Cover image for Time : its origin, its enigma, its history
Time : its origin, its enigma, its history
Waugh, Alexander.
Personal Author:
First Carroll and Graf edition.
Publication Information:
New York : Carroll & Graf, 2000.

Physical Description:
280 pages : illustrations [8] pages of plates ; 24 cm
Format :


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Material Type
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Central Library BD638 .W38 1999 Adult Non-Fiction Non-Fiction Area

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"Calendars, eons, nanoseconds, millennia - no instrument or measurement is overlooked in this wholly entertaining and intellectually bracing book which chronicles the enduring human quest to explain, utilize, and understand the enigma of time." "An informal and informative tour through science and history, it introduces a host of colorful characters ranging from the primitive homo erectus to modern time explorers, from Zeno to Caesar to Pope Gregory, Galileo, Sir Isaac Newton, and Albert Einstein, whose theory of relativity posited time as the fourth dimension of our physical universe."--BOOK JACKET.Title Summary field provided by Blackwell North America, Inc. All Rights Reserved

Reviews 2

Booklist Review

In the contrast between these two works on the shared topic of time, readers may glimpse the impressive analytical power of modern science--and its imaginative sterility. In his book, Gribbin confronts time as a theoretical puzzle: When did time begin? What is the age of the universe? As one of the scientists responsible for parsing the latest data collected with the Hubble Telescope, Gribbin well understands that since the discovery of the Big Bang, the task of gauging universal time has conflated with the challenge of measuring universal space. By measuring space with new precision, Gribbin and his colleagues have finally set plausible ages for the stars and have thereby established an unprecedented congruence between observation and theory. This feat required rare expertise, but Gribbin recounts its accomplishment with lucid economy, inviting the nonspecialist to share in the intellectual triumph and the drama that led up to it. Nor has he neglected the human emotions informing the drama: the stubbornness, the jealousies, and the credulity. Still, his analysis reduces time itself to a mathematical construct. And even a mathematical construct embracing the entire universe cannot tell us many of the things we most want to know about time. Enter Waugh. As a composer, a critic, and a generalist, he regards time not simply as a scientific riddle but rather as a mysterious current in which we humans think, feel, and act. He grants the genius of scientists (from Ptolemy to Einstein) who have tried to define and quantify that current. But the mystery remains, inspiring sublime poetry, religious fear, and bemused perplexity. Thus, although Waugh cannot match Gribbin for rigor, his witty and capacious book succeeds in conveying the richness of time as a cultural phenomenon, laden with historical irony, theological casuistry, and artistic subtlety. So while Gribbin will attract readers seeking to understand the universe, Waugh will draw those trying to understand that much larger enigma: humanity. --Bryce Christensen

Publisher's Weekly Review

From the beginning of time to the end of days, from the 60-second minute to the Roaring '20s and the first millennium, the confident Waugh (author of Classical Music: A New Way of Listening, and grandson of novelist Evelyn) has written a zippy and hard-to-classify meditation on types and ways of thinking about time. Each of Waugh's chapters covers one unit of time (seconds, centuries) or one subject related to it (the Big Bang, the afterlife). Sumerian counting methods, early medieval theology, Anglo-Dutch disputes over the spring-driven pocket watch, 19th-century essayist William Hazlitt, the rise and fall of Greenwich Mean Time and a 156-year-old tortoise (among other topics) give zest to Waugh's paragraphs. Waugh clearly has assembled this intriguing book from his own researches; he seems especially good on English folklore and on ancient Rome. Sometimes he presents legend as if it were truth, however, or makes mistakes. Zeno's paradoxes (in which a tortoise wins a race with Achilles) did not go mysteriously unsolved until the invention of quantum theory. The Greek-language Old Testament called the Septuagint wasn't really produced by six translators from each of Israel's 12 tribes. The "existence of life" cannot refute the laws of thermodynamics. And so on. Moreover, Waugh can be funny, but his attempts at verve and humor make him sound silly or glib: the ancient Sumerians brought, he writes, "a much-needed element of calm into the frantic maelstrom of ancient life"; and he says, "It is a wonder that Jesus was so thin, for food was never far from his thoughts." Plenty of readers may enjoy Waugh's work, but its flaws detract from its appeal. (May) (c) Copyright PWxyz, LLC. All rights reserved



Chapter One INITIUM Beginning `In the beginning God created Heaven and Earth, and the Earth was without form and void; and darkness was upon the face of the deep.'     Yes, yes, we all know that, but what happened before the void, before the darkness was upon the face of the deep? Or, as the philosopher Bertrand Russell asked when he was a seven-year-old schoolboy, `If God made everything, who made God?'     The Bible does not tell us what happened before the beginning, which is deeply frustrating, for we would all love to know. According to the myth of Genesis there was no before, or, at least, not in any sense that we could understand. We find it hard to grasp the idea that time, once upon a time, may have had a beginning and that one day it will probably come to an end. `That's not possible,' the inquisitive mind will urge; `if time had a beginning, what was happening two hours before it began? How can it have started without something having happened to make it start in the first place? And how could that something not have existed before the start which it was supposed to have created?'     It is not difficult for an averagely inquisitive child to find himself embroiled in a confusion like this after only a few minutes of stargazing. Gawping up at the sky on a balmy night during the summer holidays, children are particularly adept at latching on to the antinomies of time and space and asking questions that their parents, however well meaning, cannot begin to answer. For the parent, who has long ceased to ponder these problems and is living in denial, a child's fertile questioning can lead to irritability:     `Dad, what's at the end of the universe?'     `Er, more stars and stuff like that.'     `No, I mean after all the stars, what is beyond them?'     `Oh, sorry ... um ... space.'     `And what's beyond the space?'     `Nothing, just more space. Go to bed.'     `Yes, I know, but what's at the end of that?'     `Listen, God made it all. He is infinite, and he made the universe, which is also infinite, OK?'     `How did he make it?'     `He just did -- he is all-powerful.'     `But how big is the universe?'     `I told you. It is infinite. You cannot measure it -- it goes on for ever.'     `Can God measure it?'     `No.'     `But you said he is all-powerful.'     `Yes, then ... but ...'     `So, if God is all-powerful, can he make another universe that is so complicated that he cannot measure it?'     `Yes, no -- yes -- he is all-powerful.'     `You said he is all-powerful, but if he cannot make such a universe, then he cannot be all-powerful, can he? And yet, if he is able to make a universe that is so complex that he cannot measure it, then he is still not all-powerful because he cannot measure it. So, either way he cannot be all-powerful, and I thought you said ...'     `I thought I told you to go to bed.' Children are remarkably perspicacious when it comes to getting under the skin of these sorts of problems. Adults, on the other hand, are adept at brushing them aside. `They fuck you up, your mum and dad,' as the poet Philip Larkin so famously put it, and one of the ways they most persistently `fuck you up' is by not concentrating when you ask them interesting questions. `Go to bed' cannot be a satisfactory answer to the child's paradox. In the back of our minds we are all aware that questions about infinity, simple questions about the measurement of time and space or God's omnipotence, have not been satisfactorily resolved. We want to understand them, we would love to be able to stuff infinity into a nutshell and squint at it through a lens, or, as William Blake put it, To see a World in a Grain of Sand, And a Heaven in a Wild Flower, Hold Infinity in the palm of your hand, And Eternity in an hour. But a pragmatic adult usually thinks to himself, `I can either spend the rest of my life going round and round in circles trying to work it out or -- forget it.' But this is a form of mental laziness. In point of fact the child's argument can be taken apart without too much difficulty, but it needs the sort of faint effort that parents are not always willing to give. I offer three possible ripostes, each of them better than `Go to bed': 1. If Dad had been a very religious man he could have answered like this: `God is all-powerful -- that is an irrefutable tenet of my faith. The fact that you are unable to understand his omnipotence or the limitless space of his universe is simply because your own little brain is finite -- it occupies a finite space and is filled with a finite number of brain cells. Obviously, you cannot expect to understand infinity with your little finite brain. Only God can understand infinity because his own wisdom is alone infinite. It is not for us to understand infinity -- we will never be able to do that -- but only for us to believe in it as an act of faith in God.' If that does not succeed in sending the wretched youth to bed, perhaps this one will: 2. `My child, you fail to understand the nature of power. Power is about possibility. Puissance , the French word for power, is derived from the root word pouvoir -- "to be able". The more power you have, the more you are able to make possible things happen; if you are all-powerful, as God is, you are able to make all possible things happen, but no amount of power can make the impossible happen. For instance, God, who is all-powerful, cannot draw a circle which is shaped like a square; that is clearly impossible and therefore beyond the realms of power to achieve. You are suggesting that God is not all-powerful only because he cannot do something that is impossible. Your argument proves to me only that you do not understand the meaning of the word power.' This, especially if delivered in a monotone, should put the child off his keen-nosed questioning. It will certainly make him think twice next time. But there is an alternative, perhaps more compelling argument that a father might employ if he wishes to finish the thing off for good: 3. `Young whippersnapper, if God is all-powerful he must possess the power to create a universe which is so large that it cannot be measured -- not even by himself. When, and if, he creates such a universe he will no longer be all-powerful, since, in that event, he will not possess the power to measure his new universe. But that is only a possibility for the future; it relies on "when and if". For the moment he remains all-powerful. He is also infinitely wise, and it is therefore most unlikely that he would ever create an immeasurable universe which would have the effect of turning him from an all-powerful God into a God whose powers are limited, because of his inability to measure the universe that he himself created. Your argument is weak; you must be suffering from exhaustion. May I suggest you retire to your bedroom until the morning?' We have come a long way in the last few hundred years, and the human race is freer from religious dogma and political interference than it has ever been. In the Christian faith, God invented time, or more specifically invented our universal time. There was no `before that'. God inhabited his own temporal space zone into which he thankfully plopped us and our tiny universe. We are finite, but God's time rolls on for ever, around us and strangely disconnected from us. The biblical account of Genesis -- `In the beginning God created Heaven and Earth' -- was discovered in the 1870s by the English archaeologist George Smith to have been a myth copied by the Jews from the Assyrians, ancient descendants of the Sumerians. Piecing together tens of thousands of shattered fragments of cuneiform tablet inscriptions which he had found buried under a mound at Kouyunjik, opposite the town of Mosul in modern-day north-western Iraq, Smith shocked the Christian world by proving that large parts of the first book of the Bible were taken from the Chaldean account of Genesis, assimilated by the Jews at the time of their captivity in the region of Chaldea some 700 years before Christ. The Assyrians, jealous neighbours of the ancient Babylonians, were similar to the Jews and, later, to the Christians, in their belief that the Creation was caused by one all-powerful being. The Babylonians, on the other hand, held that the Creation of the world was the result of a quasi-sexual act that took place before the beginning of time in some murky underworld. Tatvu (the sea) with Absu (the deep) sludged about in the formless mud and begat Mummu, the representation of chaos. Mummu needed no sexual partner to conceive Lahma (the force of growth) and Lahama (silt). Their offspring were Kisar and Assar, a brother and sister representing the lower and upper expanse (i.e. heaven and earth in a formless, embryonic stage). Their incestuous liaison produced more births: Anu or Ouranus is born, the patriarchal god of the sky, or heaven, as well as his sister Anatu, goddess of the earth. Needless to say these two unite and spawn four more god-like figures: Vul, Bilcan, Hea and Istar (see Table 1). This at least is one version of events, and there are many others.     In the Babylonian myth of Enuma Elish, it seems that Absu (the deep) entered into a relationship with the chaotic Mummu: When on high the heaven had not been named, Firm ground below had not been called by name, Naught but primordial Absu, their begetter,. And Mummu-Tiamat, she who bore them all, Their waters comingling as a single body. The Zunis, a tribe of Pueblo Indians living along the Zuni river of New Mexico, held to similar beliefs. For the Zuni folk everything started in Anon, the nethermost world, where the seed of men and creatures took form and increased `even as eggs in warm places speedily appear. Everywhere were unfinished creatures, crawling like reptiles one over another, one spitting on another or doing other indecencies, until many among them escaped, growing wiser and more manlike.' Other myths centre on the idea of the Creation springing from a cosmic egg. One African version goes so far as to describe the impatience of one androgynous hatchling who crashes out of the egg before maturation in an attempt to control the creation process. By doing this he accidentally takes parts of the egg with him, which causes an imperfect world to be made.     All myths and religions eventually (to the scientific mind at least) fail to give a satisfactory answer to the central question: did time have a beginning or not? That is the question to which all schoolchildren are burning to have an answer -- an answer that neither religion nor myth is able to provide without requiring a leap of faith, an unwilling suspension of our disbelief and a tiresome amputation of our natural organs of logic. Socrates was, according to Xenophon, Aristophanes and Plato, one of the brightest men of his age. He was ugly to look at, maybe; statues inform us of his snub nose with grotesquely wide nostrils and a gaping mouth; he was a squat, cocky figure with a shrew called Xanthippe for a wife -- this was his external lot. To Plato, though, he was `all glorious within' and was reported to have a sense of humour in spite of his staggering conceit. But although his enemies thought Socrates the most irritating man alive, his disciples adored him. Cicero said of him that he `brought philosophy down from the heavens to earth'. Plato, some 40 years his junior, devoted a lifetime to recording the wisdom of his master. The importance of Socrates was not what he wrote (as far as we know that was nothing at all) or what he said -- it was the way he made other people think. He used to call himself `the midwife of other men's thoughts'. His famous trick was feigning ignorance (a technique now known as Socratic irony). By asking seemingly naive questions, he was able to squash his rivals in debate -- a similar technique, one supposes, to the relentless four-year-old who keeps asking `Why, Daddy, why? Daddy, why, why, why?' as a knee-jerk reaction to any adult postulate. That is why others found Socrates such a pain in the neck; but it also explains his importance.     Socrates was influenced by Parmenides, the Eleatic. It is recorded that they met, once, when Socrates was a young student and Parmenides an old man at the height of his fame. Zeno was one of Parmenides' star pupils and has for 2,000 years been but a footnote to the history of philosophy, for it was not until the nineteenth century that Charles Lutwidge Dodgson, better known as Lewis Carroll, the strange genius behind Alice in Wonderland , and later the philosopher Bertrand Russell noticed the importance of his work.     Five paradoxes are all that remain of Zeno -- not written down but passed on, the first four by Aristotle in Physics and a fifth (possibly not by Zeno) cited by Simplicius in his commentary on Aristotle. Zeno came up with his paradoxes around about 460 BC. The first is probably the most famous:     Zeno asks us to imagine an athlete. History does not relate, but one might suspect that Zeno's own narration might have involved a description of bulging biceps, well-oiled thighs and locks of golden hair that are blown by Zephyr's soft winds on the racetrack of Olympia -- for it was ever thus that the Greeks enjoyed describing their athletes. Zeno sets the problem. If the athlete is to run a race of 100 metres, how is he to pass the winning post at the far end? For to get there he will first need to pass the halfway mark at 50 metres. Once he has arrived at the 50-metre mark, he will still have an equal distance to run; yet to complete the last 50 metres he must first pass the 75-metre point. Wherever he is, however far from or close to the winning post, our oily friend has a remaining distance to travel which he cannot complete before he has run half the distance first. As we keep dividing the remaining distances in two, he will get closer and closer to the finish without ever reaching it -- so, according to this anomaly, he can run his race, but he will never reach the end. Looked at from another perspective, our beleaguered Adonis can never even start. Inverting the same argument, we can see that for him to reach the end he must get to the 50-metre mark, but to get there he must have already passed the 25-metre point. But how is he to reach the 25-metre mark if he has not already got to the 12.5-metre mark? And so on and so on. He cannot go one millimetre until he has first gone half a millimetre. If this series of divisions is infinite (and mathematics tells us that it is), then the athlete can never start his race because there will always be one more tiny subdivision that he must reach before he can proceed to the next.     It does not take a genius to work out that there is something wrong here, but the question is: what is it that causes this to be a paradox? We all know that athletes can and do run races and that they have no problems in either starting them or finishing them -- Zeno was not suggesting that they do. The fault, it seems, lies with mathematics and its relation to reality. In maths you can, in principle, divide any number higher than zero by two and get a meaningful result, but what Zeno's paradox seems to be telling us is that, in the physical world, mathematical principle does not seem to apply. If the athlete succeeds in reaching the winning post it must be that at some stage he reaches a point so close to the winning post that the remaining distance between him and it is so minute that it cannot be divided -- with the happy result that he manages to reach his destination. In other words there is a physical limit to how small a space can be. Let us call this smallest unit of space a minimum .     Now, assuming that this minimum does exist (and it certainly appears to offer a rational solution to Zeno's paradox), then we can assume that as the athlete runs towards the post, the remaining distances (which are in theory constantly dividing by two) get smaller and smaller but not ad infinitum , for when he reaches the last minimum of space, no further division is possible, with the result that he is able to cross the finishing line. The implication, then, is that movement from one end of a minimum to the other cannot take any time, because if the minimum cannot be subdivided then there can be no time in which the athlete can be said to be between the two ends. Either this, or the time it takes to traverse a minimum must be an equally minimal, indivisible unit of time. Versed scientific minds which have bothered to follow this train of thought will have noticed that we have now arrived at the gateway of quantum mechanics and Einstein's relativity. Zeno could not have been expected to understand either of these extraordinary theories from where he was sitting in his Eleatic gymnasium all those thousands of years ago, yet the raw material was there. It was with `thought experiments' such as these that Einstein first spawned the philosophical ideas about space and time which were to lead to his two gigantic scientific theories of relativity.     So Zeno tells us that space and time cannot regress by infinitely small degrees because, sooner or later, we will reach an indivisible minimum . Fine -- well, almost fine. While Zeno and others are congratulating themselves on the smooth and satisfactory course from paradox to interesting conclusion, others may have spotted a problem. An even more perplexing second paradox seems to have evolved from our conclusion to the first.     Imagine a race between something spectacularly fast (let's say a photon) and something notoriously sluggish (like a slug). Light travels, we are told, at 299,792,458 metres per second -- the fastest speed there is. Slugs, on the other hand, may not be the slowest movers in our universe, but they are unquestionably slower than light, taking perhaps more than three days to cover a kilometre. Now, if the slug and the photon were to race each other, even a chicken brain should be able to predict the result. But let's assume that the race is only one minimum long. We know that a minimum cannot be subdivided, so that neither the slug nor the photon can, at any moment in time, be perceived to be between the starting and the finishing posts. Assuming they both set off at exactly the same instant, they must arrive at the finishing post together. The slug cannot be slower than the photon. If they race over two kilometres -- a distance of x minima -- the result will consequently be the same. Oh dear, another paradox! Here we need quantum -- in the form of Heisenberg's Uncertainty Principle -- plus a decent smattering of relativity theory to help us out. But that is for later. The question that holds us here is how can Zeno's paradox help us to untangle the antinomies of time?     In the early part of the twentieth century the quantum physicist Max Planck, without reference to Zeno, established a term for the minute distance that we have been jauntily calling a minimum . He called it a `Planck length'. He also invented `Planck time' as the smallest indivisible unit of meaningful time. It had been noticed for some while that the predictable classical laws of gravity and space-time ceased to operate when observing extremely small things like atoms and particles or even less small things under extreme conditions. This observation has formed the basis of modern quantum mechanics. Extrapolating from the relative sizes of the constant of gravity, the speed of light and Planck's constant (being the relation between the wave nature and the particle energy of a proton), he was able to come up with his definition of a Planck length; described as `the smallest measurement of length which has any meaning', it is roughly [10.sup.-33] centimetres, which is [10.sup.-20] times the size of a proton. Planck time is therefore calculated as the time it takes light (the fastest of all things) to travel the distance of a Planck length, a feat apparently attainable in [10.sup.-43] of a second, thus the smallest unit of meaningful time.     The most popular theory about the birth of our universe is known as `the big bang', a babyish name coined as a term of disparagement by a Yorkshire astronomer, Sir Fred Hoyle, for a scientific theory that he once admonished for being `about as elegant as a party girl jumping out of a cake'. The theory came about after that lawyer-turned-astronomer, Edwin Hubble, discovered in the late 1920s that our galaxies are flying apart from each other. This led to the belief that all the matter in our universe is the shrapnel from one gigantic explosion flying away from a central hot point into the great unknown. Hubble's discovery of the expanding universe marked the beginning of a whole new phase in cosmology. Before that, the universe was considered to be eternal and unchanging. This idea had settled in the brains of men as deeply as an ingrained universal truth can settle -- so much so, in fact, that Einstein, working on his first theory of relativity in 1911, when he produced an algebraic sum that showed the universe to be expanding, in disbelief added an extra term to his equation to steady it -- an action he later described as the `biggest blunder' of his entire career.     Hoyle is not alone among dissenters. Professor André Linde of Stanford University, California, accepts the principle of the big-bang theory but has put forward his own version showing that our big bang might have formed just a fractional part of the act of creation. Unveiling a computerised simulation of his new theory in January 1999, Professor Linde explained: Each of these peaks is a huge new part of the universe, which you can consider as the beginning of another Big Bang. From the point of view of the general geometry of space, our part of the universe has been created, but other parts of this same universe are still being created. If life in our part of the universe were to disappear, then it will appear someplace else. So the universe as a whole becomes immortal. This is advanced thinking. Most scientists are currently holding with the theory that the universe formed from a single helium explosion some 15 billion years ago. The date is approximate but has been gleaned from a careful study of background radiation in outer space and the generous sharing of information between astronomers and physicists. Scientists believe they have an understanding of the conditions that existed from 0.0001 of a second after the moment of creation. Everything that existed was squeezed into a radioactive fireball with a density 100,000 billion times that of water, and it was hot -- very hot: 1,000 billion degrees above absolute zero. In these conditions particles of light become so energetic that they are able to convert themselves into particles of matter, swapping energy for mass, as Einstein demonstrated was possible in the most famous of all mathematical formulations: E=mc² , where E stands for energy, m for mass and c for the speed of light (Einstein's universal constant).     Lee Smolin, a visionary theoretical astrophysicist from Los Angeles, suggests that the universe might have been evolutionary, developing and correcting itself along Darwinian lines. If this is the case then a proton now might not behave like a proton used to behave 15 billion years ago and if this is true, then much of the commonly accepted data that has been collected by scientists concerning the age and development of our universe may in fact be wrong. Back to square one!     But for those who hold with the traditional view, Lee Smolin and his ilk are an irrelevance. The question they would like answered is: what happened before that 0.0001 of a second after the big bang? Here we get into the mysterious world of `singularities' and this, once again, is where the normal laws of physics inevitably break down. A singularity is a point described by Stephen Hawking and others as possessing infinite density (in this we presume him to mean mathematically, not physically infinite -- scientists are careless with words). Such points come into being as the result of the enormous gravitational forces of black holes in space. In brief, a black hole is a collapsed star; the relation of its mass to its density has reached a critical limit so the star becomes overwhelmingly dense and hot, with its corresponding force of gravity so strong that nothing, not even light, is able to escape from it. Everything that exists -- time, space, energy and matter -- is wrapped around it and squeezed down to the size of a single, invisibly tiny dot. This is what is meant by a `singularity', and it is widely believed that the big-bang explosion from which our universe was created derived from just such a singularity over 15 billion years ago.     When we consider the meaning of time, it can be explained only as a by-product of events. One thing happens, then another, so only by two events occurring can a formulation of time come into being. Einstein described things as `events' because a thing (and by this he means absolutely anything from a particle to a policeman) exists in only one form in a particular place at a particular instant in time -- at no other instant of time was it or will it be exactly the same again, for all things are changing constantly. In this way Einstein could maintain the clear notion that `things' are indeed `events'. Events, and only events, are what give us a sense of `before' and a sense of `after'. Similarly, duration (or time lapsed) has to be understood in terms of events -- there is no other way. Time can be measured only through the medium of events and so, naturally, if there were no events, time would simply cease to exist. Equally, if there were only one event, anywhere in the whole universe and nothing else outside it, time would have no conceivable meaning.     A singularity presents just such a possibility. To ask what happened before the singularity is a nonsensical question. There can be no `before', nor any `after', nor even a duration. At the point where a singularity comes into being, time just ceases to function. To a philosopher the very idea of a uniquely single object surrounded by nothing at all dictates that this must be the case. Philosophers are supported in their `thought experiments' by Einstein's algebra for Special Relativity , which demonstrates conclusively that time can be warped by the effects of gravity to such an extent that, in the extraordinary conditions of a singularity, it would simply vanish from being.     There is no point in suggesting that a singularity might be only a few billion light years from a star. The effects of a singularity are such that space and time are stopped; there can be no relative distance from a singularity to any other point outside itself as it is a closed universe. To say that our universe was created from a singularity is therefore not completely accurate, since there is no meaningful `before' or `after' where singularities are concerned. All we can say is that time began roughly 15 billion years ago and exactly one unit of Planck time (or a Zeno minimum ) into its creation. In other words the universe came into being when it was already [10.sup.-43] seconds old. Another wretched paradox? Not really, because Zeno taught us that neither time nor space, those two inseparable dimensions of being, can be divided beyond a certain point. Zeno's fancy athlete arrives at the finishing line of his race in just the same way as the first unit of time springs into being from the timeless void of a black hole singularity.     Another simple, non-mathematical way of telling that the universe, and therefore time itself, must have had a beginning lies in a solution that Edgar Allan Poe found to the long-running debate over Olbers' paradox. Poe (1809-49), admired for his ghoulish, Gothic tales and his fine poetry, was also something of an amateur scientist and, a year before he died, wrote a prose poem entitled Eureka in which he explained an ancient mystery. Heinrich Olbers, a nineteenth-century German astronomer, was not the inventor of his paradox -- someone else did that -- but by wrongly suggesting a solution to it in 1823 he broadened the debate, and the paradox was called after him.     What Olbers' paradox suggests is that in an infinite, unchanging universe (such as mankind believed it inhabited in Olbers' time) there should be no night sky. How can a dark universe be full of an infinite number of bright stars? If the night sky is really as we believe it to be, an infinite space filled with an infinite number of bright stars, then how come it is dark when we look at it? Surely, if space is really infinite then it should twinkle with brightness in every direction, for whichever way you look your line of vision should intersect with the brightness of a star. Johannes Kepler, the brilliant seventeenth-century scientist who discovered the laws of planetary motion which led to Newton's law of gravity, had toiled over this paradox too. By the end he was quite mad, had rotten breath and thought himself to be a dog. Newton and Halley had also puzzled over Olbers' paradox (though it wasn't called that then) but the obvious answer, one that was staring them in the face, remained unseen until Poe explained the phenomenon of the dark gaps between stars which he called `voids': The only mode, therefore, in which we could interpret the voids which our telescopes find in innumerable directions, would be by supposing the distance of the invisible background so immense that no ray from it has yet been able to reach us at all. To Poe this was a gigantic discovery. Eureka! But sadly, nobody paid him much attention -- after all, he was a poet and a writer of Gothic short stories, not a scientist. Why should he know anything?     Kelvin had skirted the same solution in 1904, and a follower of his, the Irish scientist Fournier D'Albe, spelt it out even more succinctly in 1907: `If the world was created 100,000 years ago, then no light from bodies more than 100,000 light years away could possibly have reached us up to the present.' The answer to Olbers' paradox lay in the simple fact that light takes time to reach us. Looking at the darkness between the stars of a night sky should have been enough to inform our ancient ancestors that the universe had a definite beginning.     So much for stargazing science. Before that, scholars attempted to calculate the age of our universe by using history, the Bible, Aristotle and any scriptural texts they could lay their hands on -- and a very unreliable method that turned out to be.     One scholarly scheme consisted of counting backwards from Jesus's time through Roman and Near Eastern eras to the ages of Abraham and Isaac, who begat Jacob the father of Judah, whose son, Perez, begat Hezron, and so on and so forth, laboriously marking each generation of this spectacularly fatuous family tree as a period of 30 years and then making the odd `leap of faith' just when the trail goes faint and the Bible gets hazy. This method usually offered some ballpark figure that could then be rounded up, or down, to the nearest 1,000 years in order to suit some fanciful millennium-creation theory. One of God's days, as we shall later see, is reckoned as 1,000 years.     In the Septuagint, a translation of the Bible undertaken by 72 Jewish scholars (six from each of the 12 tribes of Israel), there is a calculation that puts the Creation of the universe at 5,500 years before Christ. Originally a Hebrew document, the Septuagint was later used by the Christians to lend credence to certain Christian arguments; this enraged the Jews so much that they eventually abandoned the Septuagint altogether. According to the Christian reading of this sacred text, Christ was born not on the turn of a millennium as some had thought, but right in the middle of one. If God created man on the sixth day then Jesus, the beatific symbol of mankind, must have been born in the middle of the sixth millennium, so the Creation could be placed with historical confidence 5,500 years before the birth of Christ. Others worked it out differently. The Venerable Bede, for instance, dated the Creation 3,951 years before Christ, arguing vehemently that 49 years (seven times seven years) had elapsed in human terms between God's creation of light out of the void and his completion of the process on the seventh day. Therefore (and this is typical of the bizarre logic of the medieval theologian), one needs to knock off 49 years from the 4,000 which Bede claimed others had postulated as the date of the Creation, in order to arrive at the true date of the Creation: 3951 BC. Of the many theories that abounded, perhaps the most successful, or at least the one that gained the widest approval, was a calculation by the Irish divine, Archbishop James Ussher. Ussher was head of the Anglican Church in Ireland, and it was he who published in 1656, in his chronology Annales veteris testamenti a prima mundi origine deducti (The years of the Old Testament, calculated from the First Origin of the World) , the view that the Creation of the world took place in 4004 BC, precisely at midday on 23 October! The archbishop pointed out that Herod the Great was known to have died in 4 BC and that Jesus, or so the story goes, was born in the reign of this Herod. Jesus must therefore have been born in or before 4 BC. Ussher's views were hugely popular throughout most of the Christian world, where 4004 BC became widely accepted as the official date of the Creation. Which was not to say that Ussher, or any of the others for that matter, believed that time itself started then.     Time was there all along. What God did was to place the Creation of the universe into his pre-existing mould, which was made from eternal time. St Augustine, who was as obsessed by time as he was by his mother Monica, believed that God actually fashioned our universe out of time, using it as a raw material. Leibniz, the seventeenth-century German philosopher, in another piece of utterly muddled thinking, saw God's Creation of the universe as a logical reason for the world to be either non-existent or eternal: For since God does nothing without reason and no reason can be given why He did not create the world sooner, it will follow either that He created nothing at all, or that he created the world before any assignable time, that is, that the world is eternal. It beggars belief that a man of undoubted genius, a brilliant mathematician and such an inspired all-rounder as Leibniz could have wasted his brain, ink and his paper on such a shallow consideration. As he wrote these words he probably thought he was being irrefutably clever.     Must we all suffer these posthumous indignities? Will future generations spot the flaws in our own reasoning, guffaw at our foolishness and chide us for our arrogance? Probably! Copyright © 1999 Alexander Waugh. All rights reserved.

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