Plato's Perfect Number of the Divine Creature

Definition: [Astrological Ages] Some commentators, notably Jung, argue that in paragraph 546 of Plato's The Republic he was discussing the Great Year. This would be some two hundred years before Hipparchus [c 190 - 120 BC].

Plato's Perfect Number of the Divine Creature: Plato writes the following in the section of The Republic called Timarchy [Timarchy is rule by a militaristic class, Sparta being the best example known to Plato.]:

... Not only for plants that grow in the earth, but for animals that live on it, there are seasons when mind and body are productive, seasons which come when a certain period is completed, of longer duration for the long-lived, shorter for the short-lived. And though the rulers of your city are wise, reason and perception will not always enable them to hit on the right and wrong times for breeding, some time they will miss them and then children will be begotten amiss. For the divine creature, there is a period defined by a perfect number; for the human creature the number is the first in which root and square multiplications (comprising three dimensions and four limits) of basic numbers, which make like and unlike, and which increase and decrease, produce a final result in complete commensurate terms; of these basic numbers four and three coupled with five, yield two harmonies when raised to the power of four, of which one is a square with a multiple of one hundred, the other a rectangle of which one side is one hundred squares of diameters of a square of side five each diminished by one if the diameters are irrational, or by two if the diameters are rational, the other side of one hundred cubes of three.

The Argument that Plato knew of the Great Year and Therefore Precession: The above is not an easy paragraph to interpret. However, in the twentieth century a number of commentators looked at paragraph 546 and decided that in the mathematics of the latter part of that paragraph Plato was thinking of the number 36 000. Therefore, they argued, Plato knew of the rate of precession and, hence, must have known of the Great Year.

This genesis of this idea seems to go back to the Adam's edition of Plato's Republic [Cambridge University Press, 1926], in which a calculation indicating that Plato meant 36 000 years in paragraph 546 is presented. The steps of the argument then appear to be as follows:

1: Ptolemy [c 130 - 170 AD], in Al Magest, tells us that two centuries after Plato, Hipparchos [c 190 to 120 BC] defined the precessional rate as one degree per hundred years.
2: Hence 36 000 years [100 x 360] would be the Greek view of the length of a Great Year [if indeed they had such a concept.]
3: Plato's mathematics in paragraph 456 also gives 36 000 years.
4: Hence, Plato must have been aware of the length of the Great Year and the movement of the Equinoxes two centuries before Ptolemy.
5: Some commentators have taken the thesis another step: they argue that as Plato had knowledge of the Great Year, he must have understood the concept of precession, and that perhaps this knowledge even pre-dated Plato.
6: The argument for the knowledge pre-dating Plato is that Greek observational astronomy in Plato's time probably was not yet accurate enough to measure the rate of precession. Hence, it is argued, the knowledge must have come from elsewhere. [And the Babylonians, whilst the originators of much else in astrology, do not appear to have possessed the concept.] As Plato was the first to mention Atlantis in the written record, some commentators have argued that perhaps the knowledge came from there.

The Counter-Argument: Plato Knew Nothing of Precession: If Plato - perhaps the most famous of philosophers - knew of the rate of precession, it is perhaps strange that Ptolemy never mentions this: a reference to the works of Plato never did any harm to the reputation of a Classical philosopher.

The best counter-argument is paragraph 456 itself. Reading it, it is very difficult to see why anyone would think the text has any connection with the movements of anything in the heavens. It mostly seems to be concerned with child birth and the best times at which people should conceive, in order to avoid births going amiss. All the math in the second part of the paragraph relates to the numerology of human child birth. [The Greeks didn't have Algebra; they did math by doing trigonometry, hence the references to squares.] The only possible reference to something celestial are the mysterious words divine creature. This may - and then again may not - be referring to something in the heavens. However, Plato very clearly states that the breeding of the divine creature - is controlled by a perfect number.

The Greek definition of a perfect number [which is also the definition that we still use today] is an integer which is the sum of its positive proper divisors. For example, 6 can be divided properly [that is, the result is a whole number, e.g. 1, 2, 3, etc.] by the numbers 1, 2 and 3, but 6 can also be obtained by adding the numbers 1, 2 and 3. The Greeks knew the first three numbers in the series of perfect numbers, 6, 28 and 248 and perhaps they also were aware of the fourth number, 8 128, but the fifth was only discovered in modern times. It is 33 550 336, not 36 000. [Sorry about all the math!]

As the Greeks - as did most ancient cultures - saw a very strong connection between conception and the period of the Moon, the simplest explanation is that Plato - if he was thinking of the heavens at all - was referring to the perfect number 28, the approximate number of days in a Lunar month, as that of the period of the divine creature.

Which ever perfect number he was thinking of, he can not have been thinking of 36 000. Really, there is no evidence at all in that paragraph, or elsewhere in his works, that Plato knew of precession. We astrologers might be better using the expression "Hipparchos" months instead.

Plato's Spindle of Necessity: Plato does write in The Republic, paragraph 617 - 618, of something called a Spindle of Necessity, a shaft of light running straight through heaven and Earth like a pillar, the tie-rod of heaven, but this seems to be the extent of his astrology in that work. In Plato's concept the Earth was the centre of the Universe and unmoving, the planets and fixed stars revolved around it in rings, with the Spindle as the axis of revolution. There are few further details given, but equinoxes and constellations do not come into the text, which is more concerned with the Fates than with the movement of heavenly bodies. The Spindle seems to be a fairly clear allusion to the celestial axis and the circumpolar revolution of the stars. This concept was very familiar to the ancients, because they saw it with their own eyes night after night in the heavens - the rotation of constellations around the still point of Polaris as the night went on. Had Plato been aware of the Great Year - and hence the movement of this axis relative to the stars - this would have been the logical place to have mentioned it, but he does not.

Plato's Perfect Number of the Divine Creature [c 360 BC]