Not only all of this is true but my car plate is 656009
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Sent: 04 April 2015 11:12
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Subject: [lit-ideas] All Philosophy Is Mathematics
In a message dated 4/3/2015 2:30:38 P.M. Eastern Daylight Time,
jejunejesuit.geary2@xxxxxxxxx writes: "I dislike Philosophy because it always
ends up as algebra. I like Literature because it has no algebra. I do truly
like these two [poems]-- among hundreds and hundreds hundreds of other. They
add up to nothing. That's OK, I hate algebra." EWF comments: "Literature
blows, philosophy sucks."
I think Geary is right: philosophy ends up as algebra. Only perhaps Plato
would prefer arithmetic (since 'algebra' is of later vintage). In "The
Republic", Plato cites two numbers: "216" and "12,960,000". The reason why
Plato cites these two numbers is obscure.
Plato notes that 216 is equal to the cube of "6", where "6" is the number for
marriage since it is the product to the female 2 and the male 3. Plato
adds: "And, as every schoolboy knows, 2 x 3 = 6. I propose to call "6" thus
the 'nuptial number'."
Plato is also aware of the fact the sum of the cubes of the 3-4-5 Pythagorean
triple is equal to 3^3+4^3+5^3 = 216 (Livio, p. 66). On the other hand
(usually, in Plato, the right hand), in "Laws", Plato suggests that "5,040"
is the optimal number of citizens in a state (e.g. Indiana).
This is because:
1. 5,040 is the product of 12, 20, and 21.
2. The 12th part of 5.040 can still be divided by 12.
3. 5.040 has 59 proper divisors, including all numbers for 1 to 12 except 11,
and 5038--which is very close to 5040--is divisible by 11.
But doubts remain. The Republic 8.546b is a notoriously difficult passage to
understand even in Greek ("or especially in Greek," Geary adds -- "I hate
algebra", which is Arabic in origin). Geary adds: "The corresponding
translations do not allow an unambiguous interpretation, either -- and then
you think Literature is subjective!" Indeed, there is no real agreement either
about the meaning or the value of this number Plato quotes.
Plato calls it the "geometrical number" and the "nuptial number" (in Greek,
literally, the "number of the bride"). The passage in which Plato introduced
the number has been discussed ever since it was written, with no consensus in
the debate.
As for the number's actual value, "216" is the most frequently proposed value
for it, but widely divergent numerals, such as "3,600" and "12,960,000" have
also commonly considered.
Authors who have studied Plato's number include: oAristotle, Proclus, Ficino,
Cardano, Zeller, Friedrich Schleiermacher, Paul Tannery, Friedrich Hultsch and
Geary ("I hate algebra"). Further in the Republic, in a different passage --
9.587b -- another puzzling number is mentioned, known as the "Number of the
Tyrant".
Great lexical and syntactical differences are easily noted between the many
translations of the Republic. This was NOT a problem for Plato, though.
Below is a typical text from a relatively recent translation of Republic 546b
–c:
"Now for divine begettings there is a period comprehended by a perfect number,
and for mortal by the first in which augmentations dominating and dominated
when they have attained to three distances and four limits of the assimilating
and the dissimilating, the waxing and the waning, render all things
conversable and commensurable [546c] with one another, whereof a basal
four-thirds wedded to the pempad yields two harmonies at the third
augmentation, the one the product of equal factors taken one hundred times,
the other of equal length one way but oblong,-one dimension of a hundred
numbers determined by the rational diameters of the pempad lacking one in each
case, or of the irrational lacking two; the other dimension of a hundred cubes
of the triad. And this entire geometrical number is determinative of this
thing, of better and inferior births."
The 'entire geometrical number', mentioned shortly before the end of this
text, is understood to be Plato's number. The introductory words mention (a
period comprehended by) 'a perfect number' which is taken to be a reference to
Plato's perfect year mentioned in his "Timaeus" (39d). The words are presented
as uttered by the muses, so the whole passage is sometimes called the 'speech
of the muses' or something similar. Indeed Philip Melanchthon compared it to
the proverbial obscurity of the Sibyls. Cicero famously described it as
'obscure' but others have seen some playfulness in its tone.
Shortly after Plato's time his meaning apparently did not cause puzzlement as
Aristotle's casual remark attests. In the Politics, Book V, 12, 8:
Aristotle writes: "Plato only says that nothing is abiding, but that all
things change in a certain cycle: and that the origin of the change is a base
of numbers which are in the ratio of 4:3 and this when combined with a figure
of five gives two harmonies: he means when the number of this figure becomes
solid."
Half a millennium later however it was an enigma for the Neoplatonists, who
had a somewhat mystic penchant and wrote frequently about it, proposing
geometrical and numerical interpretations. Next, for nearly a thousand years
Plato's texts disappeared and it is only in the Italian Renaissance that the
enigma briefly resurfaced.
During the 19th century, when classical scholars restored original texts, the
problem reappeared. Schleiermacher interrupted for a decade his edition of
Plato while attempting to make sense of the paragraph (He also took the
opportunity to visit Alaska on a cruise).
Victor Cousin inserted a note that it has to be skipped in his French
translation of Plato's works ("It serves no purpose to Frenchmen, as far as I
can see.") In the early 20th century scholarly findings suggested a Babylonian
origin for the topic.
Most interpretators argue that the value of Plato's number is "216"
because it is the cube of 6 i.e. 6^3=216 which is remarkable for being also a
sum of the cubes for the Pythagorean triple 3,4,and 5:
3^3+4^3+5^3=6^3.\, Such considerations tend to ignore the second part of the
text where some others numbers and their relations are described. The
opinions tend to converge about their values being "480,000" and "270,000"
but there is little agreement about the details.
It has been noted that 6 raised to fourth power yields 1296 and 48 \times
27=36 \times 36=1296.
Instead of multiplication some interpretations consider the sum of these
factors: 48+27=75.
Other values that have been proposed include: Otto Weber: 17 500= 100\times
100 + 4800 + 2700.
760 000= 750000 +10000= 19\times 4\times 10000 , 19 being obtained from
(\tfrac{4}{3}+5)\times 3 and it is the number of years in the Metonic cycle.
8128=2^6 \cdot (2^7-1), a "perfect number" proposed by Cardano -- "and my wife
agrees," he adds (His wife was a Renaissance woman).
It is known that such numbers can be decomposed in the sum of consecutive odd
cubes, so 8128=1³+3³+5³+...+15³
1728=12^3=8 \cdot 12 \cdot 18 by Marsilio Ficino in 1496.
5040 =144 \times 35=(3+4+5)^2 \cdot (2^3+3^3) -- Jacob Friedrich Fries in 1823.
Cheers,
Speranza
References
Allen M., Nuptial Arithmetic:Marsilio Ficino's Commentary on the Fatal Number
in Book VIII of Plato's Republic, UCLA.
Barton G., On the Babylonian Origin of Plato's Nuptial Number, Journal of the
American Oriental Society, v.29.
Cicero, Selectae declamationes. Declamatio de periodis imperiorum, Diès A., Le
Nombre de Platon: Essai d'exégèse et d'Histoire, Paris.
Donaldson J., "On Plato's Number", Proceedings of the Philological Society,
vol.1.
Dumbrill R., Four Mathematical Texts from the Temple Library of Nippur: a
source for Plato's number.
Dupuis J., Le Nombre Geometrique de Platon, Paris: Hachette.
Weber O., De Numero Platonis, Cassel: Programm fur Shuljahre 1861/2, Lyceum
Fredericianum, 1862 Adam J., The nuptial number of Plato: its solution and
significance,
London: C.J. Clay and Sons
Laird, A.G., Plato's Geometrical Number and the Comment of Proclus, The
Collegiate
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