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Eudoxus and Ezekiel’s wheel theophany

November 4, 2014

Ezekiel’s description of the firmament in Ezekiel 1 is similar in some respects to Exodus 24:9-11. In both the Ex. 24 account and in Ezekiel, the firmament is likened to a sapphire stone, with God above, like Zeus seated above the rigid heaven.

Some scholars have suggested that there is evidence the original version of Ezekiel 1 was modified by later insertion of wheels into the vision.

Ralph W. Klein wrote: [1]

The most serious question about the integrity of the chapter deals with the account of the wheels. It is not clear how we are to conceive the connection of the wheels to the animals in general and to the legs in particular, and Othmar Keel has argued, convincingly in my judgment, that the wheels represent a shift from the basic idea of the vision.

In his commentary on Ezekiel 1, K.W. Carley stated that the Septuagint version does not contain verse 14. Referring to verse 15, he wrote: [2]

The report of the vision went directly on to describe the throne of God above the heads of the living creatures (verses 22-28a). But there has been inserted a somewhat puzzling description of wheels beside the creatures… There are secondary expansions even within this section. Verse 17 anticipates the movement of the wheels referred to in verses 19f.; verse 18 elaborates the appearance of the wheels; and verse 21, which is absent from some manuscripts, largely repeats verses 19f.

If Klein and Carly’s assessment is correct, Ezekiel’s accounts referring to the firmament and “wheels” may be additional examples of corruptions of the cosmology of the bible, that was modified in the second century BC and after by agents of Antiochus IV, the little horn of Daniel 8, who initiated the revision of the bible’s cosmology, intended to make it conform to the geocentric views of the Greek poets and philosophers. These men may have been either Gentiles, or hellenized Jews.

In Ezekiel, the redactor may have tried to introduce cosmological ideas that originated with Eudoxus of Cnidus (c. 406-355 BC).

Ezekiel 1:15-26
15 Now as I beheld the living creatures, behold one wheel upon the earth by the living creatures, with his four faces.
16 The appearance of the wheels and their work was like unto the colour of a beryl: and they four had one likeness: and their appearance and their work was as it were a wheel in the middle of a wheel.
17 When they went, they went upon their four sides: and they turned not when they went.
18 As for their rings, they were so high that they were dreadful; and their rings were full of eyes round about them four.

The reference to four rings possibly alludes to crystalline spheres proposed by Eudoxus (c. 406-355 BC) to account for the supposed motions of the sun, moon, planets, and the starry heaven.

Ezekiel 1:19-22
19 And when the living creatures went, the wheels went by them: and when the living creatures were lifted up from the earth, the wheels were lifted up.
20 Whithersoever the spirit was to go, they went, thither was their spirit to go; and the wheels were lifted up over against them: for the spirit of the living creature was in the wheels.
21 When those went, these went; and when those stood, these stood; and when those were lifted up from the earth, the wheels were lifted up over against them: for the spirit of the living creature was in the wheels.
22 And the likeness of the firmament upon the heads of the living creature was as the colour of the terrible crystal, stretched forth over their heads above.

In the hellenistic age the rigid heaven was often referred to as “crystalline.” [3]

On the work of Eudoxus, Wilbur R. Knorr wrote: [4]

Plato is said to have posed to Eudoxus the problem of “saving the phenomena” of planetary motion on the restriction to uniform circular motion. An account of Eudoxus’ scheme is transmitted by Simplicius of Cicilia (sixth century A.D.) in his commentary on Aristotle’s De Caleo (fourth century B.C.; On the Heavens). From this account a reconstruction has been worked out by the Italian historian of astronomy Giovanni Virgin-io Schiaparelli in 1875. The Eudoxean system reproduces the apparent motion of a planet by combining the rotations of a set of homocentric spheres. The planet is set on the equator of a uniformly rotating sphere. lf a second sphere is set about the first, rotating with equal speed to the first but in the opposite direction and having its axis inclined. then the planet will trace out an eight-shaped curve which the ancients called the hippopede, or horse fetter), so as to complete the full double loop once for every full revolution of the spheres. One superimposes over this a third spherical rotation, corresponding to the general progress of the planet in the ecliptic. and finally over this a fourth rotation, corresponding to the daily rotation of the whole heaven. In this way, each of the five planets requires four spheres. while the Sun and the Moon each take three. Schiaparelli’s exposition thus revealed the ingenuity of Eudoxus’ scheme for reproducing geometrically the seemingly erratic forward and backward (retrograde) motion of the planets. Nevertheless, the model proves unsuccessful in some respects; since the planets do not vary in distance from the earth (the center of their spheres), Eudoxus cannot account for their variable brightness or for asymmetries in the shape of their retrograde paths. Even worse, the values that Eudoxus had to assign for the rotations of the spheres do not produce retrogrades for Mars or Venus. and the Sun and the Moon are given uniform motions, contrary to observation. Apparently, the latter two defects were recognized, for Eudoxus’ follower Callippus introduced seven additional spheres (two each for Sun and Moon, one each for Mercury, Venus and Mars) to make the needed corrections.

The Eudoxean-Callippean scheme is enshrined in Aristotle’s Metaphysica (c. 335-323 B.C.; Metaphysics) where it serves as the mathematical basis of a comprehensive picture of the entire physical cosmos. Doubtless, Eudoxus proposed his geometric model without specific commitments on physical and cosmological issues. Nevertheless, it suited well the basic Aristotlean principles-for example, that the cosmos separates into two spherical realms, at its center, the terrestrial, and that the natural motions of matter in the central realm (for example, earthy substances moving in straight lines toward the center of the cosmos) differ from those in the outer (where motion is circular, uniform, and eternal). Ironically, these Aristotlean principles persisted in later cosmology, even after astronomers had switched from the homocentric spheres to eccentrics, epicycles, and other geometric devices.

Otto Neugebauer wrote: [5]

Few astronomical theories have exercised so deep and lasting an influence on human thought as the discovery of Eudoxus that the motion of the planets can be explained, at least qualitatively, as the combination of uniform rotations of concentric spheres about inclined axes. The sphericity of the universe, the fundamental importance of uniform circular motion, must have appeared from then on as an established fact. Combined with Aristotle’s idea of the “prime mover” the universe could be understood as one great system, truly geocentric. No wonder that this theory held its fascination for almost two thousand years over the minds of philosophers and even astronomers, in spite of the fact that serious difficulties were apparent almost from the start.

Eudoxus found that the motion of a planet could be represented as the result of four concentric rotating spheres, each with distinct axes. When the axes were suitably oriented, the planet, located on the innermost sphere, moved in a figure-eight loop called the “hippopede” or horse-fetter. When combined with the diurnal rotation, the movement resembled that of a planet in its course among the stars. In this arrangement, each planet required four spheres, while three were necessary for sun, and three for the moon, and one for the stars. The system was developed further and made even more complicated by Callippus (c. 370-300 BC) and Aristotle.

 References

1. Klein, Ralph W. 1988. Ezekiel: The prophet and his message. University of South Carolina Press. p. 18.

2. Carley, K.W. 1974. The book of the prophet Ezekiel. Cambridge University Press. Cambridge. p.17.

3. See Josephus, Ant. Jud. for examples.

4. Wilbur R. Knorr. Eudoxus of Cnidus, In: The Ancient World: Dictionary of World Biography, Volume 1, edited by Frank N. Magill. Routledge, 2003. pp. 413-414.
http://books.google.ca/books?id=7NVFUi7G6TE

5. Neugebauer, O. 1953. On the “Hippopede” of Eudoxus. Scripta Mathematica 19(4):225-229. (See p. 225.) Reprinted in: Neugebauer, O. 1983. Astronomy and History: Selected Essays. Springer-Verlag, 305-309.

Graphical representations of the planetary and celestial motions proposed by Eudoxus may be viewed at:
Henry Mendell. Eudoxos of Knidos (Eudoxus of Cnidus): astronomy and homocentric spheres

http://web.calstatela.edu/faculty/hmendel/Ancient%20Mathematics/Eudoxus/Astronomy/EudoxusHomocentricSpheres.htm

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