Ptolemy

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Claudius Ptolemy was a Greek-speaking scholar of Roman Egypt, active in Alexandria around the middle of the second century, whose mathematical works governed how Europe and the Islamic world pictured the cosmos for some fourteen hundred years. Almost nothing is known of his life — not his birthplace, not his teachers, not the years of his birth or death. What survives is the work, and the work was enough to make his name a synonym for a model of the universe.

The name itself is the one firm biographical fact. Klaudios Ptolemaios joins a Roman gentile name to a Greek given name common among the Macedonian dynasty that had ruled Egypt before Rome, and the Claudius points to a grant of Roman citizenship somewhere in his ancestry, perhaps under the emperor of that name or under Nero. He is not to be confused with the Ptolemaic kings; he was a private scholar three centuries downstream of them, working under the emperors Hadrian and Antoninus Pius. His dated observations run from the spring of 127 to the winter of 141, and a stone he set up at Canopus near the Nile delta — the so-called Canobic Inscription, which records his planetary parameters and dedicates them to a savior god — is fixed to 146 or 147. A late Byzantine writer, Theodore Meliteniotes, named Ptolemais Hermiou in Upper Egypt as his birthplace, but the claim comes a thousand years too late to carry weight. Beyond these dates and the city of his labor, the man dissolves into his books.

That city, though, is itself a kind of biography. The Alexandria of the second century was the inheritor of the great Museum and Library founded by the earlier Macedonian kings, and the one place in the Roman world where the whole apparatus of Greek mathematical science — the astronomy of Hipparchus, the geometry of Euclid and Apollonius of Perga, the trigonometry of chords — sat ready to hand. Ptolemy worked at the end of a long Alexandrian tradition rather than at its beginning, and the character of his achievement is that of a great codifier: he took the scattered Greek and Babylonian results of three centuries, supplied the missing demonstrations and the missing tables, and welded them into systems so complete that they made their own predecessors obsolete. It is partly for this reason that those predecessors are now largely lost — the Almagest preserved what it superseded only in the form of the data it absorbed.

The Almagest and the order of the heavens

His astronomical treatise, which he himself titled the Mathēmatikē Syntaxis — the Mathematical Composition — and which the Arabic tradition called al-majisṭī, “the greatest,” and which came back to Latin Europe as the Almagest, set the Earth motionless at the center and the planets, sun, and stars wheeling about it on combinations of circles. It was not a sketch but a working machine: thirteen books of tables, geometric arguments, and observational records that let an astronomer compute where any heavenly body would stand on any future night. The first book lays the cosmological foundations and the trigonometry of chords; the next pair handle the sun and the precession of the equinoxes; books four through six master the moon, its parallax, and the prediction of eclipses; books seven and eight carry the catalog of the fixed stars; and the last five books resolve the tangled motions of the five planets, including the backward loops of retrogradation.

The genius of the system lay in a small kit of geometric devices. A planet was carried on a small circle, the epicycle, whose center rode the rim of a larger circle, the deferent, turning about a point near but not at the Earth. To save the appearance of uniform motion that Greek physics demanded, Ptolemy introduced a further point, the equant, about which the deferent’s motion swept out equal angles in equal times — a subtle violation of strict uniformity that troubled later commentators and that Copernicus would single out as the model’s deepest flaw. With this apparatus of deferent, epicycle, eccentric, and equant, the irregular wanderings of the night sky became calculable quantities. The star catalog fixed the positions of over a thousand stars across forty-eight constellations, the framework of constellations Western astronomy still uses; the catalog’s coordinates, carried forward by a precession value of one degree per century that Ptolemy inherited from Hipparchus, anchored the whole edifice.

That predictive power is why the system held so long. It worked, to the accuracy the instruments of the age could check, and a model that works is hard to abandon. The Almagest passed into Arabic under the early Abbasid caliphate — al-Maʾmūn’s translators rendered it in ninth-century Baghdad — and returned to Latin Christendom when Gerard of Cremona translated it from the Arabic at Toledo, the work conventionally dated to 1175. Regiomontanus and his teacher distilled it into the influential Epitome of the Almagest, and George of Trebizond produced a full Latin version from the Greek in the fifteenth century. Only Copernicus, in 1543, and then Kepler and Galileo unseated it, and the “Ptolemaic system” became, in their hands, the name for the order they overturned — a thing so total that to overturn it was to remake the world. The companion Handy Tables repackaged the Almagest’s computations for working astronomers, and the Planetary Hypotheses went further than the mathematics, nesting the planetary spheres one inside the next to give the cosmos a physical size: the sun set at some 1,210 Earth-radii out, the sphere of the fixed stars at twenty thousand. It was a finite, bounded, snugly fitted universe, and it furnished the medieval and Renaissance imagination with the very shape of the heavens. This was the cosmos that Dante climbed in the Paradiso, the nested crystalline spheres that the Latin schools taught as settled fact, and the order against which the Renaissance revolution in astronomy would have to define itself.

The Arabic astronomers who inherited the Almagest did not merely preserve it; they tested and corrected it. The astronomers of the Maragha school in thirteenth-century Persia, troubled by the equant’s departure from true uniform motion, devised new combinations of circles to reproduce the planetary motions without it — geometrical models that recur, by paths still debated by historians, in the work of Copernicus. The Almagest’s star catalog was re-observed and its values updated by ʿAbd al-Raḥmān al-Ṣūfī in the tenth century and again at Samarqand under Ulugh Beg in the fifteenth. By the time the Islamic Golden Age handed the treatise back to a reawakening Latin West — through the Toledo translators and, for astrology, through the Sicilian and Spanish channels that carried Arabic learning into the universities — Ptolemy had become less a man than an institution, the presiding authority of two sciences at once.

The Tetrabiblos and the charter of astrology

For the later esoteric tradition the decisive book was the Tetrabiblos, his treatise in four parts on astrology — titled in Greek the Apotelesmatika, the work “on effects,” dedicated to one Syrus, and known to the Latin Middle Ages as the Quadripartitum. It is the single most consequential text in the documented history of Western astrology, and the philosophical charter on which the whole later edifice of the art was raised. Where the loose technical manuals of Hellenistic astrology — the Anthologies of Vettius Valens, the verse of Manilius, the later compendium of Firmicus Maternus — recorded the practice as a body of inherited rules, Ptolemy alone supplied a theory of why the practice should work at all.

The four books move from the general to the particular. The first sets out the principles and mounts the celebrated defense; the second treats what later ages called mundane or general astrology — the influence of eclipses, comets, and the great configurations upon nations, climates, and weather; the third and fourth descend to the individual nativity, the casting and reading of the birth-chart, with the third taking up the native’s body, soul, and inherited disposition and the fourth the outward accidents of fortune, rank, marriage, and the manner of death. Throughout, Ptolemy reasons from the four primary qualities — hot, cold, wet, dry — and assigns each planet, sign, and angle its nature by analogy with the manifest action of the two great lights. The sun warms and dries; the moon, governing the tides and the moisture of growing things, moistens; and from these undeniable powers the subtler influences of the rest are argued by extension.

There Ptolemy argued that the heavens act on the sublunary world as plainly as the sun governs the seasons and the moon the tides, and that the art of reading those influences, while fallible, was a legitimate branch of natural philosophy rather than superstition. He met the two standing objections head on. To the charge that astrology cannot be a science because its practitioners so often err, he answered that error proves the difficulty of the art and the incompetence of its bunglers, not the falsity of its foundation — the physician and the pilot also fail, and no one therefore denies that medicine and navigation rest on real knowledge. To the charge that astral prediction abolishes human freedom, he answered that the stars incline but do not compel: they shape the field of tendencies within which a soul acts, and a foreknown tendency can be tempered, much as a farmer who knows the season can guard his crop. He was careful, in short, to claim less than his successors would. He framed astrology as conjecture about tendencies, not iron decree, and he was equally careful to set its limits — discarding the catarchic and interrogatory techniques that later practice prized, and resting the art on physical causation rather than on the older language of omen and divine sign.

That guarded defense, from the same author who had given astronomy its rigor, lent the practice an authority it carried through Arabic astrology and into the Latin Middle Ages and Renaissance, where the Tetrabiblos circulated as the discipline’s standard text. Ḥunayn ibn Isḥāq rendered it into Arabic in the ninth century; Plato of Tivoli made the first Latin version from the Arabic in 1138, and the work thereafter anchored the university astrology of figures such as Pietro d’Abano, the Paduan physician-astrologer who commented on it. A spurious appendix of a hundred aphorisms, the Centiloquium or Karpos, circulated under Ptolemy’s name through the whole medieval and Renaissance period and was long taken for genuine, a measure of the authority his name conferred. When Pico della Mirandola launched the great humanist assault on astrology in 1496, it was Ptolemaic causation he took as the target worth demolishing; and when Kepler sought to reform rather than abolish the art, he reasoned from Ptolemy’s premise of celestial influence toward a geometry of aspects of his own. The Renaissance astro-magicians — Ficino, Agrippa, Fludd — built their Neoplatonic cosmologies of sympathy on a Ptolemaic skeleton, and the art that descended to the Theosophical revival and to the present still keeps the bones of his fourfold scheme.

Geography, harmonics, and the science of light

Ptolemy wrote across the mathematical sciences. The Geography — the Geōgraphikē Hyphēgēsis, the “guide to drawing a world map” — mapped the known world by coordinates: in its central books it lists some eight thousand places, each fixed by a latitude and a longitude reckoned from a prime meridian he set at the Isles of the Blessed, the westernmost land then known. Building on the earlier work of Marinus of Tyre, he criticized the flat rectangular grid as a distortion and devised two projections to lay the curved earth on a plane, the more refined of them a conic scheme curving the parallels about a pole. The work shaped cartography for a millennium, and its one great error — an underestimate of the earth’s size that stretched Eurasia far to the east and made the western ocean seem narrow — encouraged the navigators of the fifteenth century in the belief that Asia lay within easy sailing of Europe. He treated optics, music, and the projection of the sphere as well. The Optics, surviving only through a Latin rendering of a lost Arabic version, set down the first known measured study of refraction, tabulating how a ray bends as it passes between air, water, and glass. The Harmonics, in three books, took the mathematics of musical concord as a middle path between two schools — the Pythagoreans who would settle every interval by ratio alone and the followers of Aristoxenus who trusted the trained ear — insisting that reason and the senses must agree, and tested its ratios on the single-stringed monochord. Its closing turn is the one that most drew later readers: a vision in which the proportions that order sound also order the human soul and the revolutions of the heavens, the ancient doctrine of the harmony of the spheres given a mathematician’s exactness. The minor works complete the portrait of a systematizer — the Phaseis, a calendar of the risings and settings of the stars; the Analemma and Planisphaerium on the projection of the celestial sphere onto a plane, the geometry behind the astrolabe; and a lone philosophical essay, On the Criterion, on how the mind arrives at knowledge.

Two sciences, and the question of the data

Modern scholarship draws a line his readers did not. Astronomy and astrology were for Ptolemy two halves of one inquiry — the first establishing the positions of the stars, the second their meaning for earthly life — and only later centuries split the predictive science from the predictive art. The opening of the Tetrabiblos makes the partition explicit in his own terms: one study finds the configurations of sun, moon, and planets relative to one another and the earth, the other examines the changes those configurations work in what they enclose. Both, to him, were branches of the same natural philosophy, and the second followed from the first as surely as the harvest follows the season.

A second dispute is sharper, and historians have not resolved it. Some have charged that Ptolemy doctored or borrowed observations in the Almagest. The case was pressed hardest by the physicist Robert R. Newton, whose 1977 study branded him the most successful fraud in the history of science and argued that the treatise’s observations were back-computed from theory rather than taken from the sky — pointing, among other things, to an autumn equinox Ptolemy claimed to have measured with great care that falls more than a day from where modern calculation puts it. There is a related and older suspicion that the star catalog derives in large part from Hipparchus’s lost catalog of three centuries earlier, adjusted forward by a precession constant that was itself too small. Against the prosecution stand defenders such as Owen Gingerich, who granted that the Syntaxis holds some genuinely suspect numbers but read them as the selective reporting of a theorist showing his model at its best rather than as fabrication, and who urged that ancient and modern standards of what an “observation” is cannot be silently equated. The dispute turns on standards of evidence the ancient world did not share, and no consensus has settled it.

What is not in dispute is the reach. The line of transmission runs unbroken from the Alexandrian’s own hand through the translators of Baghdad and Toledo, through the medieval universities and the Renaissance presses, to the moment the geocentric heavens were dismantled and the astrological art was carried on without its physics. Few figures have furnished both a science later proved wrong and a science still practiced, and stood at the head of each for as long as he did.

Texts and scholarship

The standard modern English of the astronomical masterwork is G. J. Toomer’s Ptolemy’s Almagest (Duckworth, 1984; reissued by Princeton University Press, 1998), a close and fully annotated rendering of the Greek that supersedes all earlier translations; the underlying critical Greek text is Johan Ludvig Heiberg’s Claudii Ptolemaei opera quae exstant omnia (Teubner, 1898–1903). See books.google.com/books?id=43XvAAAAMAAJ. For the astrological treatise, F. E. Robbins’s Greek-and-English Tetrabiblos in the Loeb Classical Library (Harvard University Press, no. 435, 1940) remains the scholarly reference text, accessible through the publisher at hup.harvard.edu/books/9780674994799; the older and freely available English of J. M. Ashmand (London: Davis & Dickson, 1822) is the standard public-domain version. The transmission and the technical character of the work belong to the longer history of Western astrology, and to its formation under Hellenistic astrology. The framing of Ptolemy’s astronomy and astrology as one enterprise is argued in Mark Riley’s “Theoretical and Practical Astrology: Ptolemy and His Colleagues” in the Transactions of the American Philological Association 117 (1987), at jstor.org/stable/283969. The authenticity debate is set out, for the prosecution, in Robert R. Newton’s The Crime of Claudius Ptolemy (Johns Hopkins University Press, 1977; ISBN 0-8018-1990-3), indexed at ui.adsabs.harvard.edu/abs/1977ccp..book…N, and for the defense in Owen Gingerich’s “Was Ptolemy a Fraud?” and the ensuing exchange with Newton in the Quarterly Journal of the Royal Astronomical Society 21 (1980), 253–266 and 388–399, indexed at ui.adsabs.harvard.edu/abs/1980QJRAS..21..253G. The Geography and the world-map tradition are documented in J. Lennart Berggren and Alexander Jones’s Ptolemy’s Geography: An Annotated Translation of the Theoretical Chapters (Princeton University Press, 2000; ISBN 0-691-01042-0), books.google.com/books?id=tNrPCN3qn94C.

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