The Theory of Heliocentrism

I want to ask you to do something for me. Go outside — assuming you aren’t there already — and look up at the sky. It doesn’t matter whether it’s day or night, winter or summer, cold or hot, rainy or dry; just go. You won’t need to stay out there long.

Are you outside? Good. Now imagine that you know nothing whatsoever about astronomy, that you have no idea what the heavenly bodies you see above you actually are. What might you believe them to be? How might you believe yourself to be placed in relation to them? You would almost certainly think that you’re standing on a large, relatively flat plane, around which rotate the Sun and the Moon, the one giving off awesome amounts of heat and light, the other beaming down on you its own paler radiance. The view you see above at night might convince you that the whole apparatus is encased inside a great orb, whose inner surface is studded with thousands of tiny pinpricks of light. You would doubtless presume that a spectacle as bizarre and magnificent as this one could only be the work of the gods. You would quite likely be tempted to see signs and messages from these inscrutable beings in the day-to-day configuration of the heavens.

All of this would seem quite obvious to you. The history of astronomy is to a large extent the history of how we learned not to take the seemingly incontrovertible evidence of our senses at face value. (In that spirit, you can go back inside now if you like.)

This is not to say that we are any smarter than our more credible ancestors, nor that their understanding of the heavens was primitive. The fact is that the average person living during prehistorical times knew far more about the movements of the sky than most of us do today — for, living closer to the rhythms of nature as they did, the sky was intimately bound up with their existence. It told them when it was time to sleep and when it was time to wake up. When human beings gave up hunting and gathering their food and began to grow it for themselves, it told them when to plant and when to harvest, even as the quantity of rain that came down from it dictated whether the harvest would be successful, and thus whether they would have any food to eat that coming winter. Small wonder that so much energy and effort were devoted to placating the gods who ruled the sky, who in some cases were posited to literally be the heavenly bodies seen above. And small wonder that a heavens which already had so much influence on so many aspects of life was posited to be the key to the personalities and destinies of individual humans as well. Figuring out where the boundaries lie between astrology, which has no basis in fact, and astronomy, which does, would require millennia of investigation. In fact, this process has yet to be completed, as the millions of people who still turn to their horoscope each day will attest.

Human beings were reading the stars long before they learned to write on stone, papyrus, or parchment. Archaeologists have uncovered star maps amidst Sumerian ruins that may date back as far as 7000 BC. The famous monument of Stonehenge in southern Britain, which is believed to have been built around 3000 BC, seems to have been a giant celestial calculator, tracking the time of day as well as the time of year. Knowing the latter was essential not only for practical agriculture — when to sow and when to reap — but also for appeasing the gods whose forms and traces could be seen above; the winter and summer solstices in particular demanded prayer and sacrifices. Prehistoric peoples saw no distinction between the practical and the ceremonial.

The Egyptian Pyramids of Giza, built around 2500 BC and for almost 4000 years thereafter the tallest human-made structures on Earth, are, among their many other remarkable features, meticulously aligned so that the shafts leading from the pharaohs’ burial chambers at their centers point to due north. This was done for the convenience of the souls entombed inside: the gateway to the afterlife was believed to lie precisely 30 degrees above the northern horizon. The Egyptians were also the first people to divide the year into twelve months, each roughly as long as it took the Moon to go through one full cycle of waxing and waning. The Egyptian year began at the time that we call mid-summer, when Sirius, the brightest star of them all, first becomes visible in their part of the world. Each month thereafter was 30 days, with a five-day period of worship and festivals tacked onto the end to make the 365-day year with which we are familiar. The Egyptians even figured out that they needed to add an extra day of partying every fourth year in order to keep their calendar in sync with the movements of the heavens. (Presumably no one complained.)

The ancient Greeks built upon the knowledge of the sky which they inherited from the Egyptians and others. About half a millennium before Jesus Christ, the Greek philosopher Pythagoras founded an ascetic community of thinkers in the town of Crotene, in southern Italy. “Of all men,” wrote his contemporary or near-contemporary Heraclitus, “Pythagoras is the most assiduous inquirer.” He and his followers thought about and discussed everything, from ethics to politics, from music to religion. For this reason, it is possible that some or even most of what has been attributed to him personally really stemmed from his followers. Still, for simplicity’s sake, I will take the liberty here of speaking of Pythagorean thought as if it is Pythagoras’s alone.

So, then, Pythagoras is most remembered today as a mathematician, thanks to the Pythagorean Theorem that every first-year geometry student learns by heart: for the lengths of the sides of any right triangle, a² + b² = c². These studies in mathematics were foundational to Pythagoras’s work in astronomy. For astronomy as a discipline, then as now, often boils down to a study of angles and ratios, for which geometry — and especially the sub-category of geometry known as trigonometry — is key.

Pythagoras, wrote his Roman biographer Diogenes Laertius some 700 years after his death, “was the first person to call the Earth round, and to give the name of kosmos to the world.” Before him, many had believed that our planet took the form of a flat disc, or even of a box bobbing on celestial waters. But through a series of commonsense deductions from the observed evidence, Pythagoras concluded that we actually live on a sphere much like the ones we can see passing above us. Sailors reported to him that the southern constellations moved higher in the sky the farther south they ventured, even as Egyptian adventurers had long since written that, if you went far enough south into the interior of Africa, the Sun would one day shift position from the northerly to the southerly half of the sky; these observations made sense only if the travelers were moving over the surface of a sphere. Yet more ample evidence, Pythagoras pointed out, could be found without needing to travel so far at all. You could merely climb to the top of the nearest high hill or mountain peak, or even the tall mast of a ship at sea. If the direction in which you gazed was relatively flat, and if you were sufficiently keen-eyed, you could see the curvature of the Earth out there in the hazy distance. Further, during lunar eclipses, the shadow of the Earth could be clearly seen on the Moon — a spherical shadow. Add to all of this empirical evidence arguments from aesthetics and abstract philosophy: if all of those other heavenly bodies were spheres, why shouldn’t the Earth be as well?

This wasn’t to say that the Earth was precisely the same as those other spheres. As the special creation of the gods, home to the beings they had made in their image, it must surely have been set up at the very center of the universe, to be heated and lighted, honored and served by its seven celestial handmaidens: the Sun, the Moon, and the five planets that can be seen with the naked eye, which we still know today as Mercury, Venus, Mars, Jupiter, and Saturn, all after members of the Greco-Roman pantheon of gods.

Pythagoras drew a neat, orderly picture of the cosmos, one that his posterity would strain mightily not to let slip away completely for 2000 years to come. Standing stock still at the center is the Earth, that pride of all Creation. Around it orbit the Sun, the Moon, and the five planets, all of them moving in perfect circles on the same plane. And all of this is enclosed inside another, truly gigantic sphere, upon whose inner surface can be seen the stars when they are not obscured by the luminescence of the Sun or the Moon. (Were the stars in reality pinpricks in the surface of the sphere, letting through some of the divine light of a void of formless Energy that lay beyond it? It was tempting to think so.)

Pythagoras spoke of “the music of the spheres,” a divine fugue of harmony and proportion, playing above us all the time as the other heavenly bodies spin around the Earth. The philosopher Plato later took up the theme, describing the universe as “a body whole and perfect, made up of perfect bodies.” His student Aristotle added a fifth element to the four terrestrial ones of earth, water, air, and fire: the “aether” was the celestial pool through which the heavenly spheres moved. They had to be perfect spheres rotating in perfect circles, because spheres and circles were the most perfect of all forms, having no beginning and no end.

There was just one problem with this tidy vision of the cosmos: it was impossible to reconcile with what one actually saw in the sky from day to day. The five planets were the worst source of dissonance in Pythagoras’s music of the spheres; instead of turning around the Earth in a stately procession, they insisted on changing direction, on bobbing and weaving around in the sky almost randomly.

During the fourth century before Christ — the same period during which Aristotle was writing — a man named Heraclides Ponticus made a concerted attempt to reconcile these infuriating discrepancies between theory and empirical observation. We have nothing whatsoever that he wrote himself, only hearsay about his ideas. Yet he apparently argued that the Earth was not standing stock still, but rather spinning on its axis without otherwise moving through space; it was this motion that caused the Sun to “rise” and “set” each day. Just as significantly, he provided a new model for the universe which still had the Earth at the center, orbited by the Sun and the Moon, but had the five planets orbiting the Sun rather than the Earth. As far as we can determine, his ideas were taken very seriously in his day and after, becoming widely accepted. Astronomers were getting tantalizingly close to the truth.

And then, in the century after Heraclides, along came Aristarchus to solve the puzzle with his vision of the cosmos that was so much less satisfying and gratifying to humanity’s position in the grand scheme of things. But the ancients’ spirit of inquiry failed them here. With no really incontrovertible proof behind it, only conjecture and arguments from proportions, it was easy enough to dismiss Aristarchus’s model, so belittling to humanity’s sense of its own importance in the cosmos, as just another crackpot theory. Indeed, we don’t know to what extent even Aristarchus really believed in it, as opposed to regarding it as just another of the pure thought experiments in which Alexandrian intellectuals like him and Archimedes so loved to indulge. Archimedes does speak of it as appearing in “a book of hypotheses,” after all.

But even as it continued to get this most crucial aspect of the cosmos wrong, ancient astronomy was chalking up some remarkable achievements. A man named Eratosthenes, who may have lived and worked in Alexandria at the very same time as Aristarchus and Archimedes, calculated with extraordinary precision the size of the Earth, using a method as straightforward as it was beautiful. He measured the position of the Sun at noon on the same day of the year in Alexandria and in Aswan, a city which lay exactly 500 miles (800 kilometers) due south of his home. He found that the difference in the Sun’s position at the two places was 7.2 degrees. Given that 7.2 degrees is 2 percent of a full 360 degrees, he extrapolated that the distance between the two Egyptian cities must represent 2 percent of the total distance around the Earth. Therefore, he reckoned, the Earth must have a circumference of 24,850 miles (40,000 kilometers) — a calculation, we now know, that falls within one quarter of one percent of the real figure.

A century later, one Hipparchus, probably working from the island of Rhodes, compiled the first comprehensive written catalog of all of the stars that could be seen overhead from his part of the world. To better describe the contents of his catalog, he categorized them by brightness, or magnitude, giving the twenty brightest stars of all a magnitude of one, down to a magnitude of six for the dimmest. Incredibly, his system is still used by astronomers today (with the scale extended beyond six to include those stars that cannot be seen with the naked eye at all).

Ancient astronomy culminated around AD 150, once again in Alexandria, in the towering scholarly figure of Claudius Ptolemy. His works were so voluminous, authoritative, and comprehensive that he would be taken as the last word on all of the subjects to which he turned his attention for almost 1500 years to come. This was sometimes for the better and sometimes for the worse. For example, in his tome Geographia, Ptolemy codified the system of latitude and longitude that we still use to identify any point on the Earth’s surface, but for some reason he chose to reject Eratosthenes’s estimate of the size of our planet in favor of a figure about 27.5 percent smaller than the real one. This would cause much confusion many centuries later during the Age of Exploration. As every American schoolchild learns today, Christopher Columbus was trying to reach Asia by sailing west from Europe when he unexpectedly bumped into the so-called New World. It is less widely understood that Columbus was hewing to Ptolemy’s shrunken version of the globe when he planned his voyage. In fact, he never did allow himself to be convinced that he had discovered two whole new continents where he thought Asia ought to lie, so invested was he in the near-divine authority of Claudius Ptolemy.

As went Ptolemy’s geography, so went his astronomy. His book on that subject has been known as the Almagest since the Renaissance era; an Arabic title meaning “The Greatest,” it reflects the fact that the book first resurfaced, after being lost to Christian Europe for many hundreds of years, in an Arabic translation of the Greek original. The Almagest is a magisterial tome by any measure, by far the most comprehensive study of astronomy the ancient world would ever produce, designed to present all of its wisdom on the subject as a single, harmonious whole. It is most definitely not the work of a fool or a dabbler. Ptolemy knew his stuff, and got an incredible amount of it down on the page. For the purpose of knowing what celestial body will be where in the sky above at any given instant, it can be employed with success right down to the present day.

It’s in the conclusions that lie behind the sights we can see overhead — in the objective picture of the universe which it posits — that the infelicities  lie. For just as he rejected Eratosthenes out of hand, Ptolemy rejected Aristarchus and even Heraclides as well. The Almagest takes the geocentric model as presented by Pythagoras as its starting point, including an utterly motionless Earth at the center of it all, then bashes and hammers and saws like crazy to force it to conform with what is actually seen in the sky above.

Ptolemy solved the problem of the erratic motion of the bodies in the sky above by introducing “epicycles” into the model. Each of the planets, he claimed, was making an odd little orbit around nothing at the same time that it pursued its larger orbit around the Earth. But even this couldn’t entirely explain their observed motion, so Ptolemy also had to add a theory of the “excentric,” positing that each of the planets orbited not the Earth directly but a separate, imaginary point that was itself orbiting a short distance away from our world. Then, for the coup de grâce, he stipulated that this point as well was slowly moving back and forth in relation to the Earth. (Don’t worry if you can’t picture all of this in your head; very few people can.) In all, 39 recurring motions were required to describe the movements of just seven heavenly bodies. The math worked out that way, but the unwieldy, borderline nonsensical model that resulted resoundingly lacked the elegance that had made the simplest version of the geocentric model so attractive to Pythagoras, Plato, and Aristotle. The music of the spheres had been turned into a disjointed cacophony. Nevertheless, said Ptolemy, it would have to do.

It is all too easy to judge Ptolemy harshly for this mess. The historian of science Arthur Koestler, for example, calls him “a pedant with much patience and little originality, doggedly piling orb in orb.” But there are a couple of points that should be made in his defense. The first is that fundamental paradigm shifts are, by their very nature, hard; if there is one idea that the rest of this book will seek to impart, it is that one. When one has grown up believing in one model of the universe, when one has had that model so ingrained on one’s consciousness that it has come to seem as real and natural and self-evident as the air that one breathes, it is damnably difficult to even conceive of an alternative model as a thought experiment, much less to embrace it is as physical truth. Ptolemy would have had to be an even more exceptional thinker than he already was to have done so; that he failed to do so just makes him human, not a dullard.

The other point is that revealing the physical truth of the structure of the universe wasn’t actually the most important goal of Ptolemy. There is a peculiar hesitancy about the Almagest at times, as if even the author knows that this system of planets orbiting around nothing is a little bit ridiculous; phrases like “let us imagine” pop up with surprising frequency. The historian of astronomy J.L.E. Dreyer goes so far as to describe the Almagest and works like it as “ingenious mathematical theories which represented more or less closely the observed movements of the planets [from Earth], but whose authors by degrees came to look on these combinations of circular motion as a mere means of computing the position of each planet at any moment [from the perspective of an earthbound observer], without insisting on the actual physical truth of the system.” Rather than describing physical truth in the scientific sense, in other words, Ptolemy wanted first and foremost to provide a guide for what the earthbound observer located somewhere close to the Mediterranean Sea could expect to see in the sky at any given time. And at this, as I’ve already noted, the Almagest succeeds superbly. In fact, the system of Heraclides Ponticus, the system of Claudius Ptolemy, and the solar system as we know it to exist today can all be mathematically modeled to yield an accurate picture of what we can expect to see overhead from any given point on the Earth’s surface at any given time. When it comes to this function, they are all equally valid.

But why, you might be asking, should that function have been given so much weight? The answer is that the Almagest was, for all its magisterial scope and authority, merely a necessary prerequisite to another work by Claudius Ptolemy, commonly called the Tetrabiblos: Greek for “Four Books.”

While the Almagest remained inviolate and unquestioned in the field of astronomy for almost 1500 years, the Tetrabiblos has had an even longer run as the essential foundational text of modern astrology; for almost 2000 years now, it has been used every day by those who believe that our characters and destinies are written in the stars. Whereas the Almagest tells these folks where the stars and planets and other heavenly bodies will be at any given instant, the Tetrabiblos tells them what those stellar configurations mean for our lives on Earth. The stars are the secret code that, once cracked, can explain ourselves to ourselves. Each of the heavenly bodies is associated with specific human qualities, and their waxing and waning influences determine both the personality traits of the people born under them and the likelihood of success or failure for any enterprise they might embark upon at any particular point in time. Auspicious and inauspicious times for getting married, for having children, for starting a business, and for all the rest of life’s rich pageant are encoded in the stars. Likewise, the mutual compatibility of mates, business partners, and friends are decided by the configurations of the heavens on their respective birthdays.

The Tetrabiblios might leave those of us who are not devotees of astrology feeling confused. How could a man dedicated to sober empirical logic, as Claudius Ptolemy claimed to be, go so far astray as this? Once again, any answers we propose must be grounded in an understanding of the times in which Ptolemy lived.

As I noted at the beginning of this chapter, the world which ancient peoples saw all around them was controlled by the heavens in a very real sense, as were their own lives by extension. The heavens dictated the rhythms of agriculture, the bedrock upon which human civilization was built. In addition, there was already a strong suspicion in some quarters hundreds of years before Ptolemy that the Moon controlled the rise and fall of the tide, which in turn dictated the daily rhythm of a port city like Alexandria. And the men who sailed to and from that city in fragile wooden ships lived in awe and fear of the heavens, reading them obsessively for signs of the storms that could be their executioners and the favorable breezes that could be their saviors. If all of these natural phenomena were written in the sky, reflecting the control of life on Earth by divine beings or mechanisms which no mortal could hope to fathom, why should the shifting configurations of the heavens not also dictate the characters and destinies of individual humans?

To the Roman philosopher Seneca the Younger, who lived during the century before Claudius Ptolemy, all of this was thoroughly self-evident.

What? Think you so many thousands of stars shine on in vain? What else, indeed, is it which causes those skilled in nativities to err than that they assign us to a few stars, although all those that are above us have a share in the control of our fate? Even those stars that are motionless are not without rule and dominion over us.

Perhaps to Ptolemy’s credit, the Tetrabiblos is less fanciful than much of what would come later under the label of astrology. Fully half of it is concerned with the stars’ influence on the weather and other large-scale terrestrial events rather than their influence on individual humans. Even when Ptolemy does delve into horoscopes and star signs in its second half, he emphasizes always that his work is a highly conjectural window into a complex subject, and eschews its use as a tool for overly specific prophesying. If one sets aside all its talk of heavenly bodies, or can find a way to accept it as merely a collection of metaphors, one can see this second half of the Tetrabiblos as nothing less than the world’s first attempt at a systematic study of human psychology, of the impulses and character traits that bind us together and separate us.

At any rate, the Almagest and Tetrabiblos together represent the fullest, most mature working-out of the ancients’ understanding of the heavens. Nothing of similar scope — in fact, surprisingly little of note at all — was written afterward. For Ptolemy’s life corresponded with the absolute zenith of the Roman Empire, the most powerful and prosperous that the Western world had yet known. Its long, slow decline followed his death. Contending with increasing instability and encroaching threats of every description, men had less and less time to gaze up at the sky and think and write about what they saw there. This left Claudius Ptolemy to stand alone for a long, long time as the final word in his field.

The fifth century after Christ saw the complete collapse of the old order in and around the Mediterranean, with the imperial capital of Rome itself being sacked on several occasions by “barbarians” out of the hinterlands of Europe to the north. Alexandria fell to the burgeoning new religion of Islam in AD 642, by which time the period that some historians still refer to as the “Dark Ages” was setting in in the remaining Christian lands. Literacy rates among the population of Europe, and with it the production of new texts, declined precipitously. Those men of letters who were still to be found were virtually all associated with the Christian Church. Rather than the mathematical and empirical knowledge that had been sought by the proto-scientists of places like Alexandria, they interested themselves in divine revelations, and in parsing the fine-grained meaning of a relatively small body of already extant religious texts. Some of them even forgot that the Earth is round.

This early Medieval period gave way eventually to the High Middle Ages, during which the part of Europe that lies north of Rome came fully into its own. This time of chivalry and balladry, feudalism and Crusades was not without technological, aesthetic, and intellectual progress. Yet its concerns still tended to be either religious, agricultural, or martial, seldom scientific.

Not until the thirteenth century after Christ do we begin to see the first stirrings of what would become known as the Renaissance, as ancient texts that had been lost to the West since the fall of Rome, having been regarded by the Church as of little importance when set against the divine revelations of God, began to make their way back to Christendom from the Muslim world, whose scholars had not been possessed of such lamentable tunnel vision. The works of Claudius Ptolemy were among the very first of these legacies of the ancients to reappear in Europe, for the simple reason that they had been among the most frequently copied and widely celebrated of them all among the Muslim scholars.

As early as 1230, an English monk named John of Sacrobosco produced what may have been the first original book on astronomy to have been written in the West since the fall of Rome. De Sphaera would be used as the standard text in university astronomy courses until well into the 1600s. This was encouraging in itself, a sign of a broadening age of the mind. Yet the word “original” requires some qualification here: De Sphaera was nothing but a condensed regurgitation of the Almagest, with a few ideas from later Muslim writers thrown in for good measure. For the first glimmers of the dawning Renaissance did not immediately herald a full-fledged return to an empirical, questioning attitude toward the natural world. The early focus of the age was entirely directed toward recapturing the wisdom to be found in such texts as the Almagest rather than trying to advance the frontiers of knowledge beyond the limits of the ancient worldview. Figures like Ptolemy were regarded almost as demigods whose authority was not to be questioned.

But questioned they would be in the due course of time. The resulting conflict would pit two divergent philosophical and epistemological camps against one another. The one, still dominant view held that the ancients had already learned and written about everything that needed to be learned and written about, whether the subject was religion or astronomy or anything else, and the current, fallen generation should content themselves with imbibing their wisdom. The other, upstart view held that, while the ancient texts could certainly serve as a steppingstone, there was much that was new still waiting to be learned as well. In some cases, the ancient authorities might even be — whisper it softly! — wrong about some things. Such as, for instance, that tangled mess of a universe which Claudius Ptolemy had foisted on everyone almost a millennium and a half ago…

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(A full listing of print and online sources used will follow the final article in this series.)