mikeh wrote: 07 Sep 2018, 12:43
Another example of Pythagoreanism being used in relation to the tarot, I think, is in Piscina's Discorso, 1565 Piedmont, although only about the four suits of Swords, Batons, Cups, and Coins. It sounds more Pythagorean in the original than in the published translation. He says:
ora perchè più presto in numero quadernario che in altro potremo dire come in più perfetto anzi perfettissimo de gl'altri si come fra tutti & ispetialmente moderni il dottissimo Ficino ha scritto nel argomento fatto sopra il Timeo di Platone dal XX. Fino al 24. Cap.
And the published translation
Now why in the number of four and not another we can say because it is more perfect than all the others. Among all, and especially modern writers, this has been explained by the very learned Ficino in his discussion on Plato's Timaeus from chapters XX to 24.
A literal reading of "numero quadernario" would be "quaternary number", a Pythagorean way of talking although not exclusively so, since it is seen in Euclid, etc. But in the number theory handed down from Euclid four is decidedly not a perfect number. A perfect number is one that is the sum of its divisors, including 1or half the sum of its divisors if the number itself is included. So the first perfect number is 6, which is 1 + 2 + 3, or half of 1+2 +3+6. The next one is 28, which is 1+2+4+7+14. The divisors of 10 are 1+2+5 = 8, which falls short.
Why would Piscina call 4 a perfect number? To my knowledge Plato does not say anything of the sort in the Timaeus
, however much otherwise that work shows much Pythagorean influence. But Ficino in his commentaries brings to bear all of his learning to the text in question. Perhaps the answer is somewhere in Ficino's book. There is an English translation of Ficino's Commentary on Plato's Timaeus
, but it is not available in any library near me. I am hoping to get it from Interlibrary Loan. Until then, I offer the following speculation.
Aristotle in his Metaphysics
Book 1 Section 5 discusses the Pythagoreans. Among other things he makes fun of them, saying they invent things when their theory requires it. So we have, in the medieval Latin translation available online (http://www.logicmuseum.com/wiki/Authors ... #Chapter_5
Dico autem puta quoniam perfectus denarius esse videtur et omnem comprehendere numerorum naturam, et quae secundum celum feruntur decem quidem esse dicunt. Solum autem novem existentibus manifestis, ideo antixthonam decimam faciunt.
In W. D. Ross's translation:
E.g. as the number 10 is thought to be perfect and to comprise the whole nature of numbers, they say that the bodies which move through the heavens are ten, but as the visible bodies are only nine, to meet this they invent a tenth—the ‘counter-earth’.
Aristotle is no mathematician, and the Greek word translated as "perfect", τέλειον, teleios, also means "brought to its end, finished", which is surely the sense here (https://www.biblestudytools.com/lexicon ... leios.html
). After ten (deka), the next number is "10+1", in Greek deka + en, or 'hendeka", and so on (http://phrontistery.info/numbers.html
). Actually, twenty was not a compound of "two" and something meaning "tens", but something new, "eikosi". But that is a small point. The numbers in Greek did repeat one through nine every ten of them.
Piscina does not say that ten is a perfect number; he says "four". My hypothesis is that he is thinking of the "tetraktys", a uniquely Pythagorean notion, a triangle made of dots that shows ten as the sum of the first four numbers. While the tetraktys is 10, it also contains within it "tetra", meaning 4 (what -ktys meant, I have no idea). According to Wikipedia the Pythagoreans also called the tetraktys "the Mystical Tetrad".
That is my hypothesis for how 4 becomes a perfect number, an eminently Pythagorean notion somewhat lost in translation. If I am able to get the Ficino, I will say more.