CHAPTER SEVEN

THE MUSIC OF THE SPHERES

I saw Eternity the other night,
Like a great ring of pure and endless light,
All calm, as it was bright;
And round beneath it, Time in hours, days, years
Driv’n by the spheres
Like a vast shadow, moved; in which the world
And all her train were hurled.

Henry Vaughan, “The World,” in Silex Scintillans

 
 
The beacon on Pharos that now drew the traders of the Mediterranean to the world’s greatest emporium was also attracting other travelers. Among the scholars of the Aegean, word was out that Alexandria offered an environment where it was possible to think the unthinkable—to challenge the fundamental and apparently self-evident certainties of the world. The museum and library were fast becoming a new type of institution: a community of the world’s thinkers, working together to decipher the mysteries of the universe—the first true university.

The grain pouring out of Alexandria’s port continued to fund the work of the scholars now pouring in, giving Ptolemy II the pick of the most brilliant scholars of the age to tutor his son and heir, Ptolemy III. He in turn demonstrated as he grew up that, if anything, he was even more passionate about collecting, copying, and archiving books than his father and grandfather.

Strangely, it would not be philosophy that provided the foundation for Ptolemy III’s own rule, but war and tragedy. Following the death of his father in 246 BC, Ptolemy III succeeded to the kingdom without opposition, but the death of the old monarch had been seized on elsewhere to foment trouble. As part of a peace treaty between the Ptolemies and the rulers of the Seleucid dynasty of Syria, Ptolemy II’s daughter Berenice had been married to Antiochus II Theos, who had agreed to repudiate his previous wife, Laodice. When news of the pharaoh’s death reached Syria, Antiochus clearly considered himself no longer bound by that peace treaty and returned to his former wife. It was a deadly mistake, as Laodice immediately poisoned her former husband and declared her son the new king. Berenice and her son were bound to oppose this, and called on her brother Ptolemy III for help. War was inevitable.

By the time Ptolemy had raised an army and stormed across Egypt and up into the Middle East, news was emerging that Laodice had arranged the murder of Berenice and her son. Infuriated, the pharaoh raged through the region in a campaign that left the whole area stunned. One inscription from Adulis in Eritrea proudly compares this to the magnificent Middle Eastern exploits of the great Rameses II. When Ptolemy returned to Egypt his baggage train was laden with spoils, enough to comfortably support even the most lavish basileus. So rich was he that he offered to pay for the rebuilding of the Colossus of Rhodes. The 160-foot-tall statue (including pedestal) of the god Helios had stood at or near the harbor entrance to the island since its dedication fifty-six years earlier in thanks for Ptolemy I’s assistance in the wars of Alexander’s successors. The statue—as high as the Statue of Liberty—had recently collapsed following an earthquake, but the Rhodians, fearful they had offended the god, refused the offer to rebuild. The statue then spent another eight hundred years lying broken on the shore, although even fallen it was still a major tourist attraction, Pliny the Elder noting that few people could manage to reach their arms around the thumb.

But Ptolemy did not need the Colossus. He had other, more important statues in his baggage train. The wagons that rolled back into Alexandria brought with them the two thousand statues of Egyptian gods that the hated Persian king Cambyses had removed from Egypt. For this the people loved him and gave him the title “Euergetes”—“the Benefactor.” With Ptolemy having this title and more money than he could spend, the rest of his reign was both peaceful and prosperous. Patronizing the greatest minds of his age was thus both pleasurable and affordable, and Alexandrians could turn their minds from war to contemplating far greater things.

During the war a legend emerged which perhaps hints at the growing importance of one particular new area of science in the city. After Ptolemy left for his campaign, his wife, a Cyrenian also called Berenice, went to the temple of Aphrodite to pray for her husband. Here she promised to sacrifice her famous long hair to the goddess if Ptolemy returned safely. When he did she duly honored the pledge and cut off her hair, having it placed in the temple. The next day the offering was found to be missing, leaving the king and queen furious. Only one man could calm them, an astronomer called Conon. He told the queen that the hair had not been stolen but that the gift had so pleased the gods that they had taken it up into heaven. That night he proved it to her, showing her a small group of stars which he called “Coma Berenices”—“Berenice’s Hair”—and the constellation retains that name to this day.

 
 
By this time another astronomer and mathematician, Aristarchus of Samos, who had arrived in the city as a young man sometime before 281 BC, was also enjoying Ptolemy and Berenice’s largesse. He had turned his extraordinary mind away from the earth to contemplate the heavens, not simply to interpret signs of the zodiac so beloved by the ever-nervous rulers of the ancient world, but to understand the mechanisms of the universe itself. What he would see in the heavens was far removed from the theological ideas of gods and creation prevalent in his day, far removed even from the concepts of the universe discussed in the museum. He had brought to Alexandria a unique heritage, and to look into his world is to look into the very dawn of science.

Aristarchus came from Samos, birthplace of perhaps the most famous philosopher, mathematician, and astronomer of all time—Pythagoras. Pythagoras, who lived from around 580 BC to about 500 BC, stands almost at the dawn of rational philosophy, that is, at the point where reasoning began to supplant faith as a means of understanding how the universe, and everything in it, works. But he had one predecessor, a man who many classical writers assert actually met and taught the young Pythagoras when he was about seventy years old. His name was Thales of Miletus, and he was known throughout the classical period as “the First of the Seven Sages of Ancient Greece.”

Before Thales, those seeking answers as to how or why things occurred in the universe invariably referred to the gods. Divine interventions caused earthquakes, changed the seasons, played with the lives and health of puny mortals, and so on ad infinitum. People had only a hazy idea of the shape of the earth and the surrounding cosmos. Many believed the earth was flat and round, floating boatlike on an all-encircling ocean. They then added to the disk of earth sitting in its ocean-saucer some form of pillars or supports (the Egyptians placed them at the cardinal points and anthropomorphized them as the arms and legs of the sky goddess Nut), holding up the dome of the heavenly firmament which sun, moon, and stars traversed in a regular manner. Outside this cosmic eggshell some placed water, which could descend from above in the form of rain and snow or well up from below in springs, lakes, and wells.

But what was all this actually composed of ? What was the fundamental matter? Before Thales, and for many after him, the answer to this question was invariably divinity. Call it soul, spirit, or god, the fundamental matter was divine, untouchable, metaphysical.

Thales, however, preferred water. Water is, after all, fundamental: It can be solid, liquid, or gaseous, and without it there can be no life. Right up until the nineteenth century AD scholars believed that life could generate itself spontaneously in water. As the early metallurgists had discovered, even metals could be reduced to liquids with sufficient heat. And with the seasonal inundations of the great rivers of the ancient world—the Nile, Tigris, and Euphrates—water created earth in revitalizing silt deposits and islands in the deltas of these great rivers.

But this is where Thales made his great leap. He asserted that earthquakes were the result of waves, disturbances in the water on which the earth floated, and not the acts of irate gods. This was one of the greatest revolutionary ideas of all time.

Of course today we know that earthquakes are not caused by ripples on a cosmic ocean, but it is Thales’ idea, not his conclusion, that matters. In attributing a natural phenomenon to mechanics and not gods, he took the universe out of the hands of divinities and claimed, extraordinarily, that everything was understandable, knowable. The furious sea god Poseidon was no longer shaking the planet as he strode across it. Something physical was making the world shake. This idea alone marks the beginnings of science.

Thales is credited by all the great masters—Plato and Aristotle among them—with being the founder of natural philosophy, Aristotle reporting simply that Thales considered that he had found the “originating principle.” “Thales says it is water,” he proclaimed.

Though his own writings are lost, stories about his life and thoughts were widely reported in classical times, particularly his musings on astronomy. Diogenes Laertius devotes his first book in The Lives and Opinions of Eminent Philosophers to Thales:

 
After having been immersed in state affairs he applied himself to speculations in natural philosophy, though, as some people state, he left no writing behind him. For the book on Naval Astronomy, which is attributed to him, is said in reality to be the work of Phocus the Samian. But Callimachus was aware that he was the discoverer of the Lesser Bear [Ursa Minor]; for in his Iambics he speaks of him thus:

 
And he, ’tis said, did first compute the stars

Which beam in Charles’ wain, and guide the bark

Of the Phoenician sailor o’er the sea.

Diogenes Laertius, The Lives and Opinions
of Eminent Philosophers, book 1

 
Diogenes goes on to report that other people claimed that Thales did write two books, one on the solstice and the other on the equinox, thinking that everything else would easily be explained. Both Herodotus and Xenophanes are said to have praised him for being the first person able to predict the eclipses and motions of the sun and to have really studied astronomy—a slightly dubious claim, as the Chaldean Babylonian astronomers were considerably further advanced than the Greeks in charting the movements of the celestial bodies. Diogenes also attributes to Thales numerous other advances, all of which flowed out of his realization that the universe was rational and could be understood. He tells us that Thales affirmed the path (known as the ecliptic) along which the sun appears to move during the day, calculated the size of the sun, and was even the first person to call the last day of each month the “thirtieth,” presumably implying that he devised a new calendar. He also considered more intangible things, and we are told that

 
some again (one of whom is Choerilus the poet) say that he was the first person who affirmed that the souls of men were immortal. . . . But Aristotle and Hippias say he attributed souls also to lifeless things, forming his conjecture from the nature of the magnet and of amber.

Diogenes Laertius, The Lives and Opinions
of Eminent Philosophers, book 1

 
It was Thales’ method rather than his results that had begun a revolution, and he believed that with that method he could understand everything. Plato even credits him with being the first absentminded professor in history. He tells us that the philosopher would wander at night, gazing up at the stars and not looking where he was going. On one occasion this led him to fall into a ditch, where a pretty young girl found him and teased him, saying “that he was so eager to know what was going on in heaven, that he could not see what was before his feet,” before wryly adding, “This is applicable to all philosophers” (Plato, Theaetetus, 174A).

The heir to Thales’ innovative view of the world was a man whose name stills strikes fear into the hearts of schoolchildren—Pythagoras. Like that of Thales, none of Pythagoras’s own work has survived. In fact, the cult which he led—half religious, half scientific—followed such a tight code of secrecy that it may well be that they forbade the writing of their secret formulas and discoveries. But even in his lifetime Pythagoras was such a towering figure that his biographical details were written down by others, and some of these accounts have survived.

Many busts of the great mathematician also survive, although none are contemporary, so they probably bear little relation to what he actually looked like. The only physical feature we do know about is a striking birthmark on his thigh. His father was a merchant from Tyre (in Syria) who was granted citizenship in Samos after he donated grain to the island in a time of famine. His mother was a native of Samos. Pythagoras grew up on the small island but also traveled extensively with his father, visiting Tyre, where he was taught by Chaldean magi from Babylonia, renowned for their knowledge of astronomy and astrology, and other learned Syrians. His educators also taught him to play the lyre and to recite Homer and other poetry.

It was on his travels, the sources tell us, that he encountered both Thales and his pupil Anaximander and attended the latter’s lectures on geometry and cosmology. It is also said that Thales advised the young man to travel to Egypt to study with the priests there, just as Thales himself had done fifty years previously.

Pythagoras took the old man’s advice. At that time Samos was allied to Egypt, which apparently gave Pythagoras access to the temples and their scholar-priests, who accepted him among them. There are so many close parallels between the society which Pythagoras later set up in Italy and the operation of the Egyptian priesthood that we can assume that it was in Egypt that he developed his ideas for his own school. This would explain his cult’s emphasis on secrecy, the striving for purity, and even the refusal to eat beans or wear any sort of animal skins, all of which were Egyptian priestly taboos.

Ten years after he arrived in Egypt, the country was invaded by Cambyses II, king of Persia, and Pythagoras was captured and sent to Babylon. There, we are told by the philosopher Iamblichus,

 
he gladly associated with the Magi . . . and was instructed in their sacred rites and learnt about a very mystical worship of the gods. He also reached the height of perfection in arithmetic and music and the other mathematical sciences taught by the Chaldeans.

Iamblichus, The Life of Pythagoras

 
Around 530 BC or earlier Pythagoras left Babylon and made his way back to Samos, where he founded his school, which he called the Semicircle. There all manner of philosophical issues were discussed, his pupils sitting in a semicircle around the master. But back at his birthplace Pythagoras was again drawn into the political and diplomatic life of his people, which greatly distracted him from his philosophical work. It is also said that the local people disliked his Egyptian style of symbolic teaching, and he used this as an excuse to move the school to the Greek city-state of Croton (now Crotone) in present-day southern Italy. Here he reestablished the school with an inner circle known as the Mathematikoi who lived in the school, had no possessions, were vegetarians, and lived according to the strict regime prescribed by the master.

The members of the Semicircle were required to live by a set of tenets which stated that

• At its deepest level reality is mathematical in nature.

• Philosophy can be used for spiritual purification.

• The soul can ascend to union with the divine.

• Certain symbols have special, mystical significance.

• All brothers and sisters of the order must observe strict loyalty and secrecy.

 
Following the strictures of the group, Pythagoreans were hence the first to devise a consistent cosmos, based on pure numbers. By associating a point with 1, a line with 2, a surface with 3, and a solid with 4, they arrived at the sacred and omnipotent total number of 10. They believed that 10 would also be the key to understanding the structure of the cosmos.

A new element in this cosmic glass-bead game of mathematics and astronomy which Pythagoras introduced was music. Noting that vibrating strings produce harmonious tones when the ratios of their lengths are whole numbers, he went on to arrange the universe into similarly harmonic groups of spheres, even claiming that the Music of the Spheres really existed, though we have lost the ability to hear this background noise. According to Pliny, Pythagoras thought the musical interval between the earth and the moon was a tone, the moon to Mercury a semitone, Venus to the sun a minor third, Mars to Jupiter a semitone, and so on, so that the heavenly bodies actually played tunes as they waltzed past each other.

The Pythagoreans’ universe was one of absolute mathematical perfection. All heavenly bodies were, for them, perfectly spherical and moved in perfectly spherical orbits. At the center of the universe Pythagoras placed the earth, then the moon, then the sun, and next the planets. The whole universe was finally wrapped in an outer sphere of the fixed stars.

Arthur Koestler catches the essence of the structure perfectly: “The Pythagorean world resembles a cosmic musical box playing the same Bach prelude from eternity to eternity” (Arthur Koestler, The Sleepwalkers, p. 33).

Having turned the universe from a whim of the gods into a mathematical machine, Pythagoras set the stage for the objective study of astronomy. It was a pupil of Pythagoras, named Philolaus, who would first suggest that the reason for the rising and setting of the sun, moon, and stars might not be that these celestial bodies moved across the sky but that the earth itself was spinning. Sadly, he went on to obscure this brilliant and counterintuitive revelation by inventing two new astral bodies apparently invisible to the human eye. First he had the earth spinning around the “cosmic hearth,” an invisible fire at the center of the universe. On the same sphere there was another invisible object, a counterearth responsible for generating certain eclipses. The next sphere was our earth, then the moon, the sun, the five known planets, and finally the sphere carrying all the fixed stars, bringing the total number of celestial spheres up to the desired mystical number ten. Pythagoras would have been proud of him, had it not been such a cumbersome and fanciful creation!

The idea of a rotating earth would only be taken up again some centuries later, in Plato’s lifetime, by an astronomer named Heraclitus, who first proposed that the earth rotated once each day on its own axis. This mortally offended Plato, who still insisted that while the earth remained perfectly still at the center of the universe, every other celestial body rotated dutifully round it, and us. But this troubled Heraclitus. He had observed how some of the planets, in particular Venus, do not move smoothly through space as the perfect Pythagorean model insisted; rather, for some nights they advance, but then they stop and appear to go back on their own course for a few days. What, he asked, could make the planets wander so? It was a pressing problem, and one which even echoes into our language today, the word “planet” deriving from the Greek word for “wanderer.” For Heraclitus the solution was obvious: At least two of the planets, the so-called inner planets Venus and Mercury, must orbit around the sun, not the earth, and it was this complex movement that, viewed from the earth, seemed to make them wander. This astute model quickly caught on and became known as the “Egyptian System.” Its only flaw was that it didn’t go far enough—it still had the earth at the center of the universe, and the sun, now with its two “moons” of Venus and Mercury, obediently circling it.

This then was the confusing view of the universe that Aristarchus of Samos brought with him to Alexandria. But under her clear skies and aided by the new facilities of the museum’s observatory, that fog of confusion was about to lift, leading to one of the greatest scientific discoveries of all time.

Aristarchus had studied with Ptolemy II’s tutor, Strato of Lampsacus, a man whose devotion to the study of nature earned him the label “the Physicist.” Trained in Aristotle’s Lyceum in Athens, Strato took his master’s passion for the rational study of nature a step further by claiming that there was no need for any divine explanation of the universe. He declared that there was just nature, and that all things natural could be subjected to observation, measurement, and experimentation. In this respect he is considered the first atheist philosopher, but more important for our story, he essentially saw the universe as a mechanism which operated without the need for transcendental, divine forces. It was this idea that he impressed on the young Aristarchus, and which gave his pupil the confidence to ask a previously unasked question: If the universe is simply a machine, how does it work?

That we know the answer he devised in Alexandria is thanks only to a near fluke of history. Only one of Aristarchus’s works has come down to us, known as On the Sizes and Distances of the Sun and Moon. At first this seems disappointing, as it is largely assumed to be an early work, in which Aristarchus appears to accept the predominant, geocentric universe of those times. But on closer scrutiny even this early, fragmentary work is very revealing. First, the very notion that we can attempt to measure the size and relative positioning of the three largest-seeming celestial bodies—earth, sun, and moon—is a very bold opening gambit. It assumes that these are free-standing entities in stable relations with each other and of calculable dimensions.

It must be said that the figures he derived for the sizes of these bodies are wildly inaccurate. His own calculations led him to believe that the sun was about 20 times the size of the moon and 18 to 20 times as distant from the earth as the moon was. In fact the sun is about 450 times as far away from us as the moon is. He also calculated the diameter of the sun as about 7 times that of the earth, and therefore estimated that the sun’s volume was about 300 times the volume of the earth. In fact, the diameter of the sun is about 300 times that of the earth, its volume about 1.3 million times that of the earth. However, modern mathematicians have examined his propositions in great detail and find that effectively Aristarchus was not let down by his math (drawn from the ever-reliable Euclid) but by his observational data. So although Aristarchus was enormously wide of the mark, he hit the bull’s-eye in a far more crucial way. What he established, at least to his own satisfaction, was that the moon was the runt of the litter and that the sun was vastly bigger, more voluminous, and presumably heavier than the little earth. So why then should this huge celestial titan, at least 300 times the volume of the earth, be dutifully pirouetting around so small a planet every day? For the priests the answer had been simple: because that was how the gods had ordained it. But there were no gods in Aristarchus’s universe, so he had to seek answers elsewhere.

But at this point, just as he was about to make his great discovery, his trail appears to have gone cold. None of Aristarchus’s other work survives, and his brilliant idea might have remained unknown in the modern world were it not for a small aside in a book by another great mathematician: Archimedes.

In his book The Sand Reckoner, Archimedes set out to demonstrate methods for dealing mathematically with extremely large numbers, such as the number of grains of sand which would fill the universe (hence the title of his book). Of course to arrive at the largest number possible, he had to find a description of the largest theoretical universe known in which to place his grains, and for that he turned to Aristarchus. Having explained to his patron, King Gelon, that most astronomers believed the earth to be the center of the universe, around which everything else rotated, he added almost as an aside:

 
But Aristarchus has brought out a book consisting of certain hypotheses, wherein it appears, as a consequence of the assumptions made, that the universe is many times greater than the “universe” just mentioned. His hypotheses are that the fixed stars and the sun remain unmoved, that the earth revolves about the sun on the circumference of a circle, the sun lying in the middle of the orbit, and that the sphere of fixed stars, situated about the same centre as the sun, is so great that the circle in which he supposes the earth to revolve bears such a proportion to the distance of the fixed stars as the centre of the sphere bears to its surface.

Archimedes, The Sand Reckoner, chapter 1:4-5

 
Here then was Aristarchus’s great thought, preserved only as a reference in another book. Archimedes for his part did not even believe it to be true, only being interested in the sheer scale of the model he proposed.

The response to Aristarchus’s hypothesis of a heliocentric solar system was perhaps to be predicted and may in itself help to explain why so few of his own works survive. Contemporaries were horror-struck by the new role this Alexandrian astronomer gave to the earth and, by implication, to the people on it. How dare he take away their special position at the very heart of creation? One of them, by the name of Cleanthes, wrote a treatise entitled simply Against Aristarchus. This has since been lost, so we don’t know on what grounds he attacked Aristarchus, but Plutarch would later comment that Cleanthes

 
thought it was the duty of the Greeks to indict Aristarchus of Samos on charges of impiety for putting in motion the Hearth of the Universe (i.e. the Earth), this being the effect of his attempt to save the phenomena by supposing heaven to remain at rest and the Earth to revolve in an oblique circle, while it rotates at the same time, about its own axis.

Plutarch, On the Face Which Appears on the Orb of the Moon, book 6

 
We don’t know if Aristarchus was ever indicted, or whether a trial ensued; it would perhaps seem unlikely in the liberal atmosphere of Alexandria, though we should not forget Socrates’ fate and the threats laid upon both Plato and Aristotle. But at the very least this bold new theory provoked a reassertion of the official orthodoxy from several scholars, including Dercyllides, who argued somewhat pompously the need to assert that the Platonic model of a fixed earth with its “Hearth of the house of the gods” countered by moving planets and the rest of the heavens was correct. He claimed that it was essential to reject those who brought to rest the things that move and set in motion the things that by their nature and position are unmoved, insisting that such a supposition was contrary to the theories of mathematicians.

In the end these reactionary responses held sway. Aristarchus had no significant followers in his own generation or the following ones, and his only known disciple was a Chaldean named Seleucus who lived by the Tigris River and adopted Aristarchus’s teachings around 150 BC. Why this rejection of Aristarchus should happen is one of the greatest riddles of the ancient world. Aristarchus’s heliocentric universe seems so clearly true to us, who have the benefit of modern science and space travel to help our imaginations, that it’s hard to envisage what it must have been like to be committed to an earth-centered view of the cosmos. Yet that was the view that prevailed for thousands of years throughout antiquity, and which would continue as the only acceptable model of the solar system until the sixteenth century AD.

But there are two other profound reasons why Aristarchus’s beautifully mathematical, mechanical universe was too far ahead of its time to be acceptable, even to the scholars at the museum in Alexandria. First, we need to return to the age-old dichotomy between faith and reason, or religion and rationality. Even the great Plato had comparatively recently insisted that while our fallen, corrupted world may be analyzable using rationality, the really pure, uncontaminated cosmic bodies were to be found in the skies, or rather the heavens. Here were the seats of pure spirituality, divine beings if you like. To reduce these heavenly spheres to mere lumps of rock shunting around an infinitely huge void was tantamount to heresy: hence Cleanthes’ determination to indict Aristarchus for impiety—godlessness—not bad science.

But at an even more profound level, great minds like Archimedes balked at the idea of a sun-centered universe because it took the spotlight off us humans. An earth-centered universe is also an ego-centered universe. Why should the gods create the universe at all if not to give us humans somewhere to play, and to puzzle about? Plato had already decreed that humans were at the very zenith of creation, and that we had already gone through five phases of evolution, the last, most elevated phase being that of the philosopher—the lover of wisdom. Aristarchus’s universe was a vast and lonely place, where the earth was relegated to the role of just another planet circling around a fixed sun, shrouded in a vault of impossibly distant stars. No god marked out this earth as special—it had become just another wanderer. To demote the earth to this was to deny that the universe was built by the gods, for us. That was like denying both our descent and our ascent. Most preferred a more comfortable, human-centered universe, and this conception would survive right down to Darwin, when he scandalized Victorian society with his notion that people might be descended not from God but from mere apes.

So the cometlike genius of Aristarchus flared across the Alexandrian skies, then vanished. But not forever. In AD 1543 Copernicus published his revolutionary heliocentric model of the universe just before his death, which possibly occurred only hours after he received the first printed copy of the book. It has even been argued that Copernicus may have died of fear—fear of the wrath of the Catholic Church at a man of the cloth daring to suggest that the earth goes around the sun and not vice versa. Certainly we know that he sat upon his manuscript for decades, steadfastly refusing to publish it.

More recent research reveals, however, that his anxieties may have been driven by guilt as much as by fear. For in the original handwritten manuscript there were several references to Archimedes’ The Sand Reckoner, which of course contained his summary of Aristarchus’s book on the heliocentric universe. These references have, however, been systematically removed from the printed version of the text, and no mention is made either of Archimedes’ book or of Aristarchus. And still today nearly all of us credit Copernicus with the “discovery” of the true nature of our planet’s motion around the sun. It’s particularly ironic that Aristarchus is sometimes referred to as the “Greek Copernicus” when in fact it is Copernicus who should be referred to as the “Polish Aristarchus.”

Aristarchus’s books, including his work on the sun-centered universe, were of course lodged in the great library in Alexandria, which is very probably where Archimedes read them (he was about twenty-five years younger than Aristarchus). While Aristarchus’s great ideas never caught on in his lifetime, his work was known and read, proving that from just a small observatory on the grounds of a temple, Alexandria was already turning the universe—and the world with it—on its head. The gods had begun to release their grip, leaving humans to stagger into the daylight and begin to explore their world.

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