The Earth becomes a sphere

A marble nobody had seen

On 7 December 1972, about five hours after launching toward the moon, the crew of Apollo 17 pointed a camera back at home. From about 29,000 kilometers (18,000 miles) away, the whole sunlit earth fitted in the frame: swirled white cloud, deep blue ocean, the brown of Africa, the white of Antarctica. NASA calls the picture “The Blue Marble,” and it is among the most reproduced photographs in history. For many people it was the first time they saw their home as a thing: round, finite, and small.

It was not the first picture of the earth from above. A V-2 rocket took film from high above New Mexico in 1946, Explorer 6 sent back a crude scan of the sunlit Pacific in August 1959, and Lunar Orbiter 1 photographed the earth from the distance of the moon in August 1966. Yuri Gagarin, in April 1961, saw the curve of the horizon but not the whole disk; the first people to see the whole earth at once were the Apollo 8 crew in December 1968. The Blue Marble was simply the best picture so far.

Here is the strange part. People did not need the picture to know what it would show. For more than two thousand years, anyone who studied astronomy had known that the earth is a ball. “How could they know?” is the first question of this lesson, and “what did other peoples make of the idea?” is the second. The answer to the first is that the Greeks reasoned their way to it, long before anyone could look.

From a goddess to a drum

The Greek poet Hesiod, about 700 BCE, began his Theogony, the genealogy of the gods, with a sentence that sets the earth apart: “at first Chaos came to be, but next wide-bosomed Earth.” The first god after the void was the earth, Gaia, who then bore the sky. That is a clue to the Greek habit of mind, though Hesiod’s own earth is still a flat floor, with the underworld beneath it. Greek gods had human bodies and human passions, and Greek thinkers, this course argues, learned to ask of anything: what is its form? It is a reading of the Greeks, not a proof, but it fits what happened next.

The first Greek philosophers, in the city of Miletus on the coast of what is now Turkey, around 600 BCE, were the first to ask in a systematic way about the shape of the earth. Thales, the first of them, said the earth floats on water; Aristotle, who reports it, compares it to a log and gives no shape, so “disk” is our inference. His successor Anaximander made a daring proposal. The earth, he said, is a short cylinder, “like a column drum,” whose height is a third of its width, and it hangs in the middle of everything with nothing underneath. It does not fall, he reasoned, because it is equally far from everything else: there is no reason for it to go in one direction rather than another. Aristotle, who thought the argument ingenious but wrong, preserved it for us. Anaximander’s own pupil Anaximenes went back to a flat plate riding on air.

Look at what Anaximander did. Many peoples had put the earth on something: water, a turtle, an elephant. (The old woman who tells a scientist “it’s turtles all the way down” is famous from Stephen Hawking’s A Brief History of Time, but nobody knows where that story began; and in India the astronomers, unlike the myths, used a spherical earth: Aryabhata wrote in 499 CE of a round earth that turns.) Anaximander replaced “what holds it up?” with “which way would it go?” That removes the need for a support, and it makes the earth the center of a world with no absolute up or down. Up and down become directions toward and away from the middle. His earth was still a drum, but the step from a drum to a ball was now a short one.

Nobody knows who first said the earth is a sphere. Later writers credit Pythagoras, or Parmenides; both claims are late and shaky. By the time of Plato, around 380 BCE, Greek thinkers were already describing the earth as a ball at the center of the heavens. In Plato’s Phaedo, Socrates says he is convinced of it.

Three arguments and a sailor’s

Aristotle, in On the Heavens in the fourth century BCE, collected the reasons. The first was physical, and it was his own: all earthy matter falls toward the center of the world from every side, so it presses together into a ball, the way a heap of sand settles. The other two were observations. In every eclipse of the moon, the edge of the earth’s shadow is curved, and only a ball always throws a round shadow. And if you travel north or south, the stars change: the stars seen in Egypt and Cyprus cannot be seen farther north. On a flat earth every traveler would see the same sky.

A fourth argument is the one you can check on any shore: ships. The geographer Strabo, around the time of Christ, wrote that sailors approaching land watch the shore rise before them, and that a light too low to be seen from low down can be seen from higher up. The same fact seen from the other end is the familiar one: a ship sailing away loses its hull before its mast. On a flat sea it would only shrink to a dot. Try it below.

A ruler for the world

Once the earth is a sphere, the next question is natural: how big? Eratosthenes of Cyrene, who lived from about 276 to 195 BCE and is traditionally called the head of the great Library of Alexandria, found a way to measure it with a stick and a well. We know the story from later writers, chiefly Cleomedes, because his own book, On the Measurement of the Earth, is lost.

He had heard that at noon on the summer solstice, in the southern city of Syene (today’s Aswan), the sun shone straight down a well, lighting the water at the bottom. It was directly overhead. In Alexandria, on the same day, a vertical rod cast a shadow, and the shadow made an angle of 7.2 degrees, one fiftieth of a circle. If the sunbeams are parallel (the sun is very far away), that angle is also the angle at the center of the earth between the two cities. So the distance from Alexandria to Syene, reported as 5,000 stadia, is one fiftieth of the earth’s circumference: 250,000 stadia (later writers say 252,000).

How good was it? That depends on the length of the stadion, which we do not know for sure. With the short Egyptian stadion of about 157.5 meters, 252,000 stadia is 39,690 kilometers, within about one percent of the meridian’s true length of 40,008 kilometers. With the longer 185-meter stadion, the answer would be about 46,600 kilometers, about sixteen percent too large. The honest verdict is “remarkably close,” not “exactly right.” And his errors partly cancelled: Syene is not exactly on the Tropic and not exactly south of Alexandria.

From the Library to the open sea

About 150 CE, Ptolemy, in his Geography, chose a smaller figure for the earth: 500 stadia to a degree, or 180,000 stadia in all, roughly 30 percent too small if you use the short stadion. His book of coordinates was unknown to Western Europeans for centuries; it was translated into Latin in 1406–07, and the first printed edition, with maps, appeared in Bologna in 1477. Printed editions spread his picture of the world, and his small earth, among the geographers of the age of exploration.

Christopher Columbus took the earth’s roundness for granted, as did every educated person of his time. He, too, used a small earth: he read the figures of the Arab astronomer Alfraganus in the wrong, shorter miles, which gave a world about three quarters of its true size, and then he stretched Asia eastward with the overlong Eurasia of the ancient geographer Marinus of Tyre. The result was a Japan about 2,400 nautical miles west of the Canary Islands. The real distance is about 10,600. The experts who advised Portugal and Spain thought the plan hopeless, not because they thought the earth flat but because they knew roughly how big it was. They were right. Columbus was saved only by an unknown continent in the way, and landed in the Bahamas on 12 October 1492. In the same year a Nuremberg merchant, Martin Behaim, made the oldest surviving globe, the “Erdapfel,” “earth apple.” It has no Americas.

The first to carry the proof all the way around was an expedition begun by Ferdinand Magellan. Five ships and about 270 men left Sanlúcar de Barrameda in southern Spain on 20 September 1519. Magellan found the strait at the tip of South America in 1520, and the fleet then took about three months to cross the Pacific; he was killed in the Philippines on 27 April 1521, in a battle on the island of Mactan, and never saw home again. One ship, the Victoria, commanded by Juan Sebastián Elcano, returned to Sanlúcar on 6 September 1522, with 18 men aboard. Along the way they had found a puzzle. At the Cape Verde Islands, in July 1522, Antonio Pigafetta, whose careful log had never skipped a day, learned that the local date was a day later than his own. They had sailed west, with the sun, and lost a day: the ship’s log had measured the circuit of the earth in days.

A last point is worth stating plainly, because it is repeated everywhere: Europeans in the Middle Ages did not think the earth was flat. The English monk Bede wrote in 725 that the earth is “not circular like a shield but rather like a ball” (in Faith Wallis’s translation). The textbook that every university student read from about 1230, John of Sacrobosco’s On the Sphere, begins with a round earth, and the poet Dante built his Divine Comedy on one. There were exceptions, such as Lactantius around 310 and Cosmas Indicopleustes around 550, but they were exceptions, and even they were attacking an idea that was well known. The tale of Columbus defying churchmen who said the earth was flat is invented: it comes from Washington Irving’s 1828 biography, and was spread in the later nineteenth century by writers who wanted a story of religion against science. The historian Jeffrey Burton Russell traced the myth in Inventing the Flat Earth.

Round heaven, square earth

Chinese tradition has a famous phrase, 天圆地方 (tiān yuán dì fāng), “heaven is round, earth is square.” It looks like a flat-earth doctrine, and it is often presented as proof that China missed the sphere. The truth is more interesting, and more careful.

The phrase appears in several old books: in the Zhoubi suanjing (“the square belongs to earth, the round to heaven”), the Huainanzi (139 BCE), and the Lüshi chunqiu (239 BCE), which says “the way of heaven is round, the way of earth is square,” and spells out what it means: a ruler should hold to the round (keep moving, never stop), and his ministers should dwell in the square (each keeping to his own office). That is politics and ethics, not geometry. In a Han-dynasty collection of ritual texts, the Da Dai liji, a man asks the sage Zengzi whether it is really true that heaven is round and earth is square. Zengzi’s answer is the best-known passage on the subject: if heaven were really round and earth really square, he says, the four corners would not be covered. A commentator of the sixth century glossed the line: round and square name the “way,” not the shape.

Other writers did mean it as a picture. The Zhoubi has two: heaven like a canopy-hat, and earth like an overturned dish, curved but not a sphere. A later description of this school says “heaven is round like a spread canopy, earth square like a Go board.” Zhang Heng (78–139), the court astronomer, described a different model, the hun tian or “celestial sphere”: heaven is like a hen’s egg and earth like the yolk, alone inside it, heaven large and earth small, floating on water. In another work he wrote that heaven takes the form of yang, so it is round and moves, and earth takes the form of yin, so it is flat and still. So Chinese writers used round and square both as pictures and as philosophy, sometimes in the same text, and it is not always clear which they meant.

Notice what is not missing. Chinese astronomers could measure. In 724 CE, the monk-astronomer Yi Xing organized a survey along a line from what is now northern Vietnam to south of Lake Baikal. He found that the pole star’s height changes by one degree for each 351 li and 80 paces of travel north, roughly 130 kilometers by one reckoning (the true figure is about 111), and he declared the old rule, a shadow difference of one cun for every thousand li, false. He did not draw the conclusion that the earth curves. He wrote that the canopy school and the celestial-sphere school both failed to fit his figures, and that such debates were not needed to make a calendar. This course reads the incident as a clue: in Chinese tradition the astronomers who observed the sky and the philosophers who described the world were different groups, and nothing forced a correction to pass from one to the other.

The sphere was also known as a foreign idea. In 1267 a Muslim astronomer, Jamal al-Din, built instruments for Khubilai Khan’s court, including a wooden globe of the earth, in which “seven parts” were water, painted green, and “three parts” land, painted white, with a grid of squares for measuring distance. (The real earth is about 71 percent water.) It does not seem to have found a general audience. A few decades later the astronomer Zhao Youqin discussed the argument that the earth blocks sunlight in a lunar eclipse and rejected it, as far as his text can be read. In the thirteenth century the mathematician Li Ye had already written that the earth’s body “is not necessarily square,” and that when people call it square they mean its still, steady quality, the very argument that Ricci would later use.

That brings us to the Jesuits. The Italian Jesuit Matteo Ricci settled in China in 1583 and in 1602, in Beijing, with the Chinese scholar Li Zhizao, published a large world map, the Kunyu wanguo quantu, the first Chinese map to show the Americas. He argued the sphere in plain terms: if you travel 250 li north, the pole star rises one degree, so the earth is round; earth and sea together form one ball in the middle of the heavens “like the yolk in the white of a hen’s egg” (borrowing Zhang Heng’s own egg); and those who call the earth square “speak of its virtue, stillness, not its body.” To the question “what about the people on the other side?” he replied that wherever the feet stand is down and wherever the head points is up.

Not everyone was persuaded. In 1664–65 the scholar Yang Guangxian wrote that people stand with heads to heaven and feet on earth, and that he had never heard of people standing upside down; if the earth were a ball, he asked, why would the seas not pour off the bottom? He proposed a test with a bowl of water. (In 1668 Yang lost a calendar contest to the Jesuit Ferdinand Verbiest.) Many scholars, however, moved with the evidence. By the early 1700s the Jesuit-led mapping of the empire for the Kangxi Emperor assumed a spherical earth, and the mathematician Mei Wending (1633–1721) argued that Western methods had Chinese roots, a claim later developed into the “Western learning came from China” view. Historians describe a slow, uneven acceptance, with scholars and officials first and the wider public later; one study of the debate covers the years 1600 to 1800.