Ptolemy
Ptolemy, or in Latin Claudius Ptolemaeus (ca. 90 – ca. 168), was an ancient mathematician, philosopher, geographer, map maker, astronomer, theologian, and astrologer who lived in Alexandria, Egypt. He is most remembered as a cosmologist, because his development of the geocentric cosmological system, known as the Ptolemaic system or Ptolemaic cosmology was one of the most influential and longest-lasting intellectual-scientific achievements in human history. Almost nothing, however, is known about his life, his family background, or his physical appearance. He may have been a Hellenized Egyptian.
The first chapter of Ptolemy's most important work, now usually known as the Almagest, contains a discussion of epistemology and philosophy. Two themes are paramount and woven together there: the organization of philosophy and his reason for studying mathematics. In the ancient period philosophy included much more than is usually encompassed by that term today — then it meant the whole of human knowledge and wisdom.
Aristotle — the only philosopher to whom Ptolemy refers explicitly — had distinguished between practical and theoretical philosophy, and Ptolemy uses that distinction, noting that education is needed for theoretical philosophy but not for practical philosophy. Ptolemy also wrote that Aristotle had divided theoretical philosophy into three branches: physics, mathematics, and theology. Ptolemy followed that tripartate division, claiming that theology is the branch of theoretical philosophy that investigates the first cause of the first motion of the universe. (Taub, pp. 19 ff.)
We should note that, although both Ptolemy and Aristotle held theology to be one of the main branches of philosophy, they were Greek pagans who held to the Greek pantheon of gods and the Greek understanding of the behavior and activity of the gods. Thus we must not make the mistake of thinking that their theological investigations and speculations were necessarily equivalent or similar to what Jewish, Christian, or Muslim theologians or scholars would say about either the method(s) or the object(s) of theology. But in putting theology in with what they called physics (or what we today call natural science) and mathematics as the central concerns of philosophy, Ptolemy and Aristotle differed from present-day secular scientists, philosophers, and epistemologists who have no role for or interest in theology.
Ptolemy was the author of numerous scientific treatises, at least three of which have been of continuing importance to later Islamic and European science. The first is the astronomical treatise originally called He mathematike syntaxis ("The Mathematical Collection") which came eventually to be known as Ho megas astronomos ("The Great Astronomer"). During the 9th century Arab astronomers used the Greek superlative term Megiste for this work, which, when the definite article al was prefixed to it became Almagest, the name by which it is generally known today. (Taub, however, still uses the term Syntaxis for it.) A second of Ptolemy's main works is his Geographia, and a third of his noteworthy works is a set of books on geometry. He also wrote a treatise on astrology known as the Tetrabiblos, and additional works on music, optics, and other subjects.
Astronomy
In the Almagest, one of the most influential books of classical antiquity, Ptolemy compiled the astronomical knowledge of the ancient Greek and Babylonian world; he relied mainly on the work of Hipparchus of three centuries earlier. It was preserved, like most of Classical Greek science, in Arabic manuscripts (hence its familiar name) and only made available in Latin translation (by Gerard of Cremona) in the 12th century.
The Almagest is divided into thirteen books. Each of them deals with astronomical concepts concerning the stars and objects in the solar system. Ptolemy's geocentric model or theory put the earth at the center of the universe, a theory often known as the Ptolemaic System, or Ptolemaic Cosmology. This view was near-universally held until it was superseded by the heliocentric solar system or Sun-centered system, first put forth by Copernicus in the first three decades of the 16th Century.
Ptolemy gives various reasons why the Earth must be both the center of the universe and immovable. One of his arguments is that, since all bodies fall to the center of the universe, if the Earth were not the center things would not fall to the Earth, but the Earth itself would fall. He also argued that if the Earth moved, then things thrown vertically upward would not fall to the place from which they had been thrown, as they were observed to do. We now recognize that all those reasons are false or mistaken.
Following Aristotle, Ptolemy (and those who came after and accepted his view) made a number of philosophical assumptions that underlied their cosmology. First, they assumed that unless things are pushed and made to move, their natural state is stationary. Second, they assumed that if humans were to occupy the highest position in the universe, then they had to occupy the physical center of the universe, meaning that the Earth had to be the center. Third, they assumed that the most perfect motion was circular motion; it would not occur to people until the work of Kepler at the beginning of the 17th century that the motion of the planets is elliptical instead of circular, and even Kepler took some time to arrive at that insight. All of those assumptions are now rejected as being false.
In Ptolemy's cosmology, the Earth is first, followed by the Moon, Mercury, Venus, Sun, Mars, Jupiter, and Saturn — in his day only five planets were known to exist. In order to account for the movements of these bodies, the Ptolemaic System used large circles centered on the Earth, along with smaller circles, or epicycles, that moved around the circumferences of the larger circles.
Ptolemy's computational methods (supplemented in the 12th century with the Arabic computational Tables of Toledo) were of sufficient accuracy to satisfy the needs of astronomers, astrologers and navigators, until the time of the great explorations. They were also adopted in the Arab world and in India. The Almagest also contains a star catalogue, which is probably an updated version of a catalogue created by Hipparchus. Its list of forty-eight constellations is ancestral to the modern system of constellations, but unlike the modern system they did not cover the whole sky (only the sky Ptolemy could see).
Geography
A second of Ptolemy's influential works is his Geographia, a thorough discussion of the geographic knowledge of the Greco-Roman world. This too is a compilation of what was known about the world's geography in the Roman Empire during his time. He relied mainly on the work of an earlier geographer, Marinos of Tyre, and on gazetteers of the Roman and ancient Persian empire, but most of his sources beyond the perimeter of the Empire were unreliable.
The first part of the Geographia is a discussion of the data and of the methods he used. As with the model of the solar system in the Almagest, Ptolemy put all this information into a grand scheme. He assigned coordinates to all the places and geographic features he knew, in a grid that spanned the globe. Latitude was measured from the equator, as it is today, but Ptolemy preferred to express it as the length of the longest day rather than degrees of arc (the length of the midsummer day increases from 12h to 24h as you go from the equator to the polar circle). He put the meridian of 0 longitude at the most western land he knew, the Canary Islands.
Ptolemy also devised and provided instructions on how to create maps both of the whole inhabited world (oikoumenè) and of the Roman provinces. In the second part of the Geographia he provided the necessary topographic lists, as well as captions for the maps. His oikoumenè spanned 180 degrees of longitude from the Canary islands in the Atlantic Ocean to the middle of China, and about 80 degrees of latitude from the Arctic to the East Indies and deep into Africa. Ptolemy was well aware that he knew about only a quarter of the globe, and he knew that his information did not extend to the Eastern Sea.
The maps in surviving manuscripts of Ptolemy's Geographia, however, date only from about 1300, after the text was rediscovered by Maximus Planudes. It seems likely that the topographical tables in books 2-7 are cumulative texts - texts which were altered and added to as new knowledge became available in the centuries after Ptolemy (Bagrow 1945). This means that information contained in different parts of the Geography is likely to be of different dates.
Maps based on scientific principles had been made since the time of Eratosthenes (3rd century B.C.E.), but Ptolemy improved projections. It is known that a world map based on the Geographia was on display in Autun, France in late Roman times. In the 15th century Ptolemy's Geographia began to be printed with engraved maps; the earliest printed edition with engraved maps was produced in Bologna in 1477, followed quickly by a Roman edition in 1478 (Campbell, 1987). An edition printed at Ulm in 1482, including woodcut maps, was the first one printed north of the Alps. The maps look distorted as compared to modern maps, because Ptolemy's data were inaccurate. One reason is that Ptolemy under-estimated the size of the Earth; while Eratosthenes found 700 stadia for a degree on the globe, in the Geographia Ptolemy uses 500 stadia. It is not certain if these geographers used the same stadion, but there is no direct evidence of more than one value of the stadion. If they both used the traditional Olympic stadion of about 185 meters, then the older estimate is 1/6 too large, and Ptolemy's value is 1/6 too small.
Because Ptolemy derived most of his topographic coordinates by converting measured distances to angles, his maps get distorted. So his values for the latitude were in error by up to 2 degrees. For longitude this was even worse, because there was no reliable method to determine geographic longitude; Ptolemy was well aware of this. It remained a problem in geography until the invention of chronometers at the end of the 18th century. It must be added that his original topographic list cannot be reconstructed; the long tables with numbers were transmitted to posterity through copies containing many scribal errors, and people have always been adding to or improving the topographic data. This is a testimony to the persistent popularity of this influential work.
Geometry
Ptolemy was a first-rate geometer and mathematician who devised important new geometrical proofs and theorems. In one book, entitled Analemma, he discussed projections of points on a celestial sphere. In another work, Planispherium, he studied stereographic projection, or the forms of solid objects represented on a plane. Another book on mathematics was the two-book Hypothesis ton planomenon ("Planetary Hypothesis") in which, among other things, he attempted to give a proof of Euclid's parallel postulate.
Astrology
Another of Ptolemy's noteworthy works is his treatise on astrology known as the Tetrabiblos ("Four books" — Greek tetra means "four", biblos is "book") in which he attempted to adapt horoscopic astrology to the Aristotelian natural philosophy of his day. The Tetrabiblos was the most popular astrological work of antiquity and also enjoyed great influence in the Islamic world and the medieval Latin West. The Tetrabiblos was continually reprinted. That it did not quite attain the unrivalled status of the Almagest was perhaps because it did not cover some popular areas of the subject, particularly horary astrology (interpreting astrological charts for a particular moment to determine the outcome of a course of action to be initiated at that time), electional astrology, and medical astrology.
The great popularity that the Tetrabiblos did possess might be attributed to its exposition of the art of astrology and its being a compendium of astrological lore, rather than a manual. It speaks in general terms, avoiding illustrations and details of practice. Ptolemy was concerned to defend astrology by defining its limits, producing an compiling astronomical data that he believed was reliable, and dismissing practices (such as considering the numerological significance of names) that he believed to be without sound basis.
Much of the content of the Tetrabiblos may well have been collected from earlier sources; Ptolemy's achievement was to order his material in a systematic way, showing how the subject could, in his view, be rationalized. It is, indeed, presented as the second part of the study of astronomy of which the Almagest was the first, concerned with the influences of the celestial bodies in the sublunar sphere. Thus explanations of a sort are provided for the astrological effects of the planets, based upon their combined effects of heating, cooling, moistening, and drying.
Ptolemy's astrological outlook was quite practical. He thought that astrology was like medicine in being conjectural, because of the many variable factors to be taken into account: the race, country, and upbringing of an person affects an individual's personality as much if not more than the positions of the Sun, Moon, and planets at the precise moment of their birth. So Ptolemy saw astrology as something to be used in life but in no way relied on entirely.
Music
Ptolemy also wrote an influential work, Harmonics on music theory. After criticizing the approaches of his predecessors, Ptolemy argued for basing musical intervals on mathematical ratios (in contrast to the followers of Aristoxenus) backed up by empirical observation (in contrast to the overly theoretical approach of the Pythagoreans). He presented his own divisions of the tetrachord and the octave, which he derived with the help of a monochord. Ptolemy's astronomical interests also appeared in a discussion of the music of the spheres.
Optics
In his Optics, a work in five books which survives only in a poor Arabic translation, Ptolemy wrote about properties of light, including reflection, refraction or the way light changes direction when it passes from one medium of different density into another, and color. This was the first work on record that attempted to account for the observed phenomenon of the refraction of light. Recent attention to Ptolemy's Optics shows its "sophisticated observational basis" and that Ptolemy had conducted "a series of carefully-contrived experiemnts measuring refraction from air to water, air to glass, and water to glass." (Smith, p. 7)
Named after Ptolemy
ReferencesISBN links support NWE through referral fees
Texts and translations:
- Berggren, J. Lennart and Jones, Alexander, 2000. Ptolemy's Geography: An Annotated Translation of the Theoretical Chapters. Princeton University Press. Princeton and Oxford. ISBN 0-691-01042-0.
- Nobbe, C. F. A., ed., 1843. Claudii Ptolemaei Geographia. 3 vols. Lipsiae (Leipzig): Carolus Tauchnitus. (The most recent edition of the complete Greek text)
- Stevenson, Edward Luther. Trans. and ed., 1932. Claudius Ptolemy: The Geography. New York Public Library. Reprint: Dover, 1991. (This is the only complete English translation of Ptolemy's most famous work. Unfortunately, it is marred by numerous mistakes and the placenames are given in Latinised forms, rather than in the original Greek).
Other references:
- Bagrow, L., 1945. The Origin of Ptolemy's Geographia. Geografiska Annaler 27:318-387.
- Campbell, T., 1987. The Earliest Printed Maps. British Museum Press.
- Gingrich, Owen, 1993. The Eye of Heaven: Ptolemy, Copernicus, Kepler. New York: The American Institute of Physics.
- Smith, A. Mark, 1999. Ptolemy and the Foundations of Ancient Mathematical Optics: A Source Based Guided Study. Transactions of the American Philosophical Society Held at Philadelphia For Promoting Useful Knowledge, Vol. 89, Pt. 3. Philadelphia: American Philosophical Society.
- Taub, Liba Chaia, 1993. Ptolemy's Universe: The Natural Philosophical and Ethical Foundations of Ptolemy's Astronomy. Chicago and LaSalle, IL: Open Court.
External links
Primary sources
- Ptolemy's Tetrabiblos at LacusCurtius (English translation, with introductory material)
- Ptolemy's Geography at LacusCurtius (English translation, incomplete)
- Extracts of Ptolemy on the country of the Seres (China) (English translation)
Secondary material
- Ptolemy at SkyScript - The Life and Work of Ptolemy
- Alexander Jones, "Ptolemy and his Geography"
- Ptolemy biography (Bill Arnett's site)
- Ptolemy's Geography of Asia - Selected problems of Ptolemy's Geography of Asia (currently in German)
- Ptolemy's Geography of Northwestern Europe
- History of Cartography including a discussion of the Geographica
- Claudius Ptolemaeus (Ptolemy): Representation, Understanding, and Mathematical Labeling of the Spherical Earth
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