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.
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 Sibyls.[5]Cicero famously described it as 'obscure' but others have seen some playfulness in its tone.[1]
Interpretationsedit
An illustrated interpretation of Plato's number as 3³ + 4³ + 5³ = 6³
Shortly after Plato's time his meaning apparently did not cause puzzlement as Aristotle's casual remark attests.[6] 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 Renaissance that the enigma briefly resurfaced. During the 19th century, when classical scholars restored original texts, the problem reappeared. Schleiermacher interrupted his edition of Plato for a decade 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 century, scholarly findings suggested a Babylonian origin for the topic.[7]
Most interpreters argue that the value of Plato's number is 216 because it is the cube of 6, i.e. 63 = 216, which is remarkable for also being the sum of the cubes for the Pythagorean triple (3, 4, 5): 33 + 43 + 53 = 63.
Such considerations tend to ignore the second part of the text where some other 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 64 yields 1296 and 48 × 27 = 36 × 36 = 1296. Instead of multiplication some interpretations consider the sum of these factors: 48 + 27 = 75.
Other values that have been proposed include:
17,500 = 100 × 100 + 4800 + 2700, by Otto Weber (1862).[8]
760,000 = 750,000 + 10,000 = 19 × 4 × 10000, 19 being obtained from (4/3 + 5) × 3 and being the number of years in the Metonic cycle.[1]
8128 = 26 × (27 − 1), a perfect number proposed by Cardano. It is known that such numbers can be decomposed into the sum of consecutive odd cubes, so 8128 = 13 + 33 + 53 + ... + 153.
^ abcdfor more names and references see Dupuis J., Le Nombre Geometrique de Platon, Paris: Hachette, 1885
^ abMcNamee 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
^Translation by Paul Shorey, Plato: The Collected Dialogues, Eds. Edith Hamilton & Huntington Cairns, Princeton University Press, Princeton, N. J., 1961, (p.775)
^Erhardt E., The word of the muses, Classical Quarterly (New Series) (1986), 36: 407-420
^Selectae declamationes. Declamatio de periodis imperiorum, v.3, p. 722, Strasbourg, 1559
^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."
^Barton G., On the Babylonian Origin of Plato's Nuptial Number, Journal of the American Oriental Society, v.29, (1908), p.210-9
^Weber O., De Numero Platonis, Cassel: Programm fur Shuljahre 1861/2, Lyceum Fredericianum, 1862
^Allen M., Nuptial Arithmetic:Marsilio Ficino's Commentary on the Fatal Number in Book VIII of Plato's Republic, UCLA 1994, p75ff.
Further readingedit
Donaldson J., "On Plato's Number", Proceedings of the Philological Society, vol.1, iss. 8, p. 81-90, April 7, 1843
Adam J., The nuptial number of Plato: its solution and significance, London: C.J. Clay and Sons, 1891.
Laird, A.G., Plato's Geometrical Number and the Comment of Proclus, The Collegiate Press, George Banta Publishing Company, Menasha, Wisconsin. 1918
Diès A., Le Nombre de Platon: Essai d'exégèse et d'Histoire, Paris 1936
Allen M., Nuptial Arithmetic: Marsilio Ficino's Commentary on the Fatal Number in Book VIII of Plato's Republic UCLA 1994
Dumbrill R., Four Mathematical Texts from the Temple Library of Nippur: a source for Plato's number, ARANE 1 (2009): 27-37 [1]
plato, number, number, enigmatically, referred, plato, dialogue, republic, 546b, text, notoriously, difficult, understand, corresponding, translations, allow, unambiguous, interpretation, there, real, agreement, either, about, meaning, value, number, also, bee. 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 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 century 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 1 Plato s text 2 Interpretations 3 See also 4 References 5 Further reading 6 External linksPlato s text editGreat 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 Sibyls 5 Cicero famously described it as obscure but others have seen some playfulness in its tone 1 Interpretations edit nbsp An illustrated interpretation of Plato s number as 3 4 5 6 Shortly after Plato s time his meaning apparently did not cause puzzlement as Aristotle s casual remark attests 6 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 Renaissance that the enigma briefly resurfaced During the 19th century when classical scholars restored original texts the problem reappeared Schleiermacher interrupted his edition of Plato for a decade 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 century scholarly findings suggested a Babylonian origin for the topic 7 Most interpreters argue that the value of Plato s number is 216 because it is the cube of 6 i e 63 216 which is remarkable for also being the sum of the cubes for the Pythagorean triple 3 4 5 33 43 53 63 Such considerations tend to ignore the second part of the text where some other 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 64 yields 1296 and 48 27 36 36 1296 Instead of multiplication some interpretations consider the sum of these factors 48 27 75 Other values that have been proposed include 17 500 100 100 4800 2700 by Otto Weber 1862 8 760 000 750 000 10 000 19 4 10000 19 being obtained from 4 3 5 3 and being the number of years in the Metonic cycle 1 8128 26 27 1 a perfect number proposed by Cardano It is known that such numbers can be decomposed into the sum of consecutive odd cubes so 8128 13 33 53 153 1728 123 8 12 18 by Marsilio Ficino 1496 9 5040 144 35 3 4 5 2 23 33 by Jacob Friedrich Fries 1823 1 See also editEuler s sum of powers conjectureReferences edit a b c d for more names and references see Dupuis J Le Nombre Geometrique de Platon Paris Hachette 1885 a b McNamee K and Jacovides M Annotations to the Speech of the Muses Plato Republic 546B C Zeitschrift fur Papyrologie und Epigraphik Bd 144 2003 pp 31 50 Translation by Paul Shorey Plato The Collected Dialogues Eds Edith Hamilton amp Huntington Cairns Princeton University Press Princeton N J 1961 p 775 Erhardt E The word of the muses Classical Quarterly New Series 1986 36 407 420 Selectae declamationes Declamatio de periodis imperiorum v 3 p 722 Strasbourg 1559 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 Barton G On the Babylonian Origin of Plato s Nuptial Number Journal of the American Oriental Society v 29 1908 p 210 9 Weber O De Numero Platonis Cassel Programm fur Shuljahre 1861 2 Lyceum Fredericianum 1862 Allen M Nuptial Arithmetic Marsilio Ficino s Commentary on the Fatal Number in Book VIII of Plato s Republic UCLA 1994 p75ff Further reading editDonaldson J On Plato s Number Proceedings of the Philological Society vol 1 iss 8 p 81 90 April 7 1843 Adam J The nuptial number of Plato its solution and significance London C J Clay and Sons 1891 Laird A G Plato s Geometrical Number and the Comment of Proclus The Collegiate Press George Banta Publishing Company Menasha Wisconsin 1918 Dies A Le Nombre de Platon Essai d exegese et d Histoire Paris 1936 Allen M Nuptial Arithmetic Marsilio Ficino s Commentary on the Fatal Number in Book VIII of Plato s Republic UCLA 1994 Dumbrill R Four Mathematical Texts from the Temple Library of Nippur a source for Plato s number ARANE 1 2009 27 37 1 External links editFive translations of Rep 8 546 and 9 587 Weisstein Eric W Plato s Numbers MathWorld Ramanujan And The Cubic Equation 33 43 53 63 Math world Diophantine Equation 3rd Powers Sum of Consecutive Cubes Equals a Cube Retrieved from https en wikipedia org w index php title Plato 27s number amp oldid 1162941851, wikipedia, wiki, book, books, library,
