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 royal line that 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; it is at least as likely that he was 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 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.

It was probably Eratosthenes who first came up with the idea of superimposing onto the surface of our 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 been 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 amazingly 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. The numbers he chose were, it should be pointed out, the ones widely regarded to be the most accurate in his day. Strabo was 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 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.” He became such a respected authority that his perpetuation of Strabo’s error would persist all the way to 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 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 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, because he described 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 set the world straight.

In the broad strokes, Ptolemy’s model of the cosmos hewed to the most traditionalist of the views we met in an earlier chapter. The universe as a whole was a hollow perfect sphere, the stars pinpricks of light on its rotating inner surface. Ptolemy found 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 imagined 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 were numinous, insubstantial forms — fortunately so in that this meant they didn’t get pulled down by the attractive force to crash into the Earth.

All of the things and creatures on the Earth’s surface were anchored there by the same attractive force that held the planet itself in place. In his most notable break with received wisdom, Ptolemy rejected the hypothesis that the Earth might be spinning on its axis — a hypothesis which had been widely held by Alexandrian astronomers since the third century BC. He did so 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. And he did so even as he acknowledged 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 referred to as “wandering stars,” presented the biggest problem of all for his models. Ptolemy’s choice of adjectives wasn’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 preferred. In order to make all of the math work, he was forced to describe infamously convoluted paths for the planets, hinging on what he called “epicycles”: odd little orbits around nothing that they traveled at the same time that they pursued their often wildly eccentric orbits around the Earth.

This Renaissance-era diagram illustrates the concept of the epicycle. The Earth stands, of course, at the very center. The planet F follows not only an eccentric orbit around the Earth, but pursues another orbit around nothing within that one as it does so. The other planets all do the same. (Public Domain)

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 philosophical abstractions 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 Christian monotheism that had come to Alexandria by the time he was living and writing there.

In the end, then, our understanding of Ptolemy’s failure to see the obvious is better predicated on everyday human psychology than religious belief. 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 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, 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 long-lasting influence 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 until Europe was well into the Renaissance: 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 merely as the plebeian prerequisite for the second, more profound half of Ptolemy’s heavenly labors.

The half in question is 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 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. While the Almagest tells these folks where the stars 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 attempt. 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 — both as they appeared at the time of one’s birth and as they appear at the moment of the decision in question. Likewise, the mutual compatibility of mates, partners, and friends are decided by the configurations of the heavens on their respective birthdays.

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, 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.

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 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 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?

Four centuries or more before Claudius Ptolemy, Zeno of Citium developed the philosophy of Stoicism. His core doctrine was one of submission to and acceptance of the role of fate — 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 Mediterranean 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. We can assume that he created his grand guide to the influence of the stars 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. Perhaps to his 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.

But even as Ptolemy was writing it, a new religion was taking shape around him. It rejected out of hand the idea that our personalities, decisions, and fates might be influenced by the stars above us or by any other force of this world; one of its most sacrosanct teachings was that every individual was possessed of absolute free will. In time, it would come to dominate the life of Alexandria, from the city’s bustling streets to the rarefied environs of its museum, making the cool astral mysticism of Claudius Ptolemy as much a relic of the past as the pomp and decadence of his namesake dynasty.

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

9 Comments for "Chapter 14: The Last of the Alexandrian Star Gazers"

  • Ilmari Jauhiainen

    Great writing, as usual! Still, I think I again have to point few places, which I found problematic.

    ”If he had done so, he would have found that he could do away with his epicycles”

    I think this is unlikely considering that even Copernicus had to use epicycles in his system. It was only Kepler’s idea that ellipses could be used instead of circles (or figures made out of circles) that finally got rid of the epicycles.

    ”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”

    This might be getting more to the details than necessary, but my old philosophy professor would be ashamed if I didn’t point out that there is the inevitable third option saying that notion of free will, at least as used by laymen and jurists, is compatible with determinism. I haven’t followed the latest discussion in this particular controversy, but at least at some point the debate had shifted more to that of compatibilitists against incompatibilitists (who could then be either proponents or opponents of free will).

    ”[O]ne of these offered a surprisingly modern take on the subject almost a century before Socrates.”

    As far as I know, Democritus (born around 460 BCE) was a bit younger than Socrates (born around 470 BCE). You might be thinking of Leucippus, who is sometimes mentioned as an older proponent of atomism.

    ”Socrates, Plato, and Aristotle all loathed his ideas.”

    It’s a bit nitpicking to say this, but we only have evidence of Aristotle criticising Democritus. Still, Socrates and Plato probably also loathed his ideas, if they just had heard of them.

    • Jimmy Maher

      Thanks so much! Edits made in all cases except the second, which is indeed just a *little* bit further down in the weeds than I’d like to go with the modern debate on free will.

  • David Simon

    I’m not sure why determinism is incompatible with a justice system. Even if we cannot help but respond to the exact same stimuli in the exact same way given a particular starting state, that doesn’t rule out causing a different reaction by changing the stimuli itself.

    Society can use a justice system to self-regulate without necessarily being non-deterministic, just as a refrigerator can use a thermostat to self-regulate deterministically.

    To put it another way, there’s the old joke about a philosopher who throws his friend’s favorite book out the window. Before the friend can react, the philosopher says “Hold on, don’t be angry! I can’t be held responsible for my actions, because I have no free will. It was just cause and effect.” The friend considers this for a moment, and then she replies “In that case, I can’t be held responsible for this either,” and throws the philosopher out the window. After that, the philosopher mysteriously was never again compelled by cause and effect to throw his friend’s books out windows.

    • Jimmy Maher

      I wasn’t so interested in the practical use of a justice system, which can indeed fill the function you describe, as I was the assumptions behind it — the ones embedded in all of our discussions of it. I wouldn’t use the word “incompatible,” but there is a logical disconnect there. Historically, our justice systems have been explicitly predicated on the belief that one can *choose* how to act; perhaps this is beginning to change at the margins, with some countries choosing to emphasize rehabilitation over punishment, but I think it still largely holds true. (Of course, there’s a whole range of cases where we absolve people of responsibility, such as mental instability or incapacity, and that’s an interesting but difficult can of worms in itself…)

      In practice, determinism is so alien to our subjective impression of the world that it’s hard to imagine a life guided by it. Or rather not guided by it by conscious choice, but predetermined to be guided by it. It’s very hard to know how to even think within such a framework — which is just as well, I guess, because all thoughts are predetermined anyway…

      So, even the die-hard determinist philosopher winds up holding two versions of reality in her mind: the philosophical one and the experiential one, and switches between them as the situation demands. (Luckily, we human beings are pretty good at doing that.) I would assume that most determinist philosophers wouldn’t support overhauling the justice system on the basis of their philosophy. (A statement which itself implies a choice, and so here we go again.) I just wanted to point out some of the tensions between the determinist and subjective views, whether we’re talking about the oracle in Delphi or modern materialist philosophy. In daily life, we’re all more or less non-determinists, as your fable rather serves to illustrate. (Which opens up another question among those who believe philosophy should be useful and applicable to life about what good determinism is, but that’s yet another discussion…)

  • John Elliott

    “at the every center” -> “at the very center”

    • Jimmy Maher


  • Emmanuel Florac

    There’s a missing “time” or equivalent here: “At the same that Epicurus was writing…”

    • Jimmy Maher


  • James Norem

    ”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”

    Are philosophers still banging on at this old chestnut? Chaos theory and quantum mechanics make these arguments irrelevant.
    The two relevant observations in chaos theory are ‘sensitive dependence on initial conditions’ and ‘scale invariant complexity’ – in essence, you can have wildly different outcomes from the smallest variation in initial conditions.

    David Simon: “Even if we cannot help but respond to the exact same stimuli in the exact same way given a particular starting state”

    And here quantum theory raises its head in the form of the uncertainty principle – you cannot even KNOW the starting states – let alone hope to reproduce them, which firmly puts determinism into the same category as the spherical cow.


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