Plato's number

Last updated

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.

Contents

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".

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 546bc:

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

An illustrated interpretation of Plato's number as 33 + 43 + 53 = 63 Plato number.svg
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:

See also

Related Research Articles

<span class="mw-page-title-main">Marsilio Ficino</span> Italian philosopher and Catholic priest (1433–1499)

Marsilio T. Ficino was an Italian scholar and Catholic priest who was one of the most influential humanist philosophers of the early Italian Renaissance. He was an astrologer, a reviver of Neoplatonism in touch with the major academics of his day, and the first translator of Plato's complete extant works into Latin. His Florentine Academy, an attempt to revive Plato's Academy, influenced the direction and tenor of the Italian Renaissance and the development of European philosophy.

<span class="mw-page-title-main">Plato</span> Greek philosopher (c. 427 – 348 BC)

Plato, born Aristocles, was an ancient Greek philosopher of the Classical period who is considered a foundational thinker in Western philosophy and an innovator of the written dialogue and dialectic forms. He raised problems for what became all the major areas of both theoretical philosophy and practical philosophy, and was the founder of the Platonic Academy, a philosophical school in Athens where Plato taught the doctrines that would later become known as Platonism.

<span class="mw-page-title-main">Proclus</span> 5th-century Greek Neoplatonist philosopher

Proclus Lycius, called Proclus the Successor, was a Greek Neoplatonist philosopher, one of the last major classical philosophers of late antiquity. He set forth one of the most elaborate and fully developed systems of Neoplatonism and, through later interpreters and translators, exerted an influence on Byzantine philosophy, Early Islamic philosophy, Scholastic philosophy, and German Idealism, especially G.W.F. Hegel, who called Proclus's Platonic Theology "the true turning point or transition from ancient to modern times, from ancient philosophy to Christianity."

<span class="mw-page-title-main">Gemistos Plethon</span> 15th-century Byzantine Greek philosopher

Georgios Gemistos Plethon, commonly known as Gemistos Plethon, was a Byzantine scholar and one of the most renowned philosophers of the late Byzantine era. He was a chief pioneer of the revival of Greek scholarship in Western Europe. As revealed in his last literary work, the Nomoi or Book of Laws, which he circulated only among close friends, he rejected Christianity in favour of a return to the worship of the classical Hellenic gods, mixed with ancient wisdom based on Zoroaster and the Magi.

<span class="mw-page-title-main">Cube (algebra)</span> Number raised to the third power

In arithmetic and algebra, the cube of a number n is its third power, that is, the result of multiplying three instances of n together. The cube of a number or any other mathematical expression is denoted by a superscript 3, for example 23 = 8 or (x + 1)3.

<span class="mw-page-title-main">Renaissance philosophy</span> Period of European thought (1355–1650)

The designation "Renaissance philosophy" is used by historians of philosophy to refer to the thought of the period running in Europe roughly between 1400 and 1600. It therefore overlaps both with late medieval philosophy, which in the fourteenth and fifteenth centuries was influenced by notable figures such as Albert the Great, Thomas Aquinas, William of Ockham, and Marsilius of Padua, and early modern philosophy, which conventionally starts with René Descartes and his publication of the Discourse on Method in 1637.

<i>Parmenides</i> (dialogue) Dialogue by Plato

Parmenides is one of the dialogues of Plato. It is widely considered to be one of the most challenging and enigmatic of Plato's dialogues. The Parmenides purports to be an account of a meeting between the two great philosophers of the Eleatic school, Parmenides and Zeno of Elea, and a young Socrates. The occasion of the meeting was the reading by Zeno of his treatise defending Parmenidean monism against those partisans of plurality who asserted that Parmenides' supposition that there is a one gives rise to intolerable absurdities and contradictions. The dialogue is set during a supposed meeting between Parmenides and Zeno of Elea in Socrates' hometown of Athens. This dialogue is chronologically the earliest of all as Socrates is only nineteen years old here. It is also notable that he takes the position of the student here while Parmenides serves as the lecturer.

Syrianus was a Greek Neoplatonist philosopher, and head of Plato's Academy in Athens, succeeding his teacher Plutarch of Athens in 431/432 A.D. He is important as the teacher of Proclus, and, like Plutarch and Proclus, as a commentator on Plato and Aristotle. His best-known extant work is a commentary on the Metaphysics of Aristotle. He is said to have written also on the De Caelo and the De Interpretatione of Aristotle and on Plato's Timaeus.

In Plato's Ion Socrates discusses with the titular character, a professional rhapsode who also lectures on Homer, the question of whether the rhapsode, a performer of poetry, gives his performance on account of his skill and knowledge or by virtue of divine possession. It is one of the shortest of Plato's dialogues.

216 is the natural number following 215 and preceding 217. It is a cube, and is often called Plato's number, although it is not certain that this is the number intended by Plato.

<span class="mw-page-title-main">Platonism</span> Philosophical system

Platonism is the philosophy of Plato and philosophical systems closely derived from it, though contemporary Platonists do not necessarily accept all doctrines of Plato. Platonism has had a profound effect on Western thought. At the most fundamental level, Platonism affirms the existence of abstract objects, which are asserted to exist in a third realm distinct from both the sensible external world and from the internal world of consciousness, and is the opposite of nominalism. This can apply to properties, types, propositions, meanings, numbers, sets, truth values, and so on. Philosophers who affirm the existence of abstract objects are sometimes called Platonists; those who deny their existence are sometimes called nominalists. The terms "Platonism" and "nominalism" also have established senses in the history of philosophy. They denote positions that have little to do with the modern notion of an abstract object.

<i>Philebus</i> Work by the ancient Greek philosopher Plato

The Philebus is a work by the ancient Greek philosopher Plato, written in dialogue form. It presents a fictional conversation between Plato's teacher Socrates and two young Athenians, Philebus and Protarchus. The main topic is the ethical evaluation of pleasure.

Neoplatonism was a major influence on Christian theology throughout Late Antiquity and the Middle Ages in the East, and sometimes in the West as well. In the East, major Greek Fathers like Basil, Gregory of Nyssa and Gregory of Nazianzus were influenced by Platonism and Neoplatonism, but also Stoicism often leading towards asceticism and harsh treatment of the body, for example stylite asceticism. In the West, St. Augustine of Hippo was influenced by the early Neoplatonists Plotinus and Porphyry. Later on, in the East, the works of the Christian writer Pseudo-Dionysius the Areopagite, who was influenced by later Neoplatonists such as Proclus and Damascius, became a critical work on which Greek church fathers based their theology, like Maximus believing it was an original work of Dionysius the Areopagite.

Commentaries on Plato refers to the great mass of literature produced, especially in the ancient and medieval world, to explain and clarify the works of Plato. Many Platonist philosophers in the centuries following Plato sought to clarify and summarise his thoughts, but it was during the Roman era, that the Neoplatonists, in particular, wrote many commentaries on individual dialogues of Plato, many of which survive to the present day.

Neoplatonism is a version of Platonic philosophy that emerged in the 3rd century AD against the background of Hellenistic philosophy and religion. The term does not encapsulate a set of ideas as much as a series of thinkers. Among the common ideas it maintains is monism, the doctrine that all of reality can be derived from a single principle, "the One".

<i>Definitions</i> (Plato) Dictionary of 184 philosophical terms

The Definitions is a dictionary of 184 philosophical terms sometimes included in the corpus of Plato's works. Plato is generally not regarded as the editor of all of Definitions. Some ancient scholars attributed Definitions to Speusippus.

The Platonic Theology is a work consisting of eighteen books by Marsilio Ficino. Ficino wrote it between 1469 and 1474 and it was published in 1482. It has been described as Ficino's philosophical masterpiece.

<span class="mw-page-title-main">Allegorical interpretations of Plato</span>

Many interpreters of Plato held that his writings contain passages with double meanings, called allegories, symbols, or myths, that give the dialogues layers of figurative meaning in addition to their usual literal meaning. These allegorical interpretations of Plato were dominant for more than fifteen hundred years, from about the 1st century CE through the Renaissance and into the 18th century, and were advocated by major Platonist philosophers such as Plotinus, Porphyry, Syrianus, Proclus, and Marsilio Ficino. Beginning with Philo of Alexandria, these views influenced the Jewish, Christian, and Islamic interpretation of these religions' respective sacred scriptures. They spread widely during the Renaissance and contributed to the fashion for allegory among poets such as Dante Alighieri, Edmund Spenser, and William Shakespeare.

Plato's so-called unwritten doctrines are metaphysical theories ascribed to him by his students and other ancient philosophers but not clearly formulated in his writings. In recent research, they are sometimes known as Plato's 'principle theory' because they involve two fundamental principles from which the rest of the system derives. Plato is thought to have orally expounded these doctrines to Aristotle and the other students in the Academy and they were afterwards transmitted to later generations.

Okhêma refers to the "carrier" or "vehicle" of the soul, serving as the intermediary between the body and the soul, in Neoplatonism and the philosophical traditions it influenced.

References

  1. 1 2 3 4 for more names and references see Dupuis J., Le Nombre Geometrique de Platon, Paris: Hachette, 1885
  2. 1 2 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