During the second century AD, there lived in Alexandria a man of science who was in his way the equal of any Archimedes or Eratosthenes from an earlier epoch. Certainly Claudius Ptolemy — no known relation to the line of Egyptian kings who once bore the same name — had as voracious an appetite for empirical knowledge as any Alexandrian in history. He made it his life’s work to collect that knowledge which had come down to him courtesy of his illustrious forebears in a series of thick books, whilst building upon their foundations wherever necessary with experiments and observations of his own, which led to significant advances in geography, astronomy, mathematics, harmonics, and optics. His expressed attitude toward his work reads as strikingly modern today. The hypothesis most likely to be correct, he wrote, is the simplest that encompasses all of the facts of a case. And he cautioned his readers not to accept as definitive any experiment that hadn’t been repeated multiple times, preferably by a variety of people, and had consistently yielded the same result. “Ptolemy had the temper and patience of a true scientist,” writes Will Durant. Yet this seemingly sober-minded, thoroughgoing man of science is better remembered today for the things he got wildly wrong than for the ones he got right.
Despite his being situated closer to us in time by some 400 years, we know even less of Ptolemy’s personal life than we do of those of Archimedes and Eratosthenes. No foreign birthplace is mentioned anywhere in the ancient records, so we can assume that he was probably born in Egypt. Some have wished to connect him to an Egyptian city known as Ptolemais Hermiou, which was located far to the south of Alexandria, but this speculation is based on little more than his name; he was more likely born in Alexandria itself. He was probably of Greek rather than Egyptian ethnicity, although the latter cannot be entirely ruled out. At any rate, all of his writings were originally in Greek, as was still the norm for Alexandria’s intellectual classes even long after the coming of the Romans. And yet the combination of a first name of “Claudius” — presumably after the Roman emperor who ruled from AD 41 to 54 — paired with a family name of “Ptolemy” does reflect the influence of the Latin world order. We know the years in which he was active largely thanks to a trio of stellar observations he made which can be cross-referenced against historical configurations of the heavens: one dates from AD 127, one from 137, and one from 150. From these and other scattered clues, historians guess that he was probably born around AD 100, and died around 170.
We’ll be focusing here on Ptolemy’s work in geography, astronomy, and astrology, the fields in which he became most famous and influential. Ironically, his sheer comprehensiveness as a scholar of all three can make it difficult to assign credit for the apparent innovations he documents. Ptolemy’s books were so all-encompassing that the scholars who followed him seem to have considered them literally the last word on their subjects, and to have thrown out many of the older works he used as sources. Thus Ptolemy’s long shadow may ironically be one of the principal reasons that the works of, say, an Eratosthenes have been lost to us.
Ptolemy’s book about geography is usually called the Geographia, its name in its Latin translation, which was the first version of it to be rediscovered by European scholars during the Renaissance. (This version was actually a second-generation translation, from the Arabic rather than the original Greek.) It’s a remarkable volume in any language. “The framework and the vocabulary of our maps of the world are still shaped by Ptolemy,” notes the historian of science Daniel J. Boorstin.
By the time of Ptolemy, it had been widely recognized by men of learning for hundreds of years that the Earth was a sphere; think back to Eratosthenes’s ingenious method of determining the size of that sphere. It was probably Eratosthenes as well who first came up with the idea of superimposing onto the surface of the planet a grid of parallel lines, the earliest forerunner to our modern system of latitude and longitude. But Eratosthenes didn’t lay down his lines using regular spacing. Instead he drew them so that they passed through the major landmarks of the known world: the islands of Rhodes and Sicily, the Ethiopian city-state of Meroë, the Strait of Gibraltar, the Euphrates and Indus Rivers, the Persian Gulf, the southern tip of India. The resulting patchwork was useful for saying where these places were in relation to other places, but was tied to the political vicissitudes of its time. And the grid didn’t extend at all beyond the known world.
It was left to Hipparchus, who hailed from Rhodes but may have spent some span of time in Alexandria as well, to regularize the system in the decades after Eratosthenes’s death. Working from the latter’s estimate that the circumference of the planet must be 24,850 miles (40,000 kilometers), he drew his lines all the way around the globe at even intervals of 69 miles (111 kilometers), winding up with 360 horizontal and 360 vertical lines in all, corresponding to the 360 degrees of a circle.
Ptolemy then came along a few centuries later to complete the system. He would appear to have coined the terms “latitude” and “longitude,” and to have become the first to subdivide Hipparchus’s degrees into minutes and seconds. He then made a painstaking list of the exact locations under this system of some 8000 separate places. He also devoted much attention to the problem of translating a three-dimensional terrestrial globe to two-dimensional maps, thereby presaging much of the work of the Flemish geographer Gerardus Mercator of a millennium and a half later. He even established the standard whereby north is at the top of a map.
But in the midst of all these careful labors, Ptolemy made some devastating mistakes — not from any failing of logic in the abstract, but because he chose the wrong facts with which to build out his edifice of logic. He rejected Eratosthenes’s shockingly accurate estimate of the circumference of the Earth in favor of the later geographer Strabo’s guess of just 18,000 miles (28,968 kilometers). As a result, he wound up with lines of latitude and longitude separated from one another by only 50 miles (80 kilometers) instead of 69 miles (111 kilometers).
Conceptually unassailable, Ptolemy’s system was thus undermined by his use of the wrong numbers. His choice wasn’t, it should be pointed out, completely indefensible in the context of his day. Strabo, who had lived in Asia Minor from about 65 BC to AD 25, was still considered the leading authority in geography at the time Ptolemy began his study of the subject — considered to have superseded the likes of Eratosthenes and Hipparchus, just as Ptolemy himself would come to supersede some of what Strabo had written.
Nevertheless, the Geographia serves as an object lesson today that logic can avail one nothing without the right data to underpin it. “Ptolemy’s essential weakness was his desperate lack of facts,” admits Daniel Boorstin. Will Durant notes in a similar vein that Ptolemy “tried to rest all his conclusions upon observations”; it was just that said observations were “too seldom his own.” His mistaken estimate of the size of the Earth would persist into the Renaissance and beyond, to have some surprising effects on history. Christopher Columbus, for example, placed his faith in the Geographia when he set out to find a westward route from Europe to the Far East. His reliance on Ptolemy eventually caused him to believe that he had arrived in India when he had actually encountered a whole new, heretofore unimagined continent — a continent which Ptolemy’s cramped version of the Earth simply didn’t have room to accommodate. So, the fact that the natives of North and South America were for so many years commonly — and confusingly! — referred to as “Indians” is merely one of the many unlikely legacies of Claudius Ptolemy, ancient Alexandrian.
Still, Ptolemy’s great error in the Geographia was at the end of the day eminently correctable. Once one plugs the correct numbers into his system of the world, it hangs together perfectly. Alas, a similar claim cannot be made for his second enormously influential work, which is built upon a profoundly mistaken premise rather than mere faulty data.
Ptolemy’s extended treatise on astronomy is commonly known as the Almagest, the name it was given by its Arabic translators; it means roughly “The Greatest Compilation” in English. In spite of the gaping error that lies at its core, which we’ll get to momentarily, it remains a bracing, even inspiring volume to peruse, being filled with its author’s sense of wonder at the stately beauty of the heavens above. “Mortal as I am,” Ptolemy writes at one point, “I know that I am born but for a day, but when I follow the serried multitude of the stars in their circular course, my feet no longer touch the Earth; I ascend to Zeus himself to feast me on ambrosia, the food of the gods.”
The great error of the Almagest is, of course, that of a geocentric model of the universe. Ptolemy was definitely not alone in rejecting the insight of Aristarchus that the Earth might orbit the Sun rather than vice versa; as we have already learned, virtually everyone did so, including such luminaries as Eratosthenes and Hipparchus. But, in describing this wrong-headed model of the universe in more detail than anyone before or after him, Ptolemy would receive the lion’s share of the blame for propagating it once Nicolaus Copernicus and Galileo Galilei finally began to set the world straight.
In the broad strokes, Ptolemy’s model of the cosmos hews to the most traditionalist of the views we met earlier. The universe as a whole is a hollow perfect sphere, the stars pinpricks of light on its rotating inner surface. Ptolemy finds proof of the Earth’s location at the very center of all creation in the fact that the stars in one half of the planet’s sky don’t appear markedly larger than those in the other half, as they would seemingly have to if the planet was closer to one side of the celestial sphere than the other. He imagines some attractive force — an analogue to gravity — anchoring the Earth, the only physical heavenly body in the universe, in place in its central location. All of the other objects visible in the Earth’s sky are numinous, insubstantial forms — fortunately for all of us in that this means that they don’t get pulled down by the attractive force to crash into the Earth.
All of the things and creatures on the Earth’s surface are anchored there by the same attractive force that holds the planet itself in place. Ptolemy rejects the hypothesis that the Earth might be spinning with the commonsense argument that, if this was the case, one ought to be able to see thrown objects, flying birds, or even jumping people being left behind by its motion; he does so even as he acknowledges that a spinning Earth would simplify his mathematical models in many ways.
The five other planets visible with the naked eye from the Earth, which Ptolemy refers to as “wandering stars,” present the biggest problem for the model. Ptolemy’s choice of adjectives isn’t accidental: to the star gazer with a geocentric mindset, the planets really do seem to weave and bob about the sky almost randomly, evincing little of the clockwork orderliness which Ptolemy prefers. He is forced to describe infamously convoluted paths for the planets in order make all of the math work, hinging on what he calls “epicycles”: odd little orbits around nothing that they travel at the same time that they pursue their often wildly eccentric orbits around the Earth.
One question springs inevitably to mind when one ponders all of this: why did it never occur to Ptolemy to move the Sun to the center of his cosmos? If he had done so, he would have found that he could do away with most of his logical and mathematical contortions. His failure to recognize what strikes us as obvious seems that much more bizarre in light of his explicit statement that the hypothesis most likely to be correct in any given instance is the simplest of those which fully explain a scientist’s observations. Yes, the lack of stellar parallax appeared to argue against heliocentrism, but it was a problem that could be solved easily enough by moving the stars much farther away from the Earth — certainly a vastly simpler solution than those he employed. But Ptolemy appears never to have even considered it.
We might first be tempted to ascribe his failure to religious belief. After all, in the centuries that followed Ptolemy, the notion of a geocentric cosmos would be increasingly bound up with religious dogma: as a single god’s supreme creation, it was claimed, the Earth must necessarily stand at the center of all things. Yet the reality is that there is little sign of such dogmatic religious sentiment in the Almagest. As was becoming typical among the intellectuals of his time, Ptolemy evokes the pantheon of Greek gods more as symbols and metaphors than living entities, as in the quote above where he dreams of “ascending to Zeus” in a sort of scientific rapture. Meanwhile he gives no hint of interest in the new monotheism that had come to Alexandria (a development we’ll explore in future chapters).
In the end, then, our understanding of Ptolemy’s failure to see the obvious must hinge on human nature rather than religion or science. The framework which he so meticulously described in writing was an elaboration on the one which humanity had been carrying around with it since the beginning. Aristarchus’s alternative theory of heliocentrism, on the other hand, was an idiosyncratic notion which had garnered only passing mentions and little favor among those who studied astronomy after him. Ptolemy too was caught within the established paradigm, and never even tried to find his way out of it. Before we rush to judge him for that failure, we should perhaps ask ourselves whether we would have done any better. A heliocentric model would have struck Ptolemy as every bit as outlandish as, say, the idea that we might all be living within a computer-generated virtual reality strikes us today. Paradigms of thought are not easy prisons to escape — not even for a brilliant mind like that of Ptolemy.
By way of doing further justice to Ptolemy, I should note that he himself seemed unconvinced at times by all of his mathematical contortions, using phrases like “let us imagine” in relation to the movements of his wandering stars rather than making a more definite claim to empirical truth. The historian of astronomy J.L.E. Dreyer describes the Almagest and works like it as “ingenious mathematical theories which represented more or less closely the observed movements of the planets, 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.”
This statement turns out to be key to understanding the millennium-and-a-half-long dominance of the Almagest, despite the gnarly inelegance of its wandering stars. Profoundly wrong though its conception of the universe may have been in one way, it was more correct in another way than any model that had come before it or any model that would follow for almost 1500 years: it really did describe what you could expect to see in the sky and where you could expect to see it, at any time of day or night. Ptolemy was able to predict with impressive accuracy what the heavens above Alexandria would look like even 1000 years after his death. Even today, the Almagest remains a reasonably functional star gazer’s guide for those situated not too far away from Alexandria. Its efficacy in this regard made the physical truth of the model almost irrelevant to many or most of those who employed it: these being the ones who saw it first and foremost as the absolutely essential prerequisite for the second half of Ptolemy’s heavenly labors.
The half in question is the Tetrabiblos (Greek for “Four Books”), a comprehensive guidebook to astrology. While the Almagest remained inviolate and unquestioned for almost 1500 years, the Tetrabiblos has had an even longer run as the essential foundational text of 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 heavens. While the Almagest tells these folks where the stars will be at any given instant, the Tetrabiblos tells them what those stellar configurations mean.
But the Tetrabiblios leaves those of us who are not devotees of astrology with the same basic question as the Almagest, multiplied a hundredfold. How could a man dedicated to sober empirical logic, as Ptolemy claimed to be, wind up so far astray as this? Once again, any answers we propose must be predicated on an understanding of the times in which Ptolemy lived.
In a very real sense, the world which ancient peoples saw all around them was controlled by the heavens, as were their own lives by extension. The Sun, that bringer of light and warmth, dictated when they went to bed and when they got up. The procession of the seasons told them when to plant and when to harvest, and the fickle vagaries of sunshine and rain determined whether they would go hungry or be well-fed each year. 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 harbor like Alexandria. And of course the men who sailed to and from that city in fragile wooden ships lived in awe and fear of the heavens, reading them assiduously for signs of the storms that could be their executioners and the breezes that could be their saviors. If all of these things were written in the sky, reflecting the control of life on Earth by mechanisms no one could hope to fathom, why should the shifting configurations of the heavens not also dictate the characters and destinies of individual humans?
For the last several hundred years of our own epoch, the question of free will or the lack thereof has been one of the most hotly debated subjects in philosophy. In its most contemporary context, it comes down to those who believe that there is some ineffable essence which exists outside the physical processes of our minds and makes us independent actors, with a will separate from the universe around us, versus those who hew to the materialist position that what we call consciousness is merely a reflection of those physical processes — processes which, being entirely predictable if only we had sufficient data, can only result in the “choices” we actually make.
The more popular position among philosophers today is the materialist, deterministic view — which is, indeed, the only one that can truly be defended on a strictly empirical basis in light of what we know about the universe today. Yet most proverbial people on the street would take the opposite stance if you put the question to them, for reasons which have their own whiff of empiricism: they experience themselves to be free actors, in addition to having been raised to believe in personal accountability and responsibility for one’s actions. In fact, our societies are built upon this very premise. Courts of law, for example, take it as a given that the guilty have made a choice to commit a crime. A world guided by a strict belief in determinism would be so different as to be almost incomprehensible to us. Right and wrong would be meaningless terms if everyone accepted that the things which people did were the only things they possibly could do. Small wonder, then, that the debate over free will has been such an obsession of philosophers for so long.
And yet it hasn’t been an obsession forever. Socrates, Plato, and Aristotle, the big three of classical Greek philosophy, who engaged with most of the Big Questions that their intellectual heirs have been mulling ever since, had oddly little to say about this one. For a long time, it was commonly accepted in philosophical circles that they never gave the question of free will much attention because they simply accepted it as a given — that they “shared the plain man’s belief in free will” as a self-evident reality, as the twentieth-century philosopher W.D. Ross put it.
But was this really the case? Of late, opinion has shifted toward the belief that philosophers as late as Aristotle lacked not the concept of determinism, but rather its opposite: the concept of an absolutely sovereign individual will. Classical mythology, history, and literature are in fact shot through with a distinctly deterministic impulse. A trio of immortal women known simply as the Fates were believed to spin, measure, and finally cut the thread of every mortal’s life, while oracles such as the one in Delphi had a huge influence on international politics, thanks to their alleged ability to foresee what must inevitably come to pass. Consider the most famous story involving the oracle of Delphi, the legend of Oedipus. Informed by the oracle that he will kill his father and marry his mother, Oedipus goes to superhuman lengths to avoid doing so, only to find in the end that his very efforts to escape his destiny constituted its fulfillment. This ancient vision of literary tragedy, as a cruel cosmic joke played on a poor mortal by the inescapable Fates, stands in marked contrast to the later Shakespearean conception of the noble man with the tragic flaw, who despite his many good qualities bears ultimate moral culpability for the disaster his freely-made choices bring upon himself and others. One is a deterministic vision, while the other embraces free will.
This is not to say that the ancient version of determinism was entirely the same as its modern materialist incarnation. In a tragedy like that of Oedipus, humans are playthings of the gods and of other fickle supernatural forces beyond their control rather than part and parcel of the implacable charged particles that form their universe. In practice, then, these ancients authors are perhaps best seen as embracing a strictly circumscribed form of free will, in which humans can exercise control where the gods deign to allow it, but can never hope to escape from the larger framework which the Fates have set up for their lives. Certainly most ancient legal codes were at least as invested in the notion of punishment as our modern ones.
There were some ancient philosophers who engaged with the question of free will versus determinism in the way that Socrates, Plato, and Aristotle so conspicuously failed to do. In fact, one of these offered a surprisingly modern take on the subject during the lifetime of Socrates.
Democritus of Thrace lived from the mid-fifth to the early fourth century BC. None of his writings have survived in their complete form, but enough commentaries and quotations by later writers have reached us to give a reasonable picture of his beliefs. The first strictly materialist philosopher we know of, he’s most remembered today for his prescience in imagining a fundamental building block of nature, a least-common-denominator particle he called the atom. Just as surprisingly, he theorized that these particles behaved in a completely predictable, mechanistic way, such that everything that happened in the universe, including the choices of human beings, was already predetermined when it was first set in motion. Aristotle is on record as loathing his ideas.
But shortly after Aristotle, there came one Epicurus of Samos to at least partially embrace those same ideas. He accepted Democritus’s conception of a universe of mechanistic atoms, but displayed at the same time a clear interest in preserving the possibility of free will. To do so, he introduced a dodge: a claim that some atoms can change their courses of their own volition, and that this ability forms the basis of human consciousness. This claim is fascinating not least in that a very similar one is sometimes made today on the basis of the subjective qualities of quantum physics, in which the actions and forms of subatomic particles seem to be affected by the act of observing them through no physical mechanism we’ve yet been able to identify. This quality, some say, opens a door in science to a universe which may not be entirely deterministic.
At the same time that Epicurus was writing and teaching, another new school of philosophy was preaching a more uncompromising form of determinism. Zeno of Citium was the first of the Stoics. His core doctrine was one of submission to and acceptance of the deterministic will of the Fates — of humble acceptance of what must inevitably come to pass anyway. In the words of Will Durant:
The Stoic will shun luxury and complexity, economic or political strife; he will content himself with little, and will accept without complaint the difficulties and disappointments of life. He will be indifferent to everything but virtue and vice — to sickness and death, good or ill repute, freedom or slavery, life or death. He will suppress all feelings that may obstruct the course or question the wisdom of Nature; if his son dies he will not grieve, but will accept Fate’s decree as in some hidden way the best. He will seek so complete an absence of feeling that his peace of mind will be secure against all the attacks and vicissitudes of fortune, pity, or love. He will be a hard teacher and a stern administrator.
Crucially, the Stoics “thought of earthly affairs as in some mystic and continuous correspondence with the movements of the stars.”
This philosophy of asceticism and emotional withdrawal had a natural appeal to closeted scholars ringed in by their walls of books. It thus became immensely influential on the intellectual life of the classical world in the centuries after Zeno. Even those writers who didn’t actively call themselves Stoics absorbed many of the ideas of Stoicism. Among them must surely be numbered Claudius Ptolemy, with his comfortingly orderly portrayal of human destiny spelled out by the movements of the stars. We can assume that he developed his grand guide to their influence because he was in agreement with the Stoic philosopher Seneca the Younger:
What? Think you so many thousands 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, or because of their speed keep equal pace with the rest of the universe and seem not to move, are not without rule and dominion over us.
Ptolemy, then, endeavored to please the ghost of Seneca by assigning roles to more of the stars above us than ever before.
But even as he was doing so, another religion and accompanying philosophy of life, one which emphasized the free will of every single individual as not only extant but sacrosanct, was taking shape around him. In time, it would come to dominate the life of Alexandria, from the city’s bustling streets to the rarefied environs of its museum. So, we must turn to its origins next.
(A full listing of print and online sources used will follow the final article in this series.)