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 neither about the meaning nor about the value of the number. It has been called also the 'Geometrical number' or the 'Nuptial number' (the Number of the Bride’’),and designated by various other means. Comments on this passage have appeared ever since it has been written. Without any consensus in the argumentation 216 is a most frequently proposed value for it, but 3600 or 12960000 are also commonly considered.

An incomplete list [1] 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 c. and further new names are currently added [2].

Further in the Republic (9.587b) another number is mentioned, known as the "Number of the Tyrant".

Contents

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 [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."[3]

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[2][4]. Indeed Philip Melanchthon compared it to the proverbial obscurity of the Sybils[5]. Cicero famously described it as 'obscure' but others have seen some playfulness in its tone [1].

Interpretations

Shortly after Plato's time his meaning apparently did not cause puzzlement as Aristotle's casual remark attests[6]. Half a millenium 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 an it is only in the 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. Victor Cousin inserted a note that it has to be skipped in his French translation of Plato's works. In the early 20th c. scholarly findings suggested a Babylonian origin for the topic[7].

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%2B4^3%2B5^3=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 480000 and 270000 but there is little agreement about the details. It has been noted that 6 raised to fourth power yields 1296 and 48x27=36x36=1296. Instead of multiplication some interpretations consider the sum of these factors: 48+27=75.

Other values that have been proposed include:

References

  1. ^ a b c d for more names and references see Dupuis J., Le Nombre Geometrique de Platon, Paris: Hachette, 1885
  2. ^ a b 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
  3. ^ Translation by Paul Shorey, Plato: The Collected Dialogues, Eds. Edith Hamilton & Huntington Cairns, Princeton University Press, Princeton, N. J., 1961, (p.775)
  4. ^ Erhardt E., The word of the muses, Classical Quarterly (New Series) (1986), 36: 407-420
  5. ^ Selectae declamationes. Declamatio de periodis imperiorum, v.3, p. 722, Strasbourg, 1559
  6. ^ Aristotle, Politics, Book V, 12, 8: "He 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."
  7. ^ Barton G., On the Babylonian Origin of Plato's Nuptial Number, Journal of the American Oriental Society, v.29, (1908), p.210-9
  8. ^ Weber O., De Numero Platonis, Cassel: Programm fur Shuljahre 1861/2, Lyceum Fredericianum, 1862
  9. ^ Allen M., Nuptial Arithmetic:Marsilio Ficino's Commentary on the Fatal Number in Book VIII of Plato's Republic, UCLA 1994, p75ff.

Further Reading

External links