Реферат: Claudius Ptolemy

We will return to discuss some of the accusations made against Ptolemy after commenting briefly on his other works. He published the tables which are scattered throughout the Almagest separately under the title Handy Tables. These were not merely lifted from the Almagest however but Ptolemy made numerous improvements in their presentation, ease of use and he even made improvements in the basic parameters to give greater accuracy. We only know details of the Handy Tables through the commentary by Theon of Alexandria but in the author shows that care is required since Theon was not fully aware of Ptolemy's procedures.

Ptolemy also did what many writers of deep scientific works have done, and still do, in writing a popular account of his results under the title Planetary Hypothesis. This work, in two books, again follows the familiar route of reducing the mathematical skills needed by a reader. Ptolemy does this rather cleverly by replacing the abstract geometrical theories by mechanical ones. Ptolemy also wrote a work on astrology. It may seem strange to the modern reader that someone who wrote such excellent scientific books should write on astrology. However, Ptolemy sees it rather differently for he claims that the Almagest allows one to find the positions of the heavenly bodies, while his astrology book he sees as a companion work describing the effects of the heavenly bodies on people's lives.

In a book entitled Analemma he discussed methods of finding the angles need to construct a sundial which involves the projection of points on the celestial sphere. In Planisphaerium he is concerned with stereographic projection of the celestial sphere onto a plane. This is discussed in where it is stated:-

In the stereographic projection treated by Ptolemy in the "Planisphaerium" the celestial sphere is mapped onto the plane of the equator by projection from the south pole. Ptolemy does not prove the important property that circles on the sphere become circles on the plane.

Ptolemy's major work Geography, in eight books, attempts to map the known world giving coordinates of the major places in terms of latitude and longitude. It is not surprising that the maps given by Ptolemy were quite inaccurate in many places for he could not be expected to do more than use the available data and this was of very poor quality for anything outside the Roman Empire, and even parts of the Roman Empire are severely distorted. In Ptolemy is described as:-

... a man working [on map-construct without the support of a developed theory but within a mathematical tradition and guided by his sense of what is appropriate to the problem.

Another work on Optics is in five books and in it Ptolemy studies colour, reflection, refraction, and mirrors of various shapes. Toomer comments in:-

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".

An English translation, attempting to remove the inaccuracies introduced in the poor Arabic translation which is our only source of the Optics is given in .

The first to make accusations against Ptolemy was Tycho Brahe. He discovered that there was a systematic error of one degree in the longitudes of the stars in the star catalogue, and he claimed that, despite Ptolemy saying that it represented his own observations, it was merely a conversion of a catalogue due to Hipparchus corrected for precession to Ptolemy's date. There is of course definite problems comparing two star catalogues, one of which we have a copy of while the other is lost.

After comments by Laplace and Lalande, the next to attack Ptolemy vigorously was Delambre. He suggested that perhaps the errors came from Hipparchus and that Ptolemy might have done nothing more serious than to have failed to correct Hipparchus's data for the time between the equinoxes and solstices. However Delambre then goes on to say (see):-

One could explain everything in a less favourable 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.

However, Ptolemy was not without his supporters by any means and further analysis led to a belief that the accusations made against Ptolemy by Delambre were false. Boll writing in 1894 says:-

To all appearances, one will have to credit Ptolemy with giving an essentially richer picture of the Greek firmament after his eminent predecessors.

Vogt showed clearly in his important paper that by considering Hipparchus's Commentary on Aratus and Eudoxus and making the reasonable assumption that the data given there agreed with Hipparchus's star catalogue, then Ptolemy's star catalogue cannot have been produced from the positions of the stars as given by Hipparchus, except for a small number of stars where Ptolemy does appear to have taken the data from Hipparchus. Vogt writes:-

This allows us to consider the fixed star catalogue as of his own making, just as Ptolemy himself vigorously states.

The most recent accusations of forgery made against Ptolemy came from Newton in . He begins this book by stating clearly his views:-

This is the story of a scientific crime. ... I mean a crime committed by a scientist against fellow scientists and scholars, a betrayal of the ethics and integrity of his profession that has forever deprived mankind of fundamental information about an important area of astronomy and history.

Towards the end Newton, having claimed to prove every observation claimed by Ptolemy in the Almagest was fabricated, writes :-

[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.

Although the evidence produced by Brahe, Delambre, Newton and others certainly do show that Ptolemy's errors are not random, this last quote from is, I [EFR] believe, a crime against Ptolemy (to use Newton's own words). The book [8] is written to study validity of these accusations and it is a work which I strongly believe gives the correct interpretation. Grasshoff writes:-

... one has to assume that a substantial proportion of the Ptolemaic star catalogue is grounded on those Hipparchan observations which Hipparchus already used for the compilation of the second part of his "Commentary on Aratus". Although it cannot be ruled out that coordinates resulting from genuine Ptolemaic observations are included in the catalogue, they could not amount to more than half the catalogue.

... the assimilation of Hipparchan observations can no longer be discussed under the aspect of plagiarism. Ptolemy, whose intention was to develop a comprehensive theory of celestial phenomena, had no access to the methods of data evaluation using arithmetical means with which modern astronomers can derive from a set of varying measurement results, the one representative value needed to test a hypothesis. For methodological reason, then, Ptolemy was forced to choose from a set of measurements the one value corresponding best to what he had to consider as the most reliable data. When an intuitive selection among the data was no longer possible ... Ptolemy had to consider those values as 'observed' which could be confirmed by theoretical predictions.

As a final comment we quote the epigram which is accepted by many scholars to have been written by Ptolemy himself, and it appears in Book 1 of the Almagest, following the list of contents (see for example [11]):-

Well do I know that I am mortal, a creature of one day.

But if my mind follows the winding paths of the stars

Then my feet no longer rest on earth, but standing by

Zeus himself I take my fill of ambrosia, the divine dish.

J J O'Connor and E F Robertson