity, 306 grandfather paradox, 253–254 spontaneous creative acts compared makes rational calculation redun- dant, 229 to first cause with instan- making traversible wormholes, 245 taneity, 316 and mystery novels, 252 and stability of the long-term fu- necessarily involves spontaneity, 261 ture, 424 necessary for deep space explora- survival distinguished from order tion, 238 creation, 429 needed for space travel, 229 no causal explanation for Tim’s and tendency towards order crea- birth, 260 tion, 314 not prohibited by current physics, 238 and universal tendency towards paradoxes resolved by cosmic dis- order creation, 311 gust, 256 paradoxes resolved by the block values with, 415, 420 universe, 257 weaker than quasi-recurrence, 428 and Popper’s pond paradox, 259 time and values research on for producing new See values weapons, 238 in Sagan’s novel, 244 The Time Machine, 239, 465 slowing down the clock by time dila- time measurement tion, 233 using tachyons, 235 See also calendar using traversible wormholes, 245 See also clock Wellsian, 260 Barrow’s use of equal motions, 135 Wheeler–Feynman paradox difficulty in using natural machine, 255–256 phenomena, 324 without machines, 238 European difficulties in calculation, wormhole time machine, 243, 250 325 time=money gnomon vs mechanical clock in Europe, 326 its absence in pre-capitalist societies, 345 needed to measure length, 159 and Newton’s laws, 137 and collapse of values, 344 Newton’s rejection of equal mo- as combined with utilitarianism tions, 136 after Cold War, 348 Poincaré’s definition of proper consequences for Indian elite, 343 and corruption, 344 clock, 159 during colonialism, 345 Poincaré’s objection to Barrow and Newton, 158 Poincaré’s revised proposal of simplicity, 158 and the principle of relativity, 159 Roman difficulty in calculation, 324 and simultaneity, 158

586 INDEX and globalisation, 346 Buddhist vs values in industrial how it governs human behaviour in capitalism, 372 capitalism, 343 in capitalism, 343 human nature based on economics, and conditioned coorigination, 376– 344 377, 381 and modified utilitarian moral law, and epistemically broken time, 49, 349 174 needed for capitalist control of See also epistemically broken time, production process, 345 fatalism, time=money origin in commodification of time and future look ahead, 351 in capitalism, 343 and mundane time, 349 and railways, 345 See also mundane time, naturalistic unpunctuality as theft, 343 values wrist watch as shackle, 346 and ontically broken time, 386–387 Tipler, 50, 85, 116, 459 See also ontically broken time, al- God as a machine, 115 Ghazâlî, Duns Scotus making the singularity God ration- in pre-capitalist societies, 344 al, 114 and quasi-cyclic time, 29, 35, 357, no-return theorem, 49 387 Physics of Immortality, 88, 113 See also quasi-cyclic time, reincarna- Tolman, R. C. , 237 tion, deliverance Toynbee, Arnold, 61, 112 and structured time, 316 Study, 62 See also structured time, condi- championed apocalyptic time vs tioned coorigination Spengler’s ‘cyclic’ view, 62 and supercyclic time, 35 doubted, 64 See also supercyclic time, Stoics, and Eliot, 353 Nietzsche science as a primitive religion, 79 and the tilt in the arrow of time, seemingly right in his prediction, 64 415, 420 USA as leader of future universal See also tilt, order creation, condi- tioned coorigination state, 62 was he right about the universal time beliefs underlying utilitarianism, 349 church?, 74 triplet paradox, 232 and time=money, 349 Turing, Alan, 214–217 Vâsubandhu, 403 twin paradox, 232 Vernier, 329 Υ Vidyabhuìaä, S. C., 404 Viìäu Purâäa, 33 Udayana, 365 Ω Udyotkara, 400, 405 Ulysses, 352 Wallis, John, 334, 336 Walshe, Maurice, 401 ς Weber, Max, 391 Vaåideva Sûri, 365 Weber, Heinrich, 143 values Wells, H. G., 239–242 and apocalyptic time, 41, 43–44, Westfall, Richard, 124 406 Weyl, Hermann, 145, 176, 257 See also apocalyptic time, resurrec- Wheeler, J. A., 308–309 tion, Augustine Wheeler–Feynman, 256, 309 Buddhist contrasted with doctrine paradox machine, 255 of sin, 371 Whitehead, A. N., 52

INDEX 587 Whitrow, G. W., 326 understood that credits accumulate Whittaker, E. T., 148–149, 168, 462 around fame, 168 authority dismissed in Einstein’s Wigner, Eugene, 164 case, 150 Wilson, E. O., 426 wormhole, 243 corrected many inaccurate attribu- tions, 150 associated with a black hole, 244 can TWIST’s be made?, 245 Einstein adopted Poincaré’s name traversible, 245 for relativity, 152 Wren, Christopher, 336 Einstein knew of Poincaré’s 1904 Ψ paper, 152, 156 Yahuda, A. S., 125 influence on subsequent Young, E. D., 345 biographies of Einstein, 160 Yudhiìàhira, 359–360 Yuktibhâìâ, 334 life-sketch, 149 Pais’ response, 161 Ζ presumably aware of other cases of Zeeman, Pieter, 150–151, 154 rediscovery by Einstein, 167 Zen Buddhism, 402 publication of Poincaré’s 1905 Zermelo, Ernst, 192–193 Zoroastrianism, 41 (n. 17) paper on relativity preceded Einstein’s submission, 149 summary of his case against Einstein, 160



About the Author C. K. Raju is Professor and Head of the Centre for Computer Science, MCRP University, Bhopal. He is also an Editorial Fellow with the Project of History of Indian Science, Philosophy and Cul- ture, under the aegis of the Centre for Studies in Civilisations, New Delhi. He has been a Fellow of the Indian Institute of Advanced Study, an Affiliated Fellow of the Nehru Memorial Museum and Library, and an editor of the Journal of Indian Council of Philosophical Research. He has taught and conducted pioneering research in mathematics for several years, besides working with the Centre for Development of Advanced Computing in building India’s first su- percomputer, Param. An outstanding scientist, his previous publi- cations include Time: Towards a Consistent Theory (1994) which put forward a new system of equations for physics.