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Plato's number : ウィキペディア英語版
Plato's number
Plato’s number is a number enigmatically referred to by Plato in his dialogue the ''Republic'' (8.546b). The text is notoriously difficult to understand and its corresponding translations do not allow an unambiguous interpretation. There is no real agreement either about the meaning or the value of the number. It also has been called the "geometrical number" or the "nuptial number" (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 3,600 or 12,960,000 are also commonly considered.
An incomplete list 〔for more names and references see Dupuis J., ''Le Nombre Geometrique de Platon'', Paris: Hachette, 1885〕 of authors who mention or discourse about includes the names of Aristotle, Proclus for antiquity; Ficino and Cardano during the Renaissance; Zeller, Friedrich Schleiermacher, Paul Tannery and Friedrich Hultsch in the 19th century and further new names are currently added.〔McNamee K., and Jacovides M., '' Annotations to the Speech of the Muses (Plato "Republic" 546B-C)'', Zeitschrift für Papyrologie und Epigraphik, Bd. 144, (2003), pp. 31-50〕
Further in the ''Republic'' (9.587b) another number is mentioned, known as the "Number of the Tyrant".
==Plato's text==
Great lexical and syntactical differences are easily noted between the many translations of the ''Republic''. 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 () 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."〔Translation by Paul Shorey, ''Plato: The Collected Dialogues'', Eds. Edith Hamilton & Huntington Cairns, Princeton University Press, Princeton, N. J., 1961, (p.775)〕

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.〔〔Erhardt E., ''The word of the muses'', ''Classical Quarterly'' (New Series) (1986), 36: 407-420〕 Indeed, Philip Melanchthon compared it to the proverbial obscurity of the Sibyls.〔''Selectae declamationes. Declamatio de periodis imperiorum'', v.3, p. 722, Strasbourg, 1559〕 Cicero famously described it as 'obscure' but others have seen some playfulness in its tone.〔

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