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«Eudoxus, Callippus and the Astronomy of the Timaeus. Andrew Gregory Ancient Approaches to Plato’s Timaeus BICS Supplement 78 - 2003 Whether the ...»

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Eudoxus, Callippus and the Astronomy of the Timaeus.

Andrew Gregory

Ancient Approaches to Plato’s Timaeus

BICS Supplement 78 - 2003

Whether the astronomy of the Timaeus had any significant influence on Eudoxus' theory of

homocentric spheres is a matter of contention. Some commentators deny any such influence. Here I

argue for a view of the Timaeus' astronomy, and of Eudoxus' astronomy, whereby Eudoxus' work was

as much a natural development of the Timaeus as Callippus' work was of Eudoxus. I also argue for an important interpretative principle. This is that Plato, Eudoxus and Callippus could not account for all the phenomena they were aware of, and were aware of that fact. If the Timaeus presents a prototype, Eudoxus can then be seen to develop this astronomy, making the model more sophisticated and complex while staying within the cosmological principles, and attempting to solve the key problems which were left unsolved by the Timaeus model. He does this in much the same way as Callippus made Eudoxus' model more complex and sophisticated, and attempted to solve the leading problems in that model. I also consider some further objections to a significant interaction between Plato and Eudoxus, based on supposed philosophical differences, dating, and the evidence of later commentators. I conclude that these provide no significant obstacle to considering there to be a fruitful liaison between Plato and Eudoxus.

I The model proposed by the Timaeus was a significant advance on any previous model we are aware of, including Plato’s model in the Republic’s myth of Er.

Most notably J. Mittlestrass, Die Rettung der Phenomena, Berlin (1963), W. R. Knorr, ‘Plato and Eudoxus on the Planetary Motions’, Journal for the History of Astronomy xxi, (1990) 313-329, L.

Zhmud, ‘Plato as "Architect of Science"’, Phronesis 43/3 (1998) 211-244.

Philolaus. Republic, myth of Er.

The basic problem with these models can be put like this. The earth effectively has two motions, a daily rotation and its annual orbit of the sun. The axes of those motions are not identical.

Earth’s axes.

The earth’s axis of rotation is offset from the plane of its orbit around the sun.

If we treat the earth as being central and stable, and so transfer these motions to the heavens, there need to be two axes of rotation, one for the fixed stars and one for the sun and the other bodies of the solar system. This, in effect, is what we get forthe first time in the Timaeus.

See Aristotle De Caelo 293a18ff., cf. Metaphysics 986a.

See Plato, Republic 616b ff.

Ignoring the motion of the earth's axis of rotation, the effect of which (the precession of the equinoxes) had yet to be discovered.

–  –  –

What can this model account for, assuming that all the motions of the heavenly bodies are regular circular motions (fixed stars) or combinations of regular circular motions (sun, moon, and planets) ? If one observes the position of the sun setting on the horizon, this changes during the year from a maximum north or south of west at solstices and due west at equinoxes. If one observes which star rises at the point at which the sun set, the sun moves approximately one degree a day against the background of the fixed stars. The Timaeus model accounts very well for these phenomena, and will also have the planets in motion relative to the fixed stars along the same path as the sun.

–  –  –

One can also have good explanations of the phases of the moon and the periods of the planets, but previous models had managed these as well.

What the Timaeus model could not explain (assuming regular, circular motion (RCM)) was:

(1) The retrograde motions of the planets.

(2) Any deviation from the path of the sun by the moon or planets.

–  –  –

While the sun moves in one direction on a straight line known as the ecliptic, the planets can occasionally (appear to) reverse their motion, and they deviate from the ecliptic (change their latitude).

The band of latitude which the five naked eye visible planets move in is known as the zodiac. Some ancients, beginning with Eudoxus, believed that the sun deviated in latitude from the line through the centre of the zodiac (a commonly used ancient term, abbreviated here to ‘zodiac midline’). The

Timaeus also could not explain:

(3) The inequality of the seasons. One might expect the times between solstices and equinoxes to be equal, but in fact they are not as solstices and equinoxes are used to define the seasons, this disparity is known as the inequality of the seasons.

(4) The relation of Mercury and Venus to the sun. In distinction to the other planets, Mercury and Venus are always seen relatively close to the sun.

(5) The frequency of eclipses (is earth, sun and moon are in one plane, as the Timaeus has them, then there will be solar and lunar eclipses once a month).

The model of the Timaeus, which has the planets moving in regular circular motion in one plane (if we ignore their daily motion) cannot account for the occasional backward motion of the planets relative to the fixed stars nor can it account for any deviation in latitude.

See below for further explanation.





–  –  –

Given that the Timaeus model seems rather weak in explaining some relatively evident phenomena, are we justified in assuming RCM ? Timaeus 34a and 40b tell us that the motions of the cosmos as a whole, and those of the fixed stars are unwandering. There cannot then be a metaphysical problem with the regular motions of the heavens (i.e. that which is visible and bodily can move in a regular manner). If the ‘wanderings’ of the planets constitute time (39c), and the planets, sun and moon are the ‘guardians of time’ (38c), then unless Plato envisages a non-uniform passage of time the motions of the heavenly bodies are regular. For there to be a contrast between time and eternity, all that is required is that time moves while eternity does not. Time can move in a perfectly regular manner, as would seem to be implied by 37d (time as a movable image of eternity, moving according to number) and 38c (the 'wanderers' come into being to define and guard the numbers of time. The contrast between the fixed stars and the planets is simply that the planets have orderly motion relative to the fixed stars. If it is possible to calculate the 'perfect year' (39d) again the motions of the heavens must

be orderly. Finally, Timaeus 47a tells us that:

For more detailed argument on this issue see A. D. Gregory, Plato’s Philosophy of Science (London 2000) 105-109.

They are specifically ἀπλανές (34a5, 40b4).

Cf. Republic 529d ff.

Note the difference between the συμμετρία, 'proportions' at Republic 530a7 which deviate, and the precision of the συμμετροῦνται... ἀριτημοῖς 'commensurates in number' that we are to investigate at Timaeus 39c7.

“God devised and gave to us vision in order that we might observe the rational revolutions of the heavens and use them against the revolutions of thought that are in us, which are like them, though those are clear and ours confused, and by learning thoroughly and partaking in calculations correct according to nature (λογισμῶν κατὰ φύσιν ὀρθότητος), by imitation of the entirely unwandering (ἀπλανεῖς) revolutions of God we might stabilise the wandering (πεπλανημένας) revolutions in ourselves.” So the planets wander in the sense that they have motion relative to the fixed stars, but do not wander in the sense of having irregular motion. This is similar to the position of the Laws and Epinomis, but different from the Republic and Politicus. It is interesting to note that while both the Republic and the Politicus have the cosmos rotating on a pivot, the Timaeus has the cosmos free floating.

–  –  –

There is though a problem with simply attributing RCM to the Timaeus, which is that we are told:

“The morning star [Venus] and the star sacred to Hermes [Mercury] he placed in an orbit equal in speed to that of the sun, but possessing a contrary power (ἐναντίαν... δύναμιν) to it, whence it is that the sun, the star of Hermes and the morning star overtake and are overtaken by each other.” Some commentators have sought to extend the influence of the contrary power beyond this application to Mercury and Venus. The argument is this. Plato was aware of retrogression.

Retrogression cannot be accounted for with the Timaeus model assuming RCM. If we apply the contrary power to all the planets, then the Timaeus can account for retrogression. However, as no deviation in latitude is envisaged here, earth sun and moon are all permanently in one plane and so there will be solar and lunar eclipses once a month. We might seek a further application of the contrary power, or we might question one premise of the argument. Was the model of the Timaeus supposed to account for all the phenomena Laws 822a: "The usual opinion concerning the sun, moon, and other planets, that they at some time wander (πλανᾶται), is not the case; precisely the opposite is true. For each of these bodies always travel on one path, and not many, although this may not seem so." I accept that the Laws was 'on the wax' when Plato died and was subsequently 'published' (and edited ?) by Philip of Opus, who also 'published' (and edited/ wrote ?) the Epinomis. Quite possibly he had a greater hand in the creation of the Epinomis. With due caution, I take it to be indicative of at least what a close associate of Plato thought ought to be an appendix to the Laws, and so reflects views of Plato or someone who immediately followed him.

Republic 530ab: "Concerning the proportions (συμμετρίαν) of night to day, of these to month, of month to year, and of the other stars to these and each other, wouldn't he consider it absurd to expect these things always to behave in the same manner and never to deviate (παραλλάττειν) in any way ?" In the phase of the myth of the Politicus in which we live, the cosmos is degenerating towards chaos, and so the heavenly motions become chaotic.

Cf. Republic 616b, Politicus 270a9 and Timaeus 34a, also Timaeus 33d. It is interesting that Plato moves from a supported to an unsupported cosmos (cf. the presocratics and what supports the earth), and it is also arguable that he moves from a degenerating to a stable cosmos (see Gregory (n.7) 101Timaeus 38d2-4.

See F. M. Cornford Plato’s Cosmology (London 1937) p. 137, Knorr (op. cit. note 1) 315-137.

Plato was aware of ? We might also ask: Were the models of Eudoxus and Callippus supposed to

account for all the phenomena that they were aware of ? Simplicius tells us that:

“These [unrolling spheres] of Eudoxus' school do not save the phenomena, not only those that were found later, but also those known before and recognised by them.” The three phenomena Simplicius cites are that (1) Venus and Mars appear at times much brighter than at others (2) there is variation in the apparent size of moon (3) there are variations in the type of solar eclipses relating to the apparent size of the moon. Should we expect Plato to be different in this respect from Eudoxus and Callippus ? If so we need an argument, and a fairly strong one, that Plato believed he had accounted for all the phenomena he was aware of in the Timaeus. No one has yet provided one, and I do not see the basis for one in the Timaeus or elsewhere.

IV Which phenomena was Plato aware of ? Clearly he was aware of equinoxes and solstices.

Timaeus 47a5 tells us that:

“Sight of day and night, of months and the revolving years, of equinoxes and solstices (ἰσημερίαι καὶ τροπαὶ), have caused invention of number.”

The most interesting passage though is 40c:

“The dances of these stars and their juxtapositions (παραβολὰς) with one another, the circling backs and advances (ἐπανακυκλήσεις καὶ προσχωρήσεις) of their own cycles, which of the gods come into contact (συνάψεσιν) with each other and which into opposition, which cover (ἐπίπροσθεν) each other relative to us, and for what periods they each disappear and again re-appear (κατακαλύπτονται καὶ πάλιν ἀναφαινόμενα).” Plato would appear to be aware of retrogression. That would certainly be the most natural reading of ἐπανακυκλήσεις in this context. That he uses ἐπανακυκλήσεις, literally a 'circling back' is interesting, as planets do not directly reverse their course but undergo deviation in latitude during retrogression, typically creating loops.

Plato may also have a good knowledge of what happens when planets pass each other, depending on whether he uses different words to refer to one or several phenomena here. When planets pass each other, there are three things which may happen. They may pass each Simplicius in De Caelo 504.17 ff.

Depending on its distance from the earth, the moon sometimes covers the entire sun, while sometimes a small rim of the sun is visible around the moon. The latter is an annular eclipse.

The Loeb text omits these words, without comment, and for no good reason. They are in Burnet's Oxford text and are omitted in only one of the sources. Other passages demonstrating Plato's knowledge of solstices and equinoxes are at Phaedo 98a, Laws 767cd and 945e and Epinomis 990b.

As a contrast to προσχωρήσεις indicating forward motion, and looking directly at the sky rather than at setting positions on the horizon.

Cf. Republic 617b2.

other with sufficient distance between them that they remain two distinct objects. They may ‘touch’ each other, such that they appear to be one brighter object. One may pass in front of the other, occluding it. Now look at the words Plato uses. παραβολή can mean side by side, σύναψις can mean in contact with, and ἐπίπροσθεν before, in the sense of screen or cover. Plato may well be aware of these three separate phenomena.

Possibilities for planets passing each other in the zodiac.



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