Ferguson, Kitty (2008). The Music of Pythagoras: How an Ancient Brotherhood Cracked the Code of the Universe and Lit the Path from Antiquity to Outer Space. New York: Walker & Company. 2008. ISBN 9780802716316. Pagine 384. 31,91 €

Mi accorgo che da qualche tempo sembrano prevalere, nelle mie recensioni e dunque nel mio apprezzamento dei libri che leggo, gli aspetti negativi su quelli positivi. Ci tengo, invece, a dare di me l’immagine di un inveterato ottimista, invece che di un pedante criticone: antepongo quindi gli aspetti positivi di questo libro su quelli negativi.

La sovraccoperta, che vedete qui sopra, è bellissima e raffinatissima.

Il testo è chiaro e comprensibile.

Adesso le critiche: di Pitagora non si sa quasi nulla. Questa circostanza rende tutta la prima parte del libro – 100 pagine a essere generosi, anche di più se vogliamo aggiungere che si sa ben poco anche dei pitagorici e che con questo ci si spinge fino all’epoca romana – del tutto congetturale e un po’ inane. Insomma, non c’è semplicemente abbastanza materiale per tentare di scrivere una biografia di Pitagora (ed è qui che i tentativi di Kitty Ferguson, che vanno avanti per pagine, fanno venire la tentazione di mollare il libro). E sui primi pitagorici non andiamo molto meglio.

Il resto del volume è dedicato alle influenze di Pitagora sul pensiero medievale, moderno e contemporaneo. E qui sorge un secondo problema: data tutta l’incertezza sulla figura storica di Pitagora, che non ha scritto nemmeno un rigo e di cui è dubbia persino l’esistenza, quasi tutto quello che sappiamo di lui e delle sue dottrine è filtrato da Platone e dal platonismo. E dunque è abbastanza difficile separare l’influsso del pitagorismo da quello del platonismo e del neoplatonismo. A me – ma sarò certamente un sempliciotto – basta e avanza leggere la storia della filosofia e della scienza come percorsa dalle correnti sotterranee dell’aristotelismo (nelle sue diverse incarnazioni) e del platonismo (nelle sue diverse incarnazioni). Se poi Platone sia più figlio di Pitagora che di Socrate mi sembra una questione relativamente poco interessante.

Dev’essere colpa di Raffaello.
Platone e Aristotele

wikipedia.org

Oppure di quello che non si studia negli Stati Uniti.
La scuola di Atene

amazon.org

Occorre ammettere, però, che Kitty Ferguson è consapevole del problema, anche se lo liquida con poco più di una battuta:

When the members of Plato’s Academy before and after his death in 348/347 B. C. thought about Pythagoras and called themselves Pythagorean, they had in mind mainly Pythagoras as seen through Plato’s eyes. However, to say that Pythagoras was reinvented as a “late Platonist,” as some scholars insist, is to be too glib and overconfident about where to draw the lines between original Pythagorean thought, Pythagorean thought shortly after Pythagoras’ death, Archytas, Plato, and Plato’s pupils, some of whom attributed their own ideas to more ancient Pythagoreans and even to Pythagoras. As time passed, the line between Platonism and what called itself Pythagorean became increasingly difficult to discern. Eventually the two were indistinguishable. [pp. 145-146]

D’altro canto, la tesi che tutto quello che di Platone non ci piace venga da Pitagora era già stata esposta da Bertrand Russell nella sua Storia della filosofia occidentale e Kitty Ferguson ne è ben consapevole:

Vehemently rejecting the idea that humans have any grounds for discussion of an ideal world beyond what can be extrapolated in a reasonable manner from what we experience with our five senses, Russell was convinced that “what appears as Platonism is, when analyzed, found to be in essence Pythagoreanism.” It was from Pythagoras that Plato got the “Orphic element” in his philosophy, “the religious trend, the belief in immortality, the other-worldliness, the priestly tone, all that is involved in the simile of the cave, his respect for mathematics, and his intimate intermingling of intellect and mysticism.” Russell blamed Pythagoras for what he saw as Plato’s view that the realm of mathematics was a realm that was an ideal, of which everyday, sense-based, empirical experience would always fall short. [p. 298]

***

Qualche citazione.

The music interval of the octave was the “first consonance,” which Philolaus identified by the name harmonia. The “second consonance” was the interval of a fifth; the next was the interval of a fourth. Add the four nu,mbers in these ratios (1, 2, 3, 4) and the result is 10, the perfect number.
The numbers 1, 2, 3, and 4 had additional significance for Philolaus. They underly the progression from point to line to surface to solid. [p. 107]

[a p. 239 si cita un passe del De re aedificatoria di Leon Battista Alberti tradotta in inglese, ma io – traduzione per traduzione – vi propongo quella in italiano di Cosimo Bartoli]
Certamente io sempre più mi confermo nell’opinione di Pittagora, che la natura sia simile a se stessa in tutte le sue cose. Diffatti quei medesimi numeri, per i quali avviene che il concento delle voci apparisca gratissimo agli orecchi degli uomini, sono quelli stessi che empiono anche e gli occhi, e l’animo di piacere maraviglioso. Caveremo adunque tutta la regola del finimento dai musici, a cui perfettissimamente sono noti questi tali numeri; e da quelle cose inoltre, nelle quali la natura dimostri di se alcuna cosa degna ed onorata. [p. 450 dell'edizione facsimile in .pdf che si scarica qui]

Kepler combined the intervals into two kinds of musical scales. One had a major third and sixth in it and was the durus scale, close to what we call the major scale. (The major scale beginning on C, for example, includes the intervals C to E and C to A.) The other, with a minor third and sixth, was called the mollis scale, close to what we call the minor. (The minor scale beginning on C, for example, includes the intervals C to E flat and C to A flat.) Likewise, chords based on major thirds and sixths were durus; chords based on major thirds and sixths were mollis. [In German, dur in music still means "major"; moll is "minor": nota a piè di pagina dell'autrice] It requires no musical training to hear the difference between the two scales or chords and experience the emotional effect of this difference: the durus (major) is happy and the mollis (minor) sad. [pp. 268-269. L'esposizione di Kitty Ferguson lascia con l'impressione che sia stato Keplero a introdurre la terminologia durus/mollis, ma a me non risulta così; mi propongo di approfondire]

As Kepler calculated it, two-note harmonies of this sort occur almost every day, and Mercury, Earth, and Mars even sing three-part harmony fairly often. Venus, with so little eccentricity to its orbit, hardly varies its pitch at all, making it a sort of Johnny One-Note in the choir. If there is to be harmony with Venus, it must be when another planet slides into harmony with her, not the other way around. Four-note harmonies occur either because Mercury, Earth, and Mars are in adjustment with Venus’ monotone, or because they have waited long enough for the slow-changing bass voice of Jupiter of Saturn to ease into the right note. “Harmonies of four planets, ” wrote Kepler, “begin to spread out among the centuries; those of five planets, among myriad of years.” As for the harmony among all six planets – that grand and greatest “universal harmony” – the chord would be huge, spanning more than seven octaves. (You could not play it on most modern pianos. You would need an organ.) Kepler thought it might be possible for it to occur in the heavens only once in the entire history of the universe. Perhaps one might determine the moment of creation by calculating the past moment when all six planets joined in harmony. Kepler thought about the words of Job to Job: “Where were you when I laid the Earth’s foundation … when the morning stars sang together?” [p. 272. L'influenza di questo pensiero kepleriano – e pitagorico – conserva importanza, se non nelle scienze, almeno nella letteratura e delle arti: è uno dei temi sotterranei di Anathem di Neil Stephenson, e naturalmente del progetto Clock of the Long Now di Danny Hillis e della musica che ha ispirato a Brian Eno, January 07003: Bell Studies for the Clock of the Long Now]

The Catholic church, for centuries the guardian and bastion of learning, had turned foolish to the point of malign senility and condemned herself and Italy – the ancient home of Pythagoras – to what was virtually a new scientific dark age. The center of scientific endeavor and achievement moved, irretrievably, to northern Europe and England. [p. 278]

Masons, illuminists, and intellectual revolutionaries associated Pythagoras with prime numbers, though there had been no suggestion in antiquity of such a link. Great significance was attached to what were believed to have been the central prime numbers of Pythagorean mysticism: 1, 3, 5, and 7. […] In a moment of leftist paranoia about a possible Jesuit plot for a secret takeover of Masonry, there was a suggestion that 17 was the number needed to understand the Jesuit plan. A rightist pamphleteer turned that idea around and proceeded, ingeniously, to show how all of revolutionary history derived from the number 17. [p. 289] ( )

All that is left of him is an equation: a-squared plus b-squared equals c-squared. Every person going through basic geometry hears it. And yet for its ubiquity and almost-infinite proofs, there is very little known of the man who first discovered it in the Western world (there were earlier proofs in Babylon and India). Pythagoras (ca. 570 BCE – ca. 495 BCE) is a man surrounded by mystery. He formed a philosophical cult, but forbade anyone to write anything down, and yet his theorem survived. Kitty Ferguson’s The Music of Pythagoras attempts to separate fact from fiction on behalf of this ancient Greek thinker.

The lack of credible, contemporaneous sources make any biography of Pythagoras tricky at best. While his contributions to mathematics are indispensable, it is his philosophy that Ferguson is after. Greek historians and biographers (writing centuries after his death) described the cult of Pythagoras as an odd one. They were strict vegetarians, believed in the transmigration of souls, and that the Earth, Sun, and all other celestial bodies revolved around a Central Fire. Also central to their system was that numbers could explain the true nature of the universe.

Ferguson does her best to compile a good biography but falls at times into the same traps as others, conjecturing when the evidence is scant. After she goes through the life of Pythagoras, she posits an intellectual heritage that extends from his time through to the present day, going from Ptolemy to Kepler to Bertrand Russell. The writing is good but not stellar. On the plus side, you really learn a lot about ancient Greek philosophy. If you want a book about a mathematician that isn’t all about the math, then this one will do just fine. ( )

Chi era il 'divino'? Pitagora era così chiamato dai suoi discepoli per la sua sapienza. Anche oggi le intuizioni di Pitagora, a partire dal suo teorema, si dimostrano di estrema attualità e fondamento del sapere scientifico: basti pensare all'intuizione che alla base della natura ci sono relazioni matematiche o allo stretto legame tra la sua filosofia dell'io e le moderne teorie unificate della fisica. Questa è musica.