Cosmos
Page 3
It was an observation that someone else might easily have ignored. Sticks, shadows, reflections in wells, the position of the Sun—of what possible importance could such simple everyday matters be? But Eratosthenes was a scientist, and his musings on these commonplaces changed the world; in a way, they made the world. Eratosthenes had the presence of mind to do an experiment, actually to observe whether in Alexandria vertical sticks cast shadows near noon on June 21. And, he discovered, sticks do.
Eratosthenes asked himself how, at the same moment, a stick in Syene could cast no shadow and a stick in Alexandria, far to the north, could cast a pronounced shadow. Consider a map of ancient Egypt with two vertical sticks of equal length, one stuck in Alexandria, the other in Syene. Suppose that, at a certain moment, each stick casts no shadow at all. This is perfectly easy to understand—provided the Earth is flat. The Sun would then be directly overhead. If the two sticks cast shadows of equal length, that also would make sense on a flat Earth: the Sun’s rays would then be inclined at the same angle to the two sticks. But how could it be that at the same instant there was no shadow at Syene and a substantial shadow at Alexandria?
The only possible answer, he saw, was that the surface of the Earth is curved. Not only that: the greater the curvature, the greater the difference in the shadow lengths. The Sun is so far away that its rays are parallel when they reach the Earth. Sticks placed at different angles to the Sun’s rays cast shadows of different lengths. For the observed difference in the shadow lengths, the distance between Alexandria and Syene had to be about seven degrees along the surface of the Earth; that is, if you imagine the sticks extending down to the center of the Earth, they would there intersect at an angle of seven degrees. Seven degrees is something like one-fiftieth of three hundred and sixty degrees, the full circumference of the Earth. Eratosthenes knew that the distance between Alexandria and Syene was approximately 800 kilometers, because he hired a man to pace it out. Eight hundred kilometers times 50 is 40,000 kilometers: so that must be the circumference of the Earth.*
This is the right answer. Eratosthenes’ only tools were sticks, eyes, feet and brains, plus a taste for experiment. With them he deduced the circumference of the Earth with an error of only a few percent, a remarkable achievement for 2,200 years ago. He was the first person accurately to measure the size of a planet.
The Mediterranean world at that time was famous for seafaring. Alexandria was the greatest seaport on the planet. Once you knew the Earth to be a sphere of modest diameter, would you not be tempted to make voyages of exploration, to seek out undiscovered lands, perhaps even to attempt to sail around the planet? Four hundred years before Eratosthenes, Africa had been circumnavigated by a Phoenician fleet in the employ of the Egyptian Pharaoh Necho. They set sail, probably in frail open boats, from the Red Sea, turned down the east coast of Africa up into the Atlantic, returning through the Mediterranean. This epic journey took three years, about as long as a modern Voyager spacecraft takes to fly from Earth to Saturn.
From the shadow length in Alexandria, the angle A can be measured. But from simple geometry (“if two parallel straight lines are transected by a third line, the alternate interior angles are equal”), angle B equals angle A. So by measuring the shadow length in Alexandria, Eratosthenes concluded that Syene was A = B = 7° away on the circumference of the Earth.
After Eratosthenes’ discovery, many great voyages were attempted by brave and venturesome sailors. Their ships were tiny. They had only rudimentary navigational instruments. They used dead reckoning and followed coastlines as far as they could. In an unknown ocean they could determine their latitude, but not their longitude, by observing, night after night, the position of the constellations with respect to the horizon. The familiar constellations must have been reassuring in the midst of an unexplored ocean. The stars are the friends of explorers, then with seagoing ships on Earth and now with spacefaring ships in the sky. After Eratosthenes, some may have tried, but not until the time of Magellan did anyone succeed in circumnavigating the Earth. What tales of daring and adventure must earlier have been recounted as sailors and navigators, practical men of the world, gambled their lives on the mathematics of a scientist from Alexandria?
In Eratosthenes’ time, globes were constructed portraying the Earth as viewed from space; they were essentially correct in the well-explored Mediterranean but became more and more inaccurate the farther they strayed from home. Our present knowledge of the Cosmos shares this disagreeable but inevitable feature. In the first century, the Alexandrian geographer Strabo wrote:
Those who have returned from an attempt to circumnavigate the Earth do not say they have been prevented by an opposing continent, for the sea remained perfectly open, but, rather, through want of resolution and scarcity of provision.… Eratosthenes says that if the extent of the Atlantic Ocean were not an obstacle, we might easily pass by sea from Iberia to India.… It is quite possible that in the temperate zone there may be one or two habitable Earths.… Indeed, if [this other part of the world] is inhabited, it is not inhabited by men such as exist in our parts, and we should have to regard it as another inhabited world.
Humans were beginning to venture, in almost every sense that matters, to other worlds.
This p.: A flat map of ancient Egypt; when the sun is directly overhead, vertical obelisks cast no shadows in Alexandria or Syene. Next p., left: When the sun is not directly overhead, shadows of equal length are cast. But (next p., right) when the map is curved, the sun can be overhead in Syene and not in Alexandria; no shadow is then cast in Syene, while a pronounced shadow is cast in Alexandria.
The subsequent exploration of the Earth was a worldwide endeavor, including voyages from as well as to China and Polynesia. The culmination was, of course, the discovery of America by Christopher Columbus and the journeys of the following few centuries, which completed the geographical exploration of the Earth. Columbus’ first voyage is connected in the most straightforward way with the calculations of Eratosthenes. Columbus was fascinated by what he called “the Enterprise of the Indies,” a project to reach Japan, China and India not by following the coastline of Africa and sailing East but rather by plunging boldly into the unknown Western ocean—or, as Eratosthenes had said with startling prescience, “to pass by sea from Iberia to India.”
Columbus had been an itinerant peddler of old maps and an assiduous reader of the books by and about the ancient geographers, including Eratosthenes, Strabo and Ptolemy. But for the Enterprise of the Indies to work, for ships and crews to survive the long voyage, the Earth had to be smaller than Eratosthenes had said. Columbus therefore cheated on his calculations, as the examining faculty of the University of Salamanca quite correctly pointed out. He used the smallest possible circumference of the Earth and the greatest eastward extension of Asia he could find in all the books available to him, and then exaggerated even those. Had the Americas not been in the way, Columbus’ expeditions would have failed utterly.
The Earth is now thoroughly explored. It no longer promises new continents or lost lands. But the technology that allowed us to explore and inhabit the most remote regions of the Earth now permits us to leave our planet, to venture into space, to explore other worlds. Leaving the Earth, we are now able to view it from above, to see its solid spherical shape of Eratosthenian dimensions and the outlines of its continents, confirming that many of the ancient mapmakers were remarkably competent. What a pleasure such a view would have given to Eratosthenes and the other Alexandrian geographers.
It was in Alexandria, during the six hundred years beginning around 300 B.C., that human beings, in an important sense, began the intellectual adventure that has led us to the shores of space. But of the look and feel of that glorious marble city, nothing remains. Oppression and the fear of learning have obliterated almost all memory of ancient Alexandria. Its population was marvelously diverse. Macedonian and later Roman soldiers, Egyptian priests, Greek aristocrats, Phoenician sailors, Jewish merchants, visitors f
rom India and sub-Saharan Africa—everyone, except the vast slave population—lived together in harmony and mutual respect for most of the period of Alexandria’s greatness.
The city was founded by Alexander the Great and constructed by his former bodyguard. Alexander encouraged respect for alien cultures and the open-minded pursuit of knowledge. According to tradition—and it does not much matter whether it really happened—he descended beneath the Red Sea in the world’s first diving bell. He encouraged his generals and soldiers to marry Persian and Indian women. He respected the gods of other nations. He collected exotic lifeforms, including an elephant for Aristotle, his teacher. His city was constructed on a lavish scale, to be the world center of commerce, culture and learning. It was graced with broad avenues thirty meters wide, elegant architecture and statuary, Alexander’s monumental tomb, and an enormous lighthouse, the Pharos, one of the seven wonders of the ancient world.
But the greatest marvel of Alexandria was the library and its associated museum (literally, an institution devoted to the specialties of the Nine Muses). Of that legendary library, the most that survives today is a dank and forgotten cellar of the Serapeum, the library annex, once a temple and later reconsecrated to knowledge. A few moldering shelves may be its only physical remains. Yet this place was once the brain and glory of the greatest city on the planet, the first true research institute in the history of the world. The scholars of the library studied the entire Cosmos. Cosmos is a Greek word for the order of the universe. It is, in a way, the opposite of Chaos. It implies the deep interconnectedness of all things. It conveys awe for the intricate and subtle way in which the universe is put together. Here was a community of scholars, exploring physics, literature, medicine, astronomy, geography, philosophy, mathematics, biology, and engineering. Science and scholarship had come of age. Genius flourished there. The Alexandrian Library is where we humans first collected, seriously and systematically, the knowledge of the world.
In addition to Eratosthenes, there was the astronomer Hipparchus, who mapped the constellations and estimated the brightness of the stars; Euclid, who brilliantly systematized geometry and told his king, struggling over a difficult mathematical problem, “There is no royal road to geometry”; Dionysius of Thrace, the man who defined the parts of speech and did for the study of language what Euclid did for geometry; Herophilus, the physiologist who firmly established that the brain rather than the heart is the seat of intelligence; Heron of Alexandria, inventor of gear trains and steam engines and the author of Automata, the first book on robots; Apollonius of Perga, the mathematician who demonstrated the forms of the conic sections* —ellipse, parabola and hyperbola—the curves, as we now know, followed in their orbits by the planets, the comets and the stars; Archimedes, the greatest mechanical genius until Leonardo da Vinci; and the astronomer and geographer Ptolemy, who compiled much of what is today the pseudoscience of astrology: his Earth-centered universe held sway for 1,500 years, a reminder that intellectual capacity is no guarantee against being dead wrong. And among those great men was a great woman, Hypatia, mathematician and astronomer, the last light of the library, whose martyrdom was bound up with the destruction of the library seven centuries after its founding, a story to which we will return.
The Greek Kings of Egypt who succeeded Alexander were serious about learning. For centuries, they supported research and maintained in the library a working environment for the best minds of the age. It contained ten large research halls, each devoted to a separate subject; fountains and colonnades; botanical gardens; a zoo; dissecting rooms; an observatory; and a great dining hall where, at leisure, was conducted the critical discussion of ideas.
The heart of the library was its collection of books. The organizers combed all the cultures and languages of the world. They sent agents abroad to buy up libraries. Commercial ships docking in Alexandria were searched by the police—not for contraband, but for books. The scrolls were borrowed, copied and then returned to their owners. Accurate numbers are difficult to estimate, but it seems probable that the Library contained half a million volumes, each a handwritten papyrus scroll. What happened to all those books? The classical civilization that created them disintegrated, and the library itself was deliberately destroyed. Only a small fraction of its works survived, along with a few pathetic scattered fragments. And how tantalizing those bits and pieces are! We know, for example, that there was on the library shelves a book by the astronomer Aristarchus of Samos, who argued that the Earth is one of the planets, which like them orbits the Sun, and that the stars are enormously far away. Each of these conclusions is entirely correct, but we had to wait nearly two thousand years for their rediscovery. If we multiply by a hundred thousand our sense of loss for this work of Aristarchus, we begin to appreciate the grandeur of the achievement of classical civilization and the tragedy of its destruction.
We have far surpassed the science known to the ancient world. But there are irreparable gaps in our historical knowledge. Imagine what mysteries about our past could be solved with a borrower’s card to the Alexandrian Library. We know of a three-volume history of the world, now lost, by a Babylonian priest named Berossus. The first volume dealt with the interval from the Creation to the Flood, a period he took to be 432,000 years or about a hundred times longer than the Old Testament chronology. I wonder what was in it.
The ancients knew that the world is very old. They sought to look into the distant past. We now know that the Cosmos is far older than they ever imagined. We have examined the universe in space and seen that we live on a mote of dust circling a humdrum star in the remotest corner of an obscure galaxy. And if we are a speck in the immensity of space, we also occupy an instant in the expanse of ages. We know now that our universe—or at least its most recent incarnation—is some fifteen or twenty billion years old. This is the time since a remarkable explosive event called the Big Bang. At the beginning of this universe, there were no galaxies, stars or planets, no life or civilizations, merely a uniform, radiant fireball filling all of space. The passage from the Chaos of the Big Bang to the Cosmos that we are beginning to know is the most awesome transformation of matter and energy that we have been privileged to glimpse. And until we find more intelligent beings elsewhere, we are ourselves the most spectacular of all the transformations—the remote descendants of the Big Bang, dedicated to understanding and further transforming the Cosmos from which we spring.
*We use the American scientific convention for large numbers: one billion = 1,000,000,000 = 109; one trillion = 1,000,000,000,000 = 1012, etc. The exponent counts the number of zeroes after the one.
*Or is you like to measure things in miles, the distance between Alexandria and Syene is about 500 miles, and 500 miles × 50 = 25,000 miles.
*So called because they can be produced by slicing through a cone at various angles. Eighteen centuries later, the writings of Apellecios on comic sections would be employed by Johannes Kepler in understanding for the first time the movement of the planets.
CHAPTER II
ONE VOICE IN THE COSMIC FUGUE
Probably all the organic beings which have ever lived on this earth have descended from some one primordial form, into which life was first breathed.… There is grandeur in this view of life … that, whilst this planet has gone cycling on according to the fixed law of gravity, from so simple a beginning endless forms most beautiful and most wonderful have been, and are being, evolved.
—Charles Darwin, The Origin of Species, 1859
All my life I have wondered about the possibility of life elsewhere. What would it be like? Of what would it be made? All living things on our planet are constructed of organic molecules—complex microscopic architectures in which the carbon atom plays a central role. There was once a time before life, when the Earth was barren and utterly desolate. Our world is now overflowing with life. How did it come about? How, in the absence of life, were carbon-based organic molecules made? How did the first living things arise? How did life evolve to prod
uce beings as elaborate and complex as we, able to explore the mystery of our own origins?
And on the countless other planets that may circle other suns, is there life also? Is extraterrestrial life, if it exists, based on the same organic molecules as life on Earth? Do the beings of other worlds look much like life on Earth? Or are they stunningly different—other adaptations to other environments? What else is possible? The nature of life on Earth and the search for life elsewhere are two sides of the same question—the search for who we are.
In the great dark between the stars there are clouds of gas and dust and organic matter. Dozens of different kinds of organic molecules have been found there by radio telescopes. The abundance of these molecules suggests that the stuff of life is everywhere. Perhaps the origin and evolution of life is, given enough time, a cosmic inevitability. On some of the billions of planets in the Milky Way Galaxy, life may never arise. On others, it may arise and die out, or never evolve beyond its simplest forms. And on some small fraction of worlds there may develop intelligences and civilizations more advanced than our own.
Occasionally someone remarks on what a lucky coincidence it is that the Earth is perfectly suitable for life—moderate temperatures, liquid water, oxygen atmosphere, and so on. But this is, at least in part, a confusion of cause and effect. We earthlings are supremely well adapted to the environment of the Earth because we grew up here. Those earlier forms of life that were not well adapted died. We are descended from the organisms that did well. Organisms that evolve on a quite different world will doubtless sing its praises too.