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Philolaus’mysterious astronomical system

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Abstract

It is argued that the mysterious astronomical system traditionally attributed to Philolaus is in fact the result of a misunderstanding.

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Notes

  1. G. Galilei, lettera a Cristina di Lorena; I. Newton, De mundi systemate liber, 1.

  2. I. Boulliau, Astronomia Philolaica, Piget, Parisis, 1645.

  3. The absence of lighting effects by the central fire was noted by Graham.

  4. This argument is referred to by Aristotle in the passage given below as testimony H.

  5. The passage (Stobaeus, Anthologium, 1, 26, 3, 8–10) is quoted in Sect. 7 as testimony G.

  6. Aristotele, De caelo, 293b, 21–25. Aristotle adds that, according to "some" not better specified, around the center would turn several bodies, all invisible to us, which interposing themselves between the Sun and the Moon would make the eclipses of the Moon are much more frequent than those of the Sun.

  7. Aristotle in Metaphysica (986a, 8–12) barely mentions this topic, which was developed in his lost work on the Pythagoreans and is referred to by Alexander of Aphrodisias (In Aristotelis Metaphysica Commentaria, 40, 27–41, 2) and Simplicius (In Aristotelis quattuor libros de caelo commentaria, 511, 25–512, 9).

  8. Such is considered, for instance, in Huffman 2020.

  9. Such is considered, for instance, in Huffman 1993, 243.

  10. Τὸ πρᾶτον ἁρμοσθέν, τὸ ἕν, ἐν τῷ μέσῳ τᾶς σφαίρας ἑστία καλεῖται. (Stobaeus, Anthologium, I, 21, 8).

  11. Aristotle, De caelo, 293a, 20–21.

  12. Hicetas Syracusios, ut ait Theophrastus, caelum solem lunam stellas, supera denique omnbia stare censet neque praeter terram rem ullam in mundo moveri, quae cum circum axem se summa celeritate convertat et torqueat, eadem effici omnia quae si stante terra caelum moveretur. Atque hoc etiam Platonem in Timaeo dicere quidam arbitrantur, sed paullo obscurius (Cicero, Academica, II, xxxix).

  13. Ἡρακλείδης ὁ Ποντικὸς καὶ Ἔκφαντος ὁ Πυθαγόρειος κινοῦσι μὲν τὴν γῆν, οὐ μήν γε μεταβατικῶς, ≤ ἀλλὰ τρεπτικῶς ≥ τροχοῦ δίκην ἐνηξονισμένην, ἀπὸ δυσμῶν ἐπ’ἀνατολὰς περὶ τὸ ἴδιον αὐτῆς κέντρον. (pseudo-Plutarch, Placita philosophorum, 896A, 5–8).

  14. τὴν δὲ γῆν μέσον κόσμου κινεῖσθαι περὶ τὸ αὑτῆς κέντρον ὡς πρὸς ἀνατολήν. (Hippolytus, Refutatio omnium haeresium, I, 15, 2, 5–6).

  15. Θαλῆς καὶ οἱ ἀπ’ αὐτοῦ μίαν εἶναι τὴν γῆν. Ἱκέτης ὁ Πυθαγόρειος δύο, ταύτην καὶ τὴν ἀντίχθονα. (pseudo-Plutarch, Placita philosophorum, 895C, 7–8).

  16. καὶ τὴν γῆν κινεῖσθαι κατὰ κύκλον πρῶτον εἰπεῖν·οἱ δ’ Ἱκέταν ≤ τὸν ≥ Συρακόσιόν φασιν. (Diogenes Laertius, Vitae philosophorum, VIII, 85, 1–3).

  17. … παρὰ δὲ τοῖς νοτιωτέροις τοῦ ἰσημερινοῦ τῶν ἀντιχθόνων καλουμένων, … (Ptolemy, Syntaxis mathematica, 498, 5–7).

  18. Theon of Alexandria, Commentaria in Ptolemaei syntaxin mathematicam i–iv, 402, 1–3; Pappus, Commentaria in Ptolemaei syntaxin mathematicam v–vi, 238, 5–6.

  19. Pomponius Mela, Chorographia, I, 3.

  20. Pliny, Naturalis Historia, VI, 81.

  21. Cosmas Indicopleustes, Topographia Christiana, I, sez. 14, 4–6.

  22. Achilles Tatius, Isagoga excerpta, 30.

  23. Anonymous, Ἐξ ἑτέρων σχολίων εἰσαγωγή, 6 (in E. Maass, Commentariorum in Aratum reliquiae, Berlin: Weidmann, 1898).

  24. Cleomedes, who does not use the term "antichtones," uses the term perieci to denote those whom Achilles Tatius and the anonymous call antichtones (Cleomedes, Caelestia I, 1, 209–273, ed. Todd). Achilles Tatius and the anonymous instead use the term perieci for the inhabitants of the same place.

  25. Achilles Tatius, Isagoga excerpta, 31.

  26. In order to eliminate the contradiction various amendments to the texts of the testimonies have been proposed (see Timpanaro Cardini 626–627).

  27. This river already appears in Homer’s Odyssey (X, 513).

  28. Plato, Phaedo, 111–113 (in particular 113 B).

  29. Plutarch, De facie quae in orbe lunae apparet, 924A.

  30. This point is highlighted in the (authentic) fragment of Philolaus’ book, where it is emphasized the symmetry between up and down (Stobaeus, Anthologium, 1, 15, 7).

  31. It cannot be excluded, for example, that to start the misunderstanding was Speusippus, who had written a book On the numbers of the Pythagoreans based primarily on Philolaus, in which the decade was also studied in relation to cosmic events (Theologoumena arithmetica, 82 = Philolaous test. A13 Diels-Kranz).

  32. ἐπὶ δὲ τῶν θυραίων καὶ ὡς εἰπεῖν βεβήλων, εἰ καί ποτε τύχοι, διὰ συμβόλων ἀλλήλοις οἱ ἄνδρες ᾐνίττοντο…

    (Iamblichus, De vita Pythagorica, 227, 3–5).

  33. Τί δέ, ὦ Κέβης; οὐκ ἀκηκόατε σύ τε καὶ Σιμμίας περὶ τῶν τοιούτων Φιλολάῳ συγγεγονότες;- Οὐδέν γε σαφές, ὦ Σώκρατες. (Platone, Fedone, 61D, 6–8).

  34. ὃς καὶ δι’αἰνιγμάτων ἐδίδασκε καθάπερ ἦν ἔθος αὐτοῖς (test. 1A Diels Kranz).

  35. Τῶν Πυθαγορείων τινὲς κατὰ τὴν Ἀριστοτέλειον ἱστορίαν καὶ τὴν Φιλίππου τοῦ Ὀπουντίου ἀπόφασιν ἀντιφράξει τοτὲ μὲν τῆς γῆς, τοτὲ δὲ τῆς ἀντίχθονος. (Stobaeus, Anthologium, 1, 26, 3, 8–10).

  36. Τῷ γὰρ τιμιωτάτῳ οἴονται προσήκειν τὴν τιμιωτάτην ὑπάρχειν χώραν, εἶναι δὲ πῦρ μὲν γῆς τιμιώτερον, […]·ὥστ’ ἐκ τούτων ἀναλογιζόμενοι οὐκ οἴονται ἐπὶ τοῦ μέσου τῆς σφαίρας κεῖσθαι αὐτήν, ἀλλὰ μᾶλλον τὸ πῦρ. Ἔτι δ’ οἵ γε Πυθαγόρειοι καὶ διὰ τὸ μάλιστα προσήκειν φυλάττεσθαι τὸ κυριώτατον τοῦ παντός, τὸ δὲ μέσον εἶναι τοιοῦτον, [ὃ] Διὸς φυλακὴν ὀνομάζουσι τὸ ταύτην ἔχον τὴν χώραν πῦρ·(Aristotele, De caelo, 293a, 30–293b, 4).

  37. Φιλόλαος ὁ Πυθαγόρειος τὸ μὲν πῦρ μέσον, τοῦτο γὰρ εἶναι τοῦ παντὸς ἑστίαν· δευτέραν δὲ τὴν ἀντίχθονα, τρίτην δ’ἣν οἰκοῦμεν γῆν ἐξ ἐναντίας κειμένην τε καὶ περιφερομένην τῇ ἀντίχθονι· παρ’ ὃ καὶ μὴ ὁρᾶσθαι ὑπὸ τῶν ἐν τῇδε τοὺς ἐν ἐκείνῃ. (pseudo-Plutarco, Placita philosophorum, 895E, 4–8).

  38. τῶν πλείστων ἐπὶ τοῦ μέσου κεῖσθαι λεγόντων, ὅσοι τὸν ὅλον οὐρανὸν πεπερασμένον εἶναί φασιν, ἐναντίως οἱ περὶ τὴν Ἰταλίαν, καλούμενοι δὲ Πυθαγόρειοι λέγουσιν· ἐπὶ μὲν γὰρ τοῦ μέσου πῦρ εἶναί φασι, τὴν δὲ γῆν, ἓν τῶν ἄστρων οὖσαν, κύκλῳ φερομένην περὶ τὸ μέσον νύκτα τε καὶ ἡμέραν ποιεῖν. Ἔτι δ’ ἐναντίαν ἄλλην ταύτῃ κατασκευάζουσι γῆν, ἣν ἀντίχθονα ὄνομα καλοῦσιν. (Aristotele, De caelo, 293a, 18–24).

  39. Καὶ οὕτω μὲν αὐτὸς τὰ τῶν Πυθαγορείων ἀπεδέξατο·οἱ δὲ γνησιώτερον αὐτῶν μετασχόντες πῦρ μὲν ἐν τῷ μέσῳ λέγουσι τὴν δημιουργικὴν δύναμιν τὴν ἐκ μέσου πᾶσαν τὴν γῆν ζῳογονοῦσαν καὶ τὸ ἀπεψυγμένον αὐτῆς ἀναθάλπουσαν·διὸ οἱ μὲν Ζηνὸς πύργον αὐτὸ καλοῦσιν, ὡς αὐτὸς ἐν τοῖς Πυθαγορικοῖς ἱστόρησεν, οἱ δὲ Διὸς φυλακήν, ὡς ἐν τούτοις, οἱ δὲ Διὸς θρόνον, ὡς ἄλλοι φασίν. ἄστρον δὲ τὴν γῆν ἔλεγον ὡς ὄργανον καὶ αὐτὴν χρόνου·ἡμερῶν γάρ ἐστιν αὕτη καὶ νυκτῶν αἰτία·ἡμέραν μὲν γὰρ ποιεῖ τὸ πρὸς τῷ ἡλίῳ μέρος καταλαμπομένη, νύκτα δὲ κατὰ τὸν κῶνον τῆς γινομένης ἀπ’αὐτῆς σκιᾶς. ἀντίχθονα δὲ τὴν σελήνην ἐκάλουν οἱ Πυθαγόρειοι, […]. (Simplicius, In Aristotelis quattuor libros de caelo commentaria, 512, 9–18.

  40. Scholia in Aristotelem (Brandis), pp. 504b 42–505a 5.

  41. It is possible that Simplicius has altered the statement of the source that according to genuine Pythagorean theory the innermost of the bodies revolving around the center (which in the theory transmitted by Aristotle is the Counter-Earth), is actually the Moon.

  42. Boeckh 1852 p. 96, Schiaparelli 1925 p. 404, Timpanaro Cardini 2010 pp. 859–861. Burkert pp. 232–233, Huffman 1993 pp. 242–243.

  43. The possibility that the Pythagorean doctrine mentioned by Simplicius is posterior to Aristotle is ruled out by the considerations that the purely rotary movement of the Earth is attributed to Icetas, Hecphanthus, and Heraclides of Pontus (none of whom is later than Aristotle), and fire inside the earth is attested in Plato.

  44. Simplicius, for example, is the only source we have on Hipparchus' work on gravity.

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Acknowledgements

I am grateful to Giuseppe Cambiano for reading a preliminary version of this work and providing important suggestions.

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    Lucio Russo

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Russo, L. Philolaus’mysterious astronomical system. Rend. Fis. Acc. Lincei 33, 355–361 (2022). https://doi.org/10.1007/s12210-022-01061-0

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