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  About the Book

  Suppose you and I still wondered whether all of the pinpoints of light in the night sky are the same distance from us. Suppose none of our contemporaries could tell us whether the Sun orbits the Earth, or vice versa, or even how large the Earth is. Suppose no one had guessed there are mathematical laws underlying the motions of the heavens.

  How would – how did – anyone begin to discover these numbers and these relationships without leaving the Earth? What made anyone even think it was possible to find out “how far,” without going there? In Measuring the Universe we join our ancestors and contemporary scientists as they tease this information out of a sky full of stars. Some of the questions have turned out to be loaded, and a great deal besides mathematics and astronomy has gone into answering them. Politics, religion, philosophy and personal ambition: all have played roles in this drama.

  There are poignant personal stories, of people like Copernicus, Kepler, Newton, Herschel, and Hubble. Today scientists are attempting to determine the distance to objects near the borders of the observable universe, far beyond anything that can be seen with the naked eye in the night sky, and to measure time back to its origin. The numbers are too enormous to comprehend.

  Nevertheless, generations of curious people have figured them out, one resourceful step at a time. Progress has owed as much to raw ingenuity as to technology, and frontier inventiveness is still not out of date.

  Contents

  Cover

  About the Book

  Title Page

  Dedication

  Acknowledgements

  Prologue: Tilting at Windmills

  1. A Sphere with a View

  2. Heavenly Revolutions

  3. Dressing Up the Naked Eye

  4. An Orbit with a View

  5. Upscale Architecture

  6. The Demise of Constancy and Stability

  7. Deciphering Ancient Light

  8. The Quest for Omega

  9. Lost Horizons

  Epilogue

  Addendum

  Pictures Section

  Glossary

  Notes

  Index

  About the Author

  Also by Kitty Ferguson

  Copyright

  To my brother, David, who made himself ill as a child and caused a family crisis, worrying about the size of the universe

  Acknowledgements

  The author wishes to thank the following, who have read portions of the manuscript, answered her questions, supplied background material and information, and made suggestions and corrections. Without this help, Measuring the Universe could not have been written:

  Judy Anderson, Boyd Edwards, Caitlin Ferguson, Yale Ferguson, Carlos Frenk, Wendy Freedman, Margaret Geller, Owen Gingerich, Stephen Hawking, Jill Knapp, Helen Langhorne, P. Susie Maloney, Robert Naeye, Saul Perlmutter, Barbara Quinn, Allan Sandage, Bill Sheehan, Patrick Thaddeus and David Vetter.

  Credits for plate section photographs

  3 Sternwarte Kremsmünster; 5 Engraving attributed to Francis Place; 6, 10 Royal Astronomical Society Library; 7, 8, 9 Yerkes Observatory; 11 Harvard College Observatory; 12, 13 Victor Blanco, Wendy Roberts/CTIO/NOAO/AURA/NSF; 14 Henry E. Huntington Library; 15 NRAO/ AUI; 16 COBE Science Team, NASA, Goddard Space Flight Center; 17 NASA/Space Telescope Science Institute.

  PROLOGUE

  Tilting at Windmills 1951

  WHEN I WAS nine years old, my father suggested one morning that he and my brother and I go out and measure the height of the windmill on my grandparents’ farm. My brother and I agreed that was a fine idea.

  How would we do it? Climb the windmill, of course . . . at least my father would. My brother and I wouldn’t be allowed to try anything so dangerous as that. When my father reached the top, there would still be the problem of how to measure the height. We didn’t have a measuring tape that long. Would he take a yardstick and mark off the yards on the windmill as he climbed? Maybe he would drop the end of a long rope from up there and cut it off, and we would stand clear while the cut-off piece fell, and then we would measure it. That must be the plan, for he’d said my brother and I would help him.

  My brother suggested that my father wouldn’t need to climb the windmill at all. We could throw something over the top, just clearing it. Yes, I interrupted, attach a rope to the thing we threw, a rope with inches and feet marked on it, and then pull back on it gently so it would catch on the top of the windmill, and see what the measurement was to the ground! No, no, said my brother, who was two years younger than I but already very mathematically minded, we would measure the curve the object followed through the air. Good thinking, said my father, but, practically speaking, more difficult than the original problem of measuring the height of the windmill.

  I asked whether we might walk away from the windmill and measure how much smaller it looked as we got further away. More good thinking, said my father, but there was a better way.

  He gave us a hint. He’d thought it was a wise idea to wait for a sunny day . . . and no one would have to climb the windmill or take a walk or risk wrecking the windmill with a bad throw . . . and the only tools we’d need would be a yardstick and our eyes and brains and a pencil and paper to do some calculations. And although at this latitude it would be possible to measure the windmill precisely at noon, it would be easier at another time of day.

  Neither my brother nor I was clever enough to see where this was leading until my father said, ‘The windmill does more than just pump water, you know. It casts a shadow, and so does a yardstick,’ and then we began to understand how the trick could be done. We would stand the yardstick upright and measure its shadow. Then we would measure the windmill’s shadow. If a shadow this long went with a three-foot stick, then a shadow that long went with a windmill of thus-and-so height. My brother and I didn’t know how to make the comparison. My father taught us how and then pointed out that there was actually a more primitive way to find the answer. Wait for the time of day when the three-foot yardstick cast a three-foot shadow. At that moment the length of the windmill’s shadow would be the same as the height of the windmill. We decided to use our newly acquired mathematics first, and then we checked our answer by sitting out in the Texas sun, watching the shadow of the yardstick creep along the ground.

  That’s how we measured the windmill, while above our heads the giant structure thrummed and creaked with the watery, metallic sounds windmills in central Texas made in those days, doing its work, turning and pumping, adjusting its angle to catch a stronger breeze, not paying any attention to the mental exertions of three little people below who had captured its shadow.

  I was elated. It seemed we had outwitted the windmill without so much as touching it, and now we knew a wondrous secret: Not the height of the windmill, but how to find it out. None of us thought to ask: why are we doing this? There was no need whatsoever for any of us three to know the height of a windmill that wasn’t even our own.

  Measuring is one of the more practical uses for mathematics, but our ability and desire to measure isn’t always wrapped up with the need to know useful answers. Going with numbers where we can’t go in person – whether that’s to the top of a windmill or to the origin and borders of the universe – has been and still is one of humankind’s favourite intellectual adventures. By the beginning of the twenty-first century it had outrun our practical requirements by billions of light years.

  Compared with the adventure of finding them out, the actual measurements often seem dry as dust: The Sun is 149.5 million kilometres away (mean distance). The nearest star is 4.3 light years. The ‘Local Group’ of galaxies covers an area about 3 million light years in diameter. The distance to the edge of the observable universe is 13.7 billion light years. We shak
e our heads at how large these numbers are or admit their largeness makes them meaningless, remember them for a day or maybe long enough for a school exam . . . and then forget them. Science trivia.

  Not trivial at all when you realize how hard-won these numbers are and what ingenuity it took and still takes to find them out. Can we even begin to imagine what it would be like if no one knew them? The night sky sparkles with pinpricks of light. Are these all the same distance from us? Suppose we didn’t know. Suppose none of our contemporaries knew whether the Sun orbits the Earth, or vice versa, or even how large the Earth is. Suppose no one had guessed there are mathematical laws underlying the motion of the heavens. How would – how did – anyone begin to discover these numbers and these relationships without leaving the Earth? What made anyone even think it was possible to find out ‘how far’? Without going there. Without climbing the windmill.

  In the pages to come we’ll take many steps back, forget we know the measurements or how to make them, and join our ancestors as they tease this information out of a sky full of stars. The laboratory isn’t a neat, sterile room where carefully controlled experiments take place. Events in the heavens happen in their own good time and not before, and they are often not repeatable. We have learned to take what’s on offer and make the best of it.

  Our human point of view is sorely limited. Until recently we had no ground on which to stand and take our measurements, no possible viewing platform, other than here on Earth. In the twentieth century we travelled to the Moon and looked back at our planet from space and sent probes out into the far reaches of our solar system. But by universal standards, by the standards of the distances we’ve learned to measure and still hope to measure, how pitifully close to home that is.

  This book is a chronicle of how men and women over the course of two and a half millennia have built a ladder of measurement from our doorsteps to the borders of the known universe, and how the adventure has changed our ideas about the shape and nature of the universe and our place in it. It is not a history of all astronomy. There are fascinating discoveries, both in Western astronomy and in other cultures, that I have had to remind myself have no direct bearing on our knowledge of distances, size and shape. With regret, I have left them out, though the temptation to embark on long digressions from the main theme of the book has been almost irresistible.

  We shall however broaden our focus in another direction to examine the context in which the discoveries have taken place, for this is a story inextricably bound up with the rest of social, political and intellectual history. One of our tasks will be to look for reasons why a particular discovery or measurement happened when and where it did. What was it about that time and place, that society, that mindset or intellectual milieu, the available technology, the chain of previous discovery, the way some random occurrences fell out . . . perhaps most interesting of all, what was it about a specific individual that precipitated this advance in knowledge?

  The story of our wanting to know ‘how far’ – to make ridiculously out-of-reach measurements – must surely have begun before the beginning of recorded history. The known story of our success began some 2,200 years ago in north Africa near the mouth of the Nile with the measurement of the circumference of our own planet, long before anyone was able to circumnavigate it. The Hellenistic librarian Eratosthenes didn’t need to know the circumference of the Earth. Nevertheless, he set about measuring it and he did it in a remarkably simple way. We now call Eratosthenes the father of the science of Earth measurement, ‘geodesy’. The word has the sound of ‘odyssey’ in it.

  We learn from Eratosthenes what I learned from my father . . . and we shall see it demonstrated repeatedly in this book: what can’t be measured directly – what it is unthinkable that we should ever measure directly – can be measured in roundabout, inventive ways. In the first decade of the twenty-first century we determined the distance to the borders of the observable universe, far beyond any pinprick of light we see with the naked eye in the night sky, and measured time back to the origin of the universe. The numbers are indeed too enormous to make sense to our little minds. Nevertheless our little minds have figured them out, one resourceful step at a time, each step building upon the last. It has been a history of astounding improvement in our technology, particularly in the twentieth century, but more than that, a history of raw ingenuity. It still is. Frontier inventiveness is not out of date.

  With the benefit of hindsight we may be tempted to exclaim, ‘Of course! Why . . . I could have thought of that! The windmill has a shadow. Of course!’ for many of the methods we’ve devised to measure distances to out-of-reach places are simple enough for nearly everyone to understand – only a little more complicated than measuring my grandfather’s windmill. But to figure these things out for the first time . . . how impossibly clever!

  Kitty Ferguson,

  November 2012

  CHAPTER 1

  A Sphere with a View

  Third Century BC

  The great mind, like the small, experiments with different alternatives, works out their consequences for some distance, and thereupon guesses (much like a chess player) that one move will generate richer possibilities than the rest . . . It still remains to ask how the great mind comes to guess better than another, and to make leaps that turn out to lead further and deeper than yours or mine. We do not know.

  Jacob Bronowski

  ASK WHO ERATOSTHENES of Cyrene was, and unless you are talking to someone who specializes in the minutiae of Hellenistic culture, you are unlikely to hear that he was a man who attempted to fix the dates of the major literary and political events from the conquest of Troy until his own time in the third century BC, that he composed a treatise about theatres and theatrical apparatus and the works of the best-known comic poets of the ‘old comedy’; that he suggested a way of solving a problem that had tantalized mathematicians for two centuries – ‘duplicating a cube’; that he let his voice be heard on the subject of moral philosophy and felt it essential to criticize those who were ‘popularizing’ philosophy, accusing them of ‘dressing it up in the gaudy apparel of loose women’. It is true for Eratosthenes, as it is for many celebrated figures, that the strokes of genius for which he is revered were only a minuscule part of a lifetime of achievement, and not necessarily the part he judged most important.

  Nothing on the list above won Eratosthenes his place in the history books. Two additional accomplishments did: the invention of ‘the sieve of Eratosthenes’ – a method for sifting through all the numbers to find which are prime numbers; and his remarkably accurate measurement of the circumference of the Earth.

  Dismiss any thought that before Columbus no one knew the Earth was round. Admittedly, the shape of the Earth probably wasn’t of much daily practical interest to most people in the ancient world. However, long before even Eratosthenes, those few who were wondering about it at all were not seriously suggesting that the Earth was flat or, indeed, any shape but spherical. The Pythagoreans, a school of thinkers with particular genius for mathematics and music, had decided as early as the sixth and fifth centuries BC that the Earth is a sphere. Plato, still a century before Eratosthenes, pictured a cosmos made up of spheres within spheres, nested one within another, with a spherical Earth at the centre. Aristotle, only a little later than Plato, vigorously subscribed to the idea of a spherical Earth, and his defence proved convincing not only to the ancient world but also to the Middle Ages. The idea that scholars of the Middle Ages believed the world was flat is, in fact, a myth created in modern times.

  Aristotle used a number of arguments. During an eclipse of the Moon, the shadow cast by the Earth on the Moon is always curved. When we on the Earth move from north to south or vice versa we notice what appears to be a change in the position of the stars in relation to ourselves. In Aristotle’s words:

  There is much change, I mean, in the stars which are overhead, and the stars seen are different, as one moves northward or southward. Indeed there are some stars
seen in Egypt and in the neighborhood of Cyprus which are not seen in the northerly regions; and stars which in the north are never beyond the range of observation, in those regions rise and set. All of which goes to show not only that the Earth is circular in shape, but also that it is a sphere of no great size: for otherwise the effect of so slight a change of place would not be so quickly apparent.

  Aristotle speculated that the oceans of the extreme west and the extreme east of the known world might be ‘one’, and he reported with some sympathy the arguments of those who had noticed that elephants appeared in regions to the extreme east and the extreme west, and who thought therefore that those regions might be ‘continuous’.

  These reasons for belief in a spherical Earth came from observation, but Aristotle also argued on the basis of his philosophy. In that philosophy, five elements, earth, air, water, fire and aether, each have a natural place in the universe. The natural place for the element earth is at the centre of the universe, and for that reason earth (the element) has a natural tendency to move towards that centre, where it must inevitably arrange itself in a symmetrical fashion around the centre point, forming the sphere we call the Earth. Aristotle reported that mathematicians had estimated the Earth’s circumference to be 400,000 stades; that is, about 39,000 miles or 63,000 kilometres (more than half again as large as the modern measurement). No record survives of the method they used to arrive at that number.

  When Aristotle died in 322 BC at the age of 62, the military campaigns of his most highly achieving pupil, Alexander the Great, had just ended with the death of Alexander. Though there is a tendency to speak of ‘the Greeks’ and toss names like Eratosthenes into that file, the civilization and the culture we are dealing with after Alexander was much larger both in territory and concept than what is implied in the word ‘Greek’. Alexander’s campaigns had carried Greek knowledge, language and culture throughout Asia Minor and Mesopotamia as far east as present-day Afghanistan and Pakistan, all the way to the Indus River, as well as to Palestine and Egypt. Vastly widened intellectual horizons were part of his extraordinary legacy. The culture of Greece and its colonies and the cultures of the conquered peoples began to mix and marvellously enrich one another. This was the dawn of the Hellenistic era, as opposed to the Hellenic era. That is, Greekish, as opposed to Greek.