Approx 1600 words
One of the most influential books in the history of science is the Mathemateke Syntaxis, or Mathematical Treatises attributed to one Claudius Ptolemy of Alexandria. His catalogue of the stars visible from the Mediterranean, listing measurements of celestial longitude and latitude and visual magnitude for more than a thousand stars, remains a standard for the northern sky today.
Most students of astronomy encounter Ptolemy briefly in an Intro to Astronomy textbook. The standard narrative points to the things that Ptolemy got wrong: A geocentric model of the universe. A jumble of circles upon circles to explain the motions of the planets.
Ha, ha, ha – silly old Ptolemy!
If we look at his Treatises with modern eyes, as a work of astronomy and planetary dynamics, it’s easy to laugh at Ptolemy. But this is a fundamental misunderstanding of what Ptolemy sought to do. The Mathemateke Syntaxis was not meant to explain the motions of sun, moon and planets; instead, it taught how to measure, and how to predict these motions.
Almagest is not a work of cosmology or astrophysics, in the modern sense.
Almagest is an instruction manual for creating an ephemeris.
An ephemeris is a tabulation of the motions of the sun, and the moon, and the several planets. Past locations as measured by experienced observers, and future locations as calculated by well-studied adepts, using the geometric techniques of Ptolemy. To an astrologer, knowledge of the future positions of the planets above is knowledge of the future of the earthly world below. Certain practitioners, we presume, were happy to pay handsomely for a copy of an ephemeris prepared by a master of Ptolemy’s trigonometric arts.
Given the wide interest in astrology at the time, Ptolemy’s Treatises was not the only such manual in circulation in the 2nd, 3rd and 4th centuries CE. But early users came to agree that, of those available, Ptolemy’s manual was e Megele – the greatest.
In Arabic translation, al Magest.
As it came to pass, Ptolemy was forgotten in much of Europe during the middle ages, and was re-discovered from Arabic sources in the course of the Crusades. Hence, the modern name of Almagest for Ptolemy’s great treatise, which was rendered into Latin from Arabic translations of a Greek original, and studied by many across Europe.
The history of the text of the Mathematical Treatises is complicated.
As it came to pass, Ptolemy was forgotten in much of Europe during the middle ages, and was re-discovered from Arabic sources in the course of the Crusades. Hence, the modern name of Almagest for Ptolemy’s great treatise, which was rendered into Latin from Arabic translations of a Greek original, and studied by many across Europe.
First written in Greek, a lineage of Greek manuscripts was maintained in the Byzantine world. It’s from Greek texts that Arabic astronomers came to know Ptolemy’s Treatises. Surviving artefacts of this tradition are the basis of the modern definitive Greek text of Ptolemy, compiled by Heiberg (1898,1903). It’s from Heiberg’s text that scholarly modern translations and annotations of Ptolemy were prepared by Karl Manitius (auf Deutsch, 1912 – 1913) and G.J. Toomer (in English, 1984).
At some early date, we presume, a Latin translation was prepared, copies of which probably spread across the region of the late Roman empire and northern Europe. But with the encroaching dark age, Ptolemy faded to shadow in most of Europe, to be rediscovered centuries later in a new Latin translation from an Arabic source. We’d like to investigate this history further; reader contributions (of information or money) are welcome.
While astrologers played an important role in ensuring the survival of Almagest, we also note that both civic and religious authorities might have turned to Ptolemy. Judaism, Christianity and Islam all use solar and lunar calendars to define particular feast days, employing astronomers in drafting church calendars. Each of these religious traditions would have relied upon early astrologer/astronomers as calendar-makers.
An hypothetical: Suppose a particular feast day is scheduled for the first Sunday after the first full moon after the winter solstice. Further suppose that, in a particular year, a full moon occurs very close to the solstice. Whether the moon achieves fullness before or after the moment of sunset on the day of solstice can make a month’s difference in the timing of religious observances.
Even a church which frowns upon planetary astrology might have an interest in what Ptolemy teaches of the motions of moon and sun.
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So: Ptolemy taught of how to calculate an ephemeris.
Who might have undertaken the regimen of observation and calculation called for in ephemerogenesis?
With each generation, we suspect, a handful of adepts would study the arcane arts of geometry and astronomy with the aim of calculating the future; for there was a market for ephemerides, a market small, but wealthy.
One clever with numbers, and skilled at quantitative observation of the planets, might make a nice living selling tabulations of where the planets have been observed in the past, and where the methods of Ptolemy say they’ll be found in the future – with a special focus on determining when a planet will engage in retrograde motion, or when two planets draw close to one another in the sky, and other such omens of significance to astrologers of the day.
For these students, Ptolemy’s Mathemateke Syntaxis was their textbook and guide. It’s easy to imagine that the creation of a personal copy of Syntaxis was a rite of passage for future masters of this arcane science.
Seen that way, we understand why and how Ptolemy’s work survived the centuries known today as the Dark Ages.
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Included in Ptolemy’s manual are several reference tables.
To begin with: Trigonometry tables. (You know right off that $#!^ is getting real.)
There are also tables of past observations of the motions of the moon, sun, and planets.
And all the good stuff about calculating where the sun, the moon, and the planets will be found in the future. The stuff of ephemeris-making.
And at the heart of the book, an accounting of the starry sky still valid today.
Ptolemy’s list of stars is an astonishing historical document, an international scientific standard established thousands of years ago, still in current use – the official designations of the northern constellations known to astronomers today are rooted in the Catalogue of Almagest. An accounting of 48 constellations, 1024 [LINK] stars, with each star described in terms of its location within its figure, along with its stellar longitude, latitude and magnitude, a format instantly familiar to modern observers.
An important point regarding this list: the constellations, and the descriptions of individual stars (e.g., ‘the star in the left hand’ or ‘the third star from the north in the shield’) are not just some observer’s fancy. This was an international scientific standard, a naming of the stars which was known to observers around the Mediterranean, and beyond. It remained in common use until the early 17th century, when the nomenclature of Bayer – αOri, γUMa and such – took hold in a period of scientific revival.
Several minor constellations have been added in historical times, such as Leo Minor, Lynx, and Camelopardalis, along with southern stars unseen by the Greeks. Their histories are well documented, and won’t be addressed here.
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As to his methods: the geometric models of Ptolemy, involving nested circular orbits mapped using tools of spherical trigonomery, represented the most advanced mathematics of the day. His work might seem crude today – but remember that there was no algebra, no calculus, no automated calculation engines. Ptolemy and the astronomers of his age made do with the tools at hand, crafting models for predicting planetary motions, with calculations done manually. Awkward – but in the short term, at least, reasonably accurate.
Modern mathematicians have shown that it is possible, using the methods of Ptolemy, to accurately represent any well-behaved orbit. (Mathematicians like to deal with ‘well-behaved’ functions, for values of ‘well-behaved’ which facilitate a solution to the problem at hand.) For a remarkable illustration of this principle, pay a visit to https://www.youtube.com/watch?v=QVuU2YCwHjw ; for a more extended discussion, see https://www.youtube.com/watch?v=qS4H6PEcCCA
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So who was this person we call Ptolemy?
We don’t have a proper biography, but his bibliography is extensive.
In addition to the Mathematical Treatises, several other works are attributed to Ptolemy:
- The Tetrabiblos, a manual of astrology and signs and divination; some still consult it today
- Copies exist of a Geography, wherein he maps the world with a grid system suggestive of (but distinct from) longitude and latitude.
- Fragments of a work on optics are known, in Arabic translation.
This is not an exhaustive listing; Ptolemy was astoundingly prolific. Several other works, lost to us today, are cited by ancient authors.
Any one of these works, by itself, might represent the dedicated lifetime’s work of a gifted individual.
It’s difficult to imagine all this as the work of a single individual.
Hmmmm. . . .
What if Ptolemy is not a single person, but instead a collection of experts?
Imagine Ptolemy as the sponsor of an academy, harboring a squalor of scholars engaged in mapping the heavens and the earth, and investigating matters of natural philosophy. Or perhaps Ptolemy is nom de plume for work produced by this academy (funded by some wealthy merchant or prince or such).
At the beginning of Almagest, and at several other points in the text, the author addresses some words
to somebody named Syrus. Might this Syrus be the sponsor of the work?
Whoever Ptolemy was or were, however wrong or right we judge him today, works attributed to him/them shaped the practice of astronomy and mathematics and optics and physics for a thousand years and more. And his star catalogue remains at the core of the modern northern sky.
Silly old Ptolemy?
We think not.