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Mathematics in the Republic Book 8
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Peter Worman



Joined: 04 Jul 2007
Posts: 25
Location: Durban, South Africa

PostPosted: Tue Mar 22, 2016 6:31 am    Post subject: Reply with quote

Many thanks Pete! We need all the help we can get here in darkest Africa
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Peter Worman
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Peter Blumsom



Joined: 09 Mar 2007
Posts: 1093
Location: Wembley, London, UK

PostPosted: Sat Apr 02, 2016 8:02 pm    Post subject: Reply with quote

Dear Pete,

I’ve been pondering how to present this. Remember we have been travelling backwards through James Adam’s interpretation of sections from E to B. Sections E, D and C I am sure are correctly interpreted, but I am not completely convinced by section B on two counts which I will explain. Firstly the crucially step that Adam takes is based upon a passage from Aristotle, and not on Plato’s own words. Aristotle was not friendly towards Plato’s interest in number, especially regarding Plato’s claim that numbers are self-existing forms. Aristotle does not interpret any Pythagorean thesis sympathetically probably because they do not fit into his own metaphysical system. However, James Adam believes that the passage from Aristotle that I quoted in my earlier post is correct so let’s run with it. I will present my second objection later. I do not say Adam is incorrect I just point out the weakness of his provenance for the number 216.

So let us turn our attention to section B once more. The number 216 represents days. “It is”, Adam says, “the shortest time [hence ‘the first’] within which a child can be perfectly fashioned within the womb” and he adds “and it is during the third, fourth and fifth months after conception that the harmonies of a living organism are fulfilled.” The source of the 216 days is Aristides Quintilianus who lived a long time after Plato (3rd cent.AD) but may himself have known of an unwritten tradition going back to Plato’s time. The third, fourth and fifth months comes from Censorinus in his De di Natali, from about the same time, but he claims that his source were the ancient Chaldeans or Babylonians. It may well be true but I have no access to this work. This, by the way, would account for the ‘three distances of 3,4 and 5, within four limits of my aforementioned post. I can only think of the passage in Timaeus when the Demiurge instructs his lesser gods to construct the bodies of human beings while he will provide the immortal souls. These souls contain the same musical ratios harmonies as the World Soul itself but in miniature.

The weakness of the provenance for the 216 days leaves me wondering whether there can be another way of interpreting the ‘human number’ but there is no doubt about the other number - “a number measuring the earth” and “lord of better and worse births.” It is this number that even the Guardians have forgotten, causing them to “marry brides to bridegrooms out of season” thus bringing about the end of the benign Aristocracy that ruled men up to that point.

So, what is this great number?

It is undoubtedly 12,960,000, the number that arose from the calculations of sections E and D, explained in my post of 3rd November last year. Again it is a measure of days - the number of days in the Platonic Great Year - 12,960,000/360 days gives 36,000 years which by general consensus of Greek astronomers up to Ptolemy was the time it took for all the stars to travel a complete circuit of the heavens, that is, through all the houses of the Zodiac, and return to their original position. (we now know this to be about 25,800 years). Plato discusses this in Timaeus;

“it is still quite possible to perceive that the complete number of Time fulfils the Complete Year2 when all the eight circuits, with their relative speeds, finish together and come to a head, when measured by the revolution of the Same and Similarly-moving. In this wise and for these reasons were generated all those stars which turn themselves about as they travel through Heaven, to the end that this Universe might be as similar as possible to the perfect and intelligible Living Creature in respect of its imitation of the Eternal Nature thereof.” TIMAEUS 39d

(The individual human life, reckoned by Plato in Republic to be 100 years or 36,000 days, can be measured into this Great Year 360 times.)

Plato in his Dialogue The Statesman discusses this Great Year in a different way. Here he says that:

“During a certain period God himself goes with the universe as guide in its revolving course, but at another epoch, when the cycles have at length reached the measure of his allotted time, he lets it go, and of its own accord it turns backward in the opposite direction, since it is a living creature and is endowed with intelligence by him who fashioned it in the beginning. Now this reversal of its motion is an inevitable part of its nature for the following reason.” STATESMAN 269C

Therefore, according to the account above, once the Great Year has been completed with God’s hand on the tiller, it then retraces its path but this time under its own steam - think of winding the spring of a clock as the first period and the spring gradually loosening itself, the second.

This links to our present topic for according to Plato the first period was the golden age of Cronos, where the cosmos was under divine rule, and where the knowledge of when to marry and when to conceive was readily available to the wise men of the time. But when this lesser period began, everything was reversed and akind of blindness overtook men’s souls. This was analogous to the fall from the favoured rule of the Aristocracy.

Adam notes that this myth from the Statesman implies a double period of the Great Year and he calls it ‘The Greatest Year of 72,000 earth years. This actually fits in with Timaeus very well because this dialogue seems to start after the second or non Divine period has just ended:

“For God desired that, so far as possible, all things should be good and nothing evil; wherefore, when He took over all that was visible, seeing that it was not in a state of rest but in a state of discordant and disorderly motion, He brought it into order out of disorder, deeming that the former state is in all ways better than the latter.” TIMAEUS 30A

This is just the sort of mess the universe would be in after 36.000 years of self-rule!

Adam speculates that these two motions, the ‘directed’ and ‘undirected’, is the reason why Plato mentions two harmonies and not one, each representing a Great Year.. Both 3,600 x 3,600 and 2,700 x 4,800 produce 12,960,000.

So, Peter, now we have an interpretation that links micro and macrocosm. I have but one more post to deliver on this subject, and two more tasks, to trace back to some even more ancient sources, and to try to describe why Plato would write this extraordinary virtuoso passage of harmonics.
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