Astronomy

Astronomy offers a far richer range of examples. Koyré himself was prepared to grant that, exceptionally, Greek celestial physics was exact, but the question we must press here is whether the explanation of this

[67] Thus Posidonius' figure for the difference in altitude of Canopus (7 1/2 degrees) contrasts with an actual one of approximately 5 degrees.

[68] The problem of determining distances over land and sea continued to exercise later writers. Hero, for instance, who gives a detailed account of the construction and use of the dioptra—the chief surveying instrument used in triangulation—also describes a hodometer, a device for measuring distances on an overland journey by the automatic counting of the revolutions of a carriage wheel, thereby avoiding, as he says, the "laborious and slow" method using chains or cords (Dioptra 34.292.16ff.; cf. Vitruvius 10.9.1–4 with suggested adaptation for use at sea 10.9.5ff.: on the feasibility of such devices see most recently Sleeswyk 1979). The next chapter in the Dioptra tackles the problem of estimating greater distances, including across water, for example from Alexandria to Rome, where Hero suggests a method based on observations of a lunar eclipse (Dioptra 35.302.3ff.); see Neugebauer 1975, vol. 2, pp. 845ff. Ptolemy, in turn, discusses the difficulties in his Geographia (1.3–4) and expresses greater confidence in astronomically based calculations than in dead reckoning. Yet the former depended on accurate time-keeping, the difficulties of which we have already noted.

[69] Thus Syene is in fact some three degrees east of Alexandria, and Rhodes some one and a half degrees west of it.

exception is the one that Koyré tended to adduce, namely, the metaphysical gulf between the superlunary and the sublunary world.^[70]

First, it is as well to stress the hesitancy of the first steps the Greeks took in observational astronomy.^[71] Although attempts to determine the lengths of the solar year and the four seasons go back to the late fifth century B.C. (motivated in part, probably, by concern with calendaric problems), the number of actual observations carried out was not necessarily very great.^[72] Even Eudoxus in the fourth century may have undertaken only limited precise observational work. One of the handicaps, at this stage, was the lack of a simple coordinate system and of the division of the globe into 360 degrees, and such evidence as we have from the fragments of Eudoxus' Phaenomena suggests that he identified and located individual stars quite imprecisely. Thus "beneath the tail of the Little Bear lie the feet of Cepheus making an equilateral triangle with the tip of the tail";^[73] or, again, "over Perseus and Cassiopeia lies at no great distance the head of the Great Bear."^[74]

By Hipparchus' time, in the second century B.C. , however, the situation had changed appreciably. First, there is firmer evidence for Greek use of Babylonian observational data, and, secondly, we have more specific information for sustained observational work carried out by the Greeks themselves, first by Timocharis and Aristyllus in the late third century,^[75] and then by Hipparchus himself,^[76] even though for much of

[70] See Koyré 1948/1961, pp. 312f., 1968, p. 38; cf. Sambursky 1956b, pp. 47f., and 1965.

[71] There is a brief discussion of the development of observation in early Greek astronomy in G. E. R. Lloyd 1979, pp. 169ff., and of the topic of observational error in astronomy and elsewhere in G. E. R. Lloyd 1982.

[72] See especially Aaboe and Price 1964.

[73] See Hipparchus In Arati phaenomena (In Arat.) 1.2.11.14.13ff., and cf. 5.19.52.1ff.

[74] Hipparchus In Arat. 1.6.2.54.23ff., and cf. the similar text quoted by Hipparchus from Eudoxus' Enoptron (Mirror) at In Arat. 1.6.2.56.2ff.

[75] See Ptolemy Syntaxis 7.1–3 especially, (H) 2.3.2ff., 12.24ff., 17.15ff., 21.16ff. The datable observations assigned to Timocharis, ranging from 295 B.C. to 272 B.C. , are set out by Pedersen 1974, appendix A, pp. 410f.

[76] The datable observations ascribed by Ptolemy to Hipparchus, ranging from 162 B.C. to 127 B.C. , are set out by Pedersen 1974, appendix A, pp. 413ff.See more generally Neugebauer 1975, vol. 1, pp. 274ff., who remarks, p. 277, that in Hipparchus' time a definite system of spherical coordinates for stellar positions did not yet exist; on the question of whether it was Hipparchus or Eratosthenes who first introduced the division of the circle into 360 degrees, see Neugebauer 1975, vol. 1, p. 305 n. 27, vol. 2, p. 590.

our evidence we continue to have to rely on such sources as Ptolemy, writing much later, in the second century A.D. Ptolemy himself not only reports his predecessors' and contemporaries' observations on many occasions but also provides the first extant comprehensive star catalogue. This is particularly valuable evidence, as the observations it is based on are not subject to interference from planetary models.^[77] Books 7 and 8 of the Syntaxis give the longitudes and latitudes of over 1,000 stars in degrees and fractions of a degree, using seven simple fractions corresponding to 10', 15', 20', 30', 40', 45', and 50'.^[78] Ptolemy tells us that he used the armillary astrolabe for these and other observations, often providing a certain amount of circumstantial detail on this.

Now, whether Ptolemy actually carried out the careful observations he says he made has become, once again, in recent years, the subject of heated controversy;^[79] and the suggestion has been revived that his star catalogue in particular was plagiarised from Hipparchus.^[80] The view I have argued for elsewhere is that this is an oversimplification, to say the least. Though he has taken Hipparchus' figures as his starting-point^[81] (not to have done so would have been foolish), he has added

[77] The theory of the sun is, however, implicated when star positions are determined with reference to it or to the moon.

[78] Estimates are also given of the stars' magnitudes, though these are, of course, not based on measurement.

[79] See Newton 1973, 1974a, 1974b, 1977, 1980b, Hartner 1977, 1980, Moesgaard 1980b, Gingerich 1980, 1981. References to earlier literature will be found in G. E. R. Lloyd 1979, p. 184 n. 308.

[80] The idea that Ptolemy plagiarised an earlier Greek astronomer, Menelaus, was already suggested by Arabic astronomers: see Björnbo 1901; Dreyer 1916–17, pp. 533ff.; Vogt 1925, pp. 37f.

[81] Perhaps Newton's most telling argument is based on an analysis of the pattern of error in Ptolemy's catalogue: Newton 1977, pp. 237ff., 1979, pp. 383ff.

stars that were not included by Hipparchus, and where comparisons are possible, these suggest that he has done more than just take over Hipparchus' results and adjust these for precession.^[82] However, the ramifications of this controversy need not detain us further at this point, for the simple reason that whoever was chiefly responsible, whether Hipparchus or Ptolemy, the catalogue as we have it is excellent evidence of sustained observations. It reveals both the degree of precision aimed at (of the order of 10') and the accuracy obtained (the mean error in longitude is of the order of a degree; in latitude, of half a degree).^[83]

When we turn to the observations carried out in connection with the determinations of the parameters of astronomical models, the picture is complicated, in Ptolemy's case especially, by that controversy over the issue of the match—or mismatch—between his protestations of a concern for accuracy and his actual practice. Yet, to begin with the protestations, the evidence that both Ptolemy and, before him, Hipparchus were at pains to draw attention to the problems posed by the reliability of the data they had to work with is impressive. Ptolemy often expresses his qualms about the accuracy of some of the observations conducted by earlier astronomers, criticising their rough-and-ready character, and he indicates that Hipparchus already had similar doubts or reservations.^[84] They were also alert to the differences in reliability of different kinds of data. Those derived from eclipses or occultations were recognised as more trustworthy than those involving estimates of wide angular distances or of absolute positions. Thus, Hipparchus used lunar eclipse data for his theory of the moon, even though these presupposed, of course, his model for the sun.^[85]

Furthermore, both Hipparchus and Ptolemy drew attention to particular sources of inaccuracy in both naked eye and instrumentally

[82] G. E. R. Lloyd 1979, p. 184; cf. Gingerich 1981, pp. 42f.

[83] Cf. Toomer 1984, p. 328 n. 51.

[84] See Syntaxis 3.1 (H) 1.203.7ff., 14f., 205.15ff.; 7.1 (H) 2.2.22ff., 3.4f.; 9.2 (H) 2.209.5ff.

[85] See Syntaxis 4.5 (H) 1.294.21ff.; cf. 4.1 (H) 1.265.18ff.

aided observations.^[86] Ptolemy refers to distortions due to atmospheric conditions or to the object being close to the horizon; in his Optics (though not generally in the Syntaxis ) atmospheric refraction is discussed.^[87] The Syntaxis includes descriptions of the main astronomical instruments used, sometimes, though not always, with specifications concerning their size and construction,^[88] and it issues warnings about particular sources of inaccuracy in their use. In one notable passage, where again he is following Hipparchus' lead,^[89] Ptolemy writes of the errors arising from the faulty positioning or calibration of instruments. Referring to the use of equatorial armillaries, he notes that a deviation of a mere six minutes of arc from the equatorial plane in the setting of the instruments generates an error of six hours in determining the time of the equinox,^[90] and of the bronze rings in the Palaestra at Alexandria he remarks: "For so great is the distortion in their position, and espe-

[87] Ptolemy Optics 5.23ff. (237.20ff. Lejeune); cf. also Cleomedes 2.6.222.28ff., 224.11ff. Distortions due to the object being near the horizon are referred to in Ptolemy's Syntaxis at, for example, 1.3 (H) 1.11.20ff., 13.3ff.; 9.2 (H) 2.209.16f., 210.3ff. (where it has been thought that refraction is possibly in mind: see Toomer 1984, p. 421 n. 8).

[88] See Syntaxis 1.12 (H) 1.64.12ff., 66.5ff.; 5.1 (H) 1.351.5ff.; 5.12 (H) 1.403.9ff.; 5.14 (H) 1.417.1ff. There are useful brief surveys of ancient astronomical instruments in Dicks 1953–54 and Price 1957.

[90] Syntaxis 3.1 (H) 1.196.21ff.

cially in that of the bigger and older one, when we make our observations, that sometimes their concave surfaces twice suffer a shift in lighting in the same equinoxes."^[91]

To be sure, these expressions of a concern for accuracy have to be judged against actual performance. So far as Ptolemy goes, certain aspects of his procedures are not disputed and are indeed transparent enough. He repeatedly has recourse, throughout his calculations, to approximations and rounding procedures, some but not all of which he explicitly signals as such. Moreover, as the most recent detailed recalculation of his results goes to confirm,^[92] quite a number of those approximations are biased towards establishing a preconceived value, often one he believes to have the authority of Hipparchus in particular or of tradition in general behind it. Sometimes he may well have worked back from such a result, not merely in that it influenced the approximations he introduced but also in his selection of the observations he presented.^[93]

Equally, though, there are occasions when Ptolemy records data that do not simply confirm his conclusions—the very data on which the charge of fabrication has sometimes then been based.^[94] Furthermore, in two cases, his theories of the moon and of Mercury, he made substantial modifications in his usual epicycle-eccentric model, introducing in both instances an extra circle in addition to the epicycle and the deferent.^[95] Here the very complexities he thought necessary appear

[92] See Toomer 1984.

[93] See, for example, Czwalina 1959; cf. Newton 1977, pp. 266 and 307; Gingerich 1980, pp. 260ff.

[94] As, for example, in the case of the two sets of data presented in Ptolemy's discussion of the value of precession: Syntaxis 7.2–3 (H) 2.19.16ff., 25.13ff.

[95] For an account of the Mercury and moon models, see, for example, Pedersen 1974, pp. 159ff., especially pp. 192ff. and pp. 309ff.; Neugebauer 1975, vol. 1, pp. 68ff., 84ff., and 158ff.

to be quite gratuitous unless they are a response to what he perceived to be mismatches between the simple model and some empirical data, however and by whomsoever these were obtained.^[96] Many of his procedures would be considered sharp practice, as well as slapdash, today—in some cases also, maybe, in his own day. At the same time, there are many contexts in which his practice can be taken to bear out, at least to some extent, his expressed concern over securing a comprehensive and reliable data base.

However hesitant its beginnings, Greek astronomy eventually achieved outstanding successes in developing detailed, quantitative models to account for complex natural phenomena. The mathematical models themselves were rigorous exercises in deductive geometry. But they were evaluated not just as geometry but on how well they matched the data—an essential point we shall return to in Chapter 6.^[97] Greek astronomers were certainly neither as active nor as systematic as they might have been in confronting—or in recording the confrontations between—predicted theoretical positions and actual sightings. Yet from Hipparchus onwards, and I should say including Ptolemy, the quality of the data obtainable was a major preoccupation, not just in principle but also in practice. The rigour and exactness of the inquiry were its pride. But the point was not—or was not so much—that astronomy deals with the unchanging heavens, as, more simply, that it is based on mathematics.^[98] In particular, the realisation that the exact-

[96] Cf., e.g., Gingerich 1980, pp. 261f.: "Ptolemy must surely have put credence in some specific observations here, or he would not have ended up with such an unnecessarily complicated mechanism for Mercury."

[97] See below, Chap. 6, pp. 304ff., 312ff.

ness and reliability of the data vary in different contexts is important, since it shows that there is nothing automatic about the accuracy of the data and that the degree of accuracy was a matter that had to be evaluated in the given circumstances of each part of the inquiry.