The Eleven Pictures of Time: The Physics, Philosophy, and Politics of Time Beliefs

The Eleven Pictures of Time: The Physics, Philosophy, and Politics of Time Beliefs

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C. K. Raju

Abstract

Visit the author's Web site at http://www.11PicsOfTime.com

Time is a mystery that has perplexed humankind since time immemorial. Resolving this mystery is of significance not only to philosophers and physicists but is also a very practical concern. Our perception of time shapes our values and way of life; it also mediates the interaction between science and religion both of which rest fundamentally on assumptions about the nature of time.

C K Raju begins with a critical exposition of various time-beliefs, ranging from the earliest times through Augustine, Newton and Einstein to Stephen Hawking and current notions of chaos and time travel. He traces the role of organised religion in subverting time beliefs for its political ends. The book points out how this resulted in a facile dichotomy ...

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    Epigraph

    Saluting Time and the Goddess of Learning, Saraswati, I now begin my discourse on the knowledge of Time….

    ŖgvedaVedangaJyotiṣa

    Preface

    Time is where science meets religion. The interaction between science and culture is mediated by time beliefs: changing time beliefs changes scientific theory on the one hand, and values on the other. Mapping time beliefs thus provides a way to understand and to demonstrate how culture has influenced science, and how science is influencing culture. This science-culture interaction through time beliefs is inevitably enmeshed with politics, for cultural values govern the behaviour of very many people, and attempts to influence human behaviour by manipulating cultural values have ended up manipulating time beliefs. Such a theme naturally demands the widest possible audience.

    Some seven years ago, when I set out to write this book as a sequel to my first book on time in physics, my aim was to present to a lay audience the science-culture interaction through time beliefs. Further, I aimed to emphasize a non-Western perspective which considered science in relation to time beliefs in various religions, rather than ‘religion’ alone. To reach a large readership, I thought of presenting this book as a sort of rejoinder to books like Stephen Hawking's A Brief History of Time.

    As the book developed, the enormity of the task that I had undertaken started becoming apparent. I found the book moving from the interface of science and religion to eschatology, to church history, to current politics, to the sociology of science, to physics proper, to the philosophy and history of science, to sociology, to comparative religions, to ethics. The movement was unavoidable, since time impinges on so many aspects of our life and thought that all these subjects had necessarily to be involved in the attempt to understand that single term—time—from a fresh perspective. It seemed worthwhile to attempt to understand all this, since so much of our way of life depends upon what we believe about the nature of time. Indeed, writing this book has been a richly fulfilling experience, just because of the clarity and understanding that I acquired in the process. But it was not easy to present this understanding in a way that would be intelligible to someone with no technical background.

    Thus, the final result seems like a book which, in its entirety, will demand some persistence from an entirely lay reader; but it does not assume any specialised knowledge, and so remains accessible to the non-specialist. While the linkages of science and culture are intrinsically complex, and confusing, I have tried hard to make this book as easy as possible. I hope, therefore, that much, if not all, that I have to say, would still get across to almost everyone.

    P.S. Given the recent events in India, of rising violence in the name of religion, a postscript to this preface is essential. This book should not be misconstrued as being slanted for or against any particular religion. I believe that those who seek to attain or retain state power through religion are undoubtedly the worst enemies of the religion, whatever be the religion they claim to represent: Christianity, Islam, or Hinduism.

    Notes
    • Do feel free to read this book in bits and pieces, starting with the most interesting bits, and moving backward or forward for more details.
    • To skip a chapter, read the summary at the end of that chapter.
    • Chapter summaries are collected together at the end of the book, under The Argument, to help link chapters and parts.
    • Do check under Glossary and Persons not only for details on unfamiliar words and names, but also for some familiar words used in a specific sense.
    • Page numbers in brackets are cross-references to pages in this book.

    Prologue: Time, Science, and Religion

    There is an old story of a fisherman who saw a mermaid and instantly fell in love with her. Afraid she would disappear, he told her he loved her. The mermaid first laughed, and then cried. The puzzled fisherman asked why, and she explained that she had laughed because she was happy, for she had surfaced because she loved him. And she cried because they couldn't marry. ‘To marry me’, she said sadly, ‘you will have to lose your soul.’ So the fisherman rushed to the priest to ask how he could lose his soul. The priest refused to oblige. ‘Never part with your soul’, he warned, ‘your soul is more precious than all the gold in the world!’ But the fisherman did not heed the warning for he was madly in love. Instead, the thought of gold gave him an idea. ‘The merchant will surely want it then’, thought the fisherman, ‘and he will find a way to relieve me of my soul.’ So the fisherman ran to the merchant. But the merchant laughed. ‘I will gladly pay for your body’, he said, ‘but your soul is of no use to me!’ In the modern ending to this story, the dejected fisherman went to the scientist for help. But the scientist pooh-poohed him. ‘You don't have a soul, so how can you lose it?’ he asked. ‘Besides, there are no mermaids’, he admonished. (As if to prove the scientist right, by the time the fisherman returned, the mermaid had vanished.)

    The Priest, the Scientist, and the Merchant are the principal characters in this story of the eleven pictures of time. The Fisherman remains a bystander, a bit like you and me, trying hard to reconcile his experiences and emotions with their weighty sayings that concern the core of his being: the soul.

    What has the soul got to do with time?

  • Epilogue

    ‘Bring a fruit of that Nyagrodha tree.’

    ‘Here it is, sir.’

    ‘Break it.’

    ‘It is broken, sir.’

    ‘What do you see?’

    ‘Some seeds, extremely small, sir.’

    ‘Break one of them.’

    ‘It is broken, sir.’

    ‘What do you see?’

    ‘Nothing, sir.’

    ‘The subtle essence you do not see, and in that is the whole of the vast Nyagrodha tree…that which is the subtle essence—in that have all things there existence. That is the truth. That is the Self. And that, Svetaketu, THAT ART THOU.’

    Chandogya Upaniṣad1

    6.12.1–3.

    The Fisherman walked along disconsolate. He did not know where he was going. Nor did he know where he wanted to go. At long last he stumbled upon a wise old man. The Fisherman eagerly asked him, ‘Tell me sir, what should I do? Whom should I believe? the Priest, the Merchant, or the Scientist? What should I do to find my mermaid once again? Was she perhaps not a mermaid, after all, but only that woman from a neighbouring village, pretending to be a mermaid? What is the truth?’

    The wise man laughed loud and long. But seeing the Fisherman's distress, he took pity and said, ‘You catch fish everyday, and yet you don't understand! Well, if the fish understood your tricks, would you be able to catch them? The Priest, the Merchant, and the Scientist have trapped you like a fish, O Fisherman!’

    ‘What should I do then? How can I escape? Where will I find my mermaid?’

    The wise man beckoned to the Fisherman to come closer, and whispered something in his ear. The Fisherman sprang back startled, ‘What are you saying! I am only a poor fisherman, how can I be the Creator? the very Lord Almighty!’

    ‘Yes’, said the wise man, ‘Origen taught equity because he thought all are one with the Creator. Abu Yazīd went to meet God, and finding the throne empty he sat down on it—to discover that he was God. He was not arrogant—he was the same Abu Yazīd who stepped aside to give right of way to a dog. The Buddha and Mahavira denied God or a Creator for the world—but neither denied your ability to create.

    ‘The Priest’, continued the wise man, ‘painted the picture of an all-powerful God to frighten you into submission, and to enslave you. He took away your real soul, and gave you back only a husk in return. It is this husk of a soul he asked you never to part with, for if you throw it away, the Priest will lose his power over you, he will no longer be able to control you, through talk of reward or punishment given by his all powerful God.’

    ‘Is that why the Scientist said I have no soul?’

    ‘No’, said the wise man, ‘in the Priest's world, to obtain your reward, you had to know what God wanted. If God were capricious, it would be hard for you to know what he wanted. So, to make things easier for you, the Priest said the world is rule-bound. The Scientist seriously developed this picture of the cosmos as the clockwork of a distant God—he now thinks you are no more than a piece of this clockwork, bound to it by rigid laws. Where the Priest used a fishing line, the Scientist uses a net. Perhaps you can show him that you have a soul after all by making a hole in his net? Perhaps you can show the Scientist that the laws of the clockwork cosmos can be bent a little!’

    ‘What of the Merchant, then? why did he say he has no use for my soul?’

    ‘The Merchant lives off the work of many people—he wants them all to obey him. So, the Merchant designed a clockwork society. The Scientist only thought of you as a piece of clockwork; the Merchant changed you into one. He taught you to decide mechanically by calculating future profit. The clockwork society can be easily controlled by a few Merchant-clockmakers at the top, and it functions for their benefit. Your love for your mermaid has no place in this society—it is unprofitable for the Merchant like your thoughts about your soul.’

    ‘But’, said the Fisherman, ‘who am I to change things? How can I be the Creator? I am not all-powerful, I have only a little power. I am not all-knowing, I have only a little knowledge. I am not eternal, my life is short. I cannot be everywhere, but only live in a small hut on the shore of this vast ocean, in which my mermaid has disappeared. Can I do anything at all?’

    ‘Yes’, said the wise man, ‘what you say is quite true. You, as Creator, have created an imperfect world, to perfect which you must continue with your act of creation.’

    Will the Fisherman ever find his mermaid? Will he ever discover the truth? Will he manage to escape? Will the Fisherman someday surprise the Priest, the Scientist, and the Merchant? God certainly does not know!

    1. Modified from Swami Prabhavananda and Frederick Manchester, trans., The Upanishads, Mentor, New York, p. 70.

    Appendix: Patterns of Irrationality

    Nine ‘Proofs’ of the Existence of God

    Theorem. God exists.

    Proof 1 (by intimidation). If you don't believe in God, you will go to Hell and boil/bake/freeze/fry/roast/rot for the rest of eternity. Hence God exists.

    Proof 2 (by rewards). If you believe in God, and observe the rules, you will certainly go to Heaven and enjoy yourself for the rest of eternity. Hence God exists.

    Proof 3 (by stratification). People have believed in God from time immemorial. If God did not exist, the notion would have been discarded long ago. Hence God exists.

    Proof 4 (by numbers). So many people believe in God. They can't all be wrong, can they? Hence God exists.

    Proof 5 (by expertise). I, too, have had doubts regarding the existence of God. But they have now been clarified. See, for example [obscure reference]. Hence God exists.

    Proof 6 (by experts). Many great people have believed in God. Hence God exists.

    Proof 7 (by territory limitation). Science is all very well in the material domain, but it doesn't apply to subtler spiritual matters. Hence God exists.

    Proof 8 (by hope). If God did not exist, how could I ever hope to get all the things that I want. Hence God exists.

    Proof 9 (by example). The sea receded before Moses. Hence God exists.

    The days of hellfire-and-brimstone arguments are not over. To see this, one has only to scan a newspaper or magazine, or switch on the radio or TV. ‘If you don't use Colgate you will develop bad breath’ (intimidation). ‘If you do, you will have sparkling white teeth (see photo)’ (rewards). ‘…backed by a hundred years of experience’ (stratification). ‘Casio, the world's largest selling calculator’ (numbers). ‘Actual tests prove that Surf washes whitest’ (expertise). ‘Forhans, the toothpaste created by a dentist’ (experts). ‘Buy Cadbury and win a free trip to Timbuctoo’ (hope). ‘Sheila is a careful housewife, her choice is Rin’ (example). These advertisers certainly understand their business better than us!

    More seriously, the fact remains that proofs of the above kind are not out of date. They continue to be used, and there is an undeniable parallel between medieval theology and current-day advertising. The words may have changed, the product being sold may have changed, but the form of the ‘proofs’ remains the same. Let us compare these proofs with current ideas of a logical proof.

    What is a Logical Proof?

    We start with statements A, B, C,… that assert something. For example, ‘all philosophers are impractical fools’ is an assertive statement, as is the statement ‘a true scientists is a cold-blooded creature’. But the question: ‘are all philosophers impractical fools?’ does not assert anything, and so is not one of A, B, C,…. Assertive statements may be true or false, but they cannot be both, or neither.

    We accept some of these statements as true. These are called premises. Next, we build bridges between the premises using the following rule of reasoning.

    • If A is true then B must be true.
    • A is true.
    • Hence, B is true.

    To hide the simplicity of this rule of reasoning, let us give it a Latin name: modus ponens. Here is an example of modus ponens.

    • If Socrates was a philosopher, then Socrates was an impractical fool.
    • Socrates was a philosopher.

    Therefore,

    • Socrates was an impractical fool.

    Another rule of reasoning is called instantiation: a universally true assertion must be true in this instance. Here is an example of instantiation.

    • All philosophers are impractical fools.
    • Socrates was a philosopher.

    Therefore,

    • Socrates was an impractical fool.

    A logical proof is a repetition of these simple patterns. It uses only premises, modus ponens, instantiation, or similar ‘self-evident rules of reasoning’. The idea is that a moron or a machine, with limited intelligence but unlimited patience, should be able to check the correctness of a logical proof. In this sense every logical proof is addressed to a machine, though, in practice, it may be abbreviated to avoid tedium. Formally, a logical proof is a sequence of statements, each of which is either a premise, or is derived from some preceding statements by using a rule of reasoning such as modus ponens or instantiation. The last statement in this sequence is the assertion proved.

    The conclusion of a logical proof is only as true as its premises. In actual fact, Socrates need not have been an impractical fool. This would only mean that the first premise is false, so that there are some philosophers who are not impractical or not fools.

    On the other hand, the following is not a logical proof.

    • Philosophers have the habit of questioning everything.

    Therefore,

    • The sun rises from the east.

    We may have independent reasons to believe that the sun rises from the east, but there is no logical connection between the rising of the sun and philosophers or their habit of questioning everything. Such a non-proof is called a non-sequitur (‘it does not follow’).

    Comparison with the Nine Proofs

    From a logical point of view, each one of the nine ‘proofs’ of the existence of God is a complete non-sequitur. There are no clearly stated premises, no modus ponens, hence no proof. The tragedy is that the nine ‘proofs’ are not even fallacious. A fallacious proof might run as follows.

    • All philosophers are impractical fools.

    Therefore,

    • All impractical fools are philosophers.

    Or,

    • All scientists are rational.

    Therefore,

    • There are many rational people in this world.

    Fallacious proofs are yet impersonal (if one is not a philosopher!). Any logical proof, even a fallacious one, is addressed to a machine. In contrast, each one of the nine ‘proofs’ is addressed, implicitly or explicitly, to a person. It would be wrong to classify the nine ‘proofs’ as fallacious, because there has been no attempt at a proof. To distinguish such ‘proofs’ from the run-of-the-mill Aristotelian fallacies, we shall refer to them as irrational, although arational would, perhaps, be a better word.

    One cannot lightly dismiss irrational arguments because people do get convinced by them. Indeed, irrational arguments often carry more conviction than logical arguments. It is for this reason that advertisements use irrational arguments.

    Even a proof by intimidation may be subtle enough to carry conviction. For example, consider the following argument advanced by my uncle. ‘You should not disregard the teachings of our ancestors and question everything. You cannot know everything directly. For example, you cannot know who your father was, because that happened before you were born. But I can tell you because I attended the marriage of your parents. You are prepared to take my word for that. Likewise there are many things that I learnt from my elders. If I tell you about these things, you say ‘How do I know they are correct?’ How do you know who your father is?’ I had considerable difficulty in countering this argument: facing up to loss of face can be difficult.

    Non-Verbal Communication

    The essential message underlying an irrational proof is so simple that most animals manage to convey it without using words. One has only to sharpen one's observation a little to see this kind of communication among dogs, cats, cattle, hens, sparrows, crows, goldfish, and butterflies too.

    For example, a timid dog may tuck its tail between its legs and flee from a ferocious one. But, ‘the courage of the fugitive returns as he nears his own headquarters, while that of the pursuer sinks in proportion to the distance covered in enemy territory’. Once the timid fellow is close enough home, he will turn snarling on his tormentor. In effect, the timid one is saying, ‘I accept your superiority, but this is my territory, and if you try to drive me out of here, there will be a bloody fight. I might lose, but you are sure to get hurt’. The message, corresponding to a proof by territory limitation, predictably gets across.

    Other examples are only a little harder to find. If a butterfly sitting in a sunlit spot, in a forest, goes away for a while and returns to find another butterfly sitting there, it will inform the other butterfly of its prior claim by performing an intricate spiralling flight (proof by stratification). Sheep will follow their leader even over a cliff (proof by experts). Crows collect together to protect an injured crow (proof by numbers). Proof by expertise is, of course a little harder to come by: monkeys reportedly consult older monkeys on advice about crossing a tiger trail, or a busy road for that matter.

    To abstract still further, irrational arguments are based on the notions of status, territory, and stratification.

    Some form of status or pecking order is explicit in the behaviour of all gregarious species. The term ‘pecking order’ is used because the first reported studies in this direction were among hens. If grain is scattered among hens in a coop, the chief-hen pecks first, the vice-chief hen next, and so on down the line. Similar behaviour may be observed among human beings at, say, a formal dinner. It is impolite to begin eating before the chief guest. The clothes we wear, the perfume (e.g., soap) we use, the jewellery (e.g., watches) we flaunt, the car we drive, are all indicators of our standing in the social pecking order.

    We are occasionally amused by the fascination that lamp-posts exert on dogs. The sense of smell is very important for dogs, and a dog uses lamp-posts to mark out his territory. Vision is very important for human beings, and when we leave a table in a library, intending to come back, we usually leave behind some personal possessions—handwritten notes, a pen, or even a handkerchief—in a visually prominent place.

    It is an unwritten rule that in a crowded train, say, a seat ‘belongs’ to the person who occupies it first. This is stratification at work. Another kind of stratification is in the pecking order: promotion by seniority means that a pecking order, once established, is not to be disturbed, and all new entrants enter at the bottom of the order.

    A conflict is implicit in all the above situations. In an assembly of individuals, who should eat first and who should risk going without food? To whom does a certain piece of property or territory belong? Status, territory, and stratification correspond to the general rules for settling such conflicts.

    In a conflict between two individuals (of a given species) A is ‘right’ and B is ‘wrong’ if

    • A has a higher status than B, or
    • the conflict occurs in A’s territory, or
    • A has a prior claim to the territory now occupied by B.

    When A offers a proof by intimidation, he is trying to convince B that A, or the party on whose behalf he is pleading (perhaps God), has a higher status than B. Therefore, B should accept as correct whatever A says—the boss is always right. Other irrational proofs have similar interpretations.

    To sum up: irrational arguments are just a reflection of non-verbal behaviour in verbal behaviour. Proof by authority is convincing and widely used because of its survival value.

    Irrational arguments are deeply convincing because, being of evolutionary origin, they represent a gut response. But what is the survival value of a proof by hope? This seems obvious enough: for someone who gives up hope too soon may perish even when there is a chance of surviving. So the following example might help to clarify the question. As a child, I once watched a small grass snake trying to catch a frog. Whenever the frog hopped, the snake pursued vigorously. Whenever the frog paused, the snake froze into immobility. This continued for some time, with the snake gaining only a little. It was very difficult to understand why the snake didn't catch up while the frog was resting; it was equally difficult to understand why the frog sat still, for it could hop away when the snake had stopped. (The common wall lizard stalking an insect behaves similarly.)

    A plausible explanation is as follows. Like many animals, reptiles especially have poor vision! They can see an object only when there is relative movement between the object and the eye. So when the frog and snake were both stationary, they must have been as good as invisible to each other. Since, in this case, the speeds of the frog and snake were about equal, each was afraid that the slightest movement would reveal its whereabouts, and give the other a fractional advantage. So it is that the reaction of an animal to the first sign of danger is to stand stock still.

    With hindsight, the frog's line of thinking seems almost obvious: ‘If I can't see danger, danger cannot see me.’ For some obscure reason, it is the ostrich which reportedly makes the most use of a proof by hope. When tired of running from hunters, it simply buries its head in the sand, so that it can no longer see its pursuers.

    The ostrich seems comic, but are we humans much better in hoping that the evolutionary gut-responses that have helped us to survive till now will continue to ensure our survival regardless of the accumulation of knowledge? Are irrational gut-responses compatible with scientific theory? Is it not struthious to imagine that irrational attitudes can indefinitely exist side by side with the possession of nuclear weaponry or biotechnology? Is it not the same as handing a sword to a monkey who lacks the discrimination to use it?

    The Criteria for a Scientific Theory

    One possibility is to exercise discrimination in the manner of the law. One decides a valid argument by appealing, like the Nayyāyikas, to (a) the manifest (empirical data), (b) inference (logic, reason), and (c) testimony (authority, precedent). Another possibility is to reject authority, as the Buddhists or the materialist Lokāyata do: to rely blindly on authority is to be as indiscriminate as the ostrich (for the same reasons). On the other hand, as the Buddhists pointed out, any claim to discrimination in relying on authority cannot be justified except in terms of (a) and (b).

    • Internal consistency: Not every statement is allowed to be true. There should be some statements that are labelled as false.
    • Brevity: The theory should make as few assumptions as possible. This is also sometimes called Occam's razor. A razor is used to remove hair which we regard as superfluous; likewise Occam's razor is used to dispose off unnecessary assumptions.
    • Refutability: The theory should be testable; it should lead to some conclusions that are conceivably false. For example, the statement ‘all swans are white’ is refutable, if we are ready to call as ‘swan’ a bird which is like a swan in all respects except that it is not white. The idea is that if we do come across such a bird, we should not start hedging, and hang on to our theory by claiming that it is essential for swans to be white, so that the bird in question is not a swan at all. If we do that, there is no way the statement ‘all swans are white’ can be tested, for it is a defining characteristic of a swan that it should be white. Similarly, the statement ‘God exists’ is refutable only if we are ready to conceive of some material circumstance which would conclusively establish the statement to be false. The statement that ‘all humans are selfish’ becomes refutable only if we are able to conceive of some possible actions to which we would be ready to apply the label ‘altruistic’.
    • External consistency: The theory should not already have been refuted. A theory is refuted if an experiment shows it to be false. For example, the theory that ‘all swans are white’ is refuted if we find (or build) a black swan, in fact. The theory that ‘all human actions are selfish’ is refuted if we find an altruistic action in fact.
    • Likelihood: This is the trickiest part. Every experiment involves some possibility of error, and there is some doubt about its outcome. This forces us to choose between two or more possibilities. For example, we may accept the results of the experiment, or we may doubt the results and may want to repeat the experiment. The principle of maximum likelihood simply says that we should choose that possibility which is most likely.

    How does one decide what is most likely? This is the difficult part. One way is to repeat the experiment. If two experiments come out in favour of the theory, and ten experiments are against it, we reject the theory. In this sense this principle replaces the older principle of induction, because each repetition of the experiment updates our estimate of the likelihood of the external consistency of the theory.1

    But when we dismiss some new speculation—say Eric Lerner's ideas—as ‘interesting but very improbable’, we are naively applying this principle. This is tricky because one is tempted by territorial familiarity to dismiss all new ideas in this way. To try to assess new ideas as ‘likely’ or ‘unlikely’ on the basis of our expertise and acumen is to misuse this principle. The principle is to be applied only to decide whether external consistency holds. To apply the principle directly to hypotheses is as good or as bad as trying to guess the results of an experiment we have never performed.

    A valid scientific theory is not, however, the truth. A scientific theory is always tentative. It does not provide any certainty. Neither is there any guarantee that a series of scientific theories will take us ever closer to the truth. We have scientific theories only because we do not know the truth, so we can hardly say that a scientific theory is so close or so far from the truth. Nor even can we bring in the truth indirectly, without naming it. For example, we cannot say that successive scientific theories will come closer to each other, for a new scientific theory need not leave unchanged the core concepts of the older scientific theory it replaced—aether and phlogiston are examples.

    The Temporal Hypothesis Underlying the Criteria for a Scientific Theory

    Using the above criteria to decide between competing theories is certainly preferable to deciding truth by authority. But there are difficulties with these criteria, especially when the theories concern the nature of time. Thus the above criteria involve what might be called a layered approach. At the topmost layer there is the scientific theory about the world. Beneath that is a layer of mathematics or the process of inference which connects the hypothesis of the scientific theory to its conclusions. Beneath the mathematics is the metamathematical layer of logic. The philosophical criteria for deciding between scientific theories lies beneath all that. Each layer depends upon the one directly beneath it, so that the philosophical criteria provide the foundation for everything. But what does this foundation rest upon? Only theologians of a certain persuasion can contend that the foundation concerns principles that are universal because they are laid down by God. For, unfortunately, the chain is not such a linear one derived from God's authority: it relates back to the empirical world above the topmost layer of scientific theory!

    Specifically, the above criteria involve hypotheses about the empirical nature of time. The hypothesis typically is that of mundane time: that the structure of time is of the sort that one takes for granted in everyday life. For the present purpose this hypothesis cannot be taken for granted: the need for scientific theories arises just because unanalysed mundane experience is not the best guide to the truth. How does one go about deciding the validity of temporal hypotheses underlying the criteria of a scientific theory? However, our immediate concern is not with the validity of these hypotheses, but only with pointing out that there are such hypotheses about the nature of time underlying the above criteria. Not only does the nature of science depend strongly upon time assumptions, but the nature of what we call science also depends strongly upon time assumptions. It is, therefore, a difficult situation when the two pictures of time are different.

    Thus, consider the criterion of external consistency. When the report of an experiment is published, what one actually has are the reports of the experiment. One believes that the reports of the experiment still faithfully reflect the results of the experiment that was performed several months ago. So one has assumed, as with mundane time, that the past is linear and unchanging. This seems like a very reasonable belief, but if any interaction could propagate backward in time, the belief would not be strictly valid. Is the disagreement with mundane time sufficient ground to reject the belief that interactions can propagate backward in time? No, for the assumption of mundane time already contradicts the assumption of superlinear time used in formulating current scientific theory.

    Thus, consider the criterion of refutability. Refutability may be regarded as being of two kinds: logical refutability and empirical refutability. A statement is logically refutable if it is not a tautology. A statement is empirically refutable if one can actually carry out an empirical test. But what decides whether or not one can actually carry out such a test—our everyday experience of what one is free to do and what one is not able to do. If the past were to decide the future, this criterion might or might not filter out bad theories—for things may have been so decided that one persists with a false theory just because one can never ever carry out the critical test that could falsify the theory. In short, the criterion of refutability accepts the mundane belief that the future is open and is shaped, at least in a small way, by human actions. This is another perfectly mundane belief, but it contradicts the superlinear time of physics. One could consider modifying physics to overcome this problem,2 but what if the physical theory necessary for an open future also makes the past a little bit open?

    The Uncertainty of Deduction

    Finally, consider the criterion of internal consistency. This criterion usually assumes that the world is such that logic must necessarly be 2-valued. But the world may not be like that if time has the structure of fission-fusion time as in Chapter 9. Schrödinger's cat may then actually be both alive and dead. Changing the nature of logic would naturally change also the nature of inference, and this would change the conclusions that could be drawn from a given hypothesis. (This was forcefully demonstrated during the controversy over intuitionism in mathematics.) Thus, induction is not the only reason why a scientific theory lacks certainty. There can be no certainty even to deduction or mathematics. The certainty that has been attributed to deduction is merely cultural certainty.

    The uncertainty of deduction pertains to time perceptions. To reiterate the ground covered in Chapters 6, 10, and 11, the current definition of a mathematical proof dates back to Hilbert. The idea was that a moron or a machine should mechanically be able to check the correctness of the proof. This idea suits an industrial culture. But which logic ought one to use for this proof? Hilbert assumed the universality of 2-valued logic; and universality, or standardisation, also suits an industrial culture. Other cultures did not understand rationality or inference in this mechanical and standardised way. The Arab rationalists understood by rationality the exercise of the faculty of intelligence (aql) in the widest sense, which very much included the faculty of judgment. Buddhists would not necessarily accept such a mathematical proof as a valid argument, for they would reject both 2-valued logic, and the mathematical authority behind it: they might maintain that the assertive statement, ‘This man is good’, is both true and false. Neither would the Lokāyata—the people's philosophers of Indian tradition—have accepted Hilbert's idea of a mathematical proof; they would have been quick to point out who benefited from treating such inferences as universally valid! Thus, internal consistency and deduction both depend upon the underlying logic, and 2-valued logic is not necessarily universal, but depends upon cultural and empirical beliefs about the nature of time—beliefs that may or may not be valid.

    Summary
    • A valid scientific theory is decidedly preferable to authority, but the truth of a valid scientific theory is intrinsically uncertain.
    • The validity of a scientific theory is decided using criteria such as internal consistency, refutability, and external consistency.
    • However, these criteria involve hypotheses about the nature of time.
    • Hence, the validity of the present-day criteria of a valid scientific theory depends upon the validity of the underlying picture of time.
    • Hence, also, the validity of a picture of time cannot be decided simply by checking it against the picture of time in current scientific theory: hypotheses about the nature of time in scientific theory must be compatible with hypotheses about the nature of time used to decide the scientific nature of the theory.
    • A tilt in the arrow of time provides approximate compatibility.

    1. There is a confusing technical point here, about induction. Repeated experiments do not change the probability that the theory is externally consistent: Popper rightly pointed out that probabilities are not ampliative. But he wrongly imagined that that settles the problem of induction, for the repeated experiments do change our estimate of these probabilities. We never actually know the probabilities, and can only estimate them. See, K. R. Popper, The Open Universe: An Argument for Indeterminism, Hutchinson, London, 1982.

    2. The difficulty of assuming conflicting pictures of time, and the possible remedy of modifying physics, using a tilt in the arrow of time, is discussed in detail in C. K. Raju, Time: Towards a Consistent Theory, Kluwer Academic, Dordrecht, 1994.

    The Argument

    Part 1: Time and Eschatology
    • Life after death. Belief in the soul relates to belief in life after death. In its original form the belief in life after death involved a belief in quasi-cyclic time: it was thought that the entire cosmos went through cycles. Like days on earth, each cycle of the cosmos was believed to be much like the preceding one, though not exactly like it. It was thought that all events approximately repeated; so did individual human beings, reborn in successive cycles of the cosmos, though bodies might change a bit across cycles, somewhat the way a person grows imperceptibly older each day. People thought that death interrupted epochs of life in cosmic cycles like sleep interrupts our daily periods of wakefulness. One finds this belief across the ancient world. Some, like Socrates, even thought that with due effort one could recall the previous experiences of one's soul.

    Quite possibly our ancestors were mistaken—one can certainly imagine a world in which time is not quasi-cyclic. But that already gives us an important clue. Our ability to imagine a time that is not quasi-cyclic tells us that quasi-cyclic time, like the accompanying notion of the soul, is a physical notion—since it is refutable. But is this a valid physical notion? How does quasi-cyclic time compare with the notions of time in present-day science? Can one look forward to a life beyond the present one?

    Current physical theory does not fundamentally rule out the possibility of quasi-cyclic time. On the contrary, it is known that there are many circumstances in which quasi-cyclicity is inevitable. But present-day observation does not allow us to decide whether, in fact, these circumstances prevail.

    Conclusion: There is life after death if time is quasi-cyclic.

    Q. Is time linear or cyclic?

    • The curse on ‘cyclic’ time. A similar belief in life after death, in the context of quasi-cyclic time, existed also in early Christianity and among the ‘pagans’ in the Roman empire. This kind of life after death was not considered desirable, deliverance from it was. It was thought that deliverance from life after death was available to all. This belief in universal deliverance was used by early church fathers like Origen to support equity; a soul which repeatedly ascended to heaven and descended to earth, like a raindrop, represented complete equity—for raindrops join in streams that ultimately pour back into the ocean. After Constantine, the church found equity increasingly inconvenient; and after consummating its marriage to the Roman state, by about the middle of the 6th century, the church decisively rejected equity. If everyone would anyway be saved, why have an institution like the church? The church wanted to be needed like the state. The state is needed to mediate reward and punishment here; the church sought the role of mediating reward and punishment in the hereafter. To this end, it needed to construct an appropriate hereafter.

    Hence, the state-church cursed ‘cyclic’ time; it accepted Augustine's arguments that, for the world to be morally intelligible, the hereafter must be such that it clearly and eternally separated sinners from the virtuous. This changed idea of heaven and hell changed also the belief in life after death: instead of a sequence of lives in successive cycles of the cosmos, the church decreed that people should believe in life after death just once. Instead of universal deliverance, some now went to heaven and others to hell, both of which would last eternally. The changed picture of the hereafter changed the way of life here. The earlier ideal was dispassionate action leading to deliverance. This was replaced by a prescription better suited to purposes of state: motivation through hope of eternal reward and fear of eternal punishment in the hereafter. The Priest could guide action by explaining what act led where.

    Q. Why should this medieval curse concern us today? Can't science decide whether there is life after death ? Can't science decide whether time is ‘linear’ or ‘cyclic’?

    It can, but the decison is not so easy. The notion of time is fundamental to both science and religion, and beliefs about time in one sphere have influenced beliefs about time in the other—the curse on ‘cyclic’ time decides ideas about time in science today. For example, to try to establish that time had a beginning, at a moment of creation, Stephen Hawking reintroduced the old curse on ‘cyclic’ time as a postulate (called the ‘chronology condition’) into current physics. His arguments in support of this postulate are fundamentally the same as those used by Augustine to condemn ‘cyclic’ time.

    What were those arguments? The four key ideas are summarised in Box 10.

    All four of these ideas—(1) the confusion between distinct pictures of ‘cyclic’ and ‘linear’ time, (2) the idea that any kind of ‘cyclicity’ is contrary to ‘free will’, (3) the idea that credits for innovations can always be located in individuals, and (4) the idea that ‘free will’ can somehow be reconciled with the deterministic ‘laws’ of physics without changing them—are ideas with considerable currency in current science.

    Conclusion: Science cannot straightaway answer questions about time in a way independent of theology. Contrary to the popular image of their opposing postures in the Fisherman's story, the Priest and the Scientist have reached an understanding offstage!

    Is this conclusion hasty? While theological ideas may naturally percolate into scientific thought, through the scientist's mind, could it not be that in the case of time the Priest and the Scientist have independently arrived at the same answer? Perhaps science and religion harmonise because they express different aspects of the same truth?

    • Creation, Immortality, and the New Physics. But with which religion does science harmonise? For religions differ, so that the harmony of science with one religion may involve its discord with other religions. If science were somehow to establish the existence of God, that would be discordant with Buddhism, which denies both God and creation. ‘Religion’ in the talk of the harmony of ‘science and religion’ clearly also does not refer to Islam, for it is the conflict between science and religion that is seen to prevail in this case. That is, the new harmony between science and ‘religion’ concerns also the discord between ‘religion’ and religion. The timing of this harmony and discord is politically very significant.

    After the Cold War, further expansion in the power of the West requires investment in ‘soft power’, not nuclear weapons. Power is the capability to control the behaviour of others, and further investment in nuclear weapons will neither alter the behaviour of any more people, nor will it help to ‘fine tune’ behaviour. Thus, this agenda for a unipolar world requires globalisation of culture and values. Values have traditionally related to religion. But the perceived conflict between science and ‘religion’ has led to a loss of credibility for ‘religion’. So the credibility of ‘religion’ is sought to be restored by harmonising religion with science, which today represents a global and public set of beliefs.

    Both ‘religion’ (= Western Christianity) and science have traditionally had close links with the state. ‘Religion’ has been re-interpreted to suit the concerns of state and capital. Similar concerns have made science authoritarian, with increasing specialisation and widespread scientific illiteracy. Scientific illiterates (or over-specialised scientists) have no option but to trust some scientific authority—employed by the state or private capital. Hence, it is practically possible to adjust both science and ‘religion’ to achieve the requisite harmony—at least for the time period that is critical to the agenda of establishing a unipolar world. To achieve the harmony, it is necessary only to adjust the time beliefs that are at the interface of science and religion. The pope has explicitly outlined the minimum agenda for the new harmony of science and ‘religion’: belief in creation, and belief in immortality. These beliefs legitimise the authority of the church and the associated values.

    One expects that priests will actively pursue this agenda. And, it is evident that this harmony agenda derives support from the popular works of a number of scientists and scientific authorities (whatever their personal beliefs). These include Stephen Hawking, Roger Penrose, Ilya Prigogine, Paul Davies, F. J. Tipler, etc. Since these popular works are implicitly believed by millions of scientific illiterates, they are clearly a political matter. Much new political physics is growing around attempts to harmonise science and ‘religion’! Scientists are changing science to suit the agenda.

    The new harmony is reflected in the way the Brave New Physics treats time, especially creation (the beginning of time) and apocalypse (end of time). The big bang and Hawking-Penrose singularities have been taken as conclusive proof of creation. Tipler has written a book claiming that theology is a branch of physics, and that present-day physics can be used to calculate that there will be life after death, ‘in the flesh’, precisely once, exactly as Augustine imagined, but in the virtual reality that an apocalyptic supercomputer would create at the end of time. It is difficult to distinguish such ‘theologically correct’ claims from the ‘ideologically correct’ claims of the Russian scientist Lysenko who claimed that wheat planted in a field of corn would sprout corn.

    Part 2: Time in Current Physics

    Q. Did the original marriage of science and religion similarly influence physics?

    All social scientists believe they know the answer to this question. All become either speechless or polemical if asked, ‘Show me the cultural influences in Schrödinger's equation. Tell me how physical theory would change under different cultural circumstances.’ The answer: time is the interface between science and religion. Cultural influences have travelled from religion to science through the notion of time; they have shaped the picture of time, and the picture of time decides the equations of physics. (We postpone to Part 3 the question of how physics would change with the picture of time.)

    • Newton's secret. If one turns the pages of history, one finds that theology has helped shape science since the days of Newton. As one who was at once both a deep scientific and religious thinker, Newton symbolises the then-believed harmony of science and religion. However, the religious side of Newton is largely unknown. Newton spent 50 years of his life secretly writing an 8-volume history of the church, and diligently collecting every scrap of evidence to show how the Bible had been distorted to suit the interests of the clergy; his work on physics was, for him, almost in the nature of a distraction. Historians of science, who wrote authoritative biographies of Newton, deliberately lied about his life—they did not want people to know about this terrible religious quarrel between the Priest and so reputed a scientist. For two centuries these lies circulated widely. The secret first leaked out to people at large in the 1950s, and more material became available in the 1970s, but the final version of Newton's history of the church is still kept a secret, underlining its relevance to the current political agenda of the church.

    This secrecy has made it very difficult to examine dispassionately how prevalent theological beliefs affected Newtonian physics. Newton too was a victim of the curse on ‘cyclic’ time. The curse led to the confused dichotomy of ‘linear’ vs ‘cyclic’ time—which dichotomy was taught by his teacher, Isaac Barrow, as the non-quack view. Newton the historian chose ‘linear’ time, for no clear physical reason that Newton the physicist could supply, and perhaps because it was only the religious hope of apocalypse that brought meaning to his secret life by situating it in a wider cosmic context.

    • In Einstein's shadow. It is not widely known that Newton's physics failed exactly due to difficulties with his notion of time. This is not widely known because physics texts misrepresent the creative process by which the Newtonian theory was replaced by relativity. Most physics texts describe special relativity as Einstein's 1905 theory following from the Michelson–Morley experiment, which found that the speed of light remained the same whether the source of light was moving or stationary. Such a view is quite indefensible. To measure speed, one needs to measure time—but what are equal intervals of time? One cannot put two intervals of time side by side to compare them—one must use a clock. But which clock should one use? The difficulty with time in Newtonian physics was this: how to measure ‘equal intervals of time’ with a democracy of clocks? So the speed of light could not have been properly measured at all.

    History corroborates what physics makes evident. Barrow had defined: equal causes take equal times to produce equal effects. Poincaré modified this slightly by changing ‘equal’ to ‘almost equal’ in the preceding definition. He argued that it best suited physics to use light signals to determine equal intervals of time. Hence the velocity of light was constant by postulate. (Poincaré also derived, reported, and published all of special relativity ahead of Einstein.) Einstein, who had avidly read Poincaré, agreed that the breakthrough came at the moment it was clear that time was the problem.

    The Times headlines, the atomic bomb, and the changed political map of Arabia made Einstein a superhero. At just about that time, in 1952, one of the first histories of the subject, written by Sir Edmund Whittaker, had a chapter entitled ‘The Relativity Theory of Lorentz and Poincaré’. This suggested that Einstein had used, without acknowledgment, Poincaré's theory published earlier, even borrowing the very terms in it, such as ‘Principle of Relativity’. Einstein was probably aware that this did not legally amount to plagiarism. (To process patent applications, as a patent clerk, Einstein had to learn the legality that ideas cannot be patented.) On the other hand, Whittaker, who wrote Einstein's biography for the Royal Society, was probably aware that this was neither the first nor the last case where Einstein claimed to have independently rediscovered results reported a short while earlier by the most prominent scientists of those times. In favour of Einstein, some subsequent historians of science have repeatedly asserted, without the least factual basis, that Einstein took one step more than Poincaré. As we shall see later, Einstein, not knowing enough mathematics, actually took one step less—unlike Poincaré, he failed lifelong to appreciate a key mathematical consequence of relativity.

    This dispute also brings us face to face with another relation between time and politics: heroes and villains are decided, and reward and punishment is socially distributed by appealing to a causal analysis which serves to fix credits and blame. Any causal analysis proceeds on a picture of time. To distribute credits, scientists use the mundane picture of time, and not the picture of time in relativity. Credit is distributed among individual scientists by appealing to the same causal principles (see Step 3 in Box 10, p. 457) that are used to distribute wealth and income in a capitalist society. A special feature of this principle of locating causes in individuals is this: such a causal analysis can never be conclusive. Hence, a dispute over credits can be settled only by appeal to authority (even though the authority, like that of Einstein, may not be reliable). This enables the politically powerful to appropriate most credits, by locating causes judiciously’. The patent clerk symbolises the patent law, which is a step in this process of appropriating credits— just as much as the current attempts to universalise the patent law are a step towards hegemony.

    A priority dispute only replaces one causal analysis with another, while accepting the principle of priority—that credit should go to the one who first made a discovery. But there is another difficulty with the principle of priority.

    Q. Is the principle of priority compatible with the principle of relativity ?

    Is it possible to fix credit and blame using the notion of time in relativity? Is mundane time compatible with time in physics? Science itself stands in the way: can the Scientist go along with the Priest and the Merchant without sacrificing science?

    • Broken time: chance, chaos, computability. Theories of chance, chaos, and computability, have been widely used to try to settle this difficulty (as in Step 4, Box 10, p. 457). The theories try to show that the ‘free will’ needed to validate physics is compatible with the validity of the deterministic laws of physics. The arguments involve the idea of ‘broken’ time: in some complex situations, the laws of physics cannot be used to predict the future, so that the future, though decided by the laws, will remain unknowable. Some have argued that quantum mechanics ensures that the future is intrinsically undecided. The future will continue to surprise man. But that is not at all the point. A chocolate–ice cream machine may stuff either chocolates or ice cream into your mouth in a way that you are quite unable to predict; you may be surprised by what you eat, but that is not the same as your choosing between ice cream and chocolates. Chance, chaos, and uncomputability are, thus, beside the point—the question is not whether the future can surprise man, the question is whether man can surprise God.

    Whether or not physics decides the future, it provides no room for man to do so. Moreover, no one believes these arguments from broken time if they are applied to ‘bring about’ the past instead of the future. A similar argument from broken time was used by al-Ghazālī to support providence in the debate between rationality and providence, in Islamic theology. These arguments were subsequently attacked in medieval Christian theology, which favoured rationality: God functioned through rational laws, for repeated acts of direct divine intervention (miracles) would make the world quite unpredictable. Such a world did not suit a God who needed to punish humans, for in a completely unpredictable world it is impossible to plan, so that one cannot rationally choose between different courses of action, by comparing their consequences.

    Conclusion: Broken time destroys rationality without enabling ‘free will’. It does not help to reconcile the relativistic notion of time with the principle of locating causes in individuals. Most amusingly, the sacrifice of rationality does not ensure even that the future is surprising to man.

    Q. Is rational calculation the only way to know the future?

    • Time travel. Time travel has recently moved from SF to physics. If one can travel to the future in a time machine, the future must already be ‘out there’. One can, then, perceive the future without having to calculate it; one can report this perception on returning to the present. The possibility of time travel has brought to the forefront of physics the question of ‘free will’ vs the deterministic laws of physics: can man bring about a future not already decided by God or physics? If the future is already ‘out there’ it would seem that one can no more bring about the future than one can change the past. Changing the future becomes exactly as paradoxical as a time traveller changing the past. Suppose one uses a time machine to travel to the past to kill one's grandfather before he could procreate. Then one couldn't have been born in the first place, so who killed Grandfather? The alternative seems to be that try as one might, one is unable to kill Grandfather—he survives just because time travel is fatal to ‘free will’! Not willing to trust this, and the better to defend Grandfather, Hawking has introduced a chronology protection conjecture. To travel to the past and return to the present one must execute a closed loop in time. The chronology protection conjecture abolishes by fiat such shades of ‘cyclic’ time. Hence it prohibits time travel.

    We reconsider the Augustine-Hawking argument about closed loops in time: Tim time-travels to meet Grandfather, and returns to the present. There is no question of repeatedly going round such a closed loop, mentally incrementing a counter for each circuit. Rather, the earliest event on this loop will be spontaneous in the sense of being in-principle causally inexplicable from any past set of events. One can explain Tim's arrival by saying that he pressed the button of his time machine—but that locates the cause in the future; it is an explanation from a future event (though this future event seems to be in Tim's past). On a closed time loop, every event has a ‘cause’, but there is no first cause. There is, in principle, no explanation from past causes for the entire loop or for the earliest event on it.

    The unheralded appearance of the time traveller corresponds to an event that spontaneously creates order (reduces entropy). A machine can neither be spontaneous, nor can it create order. To create order mechanically would be to build a perpetual motion machine. In fact, it is impossible to control spontaneous order-creation mechanically either from past or from future. Hence, there can be no time machines. But the prohibition applies only to mechanical devices; time travel in the sense of information transfer between future and present is not prohibited. Living organisms may, for example, directly obtain sporadic information about the distant future, without having to calculate it, but it is not possible to repeat this feat mechanically. There is no theoretical prohibition, for example, on dreaming the future. Whether or not one actually does dream of the future is, however, a matter best decided empirically.

    Part 3: De-Theologising Physics

    Probing the ideas of time in physics has brought us back to the question with which we started.

    Q. Is time ‘linear’ or ‘cyclic’?

    • The eleven pictures of time. The conclusion is that to find answers to any questions about time, one must first de-theologise physics—one must separate the Scientist from the overpowering influence of the Priest. This involves a refutation of each of the four steps (Box 10, p. 457) involved in the curse on ‘cyclic’ time. To arrive at clarity about time, those four archetypal arguments in Western thought must all be stood on their head. This book does exactly that. Our first step is to resolve the confused categories of ‘linear’ vs ‘cyclic’ time into distinct pictures of time. This brings into the open the conflict between different ‘linear’ pictures of time. The incompatibility of ‘linear’ mundane time with the superlinear time of physics cannot be settled by the psychological trick of appealing to some imagined antagonism between all ‘linear’ and ‘cyclic’ varieties of time. One must either change physics or abandon the mundane view of time.

    As regards Step 2 (Box 10, p. 457), from Augustine to time travel it has become a fixture of Western thought that ‘cyclic’ time is anathema to ‘free will’. We have seen that the exact opposite is true. But does this understanding correspond to a picture of time that is at all physically realistic? Would it ever be possible to incorporate a nonlinear’ picture of time into a realistic physical theory?

    • The tilt in the arrow of time. This has already been done: an alternative physics with a tilt in the arrow of time has already been formulated. A tilt means partial anticipation. This involves no new physical hypothesis, but concerns an exploration of the most general form of physics after relativity.

    Einstein has been credited with relativity on the grounds that Poincaré ‘waffled’ on the question of aether. The term ‘aether’ has two meanings: Poincaré unambiguously rejected aether in the sense of absolute velocity, but Einstein hung on to aether in the original sense of action by contact used by Descartes (and the early Indian Nyāya-Vaisesika tradition). Einstein regarded action without contact as something ‘spooky’; he erred lifelong in supposing that after rejecting absolute velocity, one could hang on to aether in the sense of action by contact. (This led him to assert a mathematical absurdity in the authoritative Annals of Mathematics.) After relativity, it is necessary to reject aether in both senses; hence also it is necessary to reject the paradigm of ‘instantaneity’ used in physics till now. (Poincaré understood this correctly.) Most physicists today continue with this error, eliminated by either history-dependence or a tilt.

    But a tilt goes a step further than history-dependence. A universe with a tilt is no longer a grand piece of clockwork. Physics with a tilt is non-mechanistic: it implies spontaneity which differs from chance. Spontaneous order creation is a cooperative process, so that Step 3 of Augustine's argument is exactly denied—it is, in principle, impossible to locate the credit for creative acts within any one individual. (What one has here is not a sequential multiplicity of causes, but a simultaneous collectivity of causes, so that priority disputes cannot even be resolved through convention.)

    This picture of spontaneity is quite compatible with physics. It is not, however, compatible with the theological excess baggage of ‘causality’: it forces us to consider the equations of relativity in their most general form, corresponding to a tilt in the arrow of time.

    While this is a minimal change in physics, it does lead to many qualitative and quantitative differences.

    Part 4: Time and Values

    Q. So what difference does that make to me?

    Along with various religions, industrial capitalism too has modified time perceptions to shape values, the present way of life, and the way resources are distributed in society. A new picture of time means new values, a new way of life, and a new society.

    • Time as money. How does a changed picture of time affect our social and personal life? The quickest answer to this question is provided by examining our current value-system and way of life, which flows from the equation time=money: act so as to maximise the expected present-value of lifetime income. Howsoever dull and repetitive the work, it still is most ‘natural’ to ‘spend’ one's lifetime working harder to earn more money. People are surprised by someone who abandons a job for another which has half the salary but twice the leisure. In newly industrialised countries, these beliefs have generated the competitive pressures that make children abandon play and focus on study in the hope of getting better paid jobs later on. Time has become a commodity in modern industrial capitalist societies: one barters lifetime now for money later on.

    Early attempts to export industrial capitalism show that these transformed values, and the accompanying changes in human behaviour and society, were essential pre-requisites for the success of industrial capitalism—a lesson to be remembered in the context of the current strategic agenda to globalise convenient values.

    Industrial capitalism has been characterised by a shift from a traditional ‘cyclic’ pattern of time in agricultural societies to the modern ‘rational’, ‘linear’ picture of time in industrial societies. Significant changes in the calendar and the clock were required for the success of shipping and railways—key inputs to the industrial revolution. Equally significant changes in the human sense of time, hence human behaviour, were essential for successful control of the production process.

    We isolate the key assumptions about time that go into the making of the way of life in industrial society. For example, the profit motive, in requiring the rational calculation of future profit, assumes that the future can (only) be rationally calculated. Two distinct pictures of ‘linear’ time—mundane time and superlinear time—underlie this idea of rational choice, and the linear-cyclic dichotomy helps to mask the incoherence between these conflicting pictures of time.

    Further, there is the facile assumption that intertemporal comparisions of utility are unproblematic, and, in fact, uniform across individuals (like the rate of interest in a capitalist economy), while interpersonal comparisons of utility are anathema. Arrow's impossibility theorem is extended in Chapter 11 to show that rational choice is surely impossible if social choice is. Finally, to the extent that the assumptions about time underlying the industrial life are physical assumptions, they may be invalid.

    • The transformation of time in tradition. Industrial values exhibit a harmony between the Priest and the Merchant, and many writers have claimed that this harmony was possible because ‘linear’ time is uniquely a part of Judaeo-Christian tradition. This is qualifiedly true. First, ‘linear’ time relates to the curse on ‘cyclic’ time, which concerns a tradition commencing with 4th to 6th century religious politics: it concerns Augustine's Christianity rather than that of Jesus. And it concerns an incoherent and constant ‘reversal of perspective’ between ‘linear’ mundane time and ‘linear’ apocalyptic time.

    Second, the claim involves a profound ignorance of the pictures of time in other traditions—the rejection of ‘cyclic’ time may mean neither ‘linear’ apocalyptic time, nor superlinear time, but ‘linear’ mundane time. This was the case, for example, with the Lokāyata (‘people's philosophy’), which rejected quasi-cyclic time, a thousand years before the curse. One difference was this: while the Lokāyata rejection of ‘cyclic’ time was intended to benefit the people, by rejecting social inequity, the Western Christian curse on ‘cyclic’ time was intended to benefit the state, by rejecting equity and reinforcing hierarchy. The values related to ‘linear’ mundane time differed from those related to apocalyptic time: the Lokāyata accepted as desirable many things, like intoxicants and sexual indulgence, that Western Christianity regarded as sinful. The values related to ‘linear’ mundane time differed also from the values related to superlinear time: unlike the case of time =money, Lokāyata rejected the need to defer present consumption in the hope of future rewards, or fear of future punishment, on grounds similar to those they used to reject quasi-cyclic time.

    The bald denial of quasi-cyclic time (whether or not it led to ‘free will’) undeniably led to a sense of moral liberty, as in the story of the philosopher-King Ajātasattu, and his question addressed to the Buddha. The Buddha, without directly contesting the belief in quasi-cyclic time, denied its chief consequence—the belief in a soul. (This was the exact opposite of Augustine's decision to deny quasi-cyclic time, but accept the existence of the soul.) As is to be expected, this denial of the soul shatters the basis of morality in Western Christianity. In fact, the Buddha denied belief in the continuation of identity even from one instant to next: this realisation of change with time shatters also the basis of time=money, since it makes impossible rational choice with deferred consumption. The Buddhist notion of time endows the instant with a structure, and a non-trivial structure of time corresponding to a rejection of the very basis of classical rationality: 2-valued truth-functional logic. Finally, the Buddha's perception of time as instant replaced ‘cause’ by conditioned coorigination, and this destroys the usual justification for inequity. He established the samgha as his model for a society with equity.

    Drawing inspiration from the Neoplatonists (whom the church called pagans and pantheists), the rational theologians of Islam, like Ibn Sīnā, believed in quasi-cyclicity, as did the Sūfī-s, like Rūmī and Ibn ‘Arabī. But all today acknowledge the authority of al-Ghazālī who attacked the rationalists using ontically broken time: he contended that the rational predictability of the future depended upon God's habit, which might change unexpectedly. In that debate between rationality and providence, providence won in Islam. For al-Ghazālī the location of all creative processes in God was not a problem, for, like the Sūfī's, he subscribed to the belief in the unity of existence—that God was within man.

    But the curse on ‘cyclic’ time created a problem for providence in Christianity, for the curse had eternally separated man from God. Providence vested too much power in a God who was transcendent and vindictive. If all creative power were reserved for God, why should man be punished eternally? Hence rational theology, with its image of a rule-bound God and its vision of a rule-bound society, won in medieval Christianity: Aquinas’ arguments against al-Ghazālī came to be accepted, and the advocates of providence came to be known as Dunces. Newton's ‘laws’ were called laws exactly because of his belief in rational laws with which God governed the world, relying occasionally on providence. Eventually, Laplace's demon (p. 174) occupied even the small space reserved for providence in Newtonian physics, for the demon could rationally calculate the entire future.

    Industrial capitalism applied calculative rationality not only to production, but also to the distribution of resources. To distribute credits by cause, one must be able to identify causes. But, with the assumption of mundane time, in any realistic social context, there always is a multiplicity of causes. Hence, a dispute over credits cannot be settled except by appeal to political authority: hence credits (and resources) are inevitably distributed in proportion to political authority—an arrangement which suited industrial capitalism very well.

    The values based on the earlier varied time-beliefs of the Buddhists, the Jains, early Christians, the Advait-Vedantin-s, the Sūfī-s, the Sunni-s, etc., are all hence intrinsically incompatible with the values corresponding to the time=money of industrial capitalism. It is in this sense that industrial capitalism harmonises with Western Christianity while being discordant with other religions: both industrial capitalism and Western Christianity believe that morality begins with inequity! This harmony cannot be further restricted to a harmony with the Protestant ethic alone: the root ‘cause’ of the harmony is the very notion of cause, related to the curse on ‘cyclic’ time, for the accompanying Augustinian ethic was needed to help justify the concentration of resources with the politically powerful.

    (With calculative rationality, the unexpected refers to a situation where the calculation fails: it may, however, happen that classical rationality itself fails, for rationality rests on logic, and logic changes with the picture of time. Hence, logic may be a cultural artefact: deduction may refer to an insecure cultural truth rather than an a priori and secure universal certainty. To provide an example of this, a postscript examines in some detail the Buddhist and Jain perceptions of time and logic, pointing out the Buddha's use of a logic of four alternatives: in which, for example, Schrödinger's cat may be simultaneously both dead and alive without contradiction.)

    • Revaluation of all values. A tilt in the arrow of time, too, is intrinsically incompatible with time=money, for the temporal assumptions underlying calculative rationality fail with a tilt. A tilt too changes perception of how one ought to live, and how society ought to be organised. There is no ‘naturalist fallacy’ here, because natural inclinations link ‘is’ to ‘ought’, so a change in ‘is’-type beliefs also changes ‘ought’-type beliefs. These ‘natural inclinations’ derive from the process of biological evolution. However, a tilt modifies the Darwinian view of evolution by focusing on the neglected (cooperative) creative process (not ‘chance’) which generates mutations, rather than the (competitive) selection process which eliminates them. Hence, modifying the usual naturalistic ethic (‘survival’), a tilt suggests the principle: ‘live to increase order in the cosmos’.

    Order-creation includes the legitimate concerns of ‘survival’ and of environmental ethics, or, more generally, harmony (order preservation). But order cannot be created mechanically—machines help to dominate and to make profit, but machines necessarily create disorder, degrading the environment and making all life difficult. Only living organisms, capable of spontaneity, can possibly create order. With a tilt, order-creation is possible, and order-creation, as the very purpose of life, is valued over mindless domination in the name of ‘survival’. Order-creation is a cooperative process: credit for creating order cannot be localised in individuals, and so, with a tilt, there is no longer any justification for the iniquitous distribution of resources. Thus, contrary to time=money which makes our present life so mechanical and enforces social inequity through technology—which generates life-threatening disorder—a tilt suggests a way of life and a social organisation based upon harmony, spontaneity, and equity.

    Acknowledgments

    The writing of this book was initially and partially supported by a Fellowship of the National Institute of Science, Technology, and Development Studies, of the Council of Scientific and Industrial Research. I am grateful to Dr Ashok Jain, then Director, for making my stay at the Institute virtually painless.

    The book was conceived during an earlier Fellowship at the Indian Institute of Advanced Study. The ambience there definitely encouraged me to reflect upon possible social influences on scientific theories, though these thoughts were not incorporated in the book on ‘time’ I wrote there. I am grateful to the late Professor S. Gopal, former Chairman of the Governing Body of the Institute, for the consistent encouragement he provided both in and out of office.

    In the early stages of this book, the group discussions at the Centre for Science Communication, at the University of Delhi, greatly helped to clarify my ideas.

    I can only record my gratitude to the late Dr Paulos Mar Gregorios, Metropolitan of Delhi, and President of the World Council of Churches, for a number of long discussions, and for offering to write an introduction to this book which he unfortunately did not live to complete.

    The book was substantially improved by the comments of a number of friends and well-wishers on whom I was guilty of foisting early drafts. I am particularly very grateful to the following.

    —The late Dr Arun Ghosh, former Member, Planning Commission, for his detailed and enthusiastic comments on two such early drafts.

    —The late Professor Ravinder Kumar, former Director, Nehru Memorial Museum and Library, for the benefit of his political acumen.

    —Professor E. C. G. Sudarshan, Centre for Theoretical Physics, University of Texas at Austin, for a number of sharp observations from his vast experience, and for borrowing one of his pungent jokes without acknowledgment.

    —Professor S. Ramseshan, former Director, Indian Institute of Science, Bangalore, for not allowing his ill-health to prevent him from responding.

    —Professor Raimundo Panicker, for taking the time out from a brief visit to read and comment on the first few chapters.

    —Professor Sumit Sarkar, Department of History, University of Delhi, for pointing out some key ways in which the thesis was going astray.

    —Shri M. V. Kumar, formerly Managing Director, TTK Pharma, Chennai, for his enthusiasm, and for his candid comments.

    —Shri K. Balakrishnan, Executive Secretary, Times Research Foundation, for his consistent interest and for his advice on how to write for a mass audience.

    —Shri Praful Bidwai, columnist, and former Senior Editor of the Times of India, for taking time off from his numerous commitments to comment on the first two chapters.

    —Shri Shankar Ramaswamy, Department of Anthropology, University of Chicago, for listening to me patiently and for keeping me supplied with the latest books on ‘time’, and copies of a variety of references unavailable here.

    —Shri Kishan Ramaswamy, for responding to the book from a non-academic viewpoint.

    I am grateful to Mr V. Joshi, Librarian, NISTADS, for his constantly helpful attitude.

    In addition, personal discussions (and some acid disagreements) with the following, at various points of space and time, helped me with some of the questions raised in this book: Professors David Atkinson (Groningen), David Burston (Pittsburgh), Chris Clarke (Southampton), Paul Davies (Adelaide), Dennis Dieks (Utrecht), Gerhard Heinzmann (Nancy), Peter Landsberg (Southampton), Jayant Narlikar (Pune), Achille Papapetrou (Paris), Roger Penrose (Oxford), Huw Price (Sydney), Ilya Prigogine (Bruxelles), Jürgen Renn (Berlin), Richard Sorabji (Oxford), Franco Selleri (Bari), Frank Tipler (Tulane), Kapila Vatsyayana (New Delhi), Jean-Pierre Vigier (Paris), Dieter Zeh (Heidelberg).

    Last, but not, of course, the least, I am grateful to Jaya, Suvrat, and Archiśmān for putting up, sometimes patiently, and sometimes not so patiently, with the prolonged neglect of the family that the writing of this book entailed.

    Persons

    A one dimensional view of persons as they relate to the theme of this book. (Abbreviations: b. = born, d. = died, ca. = circa = about.)

    Abu Yazīd al-Bistāmī (d. 874). Famous Sūfī, also known as Bayazīd, from Bistām, a small town in northern Iran.

    Ajātasattu [Ajātashatru] (d. −459). Son of King Bimbisāra (b. ca. −543, a friend of the Buddha), who seized the throne by patricide (in −491) through the ‘indirect’ cause of keeping his father in chains and allowing him to starve to death. His rule lasted about thirty years, during which his Magadha empire expanded to dominate the Gangetic plains. He founded the city of Pataliputra (now Patna). He questioned various wanderers like the Buddha and Mahavira about the benefits in this world of an ascetic life. Distinct from a character of the same name in the Upanishads.

    Aquinas. See Thomas Aquinas.

    Archimedes (b. −287, d. −212). The allusion is to his work on levers, which was used to build efficient catapults, that helped sink ships attacking Greece. His well-known remark, ‘Give me a place to stand on, and I will move the earth’ is from Pappus of Alexandria.

    Aristotle (b. −384, d. −322). His father was personal physician to the grandfather of his famous pupil, Alexander the Great (d. −323). Aristotle accumulated knowledge from far-off places in two ways. (1) In deference to his teacher, Alexander appointed two persons whose only job was to collect knowledge and information from all the lands through which Alexander travelled, and report it back to Aristotle. (2) Over a thousand years after his death, Europe came to know of Aristotle through Islamic theologians, who indiscriminately attributed to Aristotle various works such as the Enneads of Plotinus.

    Arius (ca. 256–336). Pastor of the Church, rejected by the First Ecumenical Council (Nicene Council, 325), restored to favour by Constantine and his successor. His teachings were rejected again as the Arian heresy.

    Arrow, Kenneth (b. 1921). Won the Nobel prize in economics. Proved Arrow's impossibility theorem that it is impossible to talk about the good of the society as a whole, except in a dictatorship.

    al-Ash'arī, Abu'l-Hasan (d. 935). A medieval Islamic theologian. Traditionalist and founder of the Asharite school of atoms and accidents, in opposition to the Mu'tazilite philosophy of rationality in theology. He renounced reason, and announced his key idea that the contentious passages of the Ku'rān must be accepted ‘without asking how’. This precipitated the debate between rationality and providence in Islam, which later moved into Western theology.

    Athanasius (ca. 293–373). Victor at the Council of Nicaea. Was declared a heretic by Constantine II, but was then restored to favour.

    Augustine (ca. 354–430). An early medieval Christian theologian, and a judge of imperial Rome in Africa, who ‘forcefully’ argued for the idea that heaven and hell last for eternity. He thought time was subjective, and further adjusted ideas of time to enable God to make black-and-white judgments. He fought against both the majority Donatist Christians and a variety of pagans, and founded Western Christian theology. He advocated the use of force to convert people, and died when invading Vandals did to his church what he and his friends had earlier done to pagan temples. This marked the fulfilment of an earlier pagan prophecy that Christianity would disappear from Africa.

    Avicenna. See Ibn Sīnā.

    Bacon, Roger (ca. 1219–1291). Recommended the use of science in the Christian Crusades against Islam, to save Christian lives.

    Bacon, Francis (1561–1626). Prophet of modern science, and Lord Chancellor of England; allowed that ‘spooky’ things like witchcraft may be explained through action at a distance. Later on Einstein, and others working on the foundations of quantum mechanics, reversed the association, and thought that anything explained using action at a distance must be ‘spooky’.

    Barrow, Isaac (1630–77). Newton's teacher and the first Lucasian Professor. He sold his books and ran away from Cambridge to return after fighting pirates on the high seas, by which time the official doctrine had changed. Was the Dean of Trinity College when Newton, the next Lucasian Professor, was denouncing the Trinity in his secret writings. He thought scientists without a clear idea of time were quacks, and he started his lectures by clarifying the concept of time. He argued for the even tenor hypothesis, usually credited to Newton.

    Bergson, Henri (1859–1941). Winner of the Nobel prize for literature. Regarded time as durée.

    Bohr, Niels Henrik David (1885–1962). One of the founders of quantum theory, and winner of the Nobel prize. His earliest model of the atom resembled the solar system, with electrons (like planets) going round a nucleus (like the sun), except that some ‘quantization conditions’ were introduced by hand to prevent the electron from falling in.

    Boltzmann, Ludwig (1844–1906). Valiantly fought to prove the entropy law from mechanics. Committed suicide, perhaps in despair over the constant opposition he faced. His work came to be widely accepted soon after his death.

    Bruno, Giordono (1548–1600). Generally considered an early scientific martyr to Western Christianity. Burned alive by the Inquisition.

    Buddha (b. −563, d. −483). Properly known as Siddhartha Gotama. Born a prince, he abandoned his kingdom and wife and child, at age 29, to find a solution to the problem of universal suffering. On finding the solution after many years of asceticism and meditation, he assumed the title of The Buddha (‘The Enlightened One’). He taught a new notion of ‘causality’ (conditioned coorigination, praticca samuppada), through understanding which one understood also the Right Way (Law, Dharma). He founded a new social order called the Sangha, where, unlike Athens, both ‘slaves’ and women were accepted as equals. For householders, he taught compassion, and the Middle Way, the probable source of Aristotle's Doctrine of the Golden Mean. The Buddha primarily rejected the authority of Tradition (‘Scripture’), and rejected en passant those who engaged in God-discourse (Ishwaravadins), and talk of Creation. Seven hundred years later, Nagarjuna rejected this more forcefully. More than a thousand years later, when the doctrine of God as the Creator started being propagated in India by Advaita Vedantins, probably under Syrian Christian influence, the Buddhists thoroughly refuted it in all its forms, including the idea of God as Intelligent Time. Buddhism spread to S. E. Asia (where it still survives in its traditional form of Theravada), to China and Japan on one side (where it survives in its more adaptive forms like Zen), and to Syria on the other side of India, and probably deeply influenced early Christianity. The Buddha was accepted as a Christian saint (St. Jesophat) by Eastern Christian sects, and also in an embarrassing Papal error by Western Christianity. The Buddha, in one of his rare predictions, had predicted the decline of Dhamma in five hundred years, and Buddhism was driven out of Syria, Iraq, and Persia by Zoroastrianism, and out of South India by the rise of Advaita Vedanta, and the rise of God-worship and the construction of a religious hierarchy after Śankara (ca. 9th century). About eight hundred years ago, ca. 1192, Nalanda one of the two major Buddhist universities in North India, which attracted students from as far off as China for hundreds of years, was destroyed by invading Muslims, and the few surviving Buddhists fled to Tibet. In modern India, Buddhism was revived by Ambedkar, a member of the Constituent Assembly and a backward caste leader, who converted to Buddhism and urged other members of backward castes to do likewise.

    Cantor, Georg (1845–1918). Mathematician best known for his work on the theory of sets, and on how to count the elements in an infinite set.

    Chuang-tzu (b. −369, d. −286). Major exponent of Taoism, and opponent of Confucianism, whose work that bears his name is considered more definitive than that of Lao-tze, the founder of Taoism. The butterfly story comes from that book.

    Curie, Marie (1867–1934). Famous for the discovery of radium, the ethical refusal to patent it, and for winning two Nobel prizes. Nominated Poincaré for the Nobel prize.

    Cārvāka. A generic term for the ‘people's philosopher’, who articulated bitter truths, rejecting both the authority of tradition and the belief in another world. They were frowned upon by all other schools of thought in India, and the Buddha himself, possibly because of the fertility rites that they encouraged. We know of them only through their opponents. The first mention of Cārvāka is in the Mahabharata epic, where he is depicted as a man who stands up and condemns Yudhiṣṭhira, during his coronation, for having killed his teacher and brothers to obtain the crown; this Cārvāka was declared a demon and an enemy agent, and killed on the spot. The traditional date for this is ca. −1000.

    Constantine (d. 337). Pagan Roman emperor, reportedly converted to Christianity, and baptised just before his death. He was superstitiously convinced by a priest that the sign of the cross on his flag was the real ‘cause’ of his martial victories; hence he extended state support to Christianity. (This is part of the ‘fraud’ to which Gibbon alludes.) He convened the first council of Nicaea to ensure religious peace in his empire, and resolve the religious disputes through collective authority.

    Darwin, Charles Robert (1809–82). Famous for the theory of evolution. Karl Marx wanted Darwin to write a foreword to Capital, unaware that Darwin had modelled his theory on Malthus, a priest whose sellout to rich merchants is also condemned for ‘school-boyish plagiarism’ in Capital. It is, therefore, not surprising that social Darwinism is as racist, ill-founded, and empirically false as Malthus’ ideas about the relative rates of growth of population and food.

    Davies, Paul C. W. (b. 1946). Did his Ph.D. in the absorber theory of radiation. Using the background material on time, he started off with an excellent expository book on The Physics of Time Asymmetry, which he followed with a number of other expository books, winning the Templeton award in 1995.

    Dirac, Paul Adrian Maurice (1902–84). An original theoretical physicist, founder of quantum theory (the Dirac equation), winner of the 1934 Nobel prize in physics, and author of a classic text on quantum mechanics which is still used. He fearlessly used the delta function to handle infinities, possibly because of his background in electrical engineering, but opined that quantum field theory was a mere coincidence like the Bohr atom, until a better way to handle infinities (arising from, e.g., squaring that function) was found. He believed that the truth was beautiful, hence he thought the beauty of a theory was more important than its agreement with facts. While formulating his own (Fermi-Dirac) statistics, he rescued S. N. Bose from the oblivion imposed by the terminology of ‘Einstein statistics’. (Einstein translated the paper by Bose into German, without pointing out some minor corrections, which he later independently published.) He used the large-number coincidences to construct a cosmological model in which the gravitational constant varied with time. In his seventies, he wrote an elegant introduction to the theory of relativity. Dirac's kind comments were decisive when I was in deep trouble for challenging my supervisor (for ‘plagiarism’) during my Ph.D.

    Drude, Paul Karl Ludwig (1863–1906). Editor of Annalen der Physik, object of Einstein's fury in 1903.

    Einstein, Albert (1879–1955). Einstein has the image of having been a super-genius and one of the greatest scientists of the century. This image is under great strain today because of the remarkably large number of frontline theories which he seemingly independently reinvented, sometimes even ‘independently’ reinventing the very terms (like relativity) used a short while earlier by celebrated authors in papers he claimed not to have read. Unlike Poincaré, but like many historians of science, Einstein did not, until his death, quite understand the full consequences of rejecting the aether (see Chapter 9, pp. 298–303).

    Eliot, T. S. (1888–1965). Eliot is a celebrated English poet. He exemplifies how the cultural revolt against linear time may eventually return to the politics of the Western church.

    Faraday, Michael (1791–1867). Untutored genius, who performed many key experiments in electromagnetic theory, and developed the intuitive idea of lines of force.

    FitzGerald, George Francis (1851–1901). Known for the contraction effect about which he first published in Science (1889). This was of so little importance to him that when Lorentz wrote to him, he could not say whether his paper had been published by Science.

    Feynman, Richard P. (1918–88). Was best liked for his Lectures in Physics, and the book Surely you are joking Mr Feynman. Expressed moral doubts about working on the atom bomb. Along with J. A. Wheeler, he proposed the absorber theory of radiation, a modified version of which was first used to formulate a tilt in the arrow of time. He also advocated Stueckelberg's proposal that positrons are electrons travelling back in time.

    Friedmann, Alexander Alexandrovich (1888–1925). Wrote a key paper on cosmology in 1922, introducing the assumptions of homogeneity and isotropy, which we still cannot quite dispense with. All three Friedmann models correspond to the big-bang theory which they inspired.

    Galileo Galilei (1564–1642). Forced by the Pope to recant from his position that the earth moved round the sun. Graciously pardoned recently.

    al-Ghazālī (1058–1111). Celebrated Islamic traditionalist and Sufi. Used reason to destroy the arguments of the rationalists (Mu'tāzilāh) and also the philosophers (mainly Ibn Sīnā [Avicenna]), in a book called The Destruction of the Philosophers. Some of his sceptical arguments were later repeated by David Hume, who recognised them as unanswerable, but Ghazālī used them to establish the role of God as Creator. He valued ethical practice above reason, and his word is practically treated as law by the orthodox (Sunni) Muslims today.

    Gibbs, Josiah Willard (1839–1903). One of the founders of statistical mechanics, along with Boltzmann. He reportedly applied these principles to the stock market to net a tidy fortune. He was one of the people whose work Einstein reinvented. His Elementary Principles in Statistical Mechanics was published in 1902.

    Gödel, Kurt (1906–78). Gödel was a metamathematician: one who theorises about mathematics, rather than does mathematics. His paper which shattered Hilbert's dream was published in 1931. He wrote very few papers, but with each paper he sought to bring about a fundamental change in the existing thinking. This was true also of his cosmological model, challenging the extension of naive ideas of time to relativity on the 40th anniversary of relativity. He went mad in his last years, and died of self-inflicted starvation.

    Grossman, Marcel (1878–1936). Einstein's friend; helped to get Einstein his job in the patent office. It was to him that Einstein turned for learning the absolute differential geometry they both used to restate the laws of gravitation. Was a popular teacher of mathematics at Berne, and wrote a very popular text.

    Hadamard, Jacques-Salamon (1865–1963). French mathematician—famous for his proof of the prime number theorem—who gave the first example of chaotic motion at the turn of the century.

    Haldane, J. B. S. (1892–1964). British geneticist, and Marxist. Moved to India and worked at the Indian Statistical Institute founded by P. C. Mahalanobis.

    Hawking, Stephen (b. 1942). Hawking is famous for singularities, and A Brief History of Time. He is the Lucasian Professor at Cambridge. He is a member of various academies including the Papal Academy of Sciences.

    Heaviside, Oliver (1850–1925). An electrical engineer who symbolically handled infinity in a way that was successful but not appreciated by most of his contemporaries. The Dirac delta function is obtained by applying his technique of differentiation to what is now called the Heaviside function. The fundamental change that this brought to the calculus is yet to be appreciated by most physicists who are still stuck with the old calculus.

    Hilbert, David (1862–1943). He worked on the foundations of geometry during 1899–1903, and on theoretical physics from 1912–15. From 1918 onwards he remained involved with the foundations of mathematics, until Gödel proved in 1931 that Hilbert's approach was not feasible.

    Hooke, Robert (1635–1702). Worked for the Royal Society. Came up with many intuitive ideas which he did not always develop systematically. He was rather unfortunately treated by his contemporaries, and subsequent historians of science for two centuries, but has again become important as a tool against Newton.

    Ibn Sīnā (980–1037). He argued for a helically quasi-cyclic time in which creativity is all-pervading, and the soul creatively evolves from minerals to the rational soul that only humans possess.

    Ibn Fārid (1181–1235). Sufi and Arab poet who abandoned a career in law to live a solitary life near Cairo, in the Muquattam hills. His best known collection of verse is the Nazm as-suluk.

    Joyce, James (1882–1941). Well-known Irish author; treated language and time in many diverse ways in his books, particularly Ulysses and Finnegan's Wake.

    Kant, Immanuel (1724–1804). Well known German philosopher and theologian who taught a truce between science and religion.

    Keynes, John Maynard (1883–1946). Neo-classical economist elected to the Royal Society. He bought Newton's papers at the Sotheby auction, and a long-term consequence of this was that some of Newton's papers finally came into the Cambridge library as part of Keynes’ papers, after his death.

    Laplace, Pierre Simon, Marquis de (1749–1827). This famous French mathematician was Napoleon's teacher, and lived very well through several revolutionary changes of government. To explain the concept of probability he invented the ‘Intelligence’ now known as Laplace's demon, possibly because of his response to Napoleon, described in Chapter 6, Box 3, p. 174 ff.

    Larmor, Joseph (1857–1942). Became well-known for his Adams Prize essay on Aether and Matter, later published as a book. Did work on the theory of electrons, roughly comparable to that of Lorentz.

    Leibniz, Gottfried Wilhelm (1646–1716). Mathematician and philosopher, involved in a priority dispute with Newton over the origin of the calculus. This three-century-old dispute has now ended with the discovery that the calculus was already invented by the time of the 14th–15th century Kerala mathematician, Madhava of Sangamagrama, whose use of ‘Taylor's’ series to compute precise sine and cosine values was widely disseminated in the 1501 manuscript the Tantrasangraha of Neelakantha, and the ca. 1530 manuscript, the Ganitayuktibhāsā of Jyesthadeva, probably brought to Europe by some Jesuits.

    Lenard, Philipp (1862–1947). A physicist whose work fascinated Einstein when his girlfriend Mileva had to face both her exams and the birth of an illegitimate child.

    Lorentz, Hendrik Antoon (1853–1928). Introduced, independently of Fitzgerald, the contraction hypothesis to explain the null result of the Michelson-Morley experiment. Shared the 1902 Nobel prize in physics with Pieter Zeeman. Was urged by Poincaré in 1900 not to make ad hoc explanations, but to adopt a single unified explanation. Introduced the idea of ‘local time’ but admittedly did not realise its conceptual significance.

    Mahavira (b. −599?, d. −527). A contemporary of the Buddha, and teacher of the Jains. He taught asceticism and extreme non-violence, so that his followers had to invent a theory of indirect causation to justify the incidental violence that may be needed to survive or to eat cooked food. A slight extension of this enabled them to integrate well with the society, and some of the richest people in India are Jains. They engaged in bitter debates with Buddhists, especially over the role of intention in judging an act.

    Marx, Karl (1818–83). Visionary author of Capital and joint author of The Communist Manifesto. He explained how the surplus produced by labourers was appropriated by capitalists, and argued that such a state of affairs, requiring the ignorance of the labourer, could not long continue. Inspired by his vision, people all over the world revolted against capitalism, so that capitalists have invested huge amounts in propagating all kinds of falsehoods and half-truths directed against him and his followers.

    Maxwell, James Clerk (1831–79). Unified the theories of electricity and magnetism and calculated the speed of light. It was his suggestion, published posthumously, which led to the Michelson–Morley experiment.

    Michelson, Albert Abraham (1852–1931). Believed that very precise experiments were necessary because future developments in physics would affect only the seventh decimal place. Awarded the Nobel prize. Nominated Poincaré for the Nobel prize.

    Michelson–Morley. Two people joined together by a common experiment first performed during five days in July 1887. Michelson's aim was to discriminate between the competing aether theories of Fresnel and Stokes by conducting very precise experiments. Most physics textbooks misrepresent this as an experiment to measure the speed of light. The experimenters concluded in favour of Stokes’ theory, a conclusion which Lorentz could not swallow because of the now-obvious mathematical absurdity of Stokes’ theory.

    Miller, Dayton Clarence (1866–1941). Miller repeated the Michelson–Morley experiment, to arrive at the opposite conclusion in 1925. For this he received a prize of a $1,000 from the American Association for the Advancement of Science. But his experimental claim was so widely disbelieved that no one even bothered to refute it for many years. His data were subjected to statistical tests only in 1950.

    Morley, Edward Williams (1838–1923). Dedicated experimenter and Michelson's partner in the famous experiment.

    Minkowski, Hermann (1864–1909). Einstein's teacher. Invented and polemically introduced the term spacetime in 1909 for what Poincaré had called 4-dimensional space in his paper of 1905.

    Newton, Isaac (1642–1727). His father died on 6 October 1642. Author of the Principia. Widely regarded as one of the founders of physics. Jesuit priests used his theory of the solar system to dazzle the Chinese with their accurate computation of planetary movements, at a time when Europe was poor and lagged in most spheres of technology behind China, India, and the Arabs. Newton's theories held sway for two and a half centuries, and he was elevated to nearly the status of God. However, ever since the publication of parts of his heretical theological manuscripts, an easily noticeable amount of effort has been made to rake up as much 300-year-old muck about him as is possible. The last page of Stephen Hawking's A Brief History of Time provides an example.

    Nietzsche, Friedrich (1844–1900). Nietzsche argued for the German aristocracy, and against socialist ideas of equality—which latter he regarded as Christian. He fell into Augustine's trap, and mistook quasi-recurrence for eternal recurrence. Eternal recurrence was the ‘very centre’ of his thinking as elaborated by Heidegger. This idea was used in the form of the (wrong) swastika symbol by the Nazis.

    Origen (ca. 185–254). A great teacher of the early (ante-Nicene) church. See text, p. 38.

    Penrose, Roger (b. 1931). Oxford mathematician, and an examiner for Stephen Hawking's Ph.D. thesis. Originally introduced singularities to prove that even non-spherical stars collapse into black holes, if they are massive enough. (It was this idea that was later extended by Hawking.) Author of Emperor's New Mind, and Shadows of the Mind, asserting that mathematical truths are universal and ‘out there’, indicating the reality and universality of his Platonic world of ideas.

    Planck, Max Karl Ernst Ludwig (1859–1947). Influential editor of the Annals of Physics, and one of the founders of quantum theory. Identified Lorentz and Einstein as the inventors of the theory of relativity.

    Poincaré, Jules Henri (1854–1912). French mathematical genius, and a popular expositor of science, also stated the complete theory of relativity ahead of Einstein. Poincaré's recommendation was sought to get Einstein his first academic job at the ETH Zurich. Poincaré also proved the recurrence theorem, and observed that chaos reconciled determinism with chance. His criticism of Hilbert's foundational programme for mathematics was amongst the factors that motivated Hilbert to identify consistency as a key requirement. He explicitly used the idea of refutability later championed by Popper. A childhood attack of diphtheria left him with physical disabilities which he turned to his advantage—unable to see the blackboard, he did all calculations in his head. He was excessively modest and, instead of claiming, generously gave credit to others for his own work—e.g., the automorphic functions he named after Fuchs or the group of transformations he named after Lorentz.

    Popper, Karl (1902–94). Philosopher of science, most well-known for his criterion of falsifiability: a thousand experiments cannot prove a theory right, but one decisive experiment may prove it to be wrong. He used this criterion to separate science from non-science.

    Prigogine, Ilya (b. 1917). Won the 1977 Nobel prize in chemistry. Has done extensive work on thermodynamics of open systems and dissipative structures. Joint author of Order out of Chaos. He believes that physics need not be changed to establish entropy increase, and that searching ever-new mathematical techniques will eventually do the trick.

    al Rāzī, Abu Bakr Muhammad Ibn Zakariaya’ (865–932). Persian philosopher, considered to have been the greatest physician of the Islamic world. His significant medical books like Kitab al-Mansuri were translated into Latin from the 12th century, and used as standard medical texts for some four centuries in medieval Western universities. In another book, Kitab al hawi, he surveyed many early systems of medicine.

    Rumi, Jalal ud Din (1207–1273). Persian mystical poet whose famous collections of poems include the Masnawi, the Diwan-i-Shams-i-Tabriz, the Diya-al-Haqq.

    Shah Jehan (1592–1666). Moghul Emperor 1628–58 who ordered the building of the Taj Mahal, as a tomb for his beloved Mumtaz Mahal.

    Schwarzschild, Karl (1873–1916). Obtained the first rigorous solutions (black-hole solutions) of the gravitational field equations.

    de Sitter, William (1872–1934). Proposed several cosmological models, one with closed time-like curves, and one known as the Einstein–de Sitter model. Ahead of Hubble, he related cosmic expansion to stellar redshift.

    Spengler, Oswald (1880–1936). A high-school teacher who abandoned his position, to live a penurious life writing The Decline of the West, to communicate this grand idea that he had. His communication was an instant success, and his forecasts still continue to trouble sensitive Americans like Gerald Holton. Toynbee, in his monumental work, laboriously reworked the same basic idea, in a more parochial way that Spengler had rejected.

    Tipler, F. J. (b. 1947) A mathematical physicist at Tulane University in the USA, who has actively participated in many controversies, such as one claiming that intelligent extra-terrestrial life cannot possibly exist in the galaxy.

    Toynbee, Arnold Joseph (1889–1975). Historian and author of the twelve-volume A Study of History. The abridgement into 2 volumes captures the key ideas in Toynbee's own words. Some of the original ideas are like this: the disintegration of civilisations has a rhythm of 3 1/2 notes on the musical scale: rout-rally-rout-rally-rout-rally-rout.

    Thorne, Kip (b. 1940). Relativist at Caltech, and a student of Wheeler, worked in many areas including shock waves. Wrote an influential text on relativity along with Wheeler. More recently he became prominent for his work on time travel.

    Turing, Alan. (1912–54). British mathematician and logician, initially conceived his machine as a computing device that would infallibly recognise undecidable propositions. Concluded that it would need an infinity of time, i.e., that his machine would not halt on an undecidable proposition.

    Wells, H. G. (1886–1946). The father of modern science fiction, studied under T. H. Huxley. The Time Machine, whose author crash-lands in 802701 was his first major novel.

    Wheeler, John Archibald (b. 1911). Worked with the team that designed the first hydrogen (fusion) bomb in the USA. Teacher to a generation of influential physicists including Feynman and Kip Thorne. Proposed, along with Feynman, the absorber theory of radiation. Proposed the idea of quantum foam used by Thorne to make time travel plausible.

    Whitehead, Alfred North (1861–1947). Joint author with Bertrand Russell of the Principia Mathematica. Believed in a ‘process view’ of time, along with Henri Bergson.

    Whittaker, Sir Edmund Taylor (1873–1956). Elected a Fellow of the Royal Society in 1905 for his work on the Laplace equation and for having originated the confluent hypergeometric function, still widely used in mathematical physics. By that time he had already written a text on mathematical analysis, and a treatise on classical dynamics. The second volume of his History of Aether and Electricity published in 1953, 43 years after the first volume, was intended to cover the new developments in the first quarter of the 20th century.

    Wigner, Eugene Paul (b. 1902). Dirac's brother-in-law and winner of the Nobel prize for Physics in 1963. He pioneered the use of symmetry groups in physics. His basic observation of 1935, which he proved in 1971, established that quantum probabilities are fundamentally different from classical probabilities. In 1967 he published two papers asserting (incorrectly) that one could continue with instantaneity in the presence of advanced interactions.

    Zeeman, Pieter (1865–1943). Dutch physicist who observed in 1896 that if sodium is burnt between strong magnetic poles, the sharp yellow lines (D-lines) in its spectrum are broadened (through splitting into multiple lines). Awarded the Nobel prize in 1902, jointly with Lorentz.

    Dates

    A ‘non-linear’ chronology of human beliefs about time covered in this book.

    < −600, throughout the world. Belief in life after death in the physical context of quasi-cyclic time.

    ca. −600 to ca. −450, India. Rejection of quasi-cyclic time. Lokāyata: immediate present as the only reality. Rise of materialism, and collapse of values: e.g., Ajātashatru seizes kingdom by chaining his father Bimbisāra, and allowing him to starve to death. Seeks a convincing answer to the rewards of asceticism in this world.

    ca. −500, India. The Buddha expounds a new idea of ‘causation’: paticca samuppāda (conditioned coorigination) and its relation to the ‘Law’ (Dhamma), and to a truly democratic social order (samgha) and the compassionate Way of Life (Middle Way), beginning with five listeners at Gaya. Mahavira teaches extreme non-violence.

    ca. −450, India. Pāyāsi, the sceptical king, explains his 40 experiments with life after death, but converts to Buddhism after a long debate with Kumara Kassapa, the boy-Wanderer, and disciple of the Buddha.

    ca. −399, Athens. Plato's character, Socrates, peacefully consumes hemlock, firmly believing in life after death, and chides his well-wishers for their sorrow.

    ca. 200, India. Nagārjuna argues the absurdity of the belief in God and Creation. Regards the world as flux. Reassertion of conditioned coorigination and the Middle Way. Beginning of the sunyavāda philosophy currently incorporated in Zen Buddhism.

    ca. 250, Alexandria, Africa. Origen teaches quasi-cyclic time mentioned in the Bible, along with one-ness with God, both accepted by the ordinary people as well as the scholars of Alexandria.

    ca. 325, Istanbul. Constantine convenes council of Nicaea to decide what good Christians ought to believe. Athanasius prevails over Arius who is declared a heretic; the calendar is standardised to fix the dates of Easter.

    ca. 391, Alexandria. Burning down of the magnificent temple of Seraphis and the adjacent Great Library of Alexandria by rampaging Christian mobs, led by Bishop Theophilus who was later declared to be a saint.

    ca. 400, Thagaste, Africa. Augustine's rejection of quasi-cyclic time through confusion with eternal recurrence. The birth of the dichotomy between ‘linear’ and ‘cyclic’ time, and the doctrine of the eternal estrangement of Man from God in Western Christianity.

    ca 415, Alexandria. Hypatia lynched in a church by a Christian mob sent by Bishop Cyril of Alexandria, Theophilus’ nephew. Cyril is subsequently sainted.

    ca 460, Proclus of Alexandria composes a remarkable work explaining mathematics, especially geometry, as a religious discipline. Attributes authorship of some novel aspects of his work to a Euclid of Alexandria, who lived seven centuries before him but somehow remained unknown to all earlier commentators on geometry.

    ca. 529, School of Alexandria shut down by Justinian's edict banning the teaching of philosophy throughout his empire. Many scholars flee to Iran.

    542–553, Istanbul. Justinian curses ‘cyclic’ time. Convenes the 5th Ecumenical Council which concurs. This solidifies the stereotype identifying ‘cyclic’ time with ‘pagans’ and ‘linear’ apocalyptic time with Christianity.

    499, Ujjain, India. Aryabhata completes his Aryabhatīya, accurately setting out the length of the sidereal year and the dimensions of the earth, and arguing that the earth revolved on its axis. Among very many other things, he also gave a table of 24 sine and cosine values, and a value of π accurate to 5 decimal places.

    ca. 500, University of Nalanda, India. Dinnāga teaches a new logic of the Wheel of Reason, introducing logical quantifiers in a way compatible with the Buddhist teaching of transitoriness and conditioned coorigination. Bhadrabahu the Junior formulates his ten-limbed syllogism.

    ca. 750, North India. Decisive rejection of Creation by a variety of possible creators, including Time, reasserted by the Buddhists Śāntarakṣita and Kamalasīla.

    ca. 750, India, especially South India. Rise of Advaita Vedanta. Reassertion of quasi-cyclicity by Adi Śankara of Kaladi.

    ca. 750–850, Baghdad. Assertion of quasi-cyclicity and divine unity by Sūfī-s. Perhaps under Advaita Vedantic influence, Abu Yazīd al Bistāmī asserts ‘I am God, so worship me’.

    ca. 913, Baghdad. The Sūfī, al-Hallāj whipped, mutilated, crucified for 3 days, and then decapitated for asserting ‘I am the Truth’. Composes beautiful verses on the gibbet.

    ca. 750, Basra. Rise of Mu'tazilah school of Islamic rationalists. Seek to deduce everything from the two premises of divine unity and justice.

    ca. 825, Baghdad. Attempt to enforce the Mu'tazilah line of thinking by the State.

    ca. 900, Baghdad. al-Ashārī, atoms and accidents used to consolidate the tradition needed for Abbasid jurisprudence.

    ca. 1000, Baghdad. Rise of philosophers in Islam. Ibn Sīnā (Avicenna) asserts helical quasi-cyclicity. Al-Razi (Rhazes) speaks of the ‘Wheel of Birth’.

    ca. 1100, Baghdad. Destruction of the philosophers in Islam by al-Ghazālī; assertion of ontically broken time. Rise of Sūfī doctrine of Grace. Baghdad falls to Moghuls.

    ca. 1180, Seville. Ibn Rushd (Averröes) attempts to refute al-Ghazālī.

    ca. 1200. Ibn ‘Arabī and Rūmī poetically continue the idea of helical quasi-cyclicity, creative evolution, and mystic union with God.

    ca. 1192, India. Sack of the University of Nalanda by Bakhtiyar-i-Khalji. Nalanda's seven storied library razed, and all manuscripts accumulated over a thousand years burnt; survivors flee to Tibet. Bakhtiyar-i-Khalji pursues them, but is defeated and returns with only a hundred men. Eclipse of Buddhism in India. Rise of Sufism and Bhakti.

    ca. 1255, Paris. First universities commence in Europe. Censored form of Ibn Rushd's commentary on Aristotle accepted as a text at the University of Paris. Debate on Rationality and Providence inherited by Christian theology from Islam. Misrepresentation of al-Ghazālī. Thomas Aquinas repeats some of Ibn Rushd's arguments, in his tract against Averröes, and partially rejects Providence in trying to reconcile Averröes’ ‘Aristotle’ with Augustine. Rise of Scholasticism in Europe.

    1453, Istanbul. Fall of the Byzantine Empire. Church of St Sophia converted to a mosque. Greek translations of Arabic texts diffuse into Europe, inspiring the Copernican revolution.

    ca. 1400. Mādhava of Sangamagrāma near Cochin, a member of the Aryabhata school of mathematics and astronomy, uses the ‘Taylor-series’ expansion of calculus to calculate sine tables to 9 decimal-place accuracy.

    1498. Vasco da Gama, not knowing celestial navigation, reaches Calicut, near Cochin, from Melinde in Africa, with the help of an Indian pilot Malemo Cana.

    1501. Neelkantha Somayaji, another follower of Aryabhata, completes his book Tantrasangraha. He used a ‘Tychonic’ model of planetary orbits.

    ca 1530. Jyeshtadeva compiles the Ganitayuktibhāsā, setting forth the rationale used by Madhava.

    ca 1540, Goa. All Hindu temples in Goa destroyed.

    ca. 1555. Inquisition set up in India in the Portuguese territory of Goa.

    1567. Spanish government offers a prize for anyone who can provide a reliable method of navigation.

    1581. The Jesuits prepare a mission for Akbar's court, in the hope of controlling India by converting Akbar, a la Constantine. The Jesuit Matteo Ricci writes from India about his search for an ‘intelligent Brahmin or an honest Moor’, to explain the local ways of keeping time.

    1582 (5 October). Gregorian calendar reform: Europe needs a good calendar to tell the latitude from measurement of solar altitude at noon. This requires a change in the date of Easter. Pope Gregory issues a bull based on the changes proposed by the committee headed by Christoph Clavius, which collected information on the calendar from various sources including India.

    1598. The problem of determining longitude persists, and the Spanish government increases its reward. Galileo competes unsuccessfully for this reward for 15 years.

    1636. The Dutch government offers a reward for a method of navigation at sea.

    1640, Rome. Galileo forced to recant by the infallible pope.

    1666. Colbert writes to leading scholars in Europe, offering rich rewards for a method of navigation. French Royal Academy formed from the replies he received. British Royal Society formed a little later.

    ca. 1665. Cambridge. Isaac Barrow reasserts the dichotomy between ‘linear’ and ‘cyclic’ time.

    1672. Picard redetermines the size of the earth, correcting Columbus’ motivated rejection of the earlier accurate Indo-Arabic estimates. Solves the problem of determining longitude on land, using the telescope to improve the earlier Indo-Arabic method of eclipses.

    ca. 1685, Cambridge. Newton publishes Principia. Thinks that God has revealed to him His Laws, and that providential interventions are still needed.

    1711. British government declares a prize for determination of longitude at sea.

    1762. With a chronometer (robust and accurate clock), a carpenter called Harrison claims the British prize for determining longitude at sea.

    ca. 1800, Europe. Able to measure time accurately, and navigate, Europe first gains a lead in technology, and starts prospering. Rise of racism.

    ca. 1800, Paris. Laplace proves the stability of the solar system; banishes Providence, and inadvertently gives birth to Laplace's demon.

    ca. 1658, Delhi. Moghul prince and Sūfī, Dārā Shūkoh translates the Upanishads into Persian.

    ca. 1808, Hamburg. Schopenhauer reads a retranslation of the Upanishads from Dārā Shūkoh's translation. Calls it the greatest comfort of his life.

    ca. 1880, Germany. Nietzsche uses physics to prove statistical recurrence. Proposes a superman needed to transcend eternal recurrence.

    1858 (1 July), London. Charles Darwin and Alfred Russel Wallace jointly communicate the theory of evolution to the Linnaean Society.

    ca. 1885, England. The debate between T. H. Huxley and the Bishop Wilberforce on the theory of evolution. Karl Marx's Capital, Vol. II published.

    ca. 1895, London. H. G. Wells’ Time Machine published.

    1898–1905 (5 June), Paris. Complete theory of relativity formulated, named, and published by Poincaré. Decisive rejection of Newtonian time.

    1905 (September), Berne. Identical theory of relativity, with the same name, published by Einstein in Annalen der Physik (sent end-June 1905), then a patent clerk, who admitted seeing only some of Poincare's works, raising profound legal questions about priority in patenting. Einstein claimed he independently invented the theory in five weeks.

    1915 (15 November), Gottingen. David Hilbert formulates the equations of the general theory of relativity and communicates this to Einstein, who announced the independent rediscovery of essentially the same equations five days later.

    1931. Publication of Gödel's proof of the impossibility of Hilbert's metamathematical programme of mechanical proofs. Gives a definition of ‘mechanical’.

    1945, Japan. Atomic bomb dropped over the civilian population in Hiroshima, demonstrating a practical application of relativity. Claimed as a great success by the United States. Einstein responds indifferently.

    1948. The first part of Wheeler and Feynman's article on the absorber theory published. (The second part of the article had already appeared in 1945.)

    1948. Publication of Gödel's paper on cosmology presented in a symposium to celebrate the 40th anniversary of relativity.

    1951. First resolution of the infinities of quantum electrodynamics.

    1963. Publication of the Lorenz model for chaos.

    ca. 1968. Experiments to detect tachyons.

    ca. 1980. Scientists write popular accounts implicitly and explicitly bringing out the unity of science and ‘religion’ (= Western Christianity). Stephen Hawking's A Brief History of Time published. This new harmony requires an emphatic rejection of quasi-cyclicity and acceptance of creation with a bang in scientific theory.

    1985. Publication of Thorne's paper claiming the possibility of time machines.

    1990–91. End of the Cold War. Fall of the Berlin Wall. Collapse of the Soviet Union.

    1993, Vatican. The Pope pardons the dead Galileo, signalling a remarriage between science and ‘religion’.

    Glossary

    action by contact. The belief that interacting particles must be in physical contact with each other.

    aether. 1. An imaginary fluid whose particles provided contact between separated interacting bodies (like the moon interacting with the sea to produce tides). 2. By implication a reference to define absolute velocity.

    anathema. The great curse of the church, excommunicating and damning a doctrine or person.

    anticipation. The time-symmetric analogue of memory; future-dependence as opposed to history-dependence.

    apocalyptic time. Time as supposedly revealed to ‘prophets’, especially of the doomsday kind. Apocalyptic time begins with creation, focuses on the doomsday—when God apocalyptically reveals himself to all creatures—and then bifurcates to heaven and hell. Arian. A supporter of Arius, in the dispute between Arius and Athanasius in the Council of Nicea (First Ecumenical Council). By implication, one who rejects the Nicene creed, hence the Roman Catholic and Protestant churches, and would like to revert to the faith of early Christianity.

    bilking. Cheating in the game of cribbage. By implication, producing something from nothing.

    capitalism. A way of organising society so that means of production are privately owned. The traditional merchant only trades commodities produced by others; the capitalist controls the production process. Control of the production process allows him to enter into a systematically unequal exchange with labour: paying them the minimum needed for their subsistence and appropriating the surplus that they produce. Systematically unequal exchange leads to a concentration of wealth (capital), hence power, in the hands of a few individuals. While Karl Marx emphasised the unjust nature of this organisation, and its consequent instability, Max Weber, in a Machiavellian move, emphasised its harmony with the ‘Protestant ethic’: Protestants saw wealth, like caste, as a sign of divine grace. Ronald Reagan summarised the resulting system of ‘morality’: ‘rich people are good because they have money’.

    causality. 1. (Physics.) The belief that every event has a prior cause. This ‘cause’ is usually identified with initial data. 2. (Morality.) The belief that prior causes of events are the choices and actions of individual human beings.

    chance. As in games of chance like roulette, where individual outcomes cannot be systematically calculated, but a large number of outcomes have a pattern regular enough to be measured by probability—so that the house is assured of its profit!

    chaos. Sensitive dependence on initial conditions makes it difficult to predict the future state of a chaotic system. In some situations, a chaotic system may behave in an orderly way corresponding to the mythical emergence of order from chaos.

    Christianity, official.See official Christianity.

    correlation. Mutual relation or ‘co-relation’ (usually linear), distinct from a causal relation. For example, a student's marks in mathematics may correlate with her marks in language; but good marks in one subject are not the cause of better marks in another.

    complexity. Specifically algorithmic complexity. For a sufficiently complex system, an algorithm (rule-based procedure) may need infinite time for successful execution.

    counterfactual. The use of propositions contrary to fact to enable allocation of credits by implication, e.g., ‘Had there been no British Empire, India wouldn't have been united.’

    diastema. An interval or space between two successive musical notes, which could go unperceived. Hence, the unperceived, timeless gap between two discrete instants of time.

    declination. Angle which measures the north-south displacement of a celestial body (sun, moon, stars) relative to the celestial equator. (The celestial equator is the circle in which a plane through the earth's equator cuts the celestial sphere.)

    deontic logic. De-ontic logic concerns de-ontic or ‘ought’-type statements (rather than ontic or ‘is’-type statements). Hence, a logic suited to moral reasoning.

    dichotomy. Division into a pair (of opposites), such as the moral dichotomy which divides people into ‘good’ and ‘bad’. A bad dichotomy results in false similarities and conflicts: one may club as ‘bad’ an occasional liar with a mass murderer. A dichotomy between science and religion clubs all religions into one category. The dichotomy between ‘linear’ and ‘cyclic’ time clubs vaguely similar pictures of time into one class.

    ecumenical. From the Greek oikumene meaning the inhabited world; hence something which includes the entire inhabited world. An ecumenical council, therefore, was one which supposedly had representatives from the entire inhabited world. In practice, since the church historian Eusebius, the term has always been used in a way that excluded most of the inhabited world.

    entropy. A measure of disorder, explained in the text (Chapter 6).

    epistemic. Pertaining to knowledge.

    epistemically broken time. The belief that a connection between two successive states of the world may exist (e.g., in physical law or in the mind of God) but may not be known.

    eschatology. From the Greek eschaton (= last) + logos (= knowledge). Hence, knowledge of last things, specifically the four last things in Christian theology: death, judgment, heaven, and hell.

    equinox. From equi (= equal) + noct (= night), hence equal nights. 1. Either of the two times in the year when the Sun is directly above the equator, and days and nights are of equal duration. The vernal or spring equinox, around 21 March, occurs when the sun moves north across the equator, and the autumnal equinox around 23 September, when the sun crosses the equator, moving south. 2. Either of the two points in the sky where the path of the sun intersects the celestial equator. In this sense, the vernal equinox is also called the first point of Aries, and the autmnal equinox is also called the first point of Libra.

    exegesis. Exposition of the intended meaning of a difficult passage of the Bible.

    finger measurements. A traditional way of measurement, also used to determine latitude by measuring the (angular) altitude of the pole star above the horizon, using the fingers of one hand held at a distance of one span measured from the observer's nose.

    gee. On the surface of the earth, freely falling bodies (neglecting air resistance, etc.) fall with a constant acceleration, traditionally represented by the symbol g. One gee is thus the normal acceleration experienced on earth, and two gees is twice that.

    gnomon. From the Greek gnomon (= indicator). Stick stuck vertically on the ground to cast a shadow, usually to determine time as in a sundial.

    hermeneutics. From the Greek hermeneus (= interpreter; in Greek mythology, Hermes carried messages between the gods). Hence, study of the principles used to interpret the Bible, as distinct from its practical exposition (= exegesis).

    homoiousian. From the Greek homoios (= like) + ousia (= substance, essence). Hence, one who believes that Christ is of like substance, but not identical, with God.

    homoousian. From the Greek homos (= same) + ousia (= substance, essence). Hence, one who believes that Christ is not only similar, but identical with God.

    immortality. The meaning varies with the context. In Western Christian theology, ‘immortality’ refers to eternal existence in the flesh after the day of judgment. With quasi-cyclic time, ‘immortality’ means eternal cessation of existence in the flesh.

    instantaneity. The belief that the state of the world at the next instant is decided by its state at this instant. Hence the belief that physical law must be a differential equation (as distinct from, e.g., a delay or functional differential equation).

    man. Certainly includes woman, but usually used in a way that includes also all of life. The English language, being sexist, offers no appropriate alternative to this word.

    Merchant. The Merchant is obviously a metaphor for a capitalist, despite the danger that this metaphor obfuscates the very important difference between the Merchant and the capitalist, namely that the capitalist, unlike the actual traditional merchant, controls the production process.

    metempsychosis. From metem (= change) + psyche (= soul), hence a change of soul or rebirth. This euphemism is objectionable since bodies, not souls, are supposed to change at rebirth.

    modus ponens. A basic rule of inference. Also the name of a syllogism of Aristotelian logic, explained in the text and appendix, and much used in current mathematics. See alsosyllogism.

    official Christianity. It is easier to explain this in terms of who is not an ‘official Christian’. Those who believe that poverty is both unjust and man-made, and do not ascribe to God various social hierarchies and power relations are NOT ‘official Christians’. This new term is needed since current sectarian classifications—‘Protestants’, ‘Catholics’, etc.—do not capture the point of view of this book, and there are various shades even within, say, Liberation Theology. The term does not automatically exclude those who hold office: Paulos Mar Gregorios, for example, held high office, but was not an ‘official Christian’.

    ontic. Concerning what really is.

    ontically broken time. The belief that (at times) there really is no connection between two successive states of the world.

    order. The negative of entropy (= disorder).

    pagan. Originally, a ‘villager, rustic, civilian, non-militant’. Christians who called themselves ‘enrolled soldiers’ of Christ, members of his militant church, applied this term to non-Christians, particularly in the Roman empire. Despite theological denials, this is one of those words which spells out the character of Augustinian Christianity as an imperial and urban religion of the Roman empire.

    phlogiston. European scientific theories of heat in the eighteenth century associated this imaginary substance with combustion (fire).

    photon. Particle of light. Also a wave.

    pre-existence. Another euphemism for rebirth. By referring only to past lives, this leaves open the possibility that the present existence may still be the last one before apocalypse, as theologically required.

    probans. Presumably an alternative spelling of ‘probands’. From the Latin probare (= to probe, to test, to examine, to prove). A proband is an individual proposition chosen to study some generic trait. This term indicates the kinds of obscurities that arise when a Pali text translated into Tibetan is translated into English, by an Indian or Chinese translator who understands them using the Greek organisation of logic, and the Latin vocabulary with which that was studied in medieval Europe.

    proof. A valid argument according to Euclidean or modern Western logic, defined and explained in the text and appendix.

    providence. The belief that God acts through direct divine intervention. The belief in miracles.

    quasi truth-functional logic. A logic in which truth-values may not be prescribed at all, in contrast to a 3-valued logic where a sentence may be ‘true’, ‘false’, or ‘indeterminate’.

    rational theology. 1. (Islam.) The belief that one must exercise one's mental faculty (aql) to understand the word of God (kalām) in the K'urān. Opposed by those who believed that God may intervene directly in the world. Hence rational physicians deduced their line of treatment from general principles. 2. (Western Christianity.) Conceived as the attempt to convince by argument (reason) those who did not accept the authority of the scripture. Hence the belief that God runs the world through laws which the world is obliged to obey, and not through acts of direct intervention.

    refutability. Also called falsifiability, and championed by Popper; has two senses. 1. (Logical refutability.) An assertion is physically meaningful only if there are some circumstances in which it could conceivably be false. 2. (Empirical refutability.) An assertion is empirically refutable if an actual experiment can be carried out to test whether the assertion is true or false.

    ROM. Read Only Memory. A program burnt into the ROM is a program with which the computer comes to life, when it is switched on. Analogous to genetically programmed reflexive behaviour.

    seif dunes. From the Arabic ‘seif’ meaning sword. Huge orderly chains of sand dunes, visible from space, and too large and unlike the dunes formed by wind action.

    SF. Depending upon the context, this abbreviation denotes science fiction, or science fantasy, or speculative fiction.

    sidereal. From the Latin sidus (= constellation, star). Relative to the stars. The sidereal year is the time taken by the sun to return to the same position relative to the stars. This is more than 365 1/4 days, being 365 days 6 hours 9 minutes and 10 seconds, while the tropical year is less than 365 1/4 days, The traditional Indian calendar uses the sidereal year, while the Indian calendar approved by the Government after Independence is the Gregorian calendar, based on the tropical year.

    singularity. Widely regarded as a beginning or end of time, but may not actually be either.

    solstice. 1. Either of the two times in a year when the sun is farthest north or farthest south. At summer solstice, around 22 June, the sun reaches its maximum declination of about 23 degrees 27 minutes, since the rotational orbit of the earth is inclined to its orbital plane at an almost constant angle of about 66 degrees 33 minutes. At this time, the sun is directly above the Tropic of Cancer (latitude 23 degrees 27 minutes north). At the winter solstice around 22 December, the sun is directly above the Tropic of Capricorn (so it is summer there). 2. Either of the two points in the sky representing the sun's maximum deviation north or south.

    spontaneity. Causal inexplicability, in principle. Differs from chance, for no pattern need emerge even in a large number of cases. Further, spontaneity creates order while chance is believed to destroy order (create entropy).

    stochastic. From the Greek stochastikos (= to aim, to guess). Hence, concerning chance in the sense of probability.

    struthious. Ostrich-like.

    supercyclic time. The belief that time may be pictured as a circle. Analogous to a closed chain of causes. Also analogous to exact, eternal return, or an exactly periodic cosmos. Cannot be described naturally in natural language for reasons explained in the text.

    superlinear time. The belief that time may be represented by numbers on the real line.

    syllogism. An argument (or template for an argument) expressed using a (fixed) number of propositions, including a premise, and a conclusion. In Aristotelian logic the syllogism had three propositions.

    tachyon. From the Greek tachys (= fast). Hypothetical particle that travels faster than light. Tachyons have many strange properties: for example an infinite force is needed to slow a tachyon down to the speed of light.

    teleology. From the Greek telos (= end), hence the study of ends or final causes, related in Western theology to God's design of the world. More generally, a teleological explanation explains from future causes or purposes: e.g., the purpose of survival.

    tilt. Abbreviation of ‘a tilt in the arrow of time’. A picture of time in which most physical processes are history-dependent, but some are anticipatory.

    transmigration. The migration of the soul across bodies, hence rebirth. Connotes transmutation, or a change of species, hence the possibility of the soul migrating to animal bodies and vice versa. Also connotes transmogrification: a strange or grotesque transformation.

    tropical year. The tropical year of 365 days 5 hours 48 minutes and 46 seconds is the time taken for two successive occurrences of the vernal equinox. This is the year used in the Gregorian calendar.

    utilitarianism. Originally the doctrine that the greatest good of the greatest number should guide conduct; reinterpreted as a doctrine of the intelligent pursuit of self-interest; and nowadays often used as a doctrine of plain selfishness.

    vernal equinox. The equinoxes are the two days in a year when day and night are of equal duration. Vernal refers to the arrival of spring. This occurs around March 21, and relates to the date of Easter.

    West. On the earth, east and west are relative, and Rome was to the West of Constantinople (Istanbul), the shorter way round the earth. The Roman church followed Augustine's theology, creating a division between Western and Eastern Christianity—a division that later broadened into a division between Western Christianity and everyone else. According to Toynbee, every universal state must have a universal church, and Western Christianity is the religion associated with the only surviving universal state. This is the West for which capitalism is a cultural value according to Huntington.

    world. A logical world is ‘all that is the case’: a collection of propositions declared to be true, so that either a proposition or its negation is true.

    wormhole. A ‘tunnel’ through spacetime which links otherwise distant regions. The tunnel is comfortable enough for human beings to travel through, so the wormholes that concern us are also called TWISTs: Traversable Wormholes In Space Time.

    Notes

    1. gTranslation modified from Swami Prabhavananda and Frederick Manchester, trans., The Upanishads: Breath of the Eternal, Mentor, New American Library, New York, 1957, pp. 15–16.

    2. George Gallup Jr. and William Proctor, Adventures in Immortality: A Look Beyond the Threshold of Death, Coorgi Books, London, 1984. Samples were stratified geographically, and by community size. The belief in this ‘great American superstition’ declined from 77 per cent in 1952, to 75 per cent (non-whites 54 per cent, non-Christians 37 per cent, Jews 17 per cent) in 1965, to 67 per cent (scientists 32 per cent) in 1981.

    3. T. W. Rhys-Davids, trans., Dialogues of the Buddha, vol. 2, London, 1910, pp. 346–74. Reprinted by the Pali Text Society, Sacred Books of the Buddhists, vol. 2, ed. F. Max Muller, Routledge and Keagan Paul, London, 1977. Reproduced in Cārvāka/Lokāyata: An Anthology of Source Materials and some Recent Studies, ed. Debiprasad Chattopadhyaya and Mrinal Kanti Gangopadhyaya, ICPR, New Delhi, 1990, pp. 8–31.

    4. J. L. Head and S. L. Cranston, eds., Reincarnation: An East-West Anthology, Theosophical Publishing House, Wheaton, 1968, p. 102.

    5. Codex Vaticanus. In Antiquities of Mexico, ed. Lord Kingsborough, London, 1833–48, p. 240.

    6. H. A. Giles, trans., Selections from the Upanishads and the Tao-Te-King, Cunningham Press, Los Angeles, 1951, p. 91. The butterfly, incidentally, is not a substitutable symbol. The Chinese word for soul is hun, connoted by the Chinese word and symbol for ‘butterfly’ (huj). See N. J. Giradot, Myth and Meaning in Early Taoism, University of California Press, Berkeley, 1983, p. 308. For a more recent review of Chinese ideas of life after death, see Gary Arbuckle, ‘Chinese Religions’, in Harold Coward, ed., Life after Death in World Religions, Sri Satguru Publications, New Delhi, 1997, pp. 105–24.

    7. As recorded by Plato, Meno, 81–83. The Dialogues of Plato, trans. B. Jowett, vol. 7 of Great Books of the Western World, R. M. Hutchins, ed. in Chief, Encyclopaedia Britannica Press, Chicago, p. 180. As a firm believer in this theory, Socrates peacefully sipped hemlock, chiding his followers for their sorrow.

    8. Proclus, A Commentary on the First Book of Euclid's Elements, trans. Glenn R. Morrow, Princeton University Press, 1992, 45, p. 37.

    9. Proclus, Commentary on Euclid's Elements, 47, p. 38.

    10. From E. Dowden, The Life of Percy Bysshe Shelley, vol. 1, London, K. Paul Trench & Co., 1886; anecdote quoted from his friend Hogg. As quoted in J. Head and S. L. Cranston, eds., Reincarnation: An East-West Anthology, cited earlier, p. 129.

    11. J. Ducasse, Nature, Mind, and Death, Open Court, La Salle, Illinois, 1951.

    12. T. W. Rhys-Davids, trans., Dialogues of the Buddha, cited earlier, vol. 1, pp. 73–74; quoted in D. P. Chattopadhyaya, Lokāyata: a Study of Indian Materialism, People's Publishing House, New Delhi, 1973, p. 510. See also, Maurice Walshe, The Long Discourses of the Buddha: A Translation of the Dïgha Nikāya, Wisdom Publications, Boston, 1995, p. 96. Incidentally, this outburst was unconnected with the question posed by the philosopher-king Ajātasattu, who stated that this reply was as relevant to his question as a man when asked about a mango responds by talking about a bread-fruit tree. Ajātasattu's question is taken up in more detail in Chapter 11.

    13. Majid Fakhry, History of Islamic Philosophy, Columbia University Press, 1970, pp. 156–60.

    14. Krishna Chaitanya, A History of Arabic Literature, Manohar Publications, New Delhi, 1983, pp. 98–99.

    15. Krishna Chaitanya, cited above.

    16. R. A. Nicholson, trans., Translations of Eastern Prose and Poetry, Curzon Press, London, 1987, p. 155. See also Henry Corbin, Cyclical Time and Ismaili Gnosis, Keagan Paul, London, 1983. A controversy exists about Sufi beliefs in transmigration; see, e.g., Margaret Smith, ‘Transmigration and the Sufi-s’, Muslim World, 30, 1940, pp. 351–57; Jane I. Smith and Yvonne Y. Haddad, The Islamic Understanding of Death and Resurrection, SUNY, Albany, 1981; A. J. Arberry, Reason and Revelation in Islam, George Allen and Unwin, London, 1957, pp. 38–39. For more details and the pointlessness of this controversy, see C. K. Raju, ‘Time in Medieval India’, in D. P. Chattopadhyaya and Ravinder Kumar, eds., Science, Philosophy and Culture, part 2, PHISPC, New Delhi, 1997, pp. 253–78, reprinted in Indian Horizons, 46(4) and 47(1), October 1999-March 2000, pp. 40–71.

    17. Farid al-din Attar, Muslim Saints and Mystics, trans. A. J. Arberry, Arkana, 1990, pp. 117–18.

    18. R. A. Nicholson, trans., Studies in Islamic Mysticism, Cambridge University Press, 1921, p. 257, emphasis mine. The emphasis suggests that the rejection of the theory was only partial.

    19. J. M. E. McTaggart, Some Dogmas of Religion, London, 2nd ed., 1930, p. 125.

    20. Those who find this difficult should naturally consult the excellent description by Lewis Carroll!

    21. This point about everything being exactly the same has been an endless source of confusion in the West, because of its ideological connotations. In particular, the following remark of Eudemus of Rhodes attributes this belief to Pythagoreans: ‘Everything will eventually return in the self-same numerical order, and I shall converse with you staff in hand, and you will sit as you are sitting now, and so it will be in everything else; and it is reasonable to assume that time too will be the same.’ [H. Diels and W. Kranz, Fragmente der Versokratiker, 6th ed., Berlin, 1951, 58B34; cited by Milic Capek in Encyclopaedia of Philosophy, article on ‘Eternal Return’.]

    22. One could estimate this ‘long time’ at around 80 billion years. The physical significance of such a large time-span is, however, unclear: for example, there may be no proper clock by which to measure it, even if time does not ‘stop’ or start running backward. Even less does this figure have any subjective significance: for there can be no conscious appreciation of the time elapsed between death and rebirth.

    23. F. Nietzsche, Eternal Recurrence, 33. Translation adapted from O. Levy, ed., The Complete Works of Friedrich Nietzsche, vol. 16, Foulis, Edinburgh, 1911, p. 253.

    24. The Buddhists doubt the continuation of identity across two instants of time; but such doubts are postponed to Chapters 11 and 12.

    25. See, for example, C. K. Raju, Time: Towards a Consistent Theory, Kluwer Academic, Dordrecht, 1994 (Fundamental Theories of Physics, vol. 65), chap. 4. Or, ‘On Time IV: Thermodynamic Time’, Physics Education, 9(1), 1992, pp. 44–62.

    26. The Bhagvad-Gita, trans. Swami Prabhavananda and Christopher Isherwood, Martin Rodd, Hollywood, 1945.

    27. The Vishnu Purana, trans. H. H. Wilson, London, 1840, reprint, with an introduction by R. C. Hazra, Punthi Pustaka, Calcutta, 1961, chap. 3, pp. 19–24. The reduction proceeds through equations of the type ‘1 year of mortals = 1 day of the gods’. Astronomers in the Indian tradition justified this equation by appealing to the picture of a spherical earth, ‘surrounded on all sides by creatures just as the bulb of the kadamba flower is by blossoms’. They regarded day and night as due to rotation relative to the cosmic sphere, on a north-south axis, so that day and night at the poles are six-months each. The gods were supposed to stay on Mount Meru, located at the north pole, so that one day and night of the gods quite literally amounted to one year of humans! ‘The gods see the Sun, after it has risen, for half a solar year.’ Āryabhata, Āryabhatīya (Gola 6–7, 17), trans. K. S. Shukla and K. V. Sarma, Indian National Science Academy, New Delhi, 1976, pp. 118, 127. Varāhamihīra, Pancsiddhāntikā (13.27 and 13.9–13), trans. G. Thibaut and Sudhakara Dvivedi, reprinted by, Chowkhamba Sanskrit Series, Varanasi, 1968, p. 72, p. 70. Āryabhata (b. 476) firmly thought the apparent rotation of the cosmic sphere was an illusion, ‘Just as a man in a boat moving forward sees stationary objects [on the bank] moving backward’. He defined that ‘The rotations of the earth are sidereal days’, and gave the duration of a sidereal day as 23 hours, 56 minutes, and 4.1 seconds. He regarded all this as only a way to construct an accurate calendar to measure time, though he thought time itself to be ‘without beginning and end’.

    28. D. A. Mackenzie, Pre-Columbian Mythology, Gresham Publishing Co., London, c. 1920. (No date given.)

    29. Prabhavananda and Manchester, trans., The Upanishads, cited earlier, p. 118.

    30. Majid Fakhry, Islamic Philosophy, cited earlier, p. 120.

    31. J. L. Henderson and M. Oakes, The Wisdom of the Serpent: The Myths of Death, Rebirth and Resurrection, New York, Brazilier, 1963; reprint, Princeton University Press, 1990, p. 36.

    32. E. A. Wallis Budge, The Egyptian Book of the Dead, Keagan Paul, London, 1901, p. 278.

    33. There are various other symbols, like the Sun. All these symbols suffer from a cultural bias: among the Yorubas, names reveal the belief in life after death. The Yorubas may name a boy Babatunde, meaning ‘Father has returned’, or a girl Yetunde (Iyatunde) signifying ‘Mother has returned’. See E. G. Parrinder, African Traditional Religion, Society for Promotion of Christian Knowledge, London, 1962, pp. 138–40. In Ghana, the name Abaibo, ‘He has come again’, has the same significance.

    There is also, in African traditions, a more general sort of belief in life after death, related to a different belief in time. Death does not mark the end of life because the past has not ceased to exist. In these traditions, the future, by contrast, practically does not exist; time moves backwards from experienced time (Sasa) to remembered time (Zamani). Death marks the gradual removal of a person from the Sasa to Zamani; the person retains individuality till there are people alive who knew him personally. After that the dead person loses individuality and moves into the realm of collective memory. See John S. Mbiti, African Religions and Philosophy, Heinemann, London, 1969. In Chapter 11, we compare this belief in the continued existence of the past with the Buddhist belief that the past events do not cease to exist so long as they retain their causal efficacy: isn't the individual partly the cause of the memories of the individual?

    34. The phrase ‘eternal return’ is a favourite with Western authors: this oxymoron seems to mean that there is a time quite independent of events (hence a metaphysical sort of time), which stretches to infinity in the future, in which events repeat endlessly.

    35. F. Nietzsche, The Gay Science, 341. Quoted in Friedrich Nietzsche: Selected Writings, Srishti Publishers, Calcutta (in association with Creation Books, London), 1998 [1996], p. 205. See also, O. Levy, ed., The Complete Works of Friedrich Nietzsche, vol. X, The Joyful Wisdom (‘La Gaya Scienza’), Edinburgh, 1910, 2nd ed., pp. 270–71; and R. J. Hollingdale, trans., A Nietzsche Reader, Penguin Books, London, 1977, pp. 249–50.

    1. Cambridge Medieval History, vol. II, The Foundation of the Western Empire, p. 440. St. Sophia, or the ‘Great church’, dating back to Constantine, was rebuilt in 551, the principal architects being Isidore of Miletius and Anthemius of Tralles. The main novelty is its huge dome which, seen from inside, seems to float in the air. The building was again rebuilt after an earthquake in 568, and still stands. Plundered by Latin Crusaders in the 14th c, it was converted into a mosque in 1453, when Constantinople fell to Mehmet the Conqueror, and into a museum (Hagia-Sophia museum) in 1935 by Kemal Ataturk.

    2. The Nika riots so called because the crowds collected at the hippodrome kept chanting ‘Nika’, meaning victory. A. H. M. Jones, Constantine and the Conversion of Europe, Collier Books, New York, 1962. George Ostrogorsky, History of the Byzantine State, trans. Joan Hussey, Rutgers Univ. Press, New Brunswick, N.J., 1969, pp. 68–79.

    3. E. Gibbon, History of the Decline and Fall of the Roman Empire, vol. 1, chap. 40. Vol. 40 of Great Books of the Western World, ed. R. M. Hutchins, Encyclopaedia Britannica, Chicago, 1952, p. 649 and sequel. Theodora's son from a previous liaison was never again heard of, and Gibbon hints darkly that she had him murdered, an inference so offensive that to refute it Arthur Conan Doyle wrote a whole speculative fiction story. ‘The Homecoming’ in The Great

    Tales of Sir Arthur Conan Doyle, Magpie Books, London, 1993, pp. 726–40.

    4. Particularly, a powerful ecumenical politician, Theodore Askidas, Metropolitan of Caesarea in Cappadocia, and advisor to Justinian. Askidas, the Origenist, sought to out-manoeuvre those who held strictly to the creed declared at the Fourth Ecumenical Council at Chalcedon in 451. To attack the authority of Chalcedon, Askidas attacked the orthodoxy of the Three Chapters—the three bishops, Theodore of Mopsuestia, Ibas of Edessa, and Theodoret of Cyrrhus, the first of whom was accused as the father of Nestorianism, while the last two were rehabilitated at the Chalcedon council. In response to Justinian's anathemas against Origen, Askidas struck at the strict Chalcedonians by convincing Justinian to anathematise the Three Chapters, which he did. According to the Church historian Liberatus, Vigilius became Pope by promising Theodora that he would abandon the Chalcedon formula. Though Justinian did not at first envisage the need for any further confirmation of his anathemas (c. 543–545, now lost) against the Three Chapters, he eventually convened the Fifth Ecumenical Council to approve these anathemas. See Karl Baus, Hans-Georg Beck, Eugen Ewig, and Hermann Josef Vogt, The Imperial Church from Constantine to the Early Middle Ages, trans. Anselm Biggs, vol. II in History of the Church, ed. Hubert Jedin and John Dolan, Burns and Oates, London, 1980.

    5. Origen, surnamed Admantius—the man of steel or diamond—was a teacher of teachers like Dionysius the Great, Didymus the Blind, and Plotinus at the Alexandrian school. His principal work is the Peri Archon (On First Principles) translated into the Latin as De Principiis by Rufinus. Long Greek fragments from it may be found in the Philokalia of Origen compiled by the Cappadocian fathers Basil, and Gregory Nazianzen. The dispute concerned his views on apocatastasis or the final restoration of all things. See Encyclopaedia of Religion, ed. Mircea Eliade, vol. 11, Macmillan, New York, 1987, p. 108; G. W. Butterworth, trans., Origen on First Principles, 1936, reprint, Harper & Row, New York, 1966; Jean Danielou, Origen, trans. W. Mitchell, Sheed & Ward, New York, 1955; Alexander Roberts and James Donaldson, eds., The Ante-Nicene Fathers, vol. 4, T&T Clark, Edinburgh, 1866–72, reprint Wm. Eerdman, Grand Rapids, Mich., 1965.

    6. In interpreting this passage (Eccl. 1:9–12) from the Old Testament, it helps to keep in mind the following background. According to the historian Josephus Flavius, there were three sects among the Jews—the Essenes, the Pharisees, and the Sadducees—of which the first two believed in life after death, like the later Cabalists. The

    Essene belief in the survival of disembodied souls is further found in Enoch and Jubilees, works prominent among the Qumran documents (Dead Sea Scrolls). Whether there is life after death was not the dispute in Christianity, for it is a fundamental tenet of Christian belief that Christ died on the cross and was later resurrected. It is equally clear that there were divergent opinions about the sort of life to be expected after death. Under these circumstances, the natural thing would have been to turn to other sources of knowledge, and we have already glimpsed in the preceding chapter how Indian, Persian, Egyptian, and Greek traditions related to cosmic recurrence.

    7. Origen, De Principiis, as quoted in J. Head and S. L. Cranston, Reincarnation: An East-West Anthology, The Theosophical Publishing House, Wheaton, 1968, p. 36.

    8. Origen, De Principiis, Book II, chap. 9. Frederick Crombie, trans., The Writings of Origen, vol. X in Ante Nicene Christian Library, ed. Alexander Roberts and James Donaldson, T&T Clark, Edinburgh, 1895, p. 136.

    9. The similarity with Indian beliefs is not so surprising if we recollect that Alexandria, after all, is located in Egypt, where beliefs in life after death were similar to Indian beliefs. Trade between India and Egypt flourished from before the time of Alexander, whose general Nearchus travelled on this sea-route as described by Arrian. Moreover, in Origen's time, the Roman empire had a roaring trade with India, and some 120 ships sailed annually from India to Alexandria, so that the Roman historian Pliny complained that in no year did ‘India absorb less than five hundred and fifty million sesterces of our surplus, sending back merchandise to be sold to us at hundred times its prime cost’. Alexandrian (‘Greek’) scholars of the Neoplatonist school to which Origen belonged, actively studied Indian systems of knowledge, and Augustine chided Porphyry for seeking salvation by studying the ‘mores and disciplines of Indi’. Arrian, Indika, and Pliny, Natural History, Book VI, chap. 16, p. 63, cited by R. N. Saletore, Early Indian Economic History, Popular Prakashan, Bombay, 2nd ed., 1993, pp. 88, 296.

    10. Henry R. Percival, ed., The Seven Ecumenical Councils of the Undivided Church, vol. 14 in A Select Library of Nicene and Post-Nicene Fathers of the Christian Church, ed. Philip Schaff and Henry Wace, Charles Scribner's Sons, New York, 1900, pp. 318–20. Also reproduced in J. Head and S. L. Cranston, Reincarnation: An East-West Anthology, The Theosophical Publishing House, Wheaton, 1968, Appendix.

    11. There is no valid historical basis for the church propaganda that early Christians were persecuted and martyred in the Roman empire. Gibbon, cited in note 3 above, argues that the church accounts of persecution are so wildly exaggerated as to be physically impossible. My reason for believing Gibbon is that no secular account even mentions the Christians prior to the third century: the Roman empire could hardly have persecuted early Christians if it was not even aware of their existence! Moreover, prior to Constantine there is no evidence of any Roman attempt to legislate religious beliefs.

    12. It is well known that in 391 the temple of Seraphis and its adjacent great library of Alexandria were destroyed by a Christian mob. The magnificent temple of Dea Caelestis at Carthage remained open till c. 400. Under Catholic influence, many laws were passed against pagans and Donatists, and the synod of Carthage in 401 twice asked the State to implement these laws. Eventually, in 407, the Catholics took possession of Dea Caelestis, and Bishop Aurelius, Augustine's lifelong friend, triumphantly located his cathedra at the place occupied by the statue of the pagan goddess. In the countryside, there were bloody clashes between Catholics and pagans, and ultimately the latter were driven to carry their deities literally underground or into caves. See, History of the Church, ed. Jedin and Dolan, vol. II, cited earlier, p. 205. As a footnote to this footnote, the pagan prophecy of the collapse of Christianity in North Africa was fulfilled as Vandals attacked and destroyed churches in exactly the same way!

    13. Starting as a pacifist of sorts, Augustine changed his tone after a taste of power. He argued that the Donatists were mistaken because the effect of baptism depended on the miraculous qualities with which Christ imbued the water. To talk of the moral qualities of the priest performing the baptism was, therefore, a heresy against which the use of State power guided by a Catholic emperor was justified, because it was intended to be good, holy, and just. If this was persecution by the State, then it was persecution as the workers practised it in the gospel when they were sent by their master to the highways with the order ‘to coerce’ the poor ‘to come in’(Luke 14:23); it was the persecution of the shepherd who ‘persecutes’ the lost sheep, bringing it back to the flock, even against its will, and thus saves it (Matt. 18:12–14). ‘Why should not the Church compel its lost sons to return, if the lost sons compel others to their ruin?’ Augustine letters 93 and 185, Ep. 185, 6, 123, cited in History of the Church, ed. Jedin and Dolan, vol. II, cited above.

    14. More examples can be found in F. Cavallera, Saint Jérome, Université Catholique de Louvain, Louvain-Paris, 1926, pp. 115–26, and J. N. D. Kelly, Jerome. His Life, Writings, and Controversies, Duckworth, London, 1975. Jerome's about turn (c. 393) on Origen involved also a revolt against his bishop and a bitter fight with his bosom friend Rufinus. They were reconciled, and Rufinus returned to Rome to translate Apologia for Origen, adding an essay, On the Falsification of the Works of Origen, arguing that all theologically doubtful opinions of Origen were interpolations by falsifiers. In a similar vein of theological correctness, he translated Origen's Peri Archon, stating prefatorily that he was only continuing the work of that great man (Jerome) who had already translated more than 70 of Origen's homilies. Rufinus’ unfinished work was somehow forwarded to Jerome, who produced a literal translation ‘to hand over the heretical author to the Church’. Subsequently, he translated anti-Origenist propaganda which talked of the ‘blasphemous’ ‘madness’ and ‘criminal error of Origen, this Hydra of all heresies’. Rufinus defended himself, and, in response, Jerome dashed off three books, including the Apologia contra Rufinum, which begins with some rather warm polemics against Rufinus, and unscrupulously questions his honesty. Rufinus wrote a last letter, now lost, and remained silent for the remaining eight years of his life. When he died, Jerome gloated that now the scorpion lies pressed flat under the earth of Sicily; now finally the many-headed Hydra ceased to hiss. See History of the Church, ed. Jedin and Dolan, vol. II, cited earlier.

    15. J. Head and S. L. Cranston, Reincarnation in World Thought, Julian Press, New York, 1967.

    16. Origen, De Principiis, Book II, chap. 9. Frederick Crombie, trans., The Writings of Origen, vol. X in Ante Nicene Christian Library, ed. Alexander Roberts and James Donaldson, T&T Clark, Edinburgh, 1895, p. 132.

    17. Thus, in neighbouring Iran (Persia), where the Magi aspired to make Zoroastrianism a state religion, the followers of Mazdak were massacred in 528 by the leader of the Magi, reportedly in association with crown prince Khusrau. Mazdak taught not only equity, he regarded ownership of property as the root of all evils, and advocated the common ownership of property as the solution. He was patronised by Khusrau's father, Kavadh, for Mazdak's teaching's appealed to the people, though they clearly threatened the rich and the powerful. The Magi persecuted the followers of various religions, at various times, starting from Karter and his liquidation of Mani, as proclaimed in Karter's edicts at Ka'be-ye Zardusht. But it is noticeable that among the religions with a sizeable following in Iran, only the more egalitarian—viz. Mazdakism and Buddhism—were completely eliminated, while Manichaeism and Christianity continued to exist, despite the fact that Christians were viewed with suspicion as potential traitors loyal to the Roman enemy. The Magi eventually failed to assert their control, perhaps because, unlike their Christian counterparts, they stopped at physical liquidation, and do not seem to have gone on to adapt their ideology to state purposes.

    18. Augustine, City of God, XI.23, says that Origen was justly blamed’, and ‘cannot sufficiently express [his] astonishment’, for example, about Origen's ‘foolish assertion’ that better souls should be reborn in better bodies (pp. 334–35). In the popular translation, Augustine says that Origen was ‘rightly reproved’, and is ‘inexpressibly astonished’ that Origen should be so ‘stupid’ (pp. 230–31). On the other hand, Jerome had objected that Origen's ideas meant that better souls may be reborn in worse circumstances! Augustine, who commented on the quarrel between Jerome and Rufinus, presumably knew about this. Augustine's arguments were, thus, directed against the idea that bodies were neither worse nor better, but remained the same. See, Augustine, The City of God, in Augustine, trans. Marcus Dods, vol. 18 in Great Books of the Western World, ed. R. M. Hutchins, Encyclopaedia Britannica, Chicago, 1952. Popular translation: Vernon J. Bourke, ed., Saint Augustine, The City of God, abridged from the translation by Gerald G. Walsh, Demetrius B. Zema, Grace Monahan, and D. J. Honan, Image Books, New York, 1958.

    19. Augustine cites M. Aurelius (11.14): ‘All things from eternity are of like form and come round in a circle’.

    20. W. R. Inge, The Philosophy of Plotinus, vol. II, Greenwood Press Publishers, Westport, Connecticut, 1968, p. 19.

    21. Augustine, City of God, XI.13, trans. Marcus Dods, cited earlier, p. 350, emphasis mine.

    22. Unlike the millenarists, Augustine did not prophecy the precise extent of the future, or an exact date for the end of the world. But he vigorously denied pagan beliefs about the extent of the past, maintaining that the world was not more than 6000 years old, on his interpretation of the scriptures. ‘Reckoning by the sacred writings, we find that not 6000 years have yet passed’. Augustine, City of God, cited earlier, XII.10, pp. 348–49. This portion is skipped in the popular translation.

    23. Modern theologians have found technical room to argue that the curse against cyclic time is not part of the official doctrine of the Church. One claim is that Pope Vigilius, who was in Constantinople, did not sign the anathemas. Another is that the anathemas concerned an obscure chapter of ecumenical politics. Undoubtedly one can find various local elements and human dimensions in the formal condemnation of Origen, but these would have been insubstantial without the changed political role of the Church after acquiring a State-approved monopoly. As for Vigilius, he was summoned to Constantinople in 547, and remained there till 555. He vacillated during this period, excommunicating people and being himself excommunicated. To recover his reputation, he claimed that his earlier Judicatum abandoning the Three Chapters (see note 4 above) was issued under duress, but secretly gave a written and sworn assurance in 550 that he would cooperate with all his power in condemning the Three Chapters, and would undertake nothing without consulting Justinian. In his Constitutum of 14 May 553, he took a weaker stand on the Three Chapters. This became public, upon which Justinian also made public the signed minutes of the Pope's secret oath of 550, and the Pope's letter defending his earlier Judicatum. The Pope's name was expunged from the diptychs, without excommunicating him. On 2 June 553, the last day of the Council, Justinian's anathemas against the Three Chapters were accepted. To balance matters, Justinian had also proposed the anathemas against Origen about which ‘it is certain that the bishops made no difficulties…and Vigilius seems to have assented without much hesitation’ (Jedin and Dolan, eds., History of the Church, vol. II, cited earlier, p. 454). The Origenists were expelled from Palestine, and some bishops from their sees. But perhaps some more manipulations were carried out by Theodore Askidas, for there still seems to be some ambiguity about these anathemas. As for Vigilius, he again changed his mind and agreed to condemn the Three Chapters unequivocally by December 553, and published a new Constitutum in March 554. He left Constantinople for Rome in 555, but died en route.

    The precise theological interpretation of the actions of Vigilius—whether Protestants or Roman Catholics too should believe in the curse on cyclic time—is of marginal interest. The undeniable fact is that the Western Church accepted Augustine and rejected Origen, and the curse isolates the key issues involved in this fundamental ideological shift. The consequent long-term religious stigma attached to any beliefs about ‘cyclic’ time prepared the cultural predisposition which results in so many people who ‘find time-travel profoundly repugnant’ (J. F. Woodward, Foundations of Physics Letters, 8, 1995, 1–39, p. 2).

    24. Henry R. Percival, ed., The Seven Ecumenical Councils of the Undivided Church, cited earlier, pp. 318–20. Also reproduced in J. Head and S. L. Cranston, Reincarnation: An East-West Anthology, cited earlier', Appendix.

    25. Augustine, Confessions, XI.26, trans. E.B. Pusey, in Augustine, ed. Hutchins, cited earlier, p. 95.

    26. C. K. Raju, Time: Towards a Consistent Theory, Fundamental Theories of Physics, vol. 65, Kluwer Academic, Dordrecht, 1994, especially chap. 8: ‘Mundane Time’.

    27. More recently he has introduced the chronology protection conjecture, which makes closed timelike curves illegal: the laws of physics do not allow the appearance of closed timelike curves. No time machines. See Chapter 7, for Hawking's latest position, and S.W. Hawking, Physical Review D, 46, 1992, pp. 603–11. Chapter 7 also explains why the exact opposite of the claim made by Augustine and Hawking is valid: closed loops in time are exactly the way to allow spontaneity or ‘free will’ in current physics.

    28. S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Space-Time, Cambridge University Press, paperback edition, 1974, p. 189.

    29. One could, for example, eliminate these naive features, and use a more sophisticated formulation like Popper's record postulate. That postulate says simply that there is no upper limit to the length of the records one can keep. But on going round a closed time loop, every record must be destroyed for consistency. Hence there are no closed timelike curves. Incidentally, this, too, is an approach to banish ‘cyclic’ time by fiat. K. R. Popper, The Open Universe: An Argument for Indeterminism, vol. 3 of Postscript to Logic of Scientific Discovery, Hutchinson, London, 1982.

    30. ‘For, to confess that God exists and at the same time to deny that He has foreknowledge of future things, is the most manifest folly.’ Augustine, City of God, V.9, cited earlier, p. 123. Alternatively, ‘…one who does not foreknow the whole of the future is most certainly not God’, Augustine, ed. Bourke, cited earlier, p. 108.

    31. ‘…if I should choose to apply the name of fate to anything at all, I should rather say that fate belongs to the weaker of two parties, will to the stronger…than that the freedom of our will is excluded by that order of causes which, by an unusual application of the word peculiar to themselves, the Stoics call Fate.’ (Augustine, City of God V.9, cited earlier, p. 215.) ‘…if I wanted to use the word “fate” for anything at all, I should prefer to say that “fate” is the action of a weak person, while “choice” is the act of the stronger man, rather than to admit that the choice of our will is taken away by that order of causes which the Stoics arbitrarily call fate.’ (Augustine, ed. Bourke, cited earlier, pp 108–9.)

    32. F. J. Tipler, Nature, 280, 1979, pp. 203–5, and ‘General Relativity and the Eternal Return’ in F.J. Tipler, ed., Essays in General Relativity, Academic Press, New York, 1980, pp. 21–37.

    33. F. J. Tipler, The Physics of Immortality. Modern Cosmology, God and the Resurrection of the Dead. Macmillan, London, 1995.

    1. A. N. Whitehead, Science and the Modern World, Lowell Lectures, 1925, The Free Press, New York, 1967, p. 181.

    2. Isaac Asimov, ‘The Threat of Creationism’, in Creations: The Quest for Origins in Story and Science, ed. Isaac Asimov, George Zebrowski, and Martin Greenberg, Harrap, London, 1984, p. 186.

    3. Friedrich Nietzsche, The Anti-Christ, [1895], in The Twilight of the Idols and The Anti-Christ, trans. R. J. Hollingdale [1968], Penguin Books, 1990, sec. 48, pp. 175–76. (Italics original.)

    4. Jürgen Renn and Robert Schulman, eds., Albert Einstein/Mileva Mariç: The Love Letters, Princeton University Press, New Jersey, 1992, p. xix. See also Document No. 115 in The Collected Papers of Albert Einstein, vol. 1: The Early Years, 1879–1902, ed. John Stachel, Princeton University Press, New Jersey, 1987, and a companion volume with the same title, trans. Anna Beck.

    5. The withdrawal of the strictures against Galileo was no trifling matter: it was preceded by a 13-year study by the Vatican (see, e.g., The Times of India, 26 October 1996, front page). The commissioning of the 13-year study presumably followed from the deliberations of the Second Vatican Council (1962–65), which explicitly sought to change the inflexibility that had characterised Catholic thought since the Protestant Reformation.

    6. There remains, of course, the freedom of interpretation, or exegesis, to find the intended meaning of the Bible. At a more abstract level, there is the further freedom to choose the hermeneutic, i.e., the principles used to interpret the Bible. (We note in passing that Jerome, who used Origen's notes to prepare the version of the Bible, now regarded as authoritative, subscribed to the literal hermeneutic—that the Bible was the literal truth—while Origen subscribed to the moral and allegorical hermeneutic: that the Bible should be interpreted allegorically.) However, few politicians in the USA, today, would be ready to reject altogether the authority of the Bible by relegating it to, say, the status of an obsolescent text.

    7. The name derives from a series of 12 pamphlets that they wrote and circulated, called The Fundamentals.

    8. Ian Plimer, Telling Lies for God—Reason versus Creationism, Random House, 1994.

    9. A. D. White, A History of the Warfare of Science with Theology in Christendom, 2 vols, 1896; reprinted, Dover, New York, 1960.

    10. Nicolaus Copernicus, De Revolutionibus, preface and Book 1, trans. J. F. Dobson and S. Brodetsky, Royal Astronomical Society, Occasional Notes, No. 10, 1947, pp. 3–6.

    11. For example, in Brooke's book of 419 pages, all references to Buddhism and Islam would easily fit in one page (and it is not as if that page contains terse comments of great depth). J. H. Brooke, Science and Religion: Some Historical Perspectives, Cambridge University Press, Cambridge, 1991.

    12. The notion of ‘proof in the claim actually appeals to certain Platonic ideas of what constitutes a convincing demonstration. It is facile to suppose that this notion of ‘proof is universal, for the Buddha's idea's of a four-fold negation incorporated a logic quite different from the two-valued logic underlying the later Neoplatonic (‘Euclidean’) notion of ‘proof. The current Western notion of ‘proof is considered in greater detail in Chapter 6, and in the Appendix, and traditional notions of proof in Chapter 11. The current Western notion also assumes a two-valued logic, which is neither culturally universal nor empirically certain. Chapters 8 and 9 explain the possible incompatibility of two-valued logic with the structure of time in a quantum mechanical world.

    13. The Tantrasamgraha of Śāntarakṣita, With the Commentary of Kamalaśīla, trans. Ganganath Jha, reprinted Motilal Banarsidass, Delhi, 1986, vol. I, chapter VI, pp. 132–38. The Tibetan text and translation may be found in Hajime Nakamura, A History of Early Vedanta Philosophy (English translation by Trevor Leggett et al), Motilal Banarsidass, Delhi, 1983, Part 1, pp. 232–35. The notion of ‘cause’ involved here should not be assumed to be identical with the notion of ‘cause’ used in debates in traditional Christian theology, for the notion of cause, like logic, depends upon the underlying picture of time.

    14. The differences between science and Buddhism could, however, relate to (a) the kind of reason or logic underlying inference (see note 12 above), and (b) whether this logic is forever Plato-given or whether the nature of logic may itself be decided by recourse to the empirical.

    15. J.C. Polkinghorne, ‘A revived natural theology’, in Science and Religion, Papers presented at the Second European Conference on Science and Religion, March 10–13, 1988, ed. Jan Fennema and Iain Paul, Kluwer Academic Publishers, Dordrecht, 1990, p. 87.

    16. Oswald Spengler, The Decline of the West, vol. I, Form and Actuality, trans. C. F. Atkinson, George Allen & Unwin, London, 1926, p. 18. (Italics original in both quotes.) It goes without saying that talk of a Copernican revolution is itself part of a Eurocentric scheme of things!

    17. For Spengler, Cultures (rather than nations) are the appropriate entities to be studied in history: ‘Higher history, intimately related to life and to becoming, is the actualizing of possible Culture.’ Spengler, cited above, p. 55, italics original.

    18. Spengler, cited above, p. 4. Spengler devotes a whole volume to explain that his analogies are not superficial. In the ancient Nyāya tradition, analogy was regarded as one of the means of right knowledge.

    19. Arnold J. Toynbee, A Study of History, abridgement in 2 vols. by D.C. Somervell, Oxford University Press, 1957.

    20. Samuel P. Huntington, The Clash of Civilizations and the Remaking of World Order, Viking, New Delhi, 1997, p. 166.

    21. In a book called 1984, published in 1948, George Orwell had used Spengler's projection to visualise a future world divided into 3 zones perpetually at war with each other.

    22. Joseph S. Nye, Jr, ‘The Changing Nature of World Power’, Political Science Quarterly, 105, 1990, pp. 181–82.

    23. Copernicus’ book, cited earlier, may have been a revolution in European thought, but the theory was that of Ibn as Shatir, from the Maragheh observatory, and heliocentrism was a part of Arabic astronomy for centuries before that. See, Otto Neugebauer, ‘On the Planetary Theory of Copernicus’, Vistas in Astronomy, 10, 1968, pp. 89–103, and George Saliba, ‘Arabic Astronomy and Copernicus’, chapter 15 in A History of Arabic Astronomy, New York University Press, New York, 1994, p. 291. With the rise of Baghdad, in the early 9th c, Greek and Sanskrit texts were imported and translated into Arabic. By the time Baghdad fell to Hulegu, Arabic texts were being translated into Byzantine Greek. After the fall of the Byzantine empire, in 1453, many Greek translations of Arabic originals came to Europe. Copernicus translated one such book from Greek to Latin. While the mutual sharing of information is as it ought to be, the depiction of this process by Western historians of science has turned Copernicus into a heroic innovator, by transferring all credit to him. This sort of history has made science seem like a uniquely Western enterprise, and has hence made the West seem as the legitimate recipient of benefits flowing to it by force of a technological advantage—an advantage derived by monopolising information initially acquired through mutual sharing.

    24. In pre-Sassanid times, Buddhism had spread to Syria, and al Bīrūnī, the scholarly emissary of Mahmud of Ghazni, thought the Buddhists were refugees in India! Al Bīrūnī, Kitab al Hind, translated by E. C. Sachau as Alberuni's India, [Keagan Paul, 1910], Munshiram Manoharlal, New Delhi, 1992, p. 21. Nietzsche, influenced by Schopenhauer in his youth, speaks of Buddhism as a ‘kindred religion’ which he ‘should not like to have wronged’, for ‘Buddhism is the only really positivistic religion history has to show us…it no longer speaks of “the struggle against sin” but…“the struggle against suffering”… it already has… the self-deception of moral concepts behind it…it is beyond good and evil…Buddha…demands ideas which produce repose or cheerfulness…Prayer is excluded, as is asceticism; no categorical imperative, no compulsion at all…his teaching resists nothing more than it resists the feeling of revenge-fulness, of antipathy, of ressentiment (—“enmity is not ended by enmity”: the moving refrain of the whole of Buddhism…).…The precondition of Buddhism is…no militarism.’ (Italics original.) Friedrich Nietzsche, The Anti-Christ, cited earlier, sec. 20, pp. 141–42.

    25. See, e.g., A. H. M. Jones, Constantine and the Conversion of Europe, Collier Books, New York, 1962.

    26. E. Gibbon, History of the Decline and Fall of the Roman Empire, vol. I, chap. 16. Vol. 40 in The Great Books of the Western World, ed. R. M. Hutchins, Encyclopaedia Britannica, Chicago, 1952, p. 233.

    27. According to an empirical survey that I conducted, 100 per cent of a sample of 166 people who used the word ‘communism’ could not correctly discriminate between communism and socialism, in the sense of Marx, and could not explain why the Soviet Union called itself a socialist republic. The difference, incidentally, is this: ‘communism’ is a utopian situation where the state withers away, and there prevails, as in a family, the situation of ‘to each according to his needs, and from each according to his capacity’. Socialism is a transitional state between capitalism and communism.

    28. See note 12, Chapter 2.

    29. Chapter 42 of Gibbon, Decline and Fall of the Roman Empire, cited earlier.

    30. Bertrand Russell, A History of Western Philosophy, George Allen and Unwin, London, 1947, p. 387.

    31. P. S. S. Pissurlencar, ‘Govyache Khristikarana’, Shri Santadurga Quatercentenary Celebration Volume, Shaka 1488–1818, published by Durgarao Krishna Borkar, Bombay, 1966, pp. 91–122. English summary in B. S. Shastry and V. R. Navelkar, eds., Bibliography of Dr Pissurlencar Collection, part I, Goa University Publication Series, No. 3, pp. 67–69.

    32. See note 13, Chapter 2. There is, of course, no dearth of current-day apologias, e.g., H. A. Drake, ‘Lambs into Lions: Explaining Early Christian Intolerance’, Past and Present, 153, 1996, pp. 3–36.

    33. Gallup poll cited in Chapter 1, note 2. Wald points out that the USA is an outlier, an exception to the general rule that prosperity makes religion unimportant. That, however, is not relevant to the current perspective which is civilisational rather than national. Kenneth D. Wald, Religion and Politics in the United States, Popular

    Prakashan, Bombay, 1992. See also, G. Holton, Science and Anti-Science, Harvard University Press, Cambridge, Mass., 1994; J. C. Burnham, How Superstition Won and Science Lost, Rutgers University Press, New Brunswick, 1987. A Spenglerian parallel in Greece may be found in E. R. Dodds, The Greeks and the Irrational, Beacon University Press, Boston, 1957.

    34. B. Russell, ‘What is Science’, in Science Speaks, ed. H. Dow, Melbourne, Cheshire, 1955.

    35. E. Gilson, Philosophie du Moyen Age, p. 218, translation cited in Spengler, Decline of the West, cited earlier, p. 502.

    36. M. Adas, Machines as the Measure of Men, Oxford University Press, New Delhi, 1991.

    37. For example, only 7 per cent of the US adults can be called scientifically literate. See Gerald Holton, Science and Anti-Science, cited earlier, p. 147.

    38. This is generally true of any capitalist society. In India, for example, the Department of Atomic Energy got ten times the total funding given to the University Grants Commission, which concerns higher education, and higher education itself received far more funds than primary education. This is generally true of any capitalist society because profit maximisation requires constant increases in productivity, and dramatic increases in productivity can only come from technological innovation. On the other hand, the expenses on education only serve to reproduce the scientific labour which produces the innovation, and it is well understood why a capitalist society focuses on production (of commodities such as technological innovation) rather than reproduction (of scientific labour needed to produce the innovation).

    39. This, incidentally, is another reason why soft power has become important. Hard power obtained by increasing technical sophistication is more prone to sabotage by disgruntled elements. Workers in a more sophisticated system cannot be managed by an overseer with a whip, for the simple reason that the overseer may be unable to judge what is happening, so that the typical manager clings to people he thinks he can trust. This strategy may be all right with car-mechanics, where the final result at least is transparent, but it usually fails at the level of a more abstract state enterprise, such as one devoted to the development of science and technology.

    40. Arnold J. Toynbee, A Study of History, abridgement of vols. vii-x by D. C. Somervelle, Oxford University Press, 1957; reprint, Dell Publishing Co., vol. 2, p. 112.

    41. Pope John Paul II has himself told the faithful to believe that faith and science can coexist. See The Times of India, 26 October 1996.

    42. See, e.g., Asimov, ‘The Threat of Creation’, in Creations: The Quest for Origins, ed. Asimov et al. cited earlier.

    43. Friedrich Nietzsche, Twilight of the Idols and The Anti Christ, cited earlier, p. 135. (Italics original.)

    44. The ‘Award of Constantine’, or the ‘Donation of Constantine’ (Donatio Constantini) was a document, allegedly under the signature of Emperor Constantine, which granted the Vatican to the church, along with its special status as a state within a state. The document which the church at first claimed to have discovered (in the 8th c.) was later (in the 15th c.) shown to be a forgery. But this realisation did not change the status of the Vatican. See, e.g., E. F. Henderson, Select Historical Documents of the Middle Ages, George Bell, London, 1910, pp. 319–29, or The Penguin Atlas of World History, vol. 1, Penguin Books, New York, 1974, pp. 140, 212.

    45. The Times of India, 26 October 1996.

    46. Stephen Hawking, A Brief History of Time: From the Big Bang to Black Holes, Bantam, New York, 1988, p. 122.

    47. That is, no one else has actually solved the classical electrodynamic two-body problem for an electron and a proton, while theorising about the structure of the atom.

    48. The idea is that the two-body problem of electrodynamics involves functional differential equations (FDE), rather than the ordinary differential equations (ODE) that Bohr took to be the case, and which have been used by physics texts ever since. For the exact equations of motion, and for the fundamental differences between FDE and ODE, see C. K. Raju, Time: Towards a Consistent Theory, Fundamental Theories of Physics, vol. 65, Kluwer Academic, Dordrecht, 1994, chap. 5b. A preliminary solution of the equations was presented in, C. K. Raju, ‘Simulating a tilt in the arrow of time: preliminary results’, Seminar on Some Aspects of Theoretical Physics, Indian Statistical Institute, Calcutta, 14–15 May 1996; and C. K. Raju, ‘The Classical Electrodynamic 2-Body Problem and the Origin of Quantum Mechanics’, International Symposium on Uncertain Reality, India International Centre, New Delhi, 5–9 January 98, but is yet to be finalised and submitted for publication. The theory behind these calculations is explained in general terms in Chapter 9.

    49. Paul Davies, God and the New Physics, Penguin Books, London, 1990, p. 7.

    50. I cannot say what, if anything, Davies means by the term ‘Oriental cosmology’. Possibly he has in mind one of the usual utterly confused (or deliberate) misrepresentations so popular with some theologians. See, e.g., Stanley L. Jaki, Science and Creation, Scottish Academic Press, Edinburgh and London, 1974. Davies cites Jaki's later work, Cosmos and Creator, Scottish Academic Press, Edinburgh, 1981, as part of his select bibliography.

    51. There is, of course, an old dispute about what the Old Testament actually says about creation. Origen, cites the earlier Greek version of the Old Testament (the Septuagint), particularly Isaiah lxvi.22, and Ecclesiastes, in support of ‘the ages which have been before us’. He, then, goes on to point out that ‘the holy Scriptures have called the creation of the world by a new and peculiar name, calling it καταβoλη, which…signifies…to cast downwards—a word which has been…very improperly translated into Latin by the phrase “constitutio mundi”… in which καταβoλη is rendered by beginning (constitutio)…’. Origen, De Principiis, Book III, chap. V, p. 256, in A. Roberts and J. Donaldson, Ante Nicene Christian Library, vol. X, Edinburgh, 1895.

    52. Isaac Asimov in Creations, ed. Asimov et al., cited earlier, p. 6.

    53. I have translated the Sanskrit sat as ‘being’, which is the primary meaning assigned to it by, e.g., Monier-Williams’ dictionary, though it has earlier been translated as ‘existent’, and may well be translated as ‘truth’ or ‘real’. My reason is, roughly, that ‘real’ can be a confusing philosophical category, as is clear in the contemporary context of the debate on quantum mechanics. ‘Truth’ being logically prior seems a strong contender. But to say that something is true needs the verb ‘is’. M. Monier-Williams, A Sanskrit English Dictionary, reprint, Motilal Banarsidass, Delhi, 1990.

    54. But see H. A. Wolfson, ‘The identification of ex nihilo creation with emanation in Gregory of Nyssa’, Harvard Theological Review, 63, 1970, pp. 53–60; R. Sorabji, Time, Creation and the Continuum, London, Duckworth, 1983, p. 294. For the radical political difference that this makes, and for a fuller account of Gregory of Nyssa, see Paulos Gregorios, Cosmic Man, Sophia Publications, New Delhi, 1980, especially pp. 223–33. As summarised by Inge, ‘Gregory of Nyssa is an Origenist (in many of his doctrines) who has never been condemned’. W. R. Inge, The Philosophy of Plotinus, vol. 1, Greenwood Press Publishers, Westport, Connecticut, reprint, 1968, p. 103.

    55. The Vishnu Purana, trans. H. H. Wilson, cited in Chapter 1, note 27.

    56. Various concrete medieval representations of this creator in poetry and cathedral art have been examined in great detail by A. D. White, Warfare of Science with Theology, cited earlier, pp. 4–11.

    57. A. D. White, Warfare of Science with Theology, cited earlier, p. 6.

    58. As pointed out in Chapter 1, this is not entirely an ‘Oriental’ figure, for the West also measured the duration of an ordinary day and night cycle in 86,400 seconds. Note that the figure of 8.64 billion years corresponds to the duration of a cosmic cycle, and not to the age of the cosmos within the present cosmic cycle.

    59. W. R. Inge, The Philosophy of Plotinus, vol. II, Greenwood Press Publishers, Westport, Connecticut, reprint, 1968.

    60. Augustine, City, cited earlier, XII.10, pp. 348–49, ‘reckoning by the sacred writings, we find that not 6000 years have yet passed’. This portion is skipped in the popular translation.

    61. See note 50, this chapter. Jaki's book on ‘pagan’ cosmologies is cited as the authority by Davies. More recently, this book has been cited by Paul Halpern in another excessively ill-informed but supposedly authoritative account of ‘pagan’ views of time. Paul Halpern, The Cyclical Serpent, Pergamon, 1995.

    62. I think it is quite irrelevant to the issue here that a couple of people, Fred Hoyle, and his disciple Jayant Narlikar, mistakenly marketed the steady-state theory of Bondi and Gold as the theological antithesis of the big bang. As already pointed out earlier, the steady state theory requires continuous creation, which provides more scope for divine intervention.

    63. A. D. White, Warfare of Science with Theology, p. 18.

    64. E. R. Harrison, in Galactic and Extragalactic Background Radiation, ed. S. Bowyer and Ch. Lienert, Proceedings of the International Astronomers Union, No. 139, Kluwer Academic, Dordrecht, 1989, pp. 3–17.

    65. Frank E. Manuel, The Religion of Isaac Newton, Clarendon Press, Oxford, 1974.

    66. S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Space-Time, Cambridge University Press, 1974.

    67. Stephen Hawking, A Brief History of Time, pp. 52–54.

    68. More precisely, the ‘evolutionary path of a particle’ refers to a worldline.

    69. I do not recall the source which was in an anthology of SF someone borrowed from me (and never returned). This remark is attributed to Larry Niven, a former mathematician, in Black Holes, ed. Jerry Pournelle, Futura Publications, London, 1978, p. 333. ‘As we drove away from Pasadena, Larry [Niven] remarked that if we ever had proximity to a singularity, he could well imagine people praying to it. After all, their prayers probably wouldn't influence what came out of it—but they might, and certainly nothing else would.’

    70. Hawking still maintains this point of view as regards classical general relativity. In a recent publication he has stated: ‘…according to general relativity, there should be a singularity in our past. At this singularity the field equations could not be defined. Thus classical general relativity brings about its own downfall: it predicts that it can't predict the universe.’ Stephen Hawking and Roger

    Penrose, The Nature of Space and Time, Oxford University Press, Delhi, 1997, p. 75.

    71. Stephen Hawking, A Brief History of Time, cited earlier, pp. 183–84.

    72. On universal rotation, see, further, Chapter 7, note 16. On classical dynamics, rotation would make the initial configuration quite literally egg-shaped rather than spherical.

    73. More precisely, Hawking and Ellis, The Large Scale Structure of Space-Time, cited earlier, p. 362, speculate that the singularity might create information (or negative entropy as defined in Chapter 6): ‘It might be that the set of geodesics which hit these singularities (i.e. which are incomplete) was a set of measure zero. Then one might argue that the singularities would be physically insignificant. However this would not be the case because the existence of such singularities would produce…a breakdown of one's ability to predict the future. In fact this could provide a way of overcoming the entropy problem in an oscillating world model since at each cycle the singularity could inject negative entropy.’

    74. Merely punching a hole will not do, since the geodesic incompleteness could then be remedied by patching up the hole. But the idea can be suitably modified. See, C. J. S. Clarke, The Analysis of Space-Time Singularities, Cambridge University Press, Cambridge, 1993, pp. 141–53. For simplicity, we may imagine here that this hole extends inside or outside in such a way that geodesics that hit the hole are inextendible. What the external observer would ‘see’ is only a sphere with a hole amiss, as in the case of a black-hole with a small surface area, in a vast cosmos. The point of the example is only this: one tends to think of a geodesic as the path taken by a particle, but it is fallacious to suppose that every geodesic corresponds to an actual particle, so that geodesic inextendability does not mean the actual creation or destruction of a particle. The correspondence between actual particles and geodesics is far from clear in relativity; it does not seem to be one to one, for in spacetime there are an uncountable infinity of geodesics, but there may be only a finite number of actual particles. Technical difficulties have prevented the construction of a relativistic statistical mechanics so there is no clear correspondence in general relativity between the continuum and the particle description of matter.

    75. The description of matter in the theory is through the matter tensor, and no one has shown that in the presence of a Hawking-Penrose singularity some terms appear or disappear in the matter tensor. Indeed, the connection of geometry to the matter tensor is through the ‘laws of physics’—the equations of general relativity—that allegedly fail in the presence of curvature divergences that

    Hawking feels ought to be generically associated with incomplete geodesics.

    76. ‘There are examples in which geodesic incompleteness can occur with the curvature remaining bounded, but it is thought that generically the curvature will diverge along incomplete geodesics.’ Stephen Hawking and Roger Penrose, The Nature of Space and Time, Oxford University Press, Delhi, 1997, p. 15. For the examples, see C. J. S. Clarke, Analysis of Space-Time Singularities, cited earlier.

    77. Mathematically, the assumption is that the metric tensor should remain smooth (continuously differentiable, say) all the way to the singularity, without which assumption the geometric approach of singularity theory fails, and one has to shift to analytical techniques. The curvature relates to the second derivative of the metric tensor, so if the metric tensor has a kink (as in a V-shape) its first derivative would be discontinuous, and the second derivative would blow up. For shock waves in perfect fluids, these difficulties could be handled by shifting to an integral formulation of the basic equations, and deducing what happens at the point of blow-up from what happens around it. Worse divergences can arise, involving the square of the delta function, which cannot be handled so easily. These cases may arise because viscosity has a sharpening instead of a smoothing effect (see note 81, this chapter); they could also arise in the more exotic situation where the metric tensor itself becomes discontinuous, in the presence of exotic matter, say, as in the case of a ‘gravitational screen’.

    78. The exact technical meaning of this term from the theory of (hyperbolic) partial differential equations is not relevant here. Roughly speaking, these are paths along which sound travels, so that the analogy to null geodesics is exact, and does not depend on the geodesic hypothesis. Technically, the intersection of characteristics must be interpreted as indicating a shock wave; see P. D. Lax, Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves, SIAM Regional Conference Series in Appl. Math., 11, Society for Industrial and Applied Mathematics, Philadelphia, 1973.

    79. The fluid particles are hypothetical particles used in the continuum approach, and should not be confused with the molecules of the air, used in the discrete approach. In general relativity, as formulated today, only the continuum approach is available.

    80. That is, singularities have no empirical consequences that are distinct from the empirical consequences of a dense past state of the cosmos.

    81. Those interested in the technical details may consult the following of my papers. The general background papers are: ‘Products and

    Compositions with the Dirac Delta Function’, J. Phys. A: Math. Gen., 15, 1982, pp. 381–96, ‘Junction Conditions in General Relativity’, J. Phys. A: Math. Gen., 15, 1982, pp. 1785–97; ‘Distributional Matter Tensors in Relativity’, in Proc. MG5, ed. D. Blair et al. World Scientific, Singapore, 1989, pp. 421–24. The relation to quantum infinities is taken up explicitly in ‘On the Square of x−−n’, J. Phys. A: Math. Gen., 16, 1983, pp. 3739–53. Note that it does not help to talk of the smoothing properties of viscosity: on the contrary, with viscosity, the infinities involve the square of the delta function; see, ‘Navier-Stokes Shocks’, preprint, Centre for Development of Advanced Computing, Pune.

    82. In terms of singularity theory, the statement would be that the spacetime manifold can be extended, and ‘there is no absolute criterion for what sorts of extensions are ‘legitimate’, and hence no absolute criterion for what is and what is not a singularity’. C. J. S. Clarke, Analysis of Space-Time Singularities, p. 145. For the actual reinterpretation of physical law in distributional terms, see particularly my articles on the Dirac delta function, and on distributional matter tensors, cited above. It is true that uniqueness breaks down, and some further physical condition, such as the entropy law, may be needed. That, however, is in the nature of things.

    83. For a quick overview, see Stephen Hawking, ‘Classical Theory’, chap. 1 in Stephen Hawking and Roger Penrose, The Nature of Space and Time, Oxford University Press, New Delhi, 1997. For a rather more technical—and balanced—account, see C. J. S. Clarke, Analysis of Space-Time Singularities, cited earlier.

    84. Closing sentence of Hawking and Ellis, The Large Scale Structure of Space-Time, cited earlier, p. 364.

    85. Jerry Pournelle in Black Holes, ed. Jerry Pournelle, cited earlier, p. 333.

    86. Stephen Hawking, Black Holes and Baby Universes and Other Essays, Bantam Books, London, 1993, p. 158.

    87. A relativistic correction to Leibniz is needed: since spacetime is an attribute of the cosmos, God cannot also be at any time in any place!

    88. Stephen Hawking, Black Holes and Baby Universes, cited earlier, p. 85.

    89. But see F. J. Tipler, The Physics of Immortality, Macmillan, London, 1995, p. 256.

    90. Freeman J. Dyson, ‘Time without end: physics and biology in an open universe’, Rev. Mod. Phys., 51, 1979, pp. 447–60. Also, Infinite in All Directions, Harper and Row, New York, 1988.

    91. A popular account of the respective claims of Dyson and Tipler about the end of the world may be found in Paul Davies, The Last Three Minutes, Basic Books, New York, 1994.

    92. Vladimir Nabokov, The Defence, trans. Michael Scamell in collaboration with the author, Panther Books, 1967.

    93. Frederic Brown, ‘Answer’, in The Stars and Under, A Selection of Science Fiction, ed. Edmund Crispin, Faber and Faber, London, 1968, p. 110.

    94. Spengler, Decline of the West, pp. 502–4.

    95. Tipler, Physics of Immortality, pp. 256–57.

    1. Richard S. Westfall, Never at Rest: A Biography of Isaac Newton, [1980], Cambridge University Press, paperback edition, 1983, p. 49. Conduitt's memorandum of a conversation with Newton, 31 August 1726 (Keynes MS 130.10).

    2. Manuel recalls ‘Voltaire's wicked quip about the assurance of Newton's doctor that he died a virgin’. Frank E. Manuel, Isaac Newton, Historian, Harvard University Press, Cambridge, Mass., 1963, p. 253.

    3. A Freudian view may be found in Frank E. Manuel, Portrait of Isaac Newton, Cambridge, Mass., 1968, and is extended in Frank E. Manuel, Religion of Isaac Newton, Oxford University Press, Oxford, 1974.

    4. Westfall, Never at Rest, p. 319.

    5. ‘Having searched after knowledge in the prophetic scriptures, I have thought myself bound to communicate it for the benefit of others, remembering the judgment of him who hid his talent in a napkin.’ H. McLachlan, ed., Sir Isaac Newton, Theological Manuscripts, Liverpool University Press, Liverpool, 1950, p. 1. The scriptural allusion is to Luke xix, 20f; Matthew xxv, 25f The wording has been modernised, changing ‘prophetique’ to ‘prophetic’ and ‘my self to ‘myself, and ‘remembring’ to ‘remembering’. See also, Appendix A of Frank E. Manuel, Religion of Isaac Newton, p. 107.

    6. John Greaves, Miscellaneous Works, ed. Thomas Birch, vol. 2, London, 1737, pp. 405–33.

    7. The implication of this for the credibility of authoritative historians of science should not be overlooked: for centuries, historians of science have put foward their fabrications, and concealed the elementary truth about Newton.

    8. The complete quote reads: ‘a wealthy Palestinian Jew, who took his degree in Arabic studies in Germany, became Royal Professor of Medieval Rabbinics in Spain, then professr of Arabic in Germany, a lecturer in England in the 1930's and a refugee scholar in America from 1940 until his death in 1951.’ Richard H. Popkin, ‘Biblical Theology and Theological Physics’, in Newton's Scientific and Philosophical Legacy, ed. P.B. Scheuer and G. Debrock, Kluwer Academic, Dordrecht, 1988, pp. 81–97.

    9. Isaac Newton, Theological Manuscripts, selected and edited with an introduction by H. McLachlan, Liverpool, 1950. According to Westfall, cited in note 1, ‘this misbegotten volume’ ‘takes great liberty with the originals’, such as introducing paragraphs. More to the point, Newton's theological manuscripts in Keynes’ possession were not representative, since Keynes appears to have focused on Newton's alchemy, often swapping the theological manuscripts he had for alchemical one's. The Yahuda collection gives a better account of Newton's theological views.

    10. Popkin, in Newton's Legacy, ed. Scheuer and Debrock, p. 87.

    11. Popkin, in Newton's Legacy, ed. Scheuer and Debrock, p. 82; original correspondence in Yahuda MS, var. 1, Box 42.

    12. Westfall, Never at Rest, p. 876.

    13. Popkin, in Newton's Legacy, ed. Scheuer and Debrock, p. 85, states that in the Bodmer MSS ‘Newton presented his…theory of how the Church became corrupt, how it falsified the true doctrine of Christianity, and in part, how it accomplished this by tinkering with the texts of the New Testament’. That Newton's theological writing included a completed history of the church was indicated by the will of Newton's niece, Catherine Conduitt, which mentions a ‘church history compleat’; see Frank E. Manuel, Isaac Newton, Historian, Harvard University Press, 1964, p. 254. It now appears that the Bodmer MSS is part of the Sotheby lot No. 249, an incomplete 425 page treatise ‘Of the Church’, which corresponds to a later draft of the church history in Yahuda MS, var. 1, 15. See M. Goldish, ‘Newton's Of the Church: its Contents and Implications’, in Newton and Religion: Context, Nature and Influence, ed. J. Force and R. H. Popkin, International Archives of the History of Ideas 129, Kluwer, Dordrecht, 1999, pp. 145–64.

    14. An easily accessible list of the Sotheby lots may be found at the website of the Newton Project at http://www.newtonproject.ic.ac.uk/. This project, started at the Imperial College, London, in 1998, aims to end centuries of secrecy and make available all the Newton manuscripts in digital format.

    15. ‘A society of would-be clerics intent on preferment and constrained by the principle of seniority did not allow the ladder all must climb to be clogged with non-clerics who could hold their fellowships forever.’ Westfall, Never at Rest, p. 330.

    16. Barrow's argument was in response to one Francis Aston's attempt to obtain such a royal dispensation. Westfall, Never at Rest, p. 332.

    17. Ibid., p. 333.

    18. Ibid., p. 869; Keynes MSS, 130.6, Book 1; 130.7, sheet 1.

    19. More details may be found in the references in note 5, and in Frank Manuel, Isaac Newton Historian, Harvard University Press, Cambridge, Mass., 1963; I. Bernard Cohen and Robert E. Schofield, eds., Isaac Newton's Papers and Letters on Natural Philosophy, Harvard University Press, Cambridge, Mass., 1958, rev. ed. 1978; Richard S. Brooks, ‘The Relationships between Natural Philosophy, Natural Theology and Revealed Religion in the Thought of Newton and their Historiographic Relevance’, dissertation, Northwestern University, 1976; William H. Austin, ‘Isaac Newton on Science and Religion’, Journal of the History of Ideas, 31, 1970, pp. 521–40; Leonard Trengrove, ‘Newton's Theological Views’, Annals of Science, 22, 1966, pp. 277–94; Margaret Jacob, The Newtonian and the English Revolution 1689–1720, Cornell University Press, Ithaca, New York, 1976.

    20. Westfall, Never at Rest, pp. 312–13.

    21. As specific examples, Newton wrote that Athanasius had misrepresented the 3rd-century church Father, Dionysius of Alexandria, to make it appear that he accepted a term (homoousios) which, in fact, he considered heretical (Westfall, Never at Rest, p. 314, original in Yahuda MS, 2.5b, ff. 40v–41); and that words were ‘foisted in’ in the epistles of the 2nd-century Ignatius in support of trinitarianism (ibid., Yahuda MS, 14, f. 61v).

    22. Westfall, Never at Rest, p. 314; original in Keynes MS, 2, p. 77. The synod of Serdica (Sofia) met in 342 or 343 to patch a division between the eastern part of the Roman empire ruled by Conantius, and the western part ruled by his brother Constans. he eastern delegation left within a day, conemning Pope Julius and Hosius of Cordoba through whom ‘…Athanasius, and the other criminals’ had been ‘again received into the ecclesiastical community’. Jedin and Dolan, eds., History of the Church, vol. II, cited in note 4, Chapter 2, p. 38. The source of the quote is Hilary of Poitiers. In his ‘Paradoxical Questions Concerning the Morals and Actions of Athanasius and his Followers’, Newton, of course, quotes the reference to ‘the most wretched Athanasius, convicted of the most foul crimes, for which he can never be sufficiently punished—no, not though he should be ten times killed…’. McLachlan, ed., Theological Manuscripts, p. 111.

    23. After early training in Syrian Antioch, Arius was a pastor in the Church at Baucalis in Alexandria. From 318 to 319 he taught about the Logos and its relation to the Father. His bishop, Alexander, suggested a theological discussion in which the special views of Arius could be debated. Arius stated that ‘the Son of God was created out of non-being that there was a time when he did not exist, that, according to his will, he was capable of evil as well as of virtue, and that he is a creature and created’. His opponents insisted on the consubstantiality and eternity of the Son with the Father. Alexander praised both sides for their theological zeal, accepted the second opinion, and ordered Arius never again to propound his opinion. When Arius refused to accept this verdict, he and his adherents were excommunicated. Arius moved out of Egypt to Nicomedia whose Bishop Eusebius, a ‘Collucian’ (i.e., follower of the school started by Arius’ teacher, Lucian, at Antioch), supported him. He coined the term homoousios as a heretical, intolerable consequence of the anti-Arian position.

    24. Nestor was branded a heretic nominally for calling Mary ‘Mother of Christ’ because his congregation was debating whether to call her ‘Mother of God’ (Theotokos) or ‘Mother of Man’ (Anthropotokos)!

    25. Newton did think, ‘That Religion and polity, or the laws of God and the laws of man, are to be kept distinct’, McLachlan, ed., Theological Manuscripts, p. 58.

    26. Westfall, Never at Rest, p. 350; original in Yahuda MS, 9.2, ff. 99–99v.

    27. Westfall, Never at Rest, p. 318.

    28. Ibid., p. 313.

    29. Ibid., p. 350; original in Yahuda MS, 9.2, ff. 99–99v.

    30. Westfall, Never at Rest, p. 315.

    31. Ibid., p. 349.

    32. More to Sharp, 16 August 1680 in Conway Letters. The correspondence of Anne, Viscountess Conway, Henry More, and Their Friends 1642–1644, ed. Marjorie Hope Nicolson, Yale University Press, New Haven, 1930, pp. 478–79.

    33. Westfall, Never at Rest, p. 356; original in Yahuda MS, 9.2, f 157. (Emphases mine.)

    34. Westfall, Never at Rest, p. 330; original in Yahuda MS, 1.2, f. 30v. (Emphases mine.)

    35. Westfall, Never at Rest, p. 327.

    36. Westfall, Never at Rest, pp. 323–24; original in Yahuda MS, 1.4, ff. 67–68.

    37. Westfall, Never at Rest, p. 313; original in Yahuda MS, 14, f. 57v; Keynes MS, 2, pp. 19–20.

    38. Isaac Barrow, Lectiones geometricae, pp. 4–15. Lecture 1, reproduced as ‘Absolute Time’, in The Concepts of Space and Time: their Structure and their Development, ed. Milic Capek, vol. XXII of Boston Studies in the Philosophy of Science, ed. Robert S. Cohen and Marx W. Wartofsky, D. Reidel, Dordrecht, 1976, pp. 203–8.

    39. Barrow, in Space and Time, ed. Capek, p. 204. Capek points out that Gassendi, in his polemic against Descartes in 1644, had already stated, ‘Whether things exist or not, whether they move or are at rest, time always flows at an equal rate’. Milic Capek, ‘What Survives from Absolute Time’, in Newton's Legacy, ed. Scheuer and Debrock, pp. 309–19, 311.

    40. ‘Magnitudes themselves are absolute Quantums Independent on all Kinds of Measure tho’ indeed we cannot tell what their Quantity is, unless we measure them; so Time is likewise a Quantum in itself, tho’ in Order to find the Quantity of it, we are obliged to call in Motion to our Assistance.’ Barrow, cited above, p. 204.

    41. Barrow, in Space and Time, ed. Capek, p. 205. As Capek points out, Giordono Bruno had advanced a similar argument to make time (duration) independent of motion: ‘Now if it happened that all things are at rest, would this mean that they would not endure? Indeed, they would endure, they would all endure by one and the same duration.’ Capek in Newton's Legacy, p. 310

    42. The ‘Parts of Time’ corresponded to the ‘Parts of an equal Motion’, time was ‘alike in all its Parts’, and since it could be thought of as the continual ‘Flux of one Moment’, it had length alone. Barrow in Space and Time, ed. Capek, p. 205.

    43. Isaac Newton, The Mathematical Principles of Natural Philosophy, A. Motte's translation, revised by Florian Cajori, University of California Press, Berkeley and Los Angeles, 1962, vol. 1, pp. 6, 7–8. Reproduced in Concepts of Space and Time, ed. Capek, p. 209.

    44. H. Poincaré, Science and Hypothesis [1902], Eng. trans. (1905); reprint, Dover, New York, 1952, p. 141.

    45. Newton related elliptic orbits to the inverse square law using the calculus, where ‘Newton's basic discovery was that everything had to be expanded in infinite series.…Newton, although he did not strictly prove convergence, had no doubts about it.…What did Newton do in analysis? What was his main mathematical discovery? Newton invented Taylor series, the main instrument of analysis.’ V. I. Arnol'd, Barrow and Huygens, Newton and Hooke, trans. E. J. F. Primrose, Birkhauser Verlag, Basel, 1990, pp. 35–42. Taylor was a pupil of Newton whose paper dates from 1715. These infinite expansions were to analysis as decimal fractions to arithmetic. It is another matter that these infinite series expansions were not only in use, but were also explained at length in a 1501 manuscript that was in wide circulation in coastal South India in the sixteenth century, when Jesuits were busily gathering information from India. For more details, see C. K. Raju, ‘Computers, Mathematics

    Education, and the Alternative Epistemology of the Calculus in the Yuktibhāṣā’, Philosophy East and West, 51(3), 2001, pp. 325–362. Basically, the Indian calculus-related texts were imported into Europe in connection with the European navigational problem, and the related Gregorian calendar reform of 1582. These diffused into Europe through the works of Cavalieri, Fermat, etc., who had access to Jesuit sources. See further Chapter 10 and C. K. Raju, ‘The Infinitesimal Calculus: How and Why it Was Imported into Europe’, paper presented at the International Conference on East-West Transitions, National Institute of Advanced Studies, Indian Institute of Science, Bangalore, December 2000 (submitted for publication).

    46. ‘Planet Fakery Exposed. Falsified Data: Johannes Kepler’. The Times (London) 25 January 1990, 31a. The article includes large excerpts from the article by William J. Broad, ‘After 400 Years, a Challenge to Kepler: He Fabricated Data, Scholars Say’, New York Times, 23 January 1990, C1, 6. The key background article is William Donahue, ‘Kepler's Fabricated Figures: Covering Up the Mess in the New Astronomy’, Journal for the History of Astronomy, 19, 1988, p. 217–37.

    47. The poem was written c. 1730, and published in 1730. John Butt, ed., The Poems of Alexander Pope, Methuen, London, 1968, p. 808. The poem has been cited so often that it cannot possibly be spoilt by explaining that apart from the allusion to creation, ‘Light’ alludes also to Newton's work on light (optics), and that ‘light’ is, in a way, the opposite of gravity.

    48. Arab philosophy was systematically studied along with the medicine of Ibn Sīnā (called Avicenna), as part of the university syllabus for centuries in Europe. It is well documented how the scholastic philosophers, like Thomas Aquinas were deeply influenced by this philosophy, together with the works of Aristotle that it brought back to the West. It is, therefore, very likely that this dispute between rationality and providence entered Christian theology from Islamic theology.

    49. John Duns Scotus, d. 1308, was also known as Dr Subtilis, for his subtlety, and his works were used as texts until about the 16th century. Instead of subtlety, his followers developed a reputation for cavil and sophistry, and even this soon degenerated into a reputation for plain dull obstinacy.

    1. Remark to his biographer Moszkowski. Roger Highfield and Paul Carter, The Private Lives of Albert Einstein, Faber and Faber, London, 1993, p. 100.

    2. Highfield and Carter, Private Lives, p. 57. Original in Jürgen Renn and Robert Schulmann, eds., Albert Einstein/Mileva Marić, the Love Letters, Princeton University Press, Princeton, 1992, p. 19; Anna Beck and Peter Havas, trans., The Collected Papers of Albert Einstein, vol. 1, Princeton University Press, Princeton, 1987, p. 141.

    3. Highfield and Carter, Private Lives, p. 79.

    4. After getting the job at the Patent office, Einstein married Mileva in 1903, but only after his father gave him permission to do so on his deathbed. ‘She hatched another chick’, and another. The younger son was apparently mentally disturbed, while the older son remained permanently embittered from his father. The two divorced in 1919, just before Einstein became very famous, and after many years of ‘carrying on’ with his cousin Elsa, whom he later married. Physical violence is reported to have been one of the grounds for the divorce. Einstein continued his daily philanderings (including with Mileva) which were behind Elsa's back only in the sense that she deliberately went out in the morning and returned in the evening. The point of the marriage was not clear, at least not to Einstein. When asked whether the object of smoking a pipe was to clean it, he said that the object is to smoke, this gets in the way, like marriage. As she lay dying in the other room, Einstein calmly continued working, though her shrieks unnerved his collaborator P. W. Bridgman. Shortly after her death, Einstein wrote to Max Born that he had settled down splendidly at the Institute of Advanced Study. See Highfield and Carter, Private Lives, especially, p. 216.

    5. There was an attempt to do genetic matching on at least one other claim, using the preserved portions of Einstein's brain. But the tissue did not permit such matching to be carried out. See, High-field and Carter, Private Lives, p. 284.

    6. A. Einstein, ‘How I Created the Theory of Relativity’, translated from the Japanese by Yoshimasa A. Ono, in History of Physics, ed. Spencer R. Weart and Melba Phillips, Amer. Inst. Phys., 1985, p. 244. (Based on a talk given at Kyoto on 14 December 1922, when Einstein was unable to attend the Nobel prize ceremony at Stockholm, as he had already proceeded to Japan.)

    7. A. Einstein, ‘On the Electrodynamics of Moving Bodies’, in The Principle of Relativity, by H. A. Lorentz, A. Einstein, H. Minkowski, and H. Weyl, with notes by A. Sommerfeld, trans. W. Perrett, and G. R. Jeffrey, 1923; reprinted, Dover Publications, New York, 1952, p. 37. (Reprinted from Ann. Phys.17, September 1905.)

    8. I do not know what significance to attach to these contradictory answers since Einstein clearly had selective recall. He denied having had anything to do with the military, when, in fact, he worked for the US Navy on explosions, from 31 May 1943 to 30 June 1946, at a consultant's rate of twenty five dollars a day. Highfield and Carter, Private Lives, p. 245. See also, Abraham Pais, ‘Subtle is the Lord…’: The Science and the Life of Albert Einstein, Oxford University Press, Oxford, 1982, p. 529.

    9. E. T. Whittaker, A History of the Theories of Aether and Electricity, vol. II: The Modern Theories, [1951–53], American Institute of Physics, New York, 1987.

    10. Ibid., p. 30.

    11. Ibid., p. 48.

    12. Comptes rendus Acad. Sci., Paris, 140, 1905 (5 June), p. 1504.

    13. Whittaker, History of Aether and Electricity, vol. II, p. 40.

    14. H. Poincaré, Bull. des Sci. Math., (2) 28, 1904, p. 302; trans. G. B. Halstead, The Monist, 15, (January) 1905, pp. 1–24; reprinted as ‘The Principles of Mathematical Physics’, in The Value of Science, [1905] by H. Poincaré; reprint Dover, New York, 1958.

    15. This ought to be easy to decide, in principle, since a record is maintained by the University about the discussions held there.

    16. E. T. Whittaker and G. Robinson, The Calculus of Observations: A Treatise on Numerical Mathematics, Blackie & Son, London, [1924], 4th ed., reprinted 1965. Though a bit dated, the book contains nuggets like the following (p. 138): show that the sum of the 7th and 5th powers of the first n whole numbers is double the square of the sum of their cubes. [Hint: This is easy if you know how to calculate log (79!) on a computer!]

    17. Kip S. Thorne, Black Holes & Time Warps: Einstein's Outrageous Legacy, W. W. Norton, New York, 1993.

    18. Why did Lorentz take the experiment seriously? The experiment was never designed to disprove the existence of the aether. It was meant to discriminate between the theories of Fresnel and Stokes, both of which accepted the aether. The experiment was cited in favour of Stokes’ theory which was based on a mathematical impossibility, so that any hypotheses was preferable to it. For further details, see C. K. Raju, ‘The Michelson-Morley Experiment’, chap. 3a in Time: Towards a Consistent Theory, Kluwer Academic, Dordrecht, 1994.

    19. A micron is a millionth part of a meter, or one thousandth of a centimeter, so the change in length amounts to one part in 200 million.

    20. Abraham Pais, ‘Subtle is the Lord…’, p. 167.

    21. Translator's introduction to Poincaré, The Value of Science.

    22. Sir Edmund Whittaker, in Biographical Memoirs of Fellows of the Royal Society, London, 1955, p. 42.

    23. H. Poincaré, Science and Hypothesis, [1902], Eng. Trans., Dover, New York, 1952, p. 111.

    24. For those familiar with elementary calculus at the school level, the reason is simply that acceleration is the derivative of velocity; so adding a constant (vector) to the velocity does not change the acceleration.

    25. That is, a law of motion formulated as a first order differential equation. The solution would then be uniquely fixed by specifying the initial positions of all interacting particles.

    26. Poincaré, The Value of Science, cited earlier, p. 46. (Emphasis mine.)

    27. Poincaré, Science and Hypothesis, pp. 171–72.

    28. Ibid., p. 171.

    29. Poincaré, The Value of Science, p. 108.

    30. Ibid., p. 98.

    31. Poincaré, Science and Hypothesis, p. 243, pp. 175–76.

    32. Ibid., pp. 175–176.

    33. ‘The task was not easy, and if Lorentz has got through it, it is only by accumulating hypotheses’. H. Poincaré, The Value of Science, p. 99.

    34. Poincaré, Science and Hypothesis, p. 175.

    35. H. A. Lorentz, in Relativity, by Lorentz et al, p. 24.

    36. Einstein, in Relativity, by Lorentz et al, p. 63.

    37. Ibid., p. 38.

    38. Poincaré, The Value of Science, cited in note 13, p. 104.

    39. Ibid. (Emphasis mine.) Is this waffling?

    40. Ibid., p. 111.

    41. Reproduced as chapter II, in Poincaré, The Value of Science, pp. 26–36.

    42. Ibid., p 27.

    43. Ibid., p. 30.

    44. Ibid., p. 35.

    45. W. Kaufmann, Ann. Physik, 19, 1906, p. 495: ‘The measurement results are not compatible with the Lorentz–Einsteinian fundamental assumption. Pais states that ‘Einstein was unmoved’: is he looking for the reaction of a scientist or a prophet? Pais, Subtle is the Lord…, p. 159.

    46. G. Holton, Amer. J. Phys., 28, 1960, pp. 627–36.

    47. G. Scribner, Jr., Amer. J. Phys., 32, 1964, pp. 672–78.

    48. S. Goldberg, Amer. J. Phys., 35, 1967, pp. 934–44. See also, A. P. French, ed., Einstein: A Centenary Volume, Heinemann (for the International Commission on Physics Education), London, 1979, p. 80.

    49. Paul A. Schlipp, ed., Albert Einstein: Philosopher-Scientist, Library of Living Philosophers, Evanston, Illinois, 1949; including

    Autobiographical Notes by A. Einstein. P. Frank, Einstein: His Life and Times, Alfred A. Knopf, New York, 1947.

    50. R. W. Clark, Einstein: The Life and Times, World Publishing Co., New York, 1971. A. Pais, cited in note 7, and Banesh Hoffmann, with Helen Dukas, Albert Einstein: Creator and Rebel, Hart-Davis, MacGibbon, London, 1973.

    51. Hoffmann and Dukas, cited in note 49, p. 68. Poincaré's second paper, submitted in July 1905, appeared in Rend. Circ. Mat. Palermo, 21, 1906, p. 129.

    52. A. Pais, Subtle is the Lord…, p. 134.

    53. H. Poincaré, The Value of Science, pp. 98–99.

    54. C. K. Raju, Time: Towards a Consistent Theory, Appendix to chapter 3b.

    55. Poincaré, The Value of Science, p. 91.

    56. Cited in Jagdish Mehra, Einstein, Hilbert and the Theory of Gravitation, D. Reidel, Dordrecht, 1974, p. 82. Wigner briefly worked with Hilbert.

    57. Stephen Hawking, Black Holes and Baby Universes, and other Essays, Bantam Books, New York, 1993, p. 62.

    58. Jagdish Mehra, Einstein, Hilbert, and the Theory of Gravitation, cited earlier.

    59. C. Reid, Hilbert, Springer, New York, 1970, p. 142.

    60. Letter to Arnold Sommerfeld, of 15 July 1915, cited in Jagdish Mehra, p. 25.

    61. For more details, see Jagdish Mehra, pp. 25, 30, and C. Reid Hilbert, cited above.

    62. Reid, Hilbert, p. 142, Jagdish Mehra, Einstein, Hilbert, and the Theory of Gravitation, p. 25, cited above.

    63. Abraham Pais, Subtle is the Lord…, pp. 260–61.

    64. P. A. Schlipp, Albert Einstein: Philosopher Scientist, Library of Living Philosophers, 1959, p. 47. Einstein's three papers in 1902–1904 on the foundations of statistical mechanics dealt with ‘the definitions of temperature and entropy for thermal equilibrium conditions and with the equipartition theorem…, the second one with irreversibility…, the third one with fluctuations and new ways to determine the magnitude of the Boltzmann constant.’ Pais, p. 58. Einstein did not, however, submit these clearly important rediscoveries in statistical mechanics to claim his Ph.D. in 1905.

    65. P. A. Schlipp, Albert Einstein: Philosopher Scientist, p. 47; L. Infeld, Albert Einstein, Scribner's, New York, 1950, pp. 97–98.

    66. Highfield and Carter, Private Lives, p. 116.

    67. Everyone refers to this as Poincaré's lecture, but the lecture was published in 1904 itself. Einstein knew French, and the English translation of the paper was published in January 1905. To my knowledge, no one seems to have asked Einstein directly whether he knew of Poincaré's work. Given Einstein's authority, this would have seemed insulting. But let us recall Einstein's remarks on authority.

    68. Einstein's denial that he had read the paper at that time could have been just as much a case of selective recall, as his remarks on the Michelson–Morley experiment, or on working for the military.

    69. Editorial in The Times of India, 12 August 93, on the book by Highfield and Carter.

    70. A personal account. My prejudices in the matter are as follows. As an undergraduate, I was thrilled to stumble upon Einstein's paper (on Brownian motion) while browsing through old tomes in my college library, though only the formula for Avogadro's number made a little sense to me. My first scientific paper was presented at a symposium to celebrate Einstein's centenary. The praise that I heard there convinced me that Einstein was a super-genius. I appropriated a photograph of Einstein from a notice board of the Physics Department of the Indian Institute of Technology in Delhi, and hung it above my table as a source of inspiration. As a scientist I was unconcerned with history. But in 1989 I started writing a series of articles for the journal Physics Education. I wanted to explain that the text-book version of the discovery of relativity theory was wrong, and that Einstein had arrived at it by analysing the notion of time. I read Whittaker's book for the history of the Michelson-Morley experiment, and was struck by the lucidity of the book. I relied heavily on this book to draft the third article in this series. (At this time, I did not doubt that Einstein had carried out the analysis about time. That Einstein reportedly came up with a relatively low [for a super-genius] IQ of 135 was an argument I used against IQ tests.)

    To make the article more interesting for students, I wanted to put in some biographical details. I picked up Pais’ book. I was horrified by his description of Whittaker, whose book I had just read. As a mathematician I was aware of Poincaré, and I found Pais's description of Poincaré a little offensive, though I believed him at this point.

    Fortunately, I found Poincaré's two volumes in the library, and was fascinated by what I read. Poincaré had put, very much more clearly and thoroughly, exactly the argument that I wanted to present, the argument missing from the textbooks. What I had thought to be implicit in Einstein was explicit in Poincaré. I concluded that Pais was misrepresenting Poincaré. I was not absolutely sure of what had happened, but every time I looked at Einstein's photograph, the doubts assailed me. I could not bear to look anymore at the photograph which was now kept on a cupboard adjacent to my table. I turned its face to the wall.

    Five years later, I thought that I might have misjudged the situation. I found Einstein's photograph (I had shifted to a new house), dusted it and hung it in a corner. Subsequently, I managed to get Whittaker's second volume. I read the naming objection between the lines. After reading other literature, I found that others had the same reading. Many have argued for Einstein in ways that are not at all offensive, but I am beyond caring: I have now permanently dismounted the photograph.

    71. A naive but frequently asked question is this: why didn't Poincaré object? Several reasons can be offered. First, like Hilbert, Poincaré simply remained unaware (until his death in 1912) that he would be deprived of credit for his insights—for Poincaré then was famous, Einstein was largely unknown. Second, for Poincaré, science related more to the subtler aesthetics of nature than to social recognition, which he already had. Third, Poincaré was generous in giving credit to others; he understood that his work was based on that of others; probably, under no circumstances would he have brawled, like Newton with Leibniz over calculus, for credit that he could hardly claim singlehanded.

    72. We shall see that in the case of relativity, the wrong understanding of the theory relates, as in Newton's case, to the pressure of political beliefs about time.

    1. Stephen Hawking, Black Holes and Baby Universes and Other Essays, Bantam, London, 1994, p. 62.

    2. Ever since Descartes introduced his aether (=sky), probably adapted from the corresponding concepts of akāsa (sky), in the Nyāya-Vaiśeṣika system of Indian philosophy, physics has stuck to the associated ideas of action by contact. In Indian traditions, this notion of contact was long ago recognised as a linguistic matter, by, for example, the tenth century philosopher Udyotkara, who, in his arguments against Buddhism, refutes the argument that atoms must have parts for they are capable of contact. This did not happen in Western philosophy, with a lengthy debate on the above argument from the time of Leibniz and Kant to the present debate on Bell and non-locality. For a general outline of the debate see the following. Mary Hesse, Forces and Fields: The Concept of Action at a Distance in the History of Physics, Philosophical Library, New York, 1962; reprint Greenwood Press, Westport, 1970. C. K. Raju, ‘Time in Indian and Western Traditions, and Time in Physics’, in Mathematics, Astronomy and Biology in Indian Traditions, ed. D. P. Chattopadhyaya and Ravinder Kumar, PHISPC Monograph Series on History of Philosophy, Science and Culture in India, No. 3, Munshiram Manoharlal, New Delhi, 1995, pp. 56–93; C. K. Raju, ‘The Electromagnetic Field’, chapter 5 a in Time: Towards a Consistent Theory, Kluwer Academic, Dordrecht, 1994, pp. 102–115 (first published in Physics Education, 9, 1992, pp. 251–65), and references cited therein; and ‘Bell and Non-Locality’, chapter 6a in Time: Towards a Consistent Theory, pp. 139–160 (first published in Physics Education, 10, 1993, pp. 55–73).

    3. H. Poincaré, Science and Method, [1908], Dover Publications, New York, 1952.

    4. The term ‘statistical’ derives from the need to collect data to apply the laws of large numbers, and the fact that collection of data was, and still is, considered very important for purposes of the state. See, e.g., Ian Hacking, The Taming of Chance, Cambridge University Press, Cambridge, 1990.

    5. Jeremy Rifkin (with Ted Howard), Entropy: A New World View, Bantam, New York, 1981, p. 39.

    6. N. Georgescu-Roegen, Afterword in Entropy, by Rifkin, p. 267.

    7. One may want to multiply by the Boltzmann constant, and add another constant.

    8. Most texts prove this theorem for special cases, assuming Newtonian mechanics, for example. For a proof of the general case, see C. K. Raju, ‘Thermodynamics Time’, chapter 4 and its appendix in Time: Towards a Consistent Theory, pp. 79–101 (first published in Physics Education, 9, 1992, pp. 44–62). The general proof helps to understand the various ways to avoid recurrence.

    9. Complete Works of Friedrich Nietzsche, ed. O. Levy, Foulis, Edinburgh, 1911, vol. XVI, Eternal Recurrence, No. 5, p. 239.

    10. ‘The law of conservation of energy demands eternal recurrence’. F. Nietzsche, The Will to Power As Art, No. 1063, trans. W. Kaufmann and R. J. Hollingdale, ed. W. Kaufmann, 1967; reprint Vintage Books, 1968; see also, The Complete Works of Nietzsche, ed. O. Levy, vol. IX, 1909.

    11. Nietzsche, Will to Power, No. 1066, ed. Kaufmann, and also Complete Works of Nietzsche, ed. O. Levy, vol. IX.

    12. For a proof, see any standard textbook on Markov chains, or C. K. Raju, ‘Thermodynamic Time’, chap. 4 in Time: Towards a Consistent Theory.

    13. Nietzsche, Will to Power, No. 1066.

    14. Nietzsche's argument is essentially correct, notwithstanding claims that it has been refuted by some simple-minded arguments. For the alleged refutation, see W. Kaufmann, Nietzsche: Philosopher,

    Psychologist, Antichrist, Princeton University Press, New Jersey, 1974, p. 327.

    15. Nietzsche, Eternal Recurrence, No. 8.

    16. ‘This conception is not simply a mechanistic conception; for if it were that, it would not condition an infinite recurrence of identical cases, but a final state. Because the world has not reached this, mechanistic theory must be considered an imperfect and merely provisional hypothesis.’ Nietzsche, Will to Power, No. 1066, cited earlier.

    17. What is required is a manifold with constant negative curvature.

    18. That is, the trajectories locally diverge exponentially. They cannot, however, run off to infinity for the trajectories are confined to a finite region: the billiards table.

    19. H. Poincaré, Science and Method, [1908], reprinted, Dover, New York, 1952, chapter 4.

    20. Dīgha Nīkāya, trans. Maurice Walshe, The Long Discourses of the Buddha, Wisdom Publications, Boston, 1995, pp. 68–72.

    21. The plots of the Lorentz model shown here were obtained using Calcode, a programme for all calculations with ordinary differential equations.

    22. Strictly speaking the figures do not show phase portraits, for phase trajectories never intersect: they are 2-dimensional projections of the phase portraits.

    23. K. R. Popper, The Open Universe: an Argument for Indeterminism, Postscript to the Logic of Scientific Discovery, vol. 3, Hutchinson, London, 1982.

    24. Stephen Hawking, Black Holes, Baby Universes, and other Essays, Bantam, 1994.

    25. Roger Penrose, The Emperor's New Mind: Concerning Computers, Minds and the Laws of Physics, Vintage Books, London, 1990. Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness, Oxford University Press, 1994. Roger Penrose, Abner Shimony, Nancy Cartwright, and Stephen Hawking, The Large, the Small and the Human Mind, ed. Malcolm Longair, Cambridge University Press, 1997.

    26. The following is based on my talk during a debate with Roger Penrose. C. K. Raju, ‘Penrose's Theory of the Mind: a Rebuttal’, The Matter of the Mind, 22–23 December, India International Centre, New Delhi, 1997.

    27. One of the first machine learning programs, which could learn to converse was naturally called ELIZA. Joseph Weizenbaum, Computer Power and Human Reason: from Judgment to Calculation, [1976], Penguin Books, London, 1993. This made some people (Colby et al.) believe that computers could be used in psychological therapy!

    28. M. Minsky, as cited by Weizenbaum, Computer Power and Human Reason, p. 235. First published as ‘Why Programming is a Good Medium for Expressing Poorly Understood and Sloppily Formulated Ideas’, in Design and Planning II, ed. M. Krampen and P. Seeitz, Hastings House, New York, 1967, p. 121.

    29. The problem was the listing of all simple finite groups. See J. H. Conway, ‘Monsters and Moonshine’, The Mathematical Intelligencer, 2, 1980, pp. 165–71.

    30. K. Appel and W. Haken, ‘The solution of the four-color-map problem’, Scientific American, October 1977, pp. 108–21; ‘The four color proof suffices’, The Mathematical Intelligencer, 8, 1986, pp. 10–20.

    31. School geometry changed in the 1960's, after the recommendations of the US School Mathematics Study Group. School Mathematics Study Group, Geometry, Yale University Press, 1961.

    32. This confusion was specific to the cultural assimilation of the calculus in Europe, after its import by Jesuits in the 16th c. The confusion did not exist in the original Indian context because Indian mathematics had a different understanding of number, from the days of the Sulba Sūtra-s. Furthermore, in the Indian context the empirically manifest was accepted as a source of proof also in mathematics. Accordingly, the Indian approach to calculus used not ‘infinitesimals’ but ‘indivisibles’ in the sense of atomicity: the process of subdividing a circle must stop when the subdivisions reached atomic proportions. However, when the Jesuit Cavalieri, a student of Galileo, whose access to Jesuit sources in Collegio Romano is well documented, first used the same term ‘indivisible’ in exactly the same context, this invited a storm of protest in Europe. See, further, C. K. Raju, ‘Computers, Mathematics Education, and the Alternative Epistemology of the Calculus in the Yuktibhāsā’, Philosophy East and West, 51(3), 2002, pp. 325–62. W. A. Wallace, Galileo and His Sources: The Heritage of the Collegio Romano in Galileo's Science, Princeton University Press, Princeton, 1984.

    33. Proclus, A Commentary on the First Book of Euclid's Elements, trans. Glenn R. Morrow, Princeton University Press, 1992, p. 37

    34. The key change introduced into the Elements by Hilbert et al. was to change the Side-Angle-Side ‘theorem’ (proposition 1.4 of the Elements) into a postulate, since it was unprovable from the other postulates, and its original proof involved the empirical procedure of picking and carrying one triangle to place it on top of another.

    35. Richard's paradox. For an easy exposition see, e.g., R. R. Stoll, Set Theory and Logic, Eurasia Publishing House, New Delhi (by arrangement with W. H. Freeman & Co.), 1961, p. 446 and sequel. The barber paradox, by the way, has the tacit sexist assumption that the barber, and all the ‘people’ are all adult males.

    36. This is a slight correction of the game presented by Weizenbaum, Computer Power and Human Reason, pp. 51–53.

    37. For example, Penrose asserts in Emperor's New Mind, p. 539: ‘…the terms ‘algorithm’ and ‘algorithmic’ refer to anything that (in effect) can be simulated on a general purpose computer. This certainly includes “parallel action”…’ Or again, in Shadows of the Mind, p. 20, ‘It is always possible to simulate parallel action serially.’

    38. The parallel computing paradigm referred to here is that of Communicating Sequential Processes, as first implemented some 15 years ago in a computing chip called the Transputer, and in the computing language called OCCAM, which has an indeterministic construct going under the name ALT. For the knowledgeable, the formal semantics in terms of tense logic is similar to that of Schrödinger's cat: there is a PAR construct corresponding to branching, while ALT corresponds to an indeterministic selection, so that the collapse of the wavefunction faithfully implements the ALT construct. This, of course, is a parallel computer one can engineer here and now, though it would not be commercially viable. Such a parallel computer corresponds to the chocolate-ice cream machine discussed later on. For more details on the relation of OCCAM to quantum mechanics, see C. K. Raju, ‘Quantum Mechanical Time’, chap. 6b in Time: Towards a Consistent Theory. For quantum computation, see David P. DiVincenzo, ‘Quantum Computation’, Science270 (1995) pp. 255–261. For the experimental realization, see D. P. DiVincenzo, Nature393 (1998) pp. 113–114, and I. L. Chuang et al, Nature393 (1998) pp. 143–146.

    39. During the debate, ‘The Matter of the Mind’, India International Centre, New Delhi, 22–23 December 1997, cited earlier, Penrose argued that the parallel computer of the preceding note could be simulated by something ‘random’ in the sense of ‘pseudo-random’ or ‘ensemble’ as considered in Shadows of the Mind, section 3.18, pp. 168–169. In response to my question, he further clarified that the ‘ensembles’ under consideration were finite. However, pseudorandom numbers are generated algorithmically, while a finite ensemble of Turing machines is equivalent to a single Turing machine. Thus Penrose's response amounts to saying that parallel computers are algorithmic—even if the parallelism is implemented using the collapse of the wave-function in quantum mechanics. Not only is this not in accordance with existing quantum mechanics, this is not consistent with Penrose's theory of the mind which introduces a non-algorithmic element in the human brain exactly by this process of wavefunction collapse. Moreover, asserting that wavefunction collapse can be mechanically replicated would force Penrose into a hidden-variable interpretation of quantum mechanics, hence into various questions such as those about non-locality and Bell's inequalities.

    40. We need, here, a slightly different definition of ‘information’, related to what is called the Kolmogorov–Chaitin entropy or complexity. The Kolmogorov–Chaitin entropy of a string is the length in bits of the shortest computer program that will produce that string as an output. See, G. J. Chaitin, Algorithmic Information Theory, Cambridge University Press, Cambridge, 1987.

    41. David Ruelle, Chance and Chaos, Penguin Books, 1993. This refers again to the Kolmogorov–Chaitin complexity.

    42. In his Tahāfut al Falāsifā (‘Destruction of the Philosophers’), his arguments were directed against the theology of reason (aql-i-kalām), and against earlier philosophers such as Al Farābi and Ibn Sīnā (Avicenna). S. A. Kamali, Al-Ghazālī, Tahāfut al-Falāsifā, Pakistan Philosophical Congress, Lahore, 1958. S. van den Bergh, Averroes’ Tahāfut al-Tahāfut (incorporating al-Ghazālī's Tahafut al-Falasifa) translated with introduction and notes, 2 vols, Luzac, London, 1969. H. A. Wolfson, The Philosophy of the Kalām, Harvard University Press, Cambridge, Mass, 1976. Literally, kalām means word or Word of God, and the rationalists maintained that one must apply the faculty of reason/intelligence (aql) to interpret the contentious passages in the Ku'rān. As interpretations proliferated, al-Ashārī maintained that these passages must be accepted ‘without asking how’.

    43. Al-Ghazālī's Tahāfut al-Falāsifā, trans. S. A. Kamali, p. 189.

    44. The chocolate-ice cream (CHIC) machine, by the way, is a real machine which can be constructed today. It is possible to build a quantum-mechanical measuring apparatus, and it is possible to link the output of this apparatus to a digital computer which does the rest. The output of this ana-digi machine is algorithmically uncomputable, so that the criterion of uncomputability does not discriminate between human and machine. Though not a Turing machine, the chocolate-ice cream machine is, in fact, a parallel computer which faithfully implements the ALT construct of OCCAM discussed in an earlier note.

    45. M. Dummett, ‘Bringing about the past,’ Philosophical Review,73, 1964; reprinted in The Philosophy of Time, ed. R. M. Gale, Macmillan, London, 1968, pp. 252–274. For a more detailed review of the exact context of this paradox, see C. K. Raju, ‘Philosophical Time’, chapter 1 in Time: Towards a Consistent Theory, pp. 11–31.

    46. The quote continues, ‘Then, which of the virtually possible events are to be called possible under the auspices of free will? I would say, just the one that actually follows.’ This sentence is fallacious; for it easily degenerate into a tautology. E. Schrödinger, ‘Indeterminism and free will’, Nature, July 4, 1936, pp. 13–14.

    1. Paul J. Nahin, Time Machines: Time Travel in Physics, Metaphysics and Science Fiction, American Institute of Physics, New York, 1993. The difficulty that the biological clock need not be a proper clock is relevant also to time dilation due to velocity, since achieving large relative velocities would require subjecting the astronaut to prolonged periods of large accelerations, that may well speed up aging, exactly like extra weight. The need to distinguish between biological time and proper time motivated the conceptual division of time dilation as being ‘due to velocity’, and ‘due to acceleration’, in the present book. Though the biological clock cannot be affected by relative velocity, nothing guarantees that a biological clock will behave like a proper clock, when subjected to large accelerations. (In fact, the very existence of a proper clock is suspect, for nothing guarantees that any physically realizable process behaves like a proper clock over very long periods of time.)

    2. A. Einstein, ‘Electrodynamics of Moving Bodies’, in H. A. Lorentz, A. Einstein, H. Minkowski, and H. Weyl, The Principle of Relativity, trans. W. Perrett and G. B. Jeffrey, Dover Publications, New York, 1952, pp. 63–64.

    3. O. M. P. Bilaniuk, V. K. Deshpande, and E. C. G. Sudarshan, ‘“Meta” Relativity’, Amer. J. Phys., 30, 1962, pp. 718–23. O. M. Bilaniuk and E. C. G. Sudarshan, ‘Particles Beyond the Light Barrier’, Physics Today, 1969, pp. 43–51. O. M. Bilaniuk and E. C. G. Sudarshan, ‘Causality and Space-like Signals’, Nature, 223, 1969, pp. 386–87. G. Feinberg, ‘Possibility of Faster than Light Particles’, Physical Review159, 1967, pp. 1089–105.

    4. Hence also, it is irrelevant that the rest mass of a tachyon is a complex number, for a tachyon can never be brought to rest (all frames of reference are assumed to be subluminal).

    5. Bilaniuk, Deshpande, and Sudarshan, cited above, and Bilaniuk and Sudarshan, cited above.

    6. R. C. Tolman, The Theory of Relativity of Motion, University of California Press, Berkeley, 1917, pp. 54–55.

    7. G. A. Benford, D. L. Book, and W. A. Newcomb, ‘The Tachyonic Antitelephone’, Physical Review D, 2, 1970, pp. 263–65. The logic does not apply to single tachyons, nor does it apply to a collection of tachyons which cannot be used to signal to the past.

    8. Oswald Spengler, The Decline of the West, cited earlier in Chapter 3, p. 500.

    9. Strictly speaking, the surface of a photograph is 3-dimensional, and not 2-dimensional, because the photograph endures in time.

    10. M. Dummett, ‘Causal Loops’, in The Nature of Time, ed. R. Flood and M. Lockwood, Basil Blackwell, Oxford, 1986.

    11. Nahin, however, has a section on why Wells’ machine won't work, because it doesn't move through space, Paul J. Nahin, Time Machines, p. 13.

    12. M. Cook, ‘Tips for Time-Travel’, in Philosophers Look at Science Fiction, ed. N. D. Smith, Nelson-Hall, Chicago, 1982, pp. 47–55.

    13. Nahin says, ‘Wells, fortunately, never has his characters stick a hand into the space where the time machine was last seen.’ (Nahin, Time Machines, note 1 to chapter 4, p. 274.) This is incorrect. As the authority called in to support Wells’ idea of ‘diluted presentation’, the Psychologist ‘passed his hand in the space in which the machine had been. “You see?” he said, laughing.’ Wells has skillfully constructed his story, and its cast of characters. The asymmetry between the presentation of the world to the time traveller, and presentation of the time traveller to the world could also plausibly be put down in SF to psychological factors. H. G. Wells, The Time Machine, reprint, UBS Publishers, New Delhi, 1995, p. 10.

    14. See, e.g., John Earman, ‘Recent Work on Time Travel’, in Time's Arrows Today, ed. Steven F. Savitt, Cambridge University Press, 1995, pp. 268–310.

    15. The calculation is, however, suspect because it is not clear that ‘energy’ can be assigned an unambiguous meaning in the Gödel cosmos (because the Gödel cosmos is not asymptotically flat).

    16. There seem to be two common errors here. One is that a paper published by Birch, suggesting empirical evidence for universal rotation, was later shown to be wrong, but the later paper has not been noticed (e.g., Nahin, Time Machines). The other is that the ‘accepted’ analysis of the amount and kind of anisotropy (quadrupole anisotropy) one should look for has itself been more recently shown to be wrong. For further details, see C. K. Raju, ‘Cosmological Time’, chapter 7 in Time: Towards a Consistent Theory, Kluwer Academic, Dordrecht, 1994, pp. 190–211. What this means is that present-day observation may not rule out rotation of the cosmos, hence some peculiar behaviour of the cosmological arrow of time.

    17. Kip S. Thorne, Black Holes and Time Warps: Einstein's Outrageous Legacy, W. W. Norton & Co., New York, 1994. A more quantitative account may be found in M. S. Morris and K. S. Thorne, ‘Wormholes in Spacetime and their use of Interstellar Travel: A Tool for Teaching General Relativity’, Amer. J. Phys., 56, 1988, pp. 395–412.

    18. Carl Sagan, Contact, Simon and Schuster, New York, 1985. The novel was written after consultation with Kip Thorne on the question of time travel.

    19. That is, the journey should take at most one year as measured by both the traveller, and the observer stationed at the mouth of the wormhole.

    20. R. H. Price, Amer. J. Phys., 61, 1993, pp. 216–17.

    21. C. K. Raju and N. K. Dadhich, ‘Is Gravitational Screening Possible?’ in General Relativity and Gravitation (Proceedings of the Xth International Conference on General Relativity and Gravitation, Padova 1983), ed. B. Bertotti, F. de Felice, and A. Pascolini, D. Reidel, Dordrecht, 1984. A gravitational screen corresponds to a discontinuity in the metric tensor, which invalidates typical assumptions used in singularity theorems. A side effect of such a gravitational screen would be a large redshift.

    22. S. W. Hawking, ‘Chronology protection conjecture’, Physical Review, D 46, 1992, pp. 603–11. Subsequently, Hawking has changed his views on time travel in two respects. The above paper had concluded that there is excellent empirical evidence against time travel since we have not been swamped by ‘hordes of tourists’ from the future. He has now acknowledged a weakness of this argument: ‘A possible way to reconcile time travel, with the fact that we don't seem to have had any visitors from the future, would be to say that it can occur only in the future.’ The key change, however, is the restriction of his conjecture to macrophysics: ‘the Chronology Protection Conjecture: the laws of physics conspire to prevent time travel, on a macroscopic scale.’ (Emphasis added.) S. W. Hawking, ‘Space and Time Warps by S. W. Hawking as at 18/10/95’, personal communication of 16 December 1997.

    23. Except in the cases of cosmologies like the Gödel cosmology, where spacetime behaves peculiarly at infinity (it is not asymptotically flat); or in cases like black holes, where there is a singularity; or in cases where negative energy is present, so that there is a discontinuity (in the metric tensor), and Hawking's technique entirely breaks down even in the classical domain!

    24. Stephen Hawking, A Brief History of Time, Bantam Books, New York, 1988, ‘About the Author’.

    25. For a differing point of view, see, e.g. Paul Horwich, ‘Closed causal chains’, in Time's Arrows Today, ed. Steven F. Savitt, Cambridge University Press, Cambridge, 1995, pp. 259–67.

    26. Frederic Brown, ‘Experiment’, in Honeymoon in Hell, Bantam, New York, 1958. The presentation that follows does not faithfully stick to Brown's story, but uses it only to illustrate a paradox set up by Wheeler and Feynman. The point of the paradox is, of course, that any way of telling the story is wrong!

    27. J. A. Wheeler and R. P. Feynman, Rev. Mod. Phys., 21, 1949, p. 425.

    28. Some philosophers have argued that it is meaningless to speak of ‘changing’ the past, and this argument is given prominence in Nahin's book, cited earlier. I consider this argument to be a meaningless quibble over the meaning that ought to be assigned, in natural language, to the word ‘change’. One could speak, instead of ‘bringing about’ the past, in the same way as one speaks of ‘bringing about’ the future. Even more formally, one could speak of past-branching as opposed to past-linear temporal logic. Such linguistic difficulties also arise in the case of ‘cyclic’ time, which must be described by a four-place relation, rather than the binary before-after relation assumed in natural language; these difficulties are considered in Chapter 8. But as shown by the Appendix and assumption 3, the virtues associated with formalism are not above suspicion. Ultimately, meaning has to be grasped intuitively.

    29. I have not investigated this matter myself, and I am definitely sceptical about the alleged facts. But the allegation concerns Morgan Robertson's novel Futility, first published in 1898, and then republished in revised form under the title The Wreck of the Titan, in 1912, allegedly a short while before the sinking of the Titanic in 1912. It is, for instance, quite conceivable, that there was some chance similarity between the event and its description in the earlier novel, which chance similarity was brushed up after the event, and the publication of the book backdated, to make it seem like a prophecy.

    30. J. W. Dunne, An Experiment with Time, Faber & Faber, London, 1934; reprint, Macmillan, London, 1981.

    31. C. G. Jung, Synchronicity: an Acausal Connecting Principle, trans. R. F. C. Hull, ARK Paperbacks, Routledge, London 1985 [1955]. Based on Volume 8 of the Collected Works of C. G. Jung, The Structure and Dynamics of the Psyche, and an earlier essay, ‘Uber Synchronizitat’, Eranos-Jahrbuch, 1951.

    32. See, for example, J. B. Priestley, Man and Time, Aldus Books, London, 1964.

    33. Physiologically, these bursts of dreaming are associated with rapid eye movements (REM), and enhanced cerebral activity (especially in the region of the pons). By monitoring the eye movements and the EEG, one can therefore tell when a person is dreaming. REM sleep occurs five to six times in a normal night's sleep.

    1. Cited in P. J. Nahin, Time Machines: Time Travel in Physics, Metaphysics, and Science Fiction, American Institute of Physics, New York, 1993, p. 168. The view is from John Varley's novel, and later movie, Millennium.

    2. Methyl Iso-CyanatE, the chemical released in Bhopal, by the Union Carbide factory, resulting in the worst industrial disaster in history, the compensation claims of which are yet to be settled. Union Carbide used the symbol of a cat with nine lives for its batteries.

    3. There is a traditional nomenclature of ‘inductive’ and ‘deductive’ logic, which was used to denote what would today be called inductive and deductive inferences. Inductive inferences follow from empirical observations, but deductive inferences have been believed to be a priori, and independent of empirical facts. In this book, the term ‘logic’ everywhere refers to deductive logic. For inductive inferences, I have suggested the use of maximum likelihood estimation (or some similar principle of statistical inference) explained in the appendix.

    4. A fuller account may be found in Martin Bernal, Black Athena: The Afroasiatic Roots of Classical Civilization, Vol. 1: The Fabrication of Ancient Greece, Vintage, London, 1991. There are many more dimensions to this than meet the eye, e.g., the wholesale appropriation of a variety of technologies, or the appropriation of the infinitesimal calculus, for which last see C. K. Raju, ‘Computers, Mathematics Education, and the Alternative Epistemology of the Calculus in the Yuktibhāṣā,’ Philosophy East and West, 51 (3), 2001, pp. 325–62; and ‘The Infinitesimal Calculus: How and Why it was Imported into Europe’, paper presented at the International Seminar on East-West Transitions’, National Institute of Advanced Study, Bangalore, December 2000 (submitted for publication). Even ‘Euclidean’ geometry is probably such an appropriation, C. K. Raju, ‘How Should “Euclidean” Geometry be Taught’, in History of Science: Implications for Science Education, ed. G. Nagarjuna, Homi Bhabha Centre, 2002, pp. 241–60. For a popular account of better known cases, see George Geverghese Joseph, The Crest of the Peacock: Non-European Roots of Mathematics, Penguin, London, 1991.

    5. This is too long a story to get into here. Some more details in this regard are in Chapter 10. See also note 4 above, and C. K. Raju,

    ‘Computers, Mathematics Education, and the Alternative Epistemology of the Calculus in the Yuktibhāṣā’, Philosophy East and West, 51, 2002, pp. 325–62.

    6. This ‘wrapping around’ applies only to integers or whole numbers. However, this analogy might have been taken as seriously as the analogy of time to the real line, had physics developed computationally, and had the calculus continued to be done in the traditional Indian way of computational mathematics, where floating point calculations are done using large integers and a notion of ‘zeroing’ the insignificant. This would also have made ‘discreteness’ seem as natural a feature of time as continuity is today.

    7. If one chooses to quibble, one cannot ‘change’ the future either, one can only ‘bring it about’.

    8. For more details on the temporal relation, see N. Rescher and A. Urquhart, Temporal Logic, Springer, Wien, 1971, and A. N. Prior, Past, Present, and Future, Clarendon, Oxford, 1967.

    9. A more detailed account may be found in W. H. Newton-Smith, The Structure of Time, Routledge and Keagan Paul, London, 1974.

    10. These are worlds exactly in the sense of Wittgenstein's famous statement: ‘The world is all that is the case.’ L. Wittgenstein, Tractatus Logico-Philosophicus, German with English Translation by D. F. Pears and B. F. McGuinness, with an introduction by Bertrand Russell, Routledge and Keagan Paul, London, 1961.

    11. It is possible to present this paradox in a slightly different way. A theory is called physical if it is refutable or falsifiable. Refutability depends on the mundane ability to conceive of a bird which is like a swan in all respects except that it is black. This ability presupposes mundane time. This is the primary consistency problem addressed in my book, Time: Towards a Consistent Theory, Kluwer Academic, Dordrecht, 1994.

    12. C. K. Raju, ‘Quantum Mechanical Time’, chapter 6b in Time: Towards a Consistent Theory, pp. 161–89

    13. W. H. Newton-Smith, The Structure of Time, cited above.

    14. C. K. Raju, ‘Quantum-Mechanical Time’, chap. 6b, in Time: Towards a Consistent Theory, pp. 161–89.

    15. Technically, the difference is that the distributive law between and and or fails. For more details, see C. K. Raju, ‘Quantum Mechanical Time’, cited above.

    16. This is something of a technical matter, and those interested in the technical details may refer to my book cited earlier.

    1. C. K. Raju, ‘The Electromagnetic Field’, chap. 5a in Time: Towards a Consistent Theory, Kluwer Academic, Dordrecht, 1994.

    2. The Nyāya Sūtra (IV.2.17) asserts that ‘atoms are not further divisible’, and then states the objection (pūrva pakṣa) that this is impossible since ‘atoms are pervaded by aether’ (IV.2.18), ‘else aether would not be all-pervasive’ (IV.2.19). The reply is that the aether is ‘all pervasive by contact’ (IV.2.20). The Nyāya Sūtra of Gotama, trans. S. C. Vidyabhuṣaṇa, Panini Office, Allahabad, 1930; reprint Munshiram Manoharlal, New Delhi, 1977, pp. 131–32. Kanāda (‘atom-eater’), the founder of the ancient Vaiíeìika system, however stated the maxim: ‘there must be neither contact nor disjunction between cause and effect’. Vaiśeṣika Sùtra, II.2.6–11, Eng. translation in Encyclopaedia of Indian Philosophy, ed. K. H. Potter, vol. 2, Motilal Banarsidass, Delhi, 1977, p. 218.

    3. Mary Hesse, Forces and Fields, reprint Greenwood Press, Westport, CT, 1973, p. 95.

    4. What does ‘contact’ mean? Does it mean that the atoms of one object are in contact with the atoms of another object? And if atoms are capable of contact, do they have parts? This was stated as an ante-thesis (purva paksha) by Gautam, founder of the ancient Nyāya system, which believed in atomism. A linguistic resolution was proposed by Udyotkara, after a thousand-year long debate with Buddhists, but centuries before the same debate was taken up in Europe by Leibniz, Kant and others, after Descartes adopted and adapted this philosophy. A linguistic resolution would seem to create a new difficulty: what does it mean to say that two particles are not in contact? For the original statement of the paradox see, Nyāya Sūtra, IV.2.24, in The Nyāya Sūtra of Gautama, trans. Ganganath Jha, vol. 4, reprint, Motilal Banarsidass, Delhi, 1984. For Udyotkara's linguistic resolution, see Nyāya Varttika, trans. Ganganath Jha [1919], reproduced in K. H. Potter, Encyclopaedia of Indian Philosophy, vol. II, Motilal Banarsidass, Delhi, 1977, pp. 334–35. For the debate on the same question in Europe, see, Mary Hesse, Forces and Fields, pp. 160–67.

    5. C. K. Raju, ‘Newton's Time’, chap. 2 in Time: Towards a Consistent Theory, Kluwer Academic, Dordrecht, 1994, pp. 33–48.

    6. Ironically, in the priority dispute between Einstein and Poincaré, credit for relativity has been given to Einstein on the ground that he rejected the aether, while Poincaré ‘waffled’. Specifically, the term aether has two meanings in physics. The first is as a container, a reference frame with respect to which absolute velocity may be defined. The second is as an all-pervasive substratum, which ensures ‘contact’ and a ‘chain of causes’ between interacting distant objects. This is the original meaning, as used in Nyāya-Vaiśeṣika system or by Descartes. The first meaning derived from the posited all-pervasiveness of the aether. Einstein initially rejected the aether only in the first sense, while Poincaré at least stated the consequences of rejecting the aether in the Cartesian sense, namely that ‘the state of the world would depend not only on the moment just preceding, but also on much older states’. General relativity also seemed to restore in the spacetime manifold, the other sense of the aether as an absolute reference frame. F. Selleri (personal communication) informs me that Einstein believed in the aether at least from 1916 onwards as described in the book by Ludwig Kostro, Einstein and the Ether, Apeiron, Montreal, 2000.

    7. H. Poincaré, Science and Hypothesis, [1902], Eng. Trans., Dover, New York, 1952, p. 169.

    8. More precisely, what I mean here is the following. It is impossible to capture the qualitative features of the solutions of a (retarded) functional differential equation (FDE) by means of ordinary differential equations (ODEs). Hence, it is mathematically impossible to reduce FDEs to an equivalent system of ODEs, through a more complicated description of the state. On the other hand, it is mathematically possible to replace a system of FDEs by an equivalent system of partial differential equations (PDE) plus a system of ODEs, together with some ad hoc stipulations. (For example, the 2-particle FDEs of retarded electrodynamics may be replaced by Maxwell's equations for fields, plus ODEs of motion of each particle, given all other fields, together with the ad hoc stipulation that the fields in question are retarded.) But this results in a system so complicated and misleading that no one has actually solved the electrodynamic 2-body problem, and its qualitative properties have been misunderstood for a century. C. K. Raju, ‘Simulating a Tilt in the Arrow of Time: Preliminary Results’, invited paper presented at the Seminar on Some Aspects of Theoretical Physics, Indian Statistical Institute, Calcutta, 14–15 May 1996. ‘The Tachyonic Anti-Telephone and Tolman's Grandfather’, invited talk delivered at the Heisenberg Colloquium, Indian Institute of Advanced Study, Shimla, August 1997. ‘The Electrodynamic 2-Body Problem and the Origin of Quantum Mechanics’, paper presented at the International Symposium on Uncertain Reality, India International Centre, New Delhi, 5–9 January 1998, ‘Relativity: History and History Dependence’, paper presented at the On Time Seminar, British Society for History of Science, and Royal Society for History of Science, Liverpool, August 1999. ‘Time Travel’, invited talk at the International Seminar, Retrocausality Day, University of Gronningen, September 1999.

    9. To be more precise, Einstein's mathematical error was that he tried to reduce a system of retarded FDEs for the relativistic many-body problem to a system of ODEs by ‘Taylor’-expanding in powers of the delay. A. Einstein, L. Infeld, and B. Hoffmann, ‘The Gravitational Equations, and the Problem of Motion’, Ann. Math., 39, 1938, pp. 65–100; H. P. Robertson, ‘Notes on the Preceding Paper: The Two Body Problem in General Relativity’, Ann. Math., 39, 1938, pp. 101–4. This procedure is known to be incorrect. For mathematical details, see C. K. Raju, ‘Electromagnetic Time’, chap. 5b in Time: Towards a Consistent Theory, pp. 116–35.

    10. P. A. M. Dirac, ‘Classical Theory of the Radiating Electron’, Proc. R. Soc.A167, 1938, pp. 148–68.

    11. K. R. Popper, ‘The Arrow of Time;, Nature, 177, 1956, p. 538; ‘Irreversibility and Mechanics’, Nature, 178, 1956. p. 382; ‘Irreversible Processes in Physical Theory’, Nature, 179, 1957, p. 1297; ‘Irreversibility and Entropy since 1905’, Brit. J. Phil. Sci., 8, 1957, pp. 151–55; ‘Time's Arrow and Entropy’, Nature, 207, 1965, pp. 233–34 The Open Universe, Hutchinson, London, 1982.

    12. K. R. Popper, personal communication, letter dated 4 May 1990.

    13. P. A. M. Dirac, cited above.

    14. J. A. Wheeler and R. P. Feynman, ‘Interaction with the Absorber as the Mechanism of Radiation’, Rev. Mod. Phys.17, 1945, pp. 157–81; 21, 1949, pp. 425–33.

    15. That is, that the mean free path of a photon is of the order of the Hubble radius. J. E. Hogarth, ‘Cosmological Considerations of the Absorber Theory of Radiation’, Proc. R. Soc.A267, 1962, pp. 365–83.

    16. P. C. W. Davies, Proc. Camb. Phil. Soc.68, 1970, pp. 751–64; J. Phys. A, 4, 1971, pp. 836–45; ‘Extension of Wheeler-Feynman Quantum Theory to the Relativistic Domain’, J. Phys. A, 5, 1972, pp. 1025–36.

    17. F. Hoyle and J. V. Narlikar, ‘Time Symmetric Electrodynamics and the Arrow of Time in Cosmology’, Proc. R. Soc, A277, 1964, pp. 1–23; Ann. Phys.54, 1969, pp. 207–39; 62, 1971, pp. 44–97.

    18. C. K. Raju, ‘Classical Time-Symmetric Electrodynamics’, J. Phys. A, 13, 1980, pp. 3303–17.

    19. R. B. Partridge, ‘Absorber Theory of Radiation and the Future of the Universe’, Nature, 244, 1973, pp. 263–65.

    20. M. L. Heron and D. T. Pegg, J. Phys. A, 7, 1974, pp. 1965–69.

    21. The Poincaré recurrence theorem, in its most general form, fails with history-dependence, and it would be more correct to say that history-dependent processes increase entropy. See, C. K. Raju, Time: Towards a Consistent Theory, cited earlier, appendix to Chapter 4, and Chapters 5a and 5b.

    22. No doubt the process suggested above involves what has come to be known as reductionism. But I presume that most anti-reductionists 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.

    1. E. P. Thompson, ‘Time, Work-Discipline and Industrial Capitalism’, Past and Present38, 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.

    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 Quincentenary Review, 1990 (Summer), pp. 18–21.

    10. C. K. Raju, ‘Kamāl or Rāpalagai’, 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., Bhāskara I and his Works, Part III: Laghu Bhāskarīya, Department of Mathematics and Astronomy, Lucknow University, 1963. The Laghu Bhāskarīya was a widely used 6th or 7th century jyotisa 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 Bhāskarīya iii 22–23 et. seq., Maha Bhāskarīya, iii 37–38. Bhāskara 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 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 intelligente 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 Civilization. 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 translations of Arabic works, or of Byzantine Greek texts which translated Arabic works. The story of ‘Greek’ origins is thus a racist appropriation 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 Alternative Epistemology of the Calculus in the Yuktibhāṣā’, 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 Seminar on East-West Transitions, National Institute of Advanced Study, Bangalore, December 2000 (submitted for publication).

    19. For detailed quotations, etc., see C. K. Raju, ‘Kamāl or Rāpalagai’ cited earlier. Briefly, the Laghu Bhāskarīya II.8 gives a rule for determining the local longitude using a clepsydra. Bhaskara I and his works, Part II: Laghu-Bhāskarīya, ed. and trans., K. S. Shukla, Department of Mathematics and Astronomy, Lucknow University, 1963, p. 53.

    20. E. S. Kennedy, A Commentary upon Bīrūni'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, acknowledging 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 Alternative Epistemology of the Calculus in the Yuktibhāṣā’, 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 Bīrūnī. Al Bīrūnī'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 ‘Kamāl or Rāpalagai’ 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. (Extracted from ‘Lunar and seasonal calendar in the Trobriands’, J. Anthropological Institute of Great Britain and Ireland, 56–57, 1926–27.)

    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 Agricultural 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 overworked 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, 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 Colloque International pour la Danse et la Recherche Choregraphique Contemporaines (Paris: GERMS)(to appear).

    43. David Wood, The Deconstruction of Time, Humanities Press International, 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.

    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 Sāmanna Phala Sutta of the Dīgha Nikāya. 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 Visnu Purāṇa, 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 Brahmā. 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 Brahmajāla Sutta of the Dīgha Nikāya 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 Dīgha Nikāya, 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 Lokāyata or Cārvāka only from their opponents, but the relation here is marked by mutual contempt and explicit abuse. There are two meanings of ‘Lokāyata’. The first is lokesu (people) + āyatah (prevalent) = people's philosophy; the second, attributed to a 5th century CE Buddhist commentator Buddhaghosha, is loka ([this] world) + āyatana (basis) = this-worldly 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 (Jādavpur), both of whom are cited earlier in this book, it being assumed that the one referred to is clear from the context!

    8. T. W. Rhys-Davids, trans., Dialogues of the Buddha, cited earlier, vol. 1, pp. 73–74; quoted in D. P. Chattopadhyaya, Lokāyata: A Study in Ancient Indian Materialism, Peoples Publishing House, New Delhi, 1959, p. 510; cf. Dīgha Nikāya, trans. Maurice Walshe, cited above.

    9. Debiprasad Chattopadhyaya and M. K. Gangopadhyaya, eds., Cārvāka/Lokāyata: An Anthology of Source Materials and Some Recent Studies, ICPR, New Delhi, 1990, pp. 246–54. Mādhava and his brother Sāyana were ministers in the Vijayanagar empire which sent Vasco da Gama into ecstasies over the wealth in India. Sarva Darṣana 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, Lokāyata, cited earlier. He also examines in depth the related bias of patriarchy.

    12. D. P. Chattopadhyaya, in Lokāyata, 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 agriculture.

    13. D. R. Shastri, A Short History of Indian Materialism, Sensationalism and Hedonism, Calcutta, p. 36; cited in Chattopadhyaya, Lokāyata, p. 18. Reproduced in Cārvāka/Lokāyata, ed. Debiprasad Chattopadhyaya and M. K. Gangopadhyaya, pp. 394–431.

    14. D. P. Chattopadhyaya, Lokāyata, p. 31. This is an old saying, attributed to the Cārvāka mentor Brhaspati by Madhava in his Sarva Darṣana Samgraha; see Cārvāka/Lokāyata, 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'rān.

    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 Darssna Samuccaya. D. P. Chattopadhyaya, Lokāyata, pp. 29–30. Cārvāka/Lokāyata, ed. Debiprasad Chattopadhyaya and M. K. Gangopadhyaya, p. 260.

    18. Dasgupta, Indian Philosophy, vol. 3, p. 536.

    19. The elite hostility to Lokāyāta is well known. But even the Buddha rejected the teaching of Lokāyata doctrines as a dukkata offence; D. P. Chattopadhyaya, Lokāyāta, pp. 38–39; F. Max Mueller, ed., Sacred Books of the East, Oxford, 1859, vol. 20, pp. 151–52.

    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 Bhāsya 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 Ajātasattu'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. Kaccāyanagotta-Sutta, Samyukta Nīkāya, 2.17.

    31. We recall from Chapter 1 how Kassapa responded to Pāyāsi 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 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, Lokāyata, 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. Vaiśeṣika Sutra 2.10. K. H. Potter, ed., Encyclopaedia of Indian Philosophy, vol. 2, Motilal Banarsidass, Delhi 1987, p. 218.

    38. Vaiśeáika Sutra 1.15. Potter, ed., Encyclopaedia of Indian Philosophy, vol. 2, p. 216.

    39. The Nyāya Sūtra (IV.2.17) asserts that ‘atoms are not further divisible’, and then states the objection (pūrva pakṣa) that this is impossible since ‘atoms are pervaded by aether’ (IV.2.18), ‘else aether would not be all-pervasive’ (IV.2.19). The Nyāya Sūtra of Gautama, trans. Ganganath Jha, vol. 4, reprint, Motilal Banarsidass, Delhi, 1984, pp. 131–32.

    40. Nyāya Sūtra, IV.2.20. Ibid.

    41. Nyāya Sūtra, 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’. Nyāya Varttika, trans. Ganganath Jha [1919], reproduced in Encyclopaedia 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, hencemay 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 ‘Arabī, 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 Aurangazeb who slew his Sufi step-brother Dara Shūkoh. With the collapse of the Moghul empire, this tendency dissipated before it could take hold.

    53. For example, Shaikh Ahmad Sirhindi, Maktūbāt (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 examination 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 circularity.

    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 Yuktibhāṣā’, 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 Education11. Available at http://www.ex.ac.uk/~PErnest/pome/art18.htm.

    60. P. C. Mahalanobis, ‘The Foundations of Statistics (A Study in Jaina Logic)’, Dialectica8, 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. Chattopadhyaya, 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.

    65. Dīgha Nikāya, trans. Maurice Walshe, p. 97.

    66. S. C. Vidyabhuṣan, A History of Indian Logic, Calcutta, 1921, reprint Munshiram Manoharlal, New Delhi, 1977.

    67. That is, if Bhadrabāhu really was the brother of the astronomer Varāhamihīra, roughly a contemporary of Āryabhata, 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 appendix 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 Belatthaputta.

    73. Dīgha Nikāya, trans., Maurice Walshe, p. 541, footnote 62 to Sutta 1.

    74. Ibid. pp. 78–79.

    75. Mulamādhymakakārika 18.8. David J. Kalupahana, trans., Nagarjuna, SUNY, New York, 1986, p. 269.

    76. Dīgha Nikāya, 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 objective 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 Biology, 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: Mādhyamika Buddhism from Chinese Sources, Motilal Banarsidass, Delhi, 1991, p. 36. An interesting 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. Dignāga clearly has the last word in S. C. Vidyabhuśaṇ'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, Vidyabhuśaṇ, 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 Hetucakra, and the Sanskrit formulae of the Nyāyavarttika 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 Banarsidass, 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 perspective 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 Nyāyavarttika is implicitly, explicitly, and polemically against Buddhist philosophy; so I see no reason to regard Udyotkara's as the last word on Dignāga, 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) Dignāga's logic, in his Pramānasamuccaya, cannot be instantly formalised, 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 one inferred a fiery hill—from an apparently smoky hill one inferred an apparently fiery hill.

    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 statement, 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 and E.O. Wilson, Genes, Mind, and Culture, Harvard University Press, Cambridge, Mass., 1981. R. Dawkins, The Selfish Gene, Oxford 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 Sociobiology 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.

    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 Culture, 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 supercomputer, Param. An outstanding scientist, his previous publications include Time: Towards a Consistent Theory (1994) which put forward a new system of equations for physics.


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