Plato, Republic VIII 545d5 - 546d3, containing the famous "Wedding Number"
What is it about?
Even though the reviewed book was published by renowned Georg Olms Verlag which has since decades a good record in its series “Altertumswissenschaftliche Texte und Studien” (“Texts and Studies in Antiquity Sciences”), this particular work cannot be considered very well-done. The main reason for this negative outcome probably is that the author lacks specific knowledge and qualification records in antiquity sciences, rather working as a medical doctor near Zurich (Switzerland) with an apparent inclination towards alternative medicine. The reviewer tried to escape the dilemma produced by this fact by resorting to humor and an ironical view on the book; in addition, there are many florilegia in Seiler´s book (cited by the reviewer) which make one smile at least. There yet is a reason for serious consideration of this book, namely its containing certain valuable pieces of information inspiring ongoing research on Plato and his work. However, it took sizable effort by the reviewer to extract these positive features by background research to get those pieces of information shining light on Plato´s original text. The key topic which is the Platonic Number or Wedding Number (in German referred to as “Hochzeitszahl” in both Seiler´s and Fränzle´s work) is dealt with in chapter 5 of the book “Solons Götter – Platons Theologie” (Solon´s Gods – Plato´s theology) by the reviewer which is to appear in print very soon (cp. FN 13 of full-length review). The reviewer´s criticism concerns two different levels, both formal and content: 1) Form: There are technical shortcomings concerning (missing) references to data and facts from antiquity. Seiler does reproduce pictures and figures without caring about copyright issues. His language is often at odds with scientific standards and modes of diction. 2) Content: the author sometimes is confused about antique texts and biographies, f. e., (a) concerning Pythagoras and his students as well as (b) the two Ptolemies: In the latter case Seiler does identify (that is, confuse) the 2nd century-AD author with the founder of the Egyptian dynasty. (c) Most important of all, Seiler´s lacking understanding of Plato is worrying, especially his seeing similarities between Plato´s theory on an ideal state and 20th century propaganda justifications of totalitarian regimes. This does concern both eugenics (as shown in FN 17 of the review, F.-X.Ajavon, “L´eugenisme de Platon” [Paris 2002] already objected against Popper´s well-known verdict) and estimation of (what is) democracy. The reviewer gives a lengthy account of differences between modern concepts of democracy and the antique, in particular Plato´s term and notions. Switching to the positive, suggestions for research on Plato are given in the following six points (beginning at p. 291 of review): 1) Plato´s Number is linked to astronomical solar and lunar cycles (following Sonntagbauer, see FN 1 of review). 2) Seiler did mention an anonymous commentary on Plato´s Number in an Oxyrhynchus papyrus already in 2013, which points to the method of doubling a square according to Plato´s Meno, which is kind of a subtext (cp. p. 282 of review). 3) Seiler points out that doubling the area of some square is tantamount to finding a manner to calculate, determine or formulate 2½ = √2 ≈ 1.414. This is a key topic of ancient mathematics: how to deal with irrational numbers or (in geometrical terms) incommensurability of distances. 4) Relating incommensurability to the (likewise incommensurable) cycles of Sun and Moon does link Plato´s Number to his concept of time (cp. Timaeus 37c6-40d5) and to making some calendar. 5) The most important of Seiler´s work (chapter 10 = p. 113 – 121) is linking Plato´s Number to the double Olympiad cycle (oktaeteris, i. e. eight years) by drawing attention to three texts which were not at all or poorly considered in this framework, namely: a) Aristotle´s interpretation of Plato´s Number (On politics V, 1316a1-8) as a three-dimensional entity: In discussing the Wedding Number Plato at beginning and end does formulate, more or less coded, numbers 30 (corresponding to a pyramid made of unit-size balls) and 27 (corresponding to a cube), respectively. These numbers give, arrounded to next higher or lower integer number, the synodic and sidereal orbital periods of Moon around Earth in days, respectively. b) Philo of Alexandria (1st century AD, On Creation of the World according to Moses, chapter 102 = 34) does explain a hard-to-comprehend passage from Plato´s formulating the Wedding Number without crediting him, but almost literally (intertextuality). Philo derives the pyramid number 30 by arithmetics from Pythagorean tetraktys: Σx2 (1…4) = 1 + 4 + 9 + 16 = 30. c) The Roman Platonic author Aulus Gellius (2nd century AD, Attic Nights, 1.20.6/3) refers to both numbers (27 and 30) by mentioning a pyramid and referring the cube number 27 to Pythagoras as describing lunar orbit around Earth. 6) Plutarchus (about 50 – 120 AD), another Platonic scholar, published a book called “About Isis and Osiris” which gives (in chapter 56) an interesting Egypt-based interpretation of the Pythagorean triangle, and thus Plato´s Number. The oncoming monographical volume by the reviewer (cp. FN 13 in the review) will provide novel insight into both Philo´s and Plutarchus´s evidence on the Unwritten Teachings (or Opinions) of Plato distributed within the Academy (“Exkurs I” in chapter 4.6) and deal with “Faszination Ägypten bei Platon” (Plato´s fascination with Egypt, “Exkurs” in chapter 5.3.3.5). Translation by Stefan Fränzle
Why is it important?
The Platonic or Wedding Number is in fact the most difficult passage of the whole corpus of Plato´s writings. My book review and my study announced therein about this matter ("Solon´s Gods - Plato´s Theology", chapter 5) will help to understand Plato´s formulating and will decifer coding this number.