The great Ptolemy-Hipparchus dispute.
Was the greatest of ancient astronomers a liar and a fraud? New evidence brings some perspective to this long-boiling controversy.The Almagest was the most important astronomy book to come out of the ancient world. Written by Claudius Ptolemy at Alexandria, Egypt, in the 2nd century A.D., it presents an intricate, Earth-centered model of the then-known universe, designed to predict the complex motions of the Sun, Moon, and planets. It also contains a catalog of the positions and brightnesses of slightly more than 1,000 stars.
The Almagest's name is a corruption of the Arabic meaning "the greatest," and indeed, among ancient astronomy books it is by far the greatest both in name and fact. It presents large amounts of data for mathematical analysis within a geometric model that served as the exemplar of Greek rational science, the forerunner of modern science. For 1,500 years the Almagest dominated western astronomy.
But is Ptolemy the greatest fraud in all science? For four centuries, science historians have debated how much of the data in the Almagest was stolen or fabricated. This bitter feud has become hotter in recent times than ever. Virtually nothing is known of Ptolemy's life; we can judge him only by his books (which include definitive works on geography and astrology as well as astronomy). Ptolemy freely credits many observations to other astronomers, but he explicitly says that he measured star positions himself and tells details of his procedures. Despite this statement, many have suspected that the star positions in the Almagest were actually stolen from an earlier catalog by Hipparchus.
Hipparchus is the only rival to Ptolemy as the greatest astronomer of antiquity. He lived on the Greek island of Rhodes in the 2nd century B.C. His greatest discovery was the precession of the equinoxes, the gradual creep of a star's celestial coordinates over the centuries (in a direction parallel to the ecliptic) due to a drift in the orientation of the Earth's axis. Little of Hipparchus's writings have survived to the present, but we do know that he recorded positional data for more than 300 stars.
The question of fraud was raised by Tycho Brahe around 1600, based on his comparison of his own accurately measured star positions with those of the Almagest. In 1792, Joseph-Jerome le Francais de Lalande made the accusation that Ptolemy "took everything which is good in his work from Hipparchus and his other predecessors." Nor could he forgive Ptolemy for believing in astrology. In 1817, Jean-Baptiste-Joseph Delambre went further and accused Ptolemy of fabricating observations to conform with his great theory. Ptolemy's honesty then became a topic of a continuous dispute.
The Modern Debate
The intensity of the Ptolemy-Hipparchus dispute was inflamed in 1977 with the publication of a book by Robert R. Newton titled The Crime of Claudius Ptolemy. Newton pointed out many inaccuracies in both theory and observation and concluded that Ptolemy's model of the solar system was a failure on its own terms, that all of his observations were fabricated, and that Ptolemy "is the most successful fraud in the history of science."
Newton's frequent argument was to take some observation in the Almagest, point out that it is significantly inaccurate by modern calculation, emphasize that it does, however, closely match Ptolemy's model, and conclude that this proves Ptolemy faked the observation. One example concerns Ptolemy's report that he observed the time of an autumnal equinox to be 2 p.m. on September 25, 132. Modern calculation shows that the equinox actually came 30 hours earlier. Christian Severin (around 1600) and Tobias Mayer (in 1753) realized that Ptolemy's claimed time was suspiciously close to that which could be calculated from old data, for example by adding 278 years (using Hipparchus's length for the year) to a timing made by Hipparchus. However, in a doctoral thesis at Yale in 1967, John Britton showed that ordinary atmospheric refraction would cause just such a one-day error about half the time. Refraction enters the picture by altering the apparent position of the Sun near sunrise and sunset, which is how the equinoxes were determined. So for this sample discrepancy, we have both a guilty and an innocent explanation.
Unfortunately, the rancor in Newton's writing and the attempts to oversell his case have alienated many historians. Starting in 1980, Harvard-Smithsonian astronomy historian Owen Gingerich and Newton went through a series of replies and counter-replies in the Quarterly Journal of the Royal Astronomical Society. The main arguments against Newton were that he was trying to apply modern standards to ancient actions (a blunder for historians) and that Ptolemy's lack of a statistical theory of errors forced him to select between conflicting data--and, faced with a choice, he would naturally have selected those that agreed with his model. The feuding sides attracted adherents who can be stereotyped as a pro-Ptolemy establishment versus an anti-Ptolemy group of mavericks.
Dennis Rawlins is a disciple of Newton, and he started adding to the evidence against Ptolemy. In 1982 in the Publications of the Astronomical Society of the Pacific, he presented a new argument: that the Almagest's errors in the ecliptic latitudes of stars vary sinusoidally around the ecliptic in a manner that could have arisen if Ptolemy stole Hipparchus's star catalog and applied an inadequate precession correction. Rawlins submitted one of his papers to the premier Journal for the History of Astronomy (JHA), based in Cambridge, England, and edited by Michael Hoskin. The manuscript was ultimately rejected for publication after Rawlins refused to remove the claim that Ptolemy was a liar, and thereafter Rawlins fought what he perceived as censorship. He started sending abusive letters to Hoskin, who soon stopped opening them.
Rawlins took this to be blacklisting by the establishment. As a counter, he started privately publishing his own journal, Dio (subtitled The Journal for Hysterical Astronomy), devoted to bashing the establishment and exposing fraud by famous explorers.
In the first issue, Rawlins writes, "Please note that criticisms & satires in DIO's supplemental J.HA will be primarily aimed not at the small or the powerless, but at [1] the lordliest archons of academe (largely reviewing their Hist.sci effusions), and-or [2] he who tries to kiss these lords' brains, by attempting (safe in their captive journals) to bully-trash dissenters' creativity...." Dio has a very small circulation and is written mostly by Rawlins himself.
A formal debate was held on July 3, 1999, during the Fourth Biennial History of Astronomy Workshop at Notre Dame University. Owen Gingerich and James Evans represented the pro-Ptolemy camp. They did not present an extreme pro-Ptolemy position but readily acknowledged that the Almagest may have a considerable heritage from Hipparchus. Keith Pickering and Hugh Thurston argued the anti-Ptolemy side.
During the debate Pickering presented many arguments for why the star catalog must have been stolen from Hipparchus, while Thurston pointed out evidences of other fraud by Ptolemy, including some reports of Venus's elongations. Gingerich presented innocent explanations for the alleged fraudulent data. Evans pointed out how far Ptolemy's planetary theory was ahead of that of his contemporaries and argued that Ptolemy's originality can be seen in the improvements in his treatment of some subjects between works he wrote early in his life and works he wrote later. Reports from the scene say that no one was converted in either direction.
The Ptolemy-Hipparchus feud has led to many unprofessional acts. These include shunning of people at conferences and spammed hate mail. Why should such an arcane question as the identity of the Almagest's observer cause such furor in a field that is generally perceived as staid? I have no sure answers, but I think the passions arise from just a few individuals wanting to buck the establishment, and the subsequent reaction to them. Fortunately, the bitterness of this feud is virtually unique in astronomy. Even better, most of it centers on evidence-based arguments, and this is what distinguishes science from politics.
Ambiguities
So who was the observer for the Almagest star catalog? The arguments are many and widely varied, and all go several layers deep. The schism among astronomy historians shows that the case is not decisive. I have selected two of the characteristic arguments to illustrate the fundamental ambiguity of much of the evidence.
The first argument is the original one that dates back to Tycho. It is based on the fact that the Almagest's star longitudes are systematically wrong by about 1°. The anti-Ptolemy camp explains this by saying that Ptolemy (writing around A.D. 137) used the data from Hipparchus's star catalog (around 128 B.C.) and simply added a correction for precession to cover the intervening 2 2/3 centuries. If Ptolemy used Hipparchus's rate of precession of 1° per century, the alleged shift would be 2 2/3°. We now know that the actual rate of precession resulted in a 3 2/3° shift, which accounts for the systematic 1° error.
In 1796 Pierre-Simon Laplace suggested an alternative that did not involve theft. Ptolemy tells us that he used Hipparchus's theory of the Sun's position, which by A.D. 137 had accumulated an error of 1°. Ptolemy says that his star positions were ultimately measured with respect to the Sun--so they too must suffer the 1° error. We now have two plausible explanations for the 1° shift in the stars' ecliptic longitude, one involving plagiarism and the other involving normal experimental problems.
The second argument was presented by A. K. Dambis and Y. N. Efremov in the JHA for the year 2000. They point out that many stars move slowly with respect to their neighbors, an effect we call proper motion. The Almagest positions for these stars might provide a type of "clock" to distinguish whether the stars were observed in A.D. 137 or 128 B.C. Dambis and Efremov analyzed the 40 fastest-moving stars by comparing each with its six nearest neighbors. The derived date is around one century B.C. They claimed that the "coordinates of at least the bulk of 40 stars were measured during the Hipparchan epoch and this conclusion seems to be unescapable."
However, Dennis Duke has reexamined their analysis, as described in an article now in press with the JHA. In a detailed statistical analysis, Duke proves that the original errors of measurement were greatly underestimated. He calculates that the typical measurement error is 0.6°, much larger than any of the stars' proper motion. For example, the fastest-moving star in the Almagest ([omicron.sup.2] Eridani) moves only 0.3° in 2 2/3 centuries, while the third fastest (Arcturus) moves 0.17°. So proper motions can shed no light on the authorship.
Recent Results
Two recent calculations bring strong new evidence. Both offer constraints that are unambiguous. And yet they appear to contradict each other.
The first is my own analysis, based on which stars are listed in the Almagest and which are not. The idea is that the magnitude limit for the included stars will brighten for those at more southerly declinations, due to the dimming of their light near the southern horizon by haze and atmospheric absorption. The catalog might have a typical limit of magnitude 4.7 near the zenith, 4.2 at a declination where stars reach a maximum altitude of only 20°, magnitude 3.6 for an altitude of 10°, and only a few bright stars lower down. The rate by which the Almagest stars diminish toward the south then gives the declination of the horizon, and hence the latitude of the observer. With Ptolemy in Alexandria (latitude 31.2° north) and Hipparchus in Rhodes (36.4° north), the selection of stars in the Almagest should clearly discriminate between who selected them.
This is an old idea that has been used many times, but always with fundamental errors. Only in the last few years have the technical models and computing power become available to do a correct job. I presented my results in a long paper last year in the JHA.
I find a somewhat complex situation. Roughly three-quarters of the sky was observed from a deduced latitude of 32.0° ± 0.8°, with Hipparchus being definitively ruled out. However, the remaining quarter of the sky has a deduced latitude of 35.7° ± 1.1°, which argues strongly against Ptolemy. So where does this leave us? Apparently the selection of stars for inclusion in the Almagest was mostly made by Ptolemy but with a fraction taken from Hipparchus.
The second recent calculation involves a comparison between Hipparchus's own star data and the versions in the Almagest. Hipparchus's star catalog itself was lost sometime after Ptolemy, but adequate positional information was given for roughly a hundred stars in Hipparchus's Commentary, which we have. With modern data, we can determine the positional errors of stars in both the Commentary and the Almagest. Starting in 1925 with H. Vogt, analysts have done just this. Vogt pointed out that the errors were not identical, and hence the Almagest positions were not from Hipparchus. But in 1990, Gerd Grasshoff showed that the two sets of errors are strongly correlated and so must be causally connected. Indeed, 13 stars have huge individual errors of more than 1° in the Hipparchus data, and these same stars have similar huge errors in the Almagest. These large correlated mistakes already prove that the Almagest has at least some heritage from the earlier catalog.
Noel Swerdlow has calculated that 5 to 14 percent of the Almagest is dependent on Hipparchus's data, while James Evans independently estimated that "as few as 21 percent of the stars need to have been borrowed."
Now, Dennis Duke has made a thorough analysis of the correlations between the two ancient star catalogs. He first proves how the analyses by Vogt and Swerdlow are incorrect and argues that the Evans estimate is inconclusive. Then he demonstrates that both the systematic and random errors in the two catalogs are strongly related. This is true even if the stars with errors of more than 1° are ignored. The implication is that perhaps the majority of the star positions in the Almagest are indeed derived from Hipparchus.
A Complex Patchwork
The results from these two new calculations appear contradictory. How can both Ptolemy and Hipparchus contribute the majority of the data in the Almagest star catalog? A simple answer is that their contributions are to different aspects of the catalog. Ptolemy could easily have selected the stars from his own observations, then included many of their measured positions from Hipparchus.
There are two other subtle indications of multiple sources in the Almagest. Of the 48 constellations, a little more than half have many stars' reported latitudes ending with fractional values of 1/4° or 3/4°, while stars in the rest of the constellations have these endings only rarely. This bimodal (two-peaked) distribution suggests that two different armillary spheres were used to measure the stars' positions in the sky, presumably by two different observers. Also, the average longitude error for zodiacal constellations is bimodal, again suggesting two observers.
All of the various indicators identify sets of constellations that were presumably measured by one observer, but unfortunately these sets all differ from each other! It is as if Ptolemy compiled his catalog by taking the input for each measured quantity from old and new data in a different patchwork across the sky. For example, he might have known that his own measured longitudes had problems across a certain part of the sky, so here he used the values from Hipparchus for his own selected stars. It would be natural for a compiler to choose the best available data for presentation.
By way of comparison, the modern version of the Almagest is the Yale Bright Star Catalogue, edited by Dorrit Hoffleit. Here we find that every type of stellar data has a different observer and often multiple observers, creating a confusing patchwork. Some electronic versions of the modern catalog have the attributions to observers stripped off, and all credits might be lost two millennia from now.
Was Ptolemy a criminal? Apparently he did include substantial amounts of data from earlier observers without giving explicit credit that has survived, even while he did give attributions for large numbers of other observations. Such lack of references is common even in modern books, and in any case it is dangerous to apply modern standards, especially when we don't really know any of the details from long ago.
As for theory, Ptolemy's model of the universe remains impressive in scope, accuracy, and insight, making it truly "the greatest" epitome of astronomy until the scientific revolution of the 17th century. It now appears that both extremes in the controversy are wrong. For substantial portions of the Almagest Ptolemy was the observer--yet he included data from Hipparchus too. The construction of the star catalog had a complex history that we can view only dimly with scant evidence after almost two millennia.
BRADLEY E. SCHAEFER and his wife, Martha, have just come back from a trip to Australia to see the Leonid meteor shower at its best.
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| Author: | Schaefer, Bradley E. |
|---|---|
| Publication: | Sky & Telescope |
| Date: | Feb 1, 2002 |
| Words: | 2871 |
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