Theon of Smyrna

Theon of Smyrna ( ancient Greek Θέων Théōn ; † after 132) was an ancient Greek philosopher ( Platonist ), mathematician and astronomer from Smyrna (today İzmir in Turkey, port city on the Aegean coast ). He lived under Emperor Hadrian .

identity

The identity of the philosopher Theon with the mathematician of this name, whom Klaudios Ptolemaios quoted in his Syntaxis ( Almagest ) and whom Theon of Alexandria called the "old Theon" in his Almagest commentary in the 4th century , was previously doubted. Today, however, it is considered very likely. Ptolemy mentions Theon's observations of Venus and Mercury in the period 127–132. Otherwise nothing is known about Theon's life, but his appearance is known thanks to a bust that his son of the same name had made (today in the Capitoline Museums , Rome).

Works

A page from Theon's book The Mathematical Knowledge Useful for Reading Plato in a 12th century manuscript owned by Cardinal Bessarion . Venice, Biblioteca Nazionale Marciana , Gr. 307, fol. 98v

Only one of Theon's writings has survived, the work The mathematical knowledge useful for reading Plato's . It is a general introduction to mathematics, music theory, and astronomy for the needs of Plato readers. It contains valuable quotations from lost older literature. Theon names numerous authors from whom he draws his knowledge, and reports on their views, often leaving contradictions without trying to clear up or take a position. In the first part he deals with arithmetic and music and goes into detail on the Pythagorean Tetraktys . In the second, more extensive part, he deals with astronomy. The topics include evidence of the spherical shape of the earth, the determination of the earth's circumference, the planetary orbits and the explanation of solar and lunar eclipses. Theon also deals with the harmony of the spheres , but there is no separate treatment of this topic, which has been repeatedly announced for the end, which gives rise to the assumption that the work is incomplete.

Theon also wrote two other works: a commentary on Plato's dialogue Politeia , which has not survived, and a text on the order in which one should read Plato's works and on their titles. This writing, probably an introduction to Plato's works, was available in the 10th century to the scholar ibn an-Nadīm , who used it in his kitāb al-Fihrist . It is only preserved in fragments in Arabic translation. In this work Theon dealt with the order of tetralogies , the division of Plato's works into groups of four; It probably also contained a biography of Plato, from which passages in Arabic translation have come down to us.

philosophy

Theon compares the immersion in Platonic philosophy with five levels of initiation into the mysteries of Eleusis, which he assumed . The first stage is purification; it happens "from child up" by practicing the mathematical teachings that prepare for philosophy ( propaedeutics ). Theon understands the “mathematical sciences”, following Plato's explanations in the Politeia , to be arithmetic, geometry (that is, planimetry ), stereometry , music theory and astronomy. The second stage, the reception of consecration in the mysteries, consists in Platonism in communicating the philosophical teachings of Plato (logic, political philosophy , natural philosophy ). The third level of the mysteries, the “vision” ( epopteía ), corresponds to the preoccupation with ideas , which is also understood as a vision. The fourth stage in the mysteries is the putting on of the head bandages and the wreath, which expresses that the initiate can pass on the ordinations he has received. In Platonism it corresponds to the acquisition of the ability to teach philosophy, which enables others to see. The fifth and final stage in both the mysteries and philosophy is eudaimonia (bliss). In the Mysteries it is achieved through the now possible contact with the gods, in Platonism - as Theon expresses it with a phrase from Plato - through "assimilation to God as far as possible". Theon's scheme of the initiation rites of the Mysteries, however, differs from the actual course in Eleusis.

mathematics

"Theon's Head"

In his book Das an Mathematischen Wissen für die Plato ( Theory of Mathematical Knowledge Useful for Reading Plato) , Theon describes a mathematical method that is suitable for determining the relationship between “side numbers” and “diagonal numbers”, namely the side of the square to its diagonal. First he notes that the unit (1) as the origin of all numbers is both the side and the diagonal. This gives him the first approximate value: side number 1 and diagonal number also 1. Then he takes two units, one side and one diagonal unit. A new page is created by adding the diagonal unit to the side unit, and a new diagonal by adding the side unit twice to the diagonal unit: 1 + 1 = 2, 1 + 2 = 3 The new page number is therefore 2, the new diagonal number 3. For the next page number, the previous page number and the previous diagonal number are added, i.e. 2 + 3 = 5, and for the next diagonal number the previous diagonal number and twice the previous page number, i.e. 3 + 2 × 2 = 7.

This method provides an approximation if the diagonal number is divided by the corresponding page number. The quotients approach the value by alternately supplying a lower and an upper limit for the root. The method can easily be generalized to compute arbitrary square roots. It is called "Theon's Ladder" in English; each quotient forms one rung of the "ladder". ${\displaystyle {\sqrt {2}}}$ ${\displaystyle y_{n}/x_{n}}$ ${\displaystyle {\sqrt {2}}}$

The starting point for Theon were Plato's considerations about the “wedding number” in the Politeia . Proclus later followed up on this in his commentary on the Politeia , where he cites the same procedure as Theon.

Theon only describes the procedure but offers no proof.

astronomy

Theon mentions that he constructed a model of the celestial spheres based on Plato's information. He is convinced that a correct astronomical theory not only enables calculations that agree with the observation results, but also faithfully reproduces physical reality. When comparing the Babylonian and Egyptian astronomy with the Greek, he points out that only the Greek includes "physiology", i.e. establishing a relationship between the calculations and the physical basis of astronomy.

reception

In the Islamic world, Theon's now-lost work on the order in which one should read Plato's works and their titles was still accessible in the Middle Ages. It was used by ibn an-Nadīm in the 10th century and later by ibn al-Qifṭī (1172-1248).

The moon crater Theon Senior is named after Theon .

Text editions and translations

• Jean Dupuis (ed.): Théon de Smyrne: Exposition des connaissances mathématiques utiles pour la lecture de Platon . Culture et civilization, Bruxelles 1966 (reprint of the Paris 1892 edition; Greek text and French translation; online )
• Eduard Hiller (Ed.): Theonis Smyrnaei philosophi Platonici expositio rerum mathematicarum ad legendum Platonem utilium . Teubner, Stuttgart 1995, ISBN 3-519-01853-5 (reprint of the Leipzig 1878 edition; critical edition without translation; online )
• Robert Lawlor, Deborah Lawlor (translator): Theon of Smyrna, Mathematics Useful for Understanding Plato . Wizards Bookshelf, San Diego 1979 (English translation)

literature

Overview representations in manuals

• Franco Ferrari: Theon of Smyrna. In: Christoph Riedweg et al. (Hrsg.): Philosophy of the imperial era and late antiquity (= outline of the history of philosophy . The philosophy of antiquity. Volume 5/1). Schwabe, Basel 2018, ISBN 978-3-7965-3698-4 , pp. 580-583, 686 f.
• Kurt von Fritz : Theon from Smyrna. In: Paulys Realencyclopadie der classischen Antiquity Science (RE). Volume VA, 2, Stuttgart 1934, Sp. 2067-2075.
• Federico M. Petrucci, Jörn Lang: Théon de Smyrne. In: Richard Goulet (ed.): Dictionnaire des philosophes antiques. Volume 6, CNRS Éditions, Paris 2016, ISBN 978-2-271-08989-2 , pp. 1016-1028

Investigations

• Joëlle Delattre: Théon de Smyrne: modèles mécaniques en astronomie . In: Gilbert Argoud, Jean-Yves Guillaumin (eds.): Sciences exactes et sciences appliquées à Alexandrie . Publications de l'Université de Saint-Étienne, Saint-Étienne 1998, ISBN 2-86272-120-4 , pp. 371-395.
• Luca Simeoni: Teone di Smirne e le scienze esatte . In: Elenchos 21, 2000, pp. 271-302.
• George Clarence Vedova: Notes on Theon of Smyrna . In: The American Mathematical Monthly 58, 1951, pp. 675-683

Web links

• John J. O'Connor, Edmund F. Robertson :  Theon of Smyrna. In: MacTutor History of Mathematics archive .

Remarks

1. ^ Gisela MA Richter : The Portraits of the Greeks , Vol. 3, London 1965, p. 285 and illustration 2038.
2. ↑ On the structure of Theon's presentation of music and astronomy see Joëlle Delattre-Biencourt, Daniel Delattre: La théorie de la musique et de l'astronomie d'après Théon de Smyrne . In: Carlos Lévy u. a. (Ed.): Ars et ratio , Bruxelles 2003, pp. 243-258, here: 244-248.
3. ↑ Michael R. Dunn: The organization of the Platonic corpus between the first century BC and the second century AD , Yale 1974 (dissertation), pp. 120-126, 130-141; Harold Tarrant: Thrasyllan Platonism , Ithaca 1993, pp. 58-84.
4. ^ Heinrich Dörrie , Matthias Baltes : The Platonism in the Ancient World , Vol. 4, Stuttgart-Bad Cannstatt 1996, pp. 36–39 (Greek text and translation), 250–253 (commentary); Harold Tarrant: Thrasyllan Platonism , Ithaca 1993, pp. 98-103; Christoph Riedweg : Mystery terminology in Plato, Philon and Klemens von Alexandrien , Berlin 1987, pp. 125–127.
5. ↑ See on Theon's understanding of this method Árpád Szabó : Beginnings of Greek Mathematics , Munich 1969, pp. 272–275; David H. Fowler: The Mathematics of Plato's Academy , Oxford 1987, pp. 58 f., 100-104.
6. ↑ Plato, Politeia 546b – d.
7. ↑ Theon von Smyrna, The usefulness of mathematical knowledge for reading Plato's , ed. Eduard Hiller, Leipzig 1878, p. 146, line 4 f.
8. ^ Geoffrey ER Lloyd : Saving the Appearances . In: The Classical Quarterly NS 28, 1978, pp. 202-222, here: 218.
9. ↑ Michael R. Dunn: The organization of the Platonic corpus between the first century BC and the second century AD , Yale 1974 (dissertation), pp. 120-126; Harold Tarrant: Thrasyllan Platonism , Ithaca 1993, p. 59 f.