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Ptolemy: Integrity at Question Ptolemy (about 85 about 165), until recently, was considered to be one of the most prominent and influential astronomers of ancient Greece who introduced the geocentric theory in a manner that prevailed for more than 1000 years. However, after the recent findings, the authenticity of Ptolemy's works was submitted to more argument and discussion than any other Greek mathematicians discoveries. Scientists and historians are now divided into 2 warring groups, the first one arguing that Ptolemy was one of the top mathematicians, while the second provides the proof that he was no other than a perfect expositor, with some historians even claiming that Ptolemy committed a crime, a fraud against his fellow scientists betraying the integrity and ethics of his profession. (J. J. OConnor, E. F.
Robertson, 1999) Although major Ptolemy's works have been preserved to our days, it is only one that creates the most controversy the Almagest, originally named The Mathematical Compilation. It is the earliest of books written by Ptolemy and explains in detail the mathematical theories of the Sun, Moon and planets motions. The Almagest was not superseded for more than a thousand years, until the heliocentric theory was presented by Copernicus in his De Revolutionibus in 1543. Ptolemy's Almagest shares with Euclid's Elements the glory of being the scientific text longest in use. From its conception in the second century up to the late Renaissance, this work determined astronomy as a science. (cited in Claudius Ptolemy by J. J.
OConnor, E. F. Robertson, 1999) So what is wrong with this monumental, thirteen volume, profound compilation, which included practically all available at that time achievements of mathematics and astronomy and even improved or corrected some of them? As it turns out, a lot of things.
The first one to recognize the need to reconsider the reliability and authority of Ptolemy's data was Johannes Kepler, who was later supported by J. B. J. Delambre and by Robert Newton. They discovered that the most substantial treatise on ancient Greek astronomy, the Almagest, could not be trusted and that Ptolemy misrepresented much of his data. (Thurston, 2002) As Hugh Thurston writes in his article Greek Mathematical Astronomy Reconsidered (2002), Ptolemy's calculation of the year length is the clearest example of his misreporting. He claimed to divide the time between two summer solstices by the number of years between them, indicating that he himself observed the second solstice.
He followed the same pattern with two spring and two autumn equinoxes, each time getting the same result as Hipparchus, which is around 5 minutes too short. In order to get such result, equinoxes and solstice that he observed had to be more than 24 hours too early, which was really so according to the data provided by Hipparchus around 300 years ago. The times Ptolemy said to observe the equinoxes and solstice were exactly the ones obtained by Hipparchus as per his own calculations from earlier observations and his value of the year length. Having calculated and predicted equinoxes and solstices this way, Hipparchus got most of them right, however there were some mistakes. The fact that Ptolemy instead of observing simply calculated the time using his predecessors formula seems obvious and therefore, the conclusion can be made that he was not telling the truth. (Thurston, 2002) Delambre, too, suggested that the errors were made by Hipparchus and Ptolemy simply failed to correct his data, going on with his erroneous calculations: One could explain everything in a less favorable but all the simpler manner by denying Ptolemy the observation of the stars and equinoxes, and by claiming that he assimilated everything from Hipparchus, using the minimal value of the latter for the precession motion. (cited in Claudius Ptolemy by J. J.
OConnor, E. F. Robertson, 1999) There are numerous other examples of Ptolemy reporting measurements that couldnt take place in real but agreed precisely with the results he wanted to deduce. His calculation of the Saturn longitude was proven incorrect by John Britton who, using modern theory, calculated where Saturn and the moon were at the time of Ptolemy. He found that the moon in fact covered Saturn and was nowhere Ptolemy stated to observe it was. There are similar examples of error in Ptolemy's calculations of the Venus apogee and the apogee of Mercury which only were too close to what he wanted to obtain but completely disagreed with reality. (Thurston, 2002) Newton writes about this, [Ptolemy] developed certain astronomical theories and discovered that they were not consistent with observation.
Instead of abandoning the theories, he deliberately fabricated observations from the theories so that he could claim that the observations prove the validity of his theories. In every scientific or scholarly setting known, this practice is called fraud, and it is a crime against science and scholarship. (cited in Claudius Ptolemy by J. J. OConnor, E. F.
Robertson, 1999) Ptolemy's catalogue of stars included in the Almagest created the most suspicion about the very fact that he actually observed the stars reported in the catalogue. Scientists who were investigating Ptolemy's original data noticed that he didnt observe clearly visible stars in Alexandria while he remarkably well saw the stars visible from Rhodes, where Hipparchus lived and worked. As Dennis W. Duke writes in his work On the Clarity of Visibility Tests (2002), the Almagest star catalog has for centuries invited speculation about who actually compiled it. Of its many curious features, the fact that the catalog contains no stars which are visible in Alexandria but not visible in Rhodes suggested to Delambre that perhaps the catalog was actually compiled by Hipparchus, who is known to have lived in Rhodes (at about 36 north latitude), and not by Ptolemy, the author of the Almagest, who is known to have lived in Alexandria (at about 31 north latitude). (Duke, 2002) Ptolemy does give credit to Hipparchus in the Almagest by attributing 3 timed longitudes of the sun to him.
This agrees with Hipparchus solar theory but not the one Ptolemy adopted. The latter indicated that Hipparchus had calculated the longitude from the dates incorrectly and re-calculated them using the theory in the Almagest, quoting the mean longitudes as well. Coincidentally, both theories produced the same longitude, with different mean longitude, for the middle observation. However, the mean longitude quoted by Ptolemy agreed with the theory of Hipparchus, and not his own. So, probably, when writing the Almagest, Ptolemy remembered the middle observation longitude to be correct and copied the mean longitude as calculated by Hipparchus as well. (Thurston, 2002) So, taking into account all the controversy and contradiction, it is difficult to find out now exactly which achievements and discoveries belonged to whom. After all, Ptolemy, even if faking and stealing his data from his fellow scientist, also made certain contributions to mathematics as well as astronomy.
His heritage, however, is easier to research as his major works have survived. It is much more troublesome to investigate the details of Hipparchus work since they are disappointingly few, with only one Commentary on Arts and Eudoxus seeing our days. There is some information about Hipparchus in Ptolemy's Almagest, too, even though he obviously had studied Hipparchus writings thoroughly and had a deep respect for his work, his main concern was not to transmit it to posterity but to use it and, where possible, improve upon it in constructing his own astronomical system. (cited in Hipparchus of Rhodes by J. J. OConnor, E. F.
Robertson, 1999) In any case, we know that Hipparchus contributed much to trigonometry introducing a table of chords, the purpose of which was to give a pattern for solving triangles that avoided solving from first principles. He also produced the division of a circle in 360 degrees. Hipparchus is credited with calculating the length of the year with 6. 5 -minute exactness and discovering the precession of the equinoxes. J. J. OConnor and E.
F. Robertson in their article Hipparchus of Rhodes write that his value of 46 " for the annual precession is good compared with the modern value of 50. 26 " and much better than the figure of 36 " that Ptolemy was to obtain nearly 300 years later. Hipparchus is also believed to have created star catalogue of about 850 stars in 129 BC, which has been allegedly used by Ptolemy in the Almagest. (J. J. OConnor, E. F.
Robertson, 1999) Ptolemy seems to gain from each and every of these achievements, not only basing his calculations on formula produced by Hipparchus, but also claiming some of these observations to be his own. However, there are some of his original contributions among which his planetary theory discussed in the final five books of the Almagest. Ptolemy created a complex mathematical model, which represents the motions of the planets rather well, fitting the observational data that was very scarce before. Ptolemy's another work is also worth mentioning here since its considered to be the representation of his original achievements Optics, where he studies color, refraction, and reflection. The establishment of theory by experiment, frequently by constructing special apparatus, is the most striking feature of Ptolemy's Optics. Whether the subject matter is largely derived or original, the Optics is an impressive example of the development of a mathematical science with due regard to physical data, and is worthy of the author of the Almagest.
As it is, even though Ptolemy based a lot of his achievements on those by Hipparchus, at the very least, he can be credited with providing astronomy with an orderly compilation of the data available at that time. In fact, Ptolemy made such an orderly compilation and made predictions of the planets motions with such high accuracy, that his work remained the major one for over a thousand years. As Tower writes about the Almagest, - As a didactic work the Almagest is a masterpiece of clarity and method, superior to any ancient scientific textbook and with few peers from any period. (cited in Claudius Ptolemy by J. J. OConnor, E.
F. Robertson, 1999) References: J. J. OConnor, E.
F. Robertson, Hipparchus of Rhodes, 1999 (web) J. J. OConnor, E. F. Robertson, Claudius Ptolemy, 1999 (web) H.
Thurston, Greek Mathematical Astronomy Reconsidered, ISIS, The History of Science Society, 2002 D. W. Duke, On the Clarity of Visibility Tests, Florida State University, 2002 (web)
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