Politeia VIII

Plato continues about the ideal type of state: the aristocracy as discussed above guided by the most just, best educated people namely sincere philosophers and four other types of state: the state Sparta, the oligarchy, democracy and tyranny. From aristocracy a sixth type of state may rise and this must be seen as a deterioration: the timocracy, a society based on ambition. An aristocracy may dwindle down into a timocracy when men and women procreate at the wrong moment*, begetting weaker offspring and leading to the different classes of people starting to mingle. Society knows respectively a golden, silver, cupper and iron type of man. Mingling leads to disappearance of the most just and educated people: golden and silver people and thus to disharmony, struggle, hostility and finally a civil war. The leaders of a timocracy are practical, more interested in physical activity and ambitious for short term goals that match this attitude. They neglect the highest intellectual and moral standards. A timocracy in turmoil may deteriorate into an oligarchy: a society focused on possession, ruled by an avaricious type of leader, avaricious to both others and themselves. In a society focused on possession a gap grows between rich and poor, leading to a struggle. If the poor win, the wealthy will be expelled or killed and from then on all people may participate in society and governance on an equal footing. This is the birth of democracy: society based on freedom. Slaves, even animals enjoy the same freedom as their masters. People may say what they want, no restrictions or sanctions really exist, because there is no single moral standard. The mood goes with the flow of a then prevalent influence. If the prevalent influence is somehow harmful or demoralizing, opportunists grab their chance to win over those with whom power truly resides in a democracy: the large majority of poor people. This opportunist leads the people into a rebellion against remaining (and new) oligarchs and proclaims himself as a protector of the people. Such a position can only be maintained with violence: war fare and extermination of critics. Critics will disapprove of the lack of freedom under patronage of the leader. The tyrannic leader has to surround himself with a large staff of protectors and  guards. Thus democracy ends in a tyranny. Plato compares the tyrant with a son killing his father: a popular leader brought forth by an enslaved people finally enslaves his people again. Living under tyranny is being enslaved by  slaves.

*The wrong moment: Plato gave an arithmetic explanation of ‘the wrong’ moment to give birth: the moral and intellectual potential of each newly born is determined by logarithmic succession of numbers: the Platonic nuptial number. All of it seems mystical; many explanations have been given. Most likely the nuptial number corresponds with the number 12,960,000, an important number in Babylonian numerology that equals 60^4 =12,960,000, but it may also correspond with Plato’s number of citizens for the ideal state: 1 x 2 x 3 x 4 x 5 x 6 x 7 = 5,040. The ideal period to give birth, however, consists of a lapse of 3, 4 and 5 months in a mathematical combination:

3^3 + 4^3 + 5^3 = 6^3 = 216. However, 3 + 4 + 5 = 12, which may be 12 months. The numbers 3, 4, and 5 can also be used as lengths of the lines in a triple. When we go further with new combinations, we arrive again at 12,960,000:

5 x 12 = 60

60 x 60 = 3,600

3,600 x 60 = 216,000

216,000 x 60 =12,960,000.

36 x 36 = 1296 and 100 x 100 = 10,000 and 1,296 x 10,000 = 12,960,000

A perfect square may have sides of each 3,600 and thus a surface of 12,960,000 in a relation of 1 : 1. The relation equals the harmony of unisound in music.

Then we add Pythagoras’ hypothesis on another perfect square, with sides of each 5 and corners named A, B, C and D and cut it in two at corners B and D:

AB^2 + AD^2 = BD^2

25 + 25 = 50.

The real length of BD, however, is 7. Plato used this problem to arrive at his nuptial number in another way:

BD^2 – 1 = √50^2 – 2 = 48.

(4800 x 100) x (2700 x 100) = 1,2960,000

‘The relation 4,800 : 3,600 is used in Greek music structure, now used in all music in the West: minor seventh’, a commentator on Plato said. (Stichting Ars Floreat Without entering a full disclosure of tone scales in western music: it consists of seven basic tones, called root tones, from A to G. Sometimes a tone scale starts at C, sometimes G, sometimes F, A, it depends on the intended mood of the music and the instrument. On a C scale we count from C to exactly the same, higher tone above it: C. In total eight notes. Between the root tones half tones exist. Major tone scales maintain a bigger distance between tones; chords or harmonies then have a more contrasting, higher, brighter sound; minor tone scales sound deeper, darker, more melancholic, sometimes dissonant,    because of smaller distance between tones, more half distances. Minor scales differ between second and third note only a half tone and major scales between third and fourth and between seventh and eighth note only a half note, generally speaking.

This extra elaboration on music and math has to do with Plato’s fascination for any correspondence between them; his use of numbers in geometry somehow corresponds with tone scales and he must have seen beauty in it and a philosophical lesson. Though many commentators have speculated about it.

Sources:
Works by Plato, The Internet Archive http://classics.mit.edu/Browse/browse-Plato.html
Wikipedia.org
Philebus http://classics.mit.edu/Plato/philebus.html
Plato’s Politeia http://www.arsfloreat.nl
http://mathsforeurope.digibel.be/story.htm
Suite101.com http://www.suite101.com/content/minor-seventh-chords-a113729
‘Wiskunde op het net’ http://wiskunde.ebrodesign.com/index.php?id=20&gr=1
Chord Mine http://www.chordmine.com/guitar-chords/chord/chord_3.aspx

 

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