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Oliver Primavesi

Empedocles’ Cosmic Cycle and the Pythagorean Tetractys, p. 5–29.

Abstract: Empedocles posits six fundamental principles of the world: Love, Strife and the four elements (rhizōmata). On the cosmic level, he describes the interaction of the principles as an eternal recurrence of the same, i.e. as a cosmic cycle. The cycle is subject to a time-table the evidence for which was discovered by Marwan Rashed and has been edited by him in 2001 and 2014. The purpose of the present paper is to show that this timetable is based on the numerical ratios of the Pythagorean tetractys.

P. 8 : While living beings are an extremely short-lived aggregate of those elements, the elements themselves neither arise nor pass away; thus, if we are anything at all, we are the divine elements. As first shown by the Strasbourg Empedocles papyrus, the mortal teacher of the Physica expresses this quite aptly by occasionally passing over the transitory individuality of the isolated combinations altogether and speaking instead directly in the name of the four elements themselves: “Under Love’s dominion, we [= the elements] come together into the Sphairos”.

P. 9 : The eye contains within itself both fire (which is light) and water (which is dark). It is also covered with membranes (that is, the cornea) that are made up of air and earth and equipped with pores that are permeable to fire as well as with others that are permeable to water.

P. 11 : The process of mixture brought about by Love’s expansion leads to a state of rest in which the four elements are completely mixed and combined into a spherical god, the Sphairos; the latter is probably also referred to as Apollo.29 Strife’s centripetal invasion, by contrast, leads to a state in which the four elements have assembled themselves [...] Like the Sphairos (Apollo), these four perfect masses are regarded as gods, which also justifies the attribution of the names of two divine couples to the four elements as such – Zeus (Fire) & Hera (Air), Aidoneus/Hades (Earth) & Nestis (Water).30 Yet in the full sense of [...]

Note 29. Empedocles text 192b Mansfeld/Primavesi (Ammonius In int. p. 249,1–10 Busse; the text of the embedded Empedoclean quotation [DK 31 B 134] is here corrected after Olympiod. In Gorg. 4.3, Cod. Marc. Gr. Z. 196 [=743] in margine): [...] οὔτε γὰρ ἀνδρομέηι κεφαλῆι κατὰ γυῖα κέκασται, / οὐ χέρες, οὐ θοὰ γοῦν᾿, οὐ μήδεα λαχνήεντα, / ἀλλὰ φρὴν ἱερὴ καὶ ἀθέσφατος ἔπλετο μοῦνον, / φροντίσι κόσμον ἅπαντα καταΐσσουσα θοῆισιν.

Note 30. [...] The identification of Zeus with fire is put beyond reasonable doubt by the epithet ἀργής. For the couple Aidōneus (= Earth) & Nēstis (= Water) see Heyne (1776), p. IX, n.* to p. VIII (continued) [...] 

P. 11-12 : Yet in the full sense of the word, the elements are “gods” only during their full separation; in the remaining parts of the cycle, by contrast, their divine individuality is compromised and diminished.

P. 12 : for the phase of increasing mixture presided over by Love and for that of increasing separation presided over by Strife [...] in these periods the elements are referred to merely as daimones (δαίμονες) rather than theoi (θεοί).31

Note 31. Empedocles text 155 Mansfeld/Primavesi (DK 31 B 59): [...]

A fortiori, the same holds also for the period of total unity and rest, i.e. for the Sphairos, the single god who has, as it were, swallowed the four gods.

P. 12 : what we know as the sun is in fact a mere reflection of the fire that already covers an entire half of the firmament, the half that faces away from us during the day.

This fire first illuminates the half of the firmament that is covered with air and visible to us in the daytime, which then reflects it onto the earth, which in turn, like a lens, reflects it back on the visible heaven in the form of a equally visible disk. [...] The path of this disk in the heavens may then be explained by the rotation of the firmament [...]

P. 13 : Rashed has deduced the following basic structure of the timetable as attested by the Byzantine scholia: Love’s centrifugal expansion lasts sixty time units (chronoi), the Sphairos lasts forty time units, and Strife’s centripetal invasion lasts again sixty time units; the latter is immediately followed by the next revolution of the cycle which starts with Love’s

expansion (PLATE 1). Rashed’s deduction is entirely convincing, and it will be taken for granted in the following argument.

P. 15 : the Pythagorean oath alludes to Empedoclean physics, and since pēgē in Empedocles refers to the stream of life in its entirety, the equation of the tetractys (1 : 2 : 3 : 4) with a paga physeos amounts to ascribing the numerical ratios of the tetractys to Empedocles’ cosmic cycle. This ascription, in turn, sheds unexpected light on the cosmic timetable as transmitted by the Byzantine

scholia. [...] two tetractyes, one increasing and one decreasing, which have the 40 times of the Sphairos in common. On this reading, the first 60 times-period (Love’s expansion) consists of 10 + 20 + 30 times, and the second 60 times-period (Strife’s invasion) consists of 30 + 20 + 10 times [...]

P. 18 : For the proper understanding of this doctrine, it is important to realize that by “mortal beings” (θνητά) Empedocles means only the short-lived heterogeneous combinations of elements, in explicit contrast to the long-lived gods (theoi dolichaiōnes) of Empedoclean physics as for instance the divine Sphairos, whose dominion is now reported to last forty time-units.

[...] Love forms particular combinations of the elements both in the phase of increasing fusion, when it is gradually gaining strength, as well as in that of increasing separation, although it is getting weaker and weaker.

P. 20-21 :  [...] when fire, in its ascent, has reached the periphery of the cosmos; at this very moment Strife demonstrates its increasing strength by violently splitting the uniform, unarticulated beings of the third stage into halves, male and female. So when the sun rises for the first time, the living beings, which have been mute up to this point, produce their first sound, the cry of pain with which they react to their division; and from now on they carry within themselves the desire for sexual (re)union.70 Thus, the transition from the third to the fourth stage is brought about by splitting the whole-natured beings of the third stage into halves; and both stages are caused by a continuous centrifugal movement of fire.

P. 21 : The combined evidence of the indirect tradition and of the Strasbourg papyrus rather shows that both Love’s expansion and Strife’s invasion involve, in addition to their respective zoogonic stages, one abiotic stage each, which is characterized by the absence of individual living beings. The two abiotic stages in question immediately precede and follow the turning point of the cosmic cycle, i.e. the transition from Strife’s invasion to Love’s expansion.

P. 21-22 : Strife’s invasion comes to a natural end when Strife, closing in from all sides, has compressed Love into a single point, the “centre of the whirlwind”, that is, the centre of the earth.

P. 22 : But when the first compounds are formed, the elements suddenly become mortal, whereas before they had learnt to be immortal (ἀθάνατα). [...] If the total separation were “not a condition that can endure”, as O’Brien maintained, it could scarcely count as a state of immortality, since a merely instantaneous freedom of mixture and dissolution is neither a very meaningful concept, nor a state which the elements can have learned to be in. We conclude that the first of the three stages of Love’s expansion is the life-time of the four divine pure masses, and that these divine masses are, like the Sphairos, to be reckoned among the long-lived gods (theoi dolichaiōnes) of Empedoclean physics.

A second abiotic stage will occur towards the end of Strife’s invasion, immediately before the turning point of the cycle.

P. 24 :

The increasing duration of the stages of Love’s tetractys corresponds to the decreasing speed of the overall movement during Love’s expansion, from the rotation of the four masses at maximum speed to the immobility of the Sphairos [...]

P. 25 : The rest period of Love and Strife—the dominion of the Sphairos—comes to an end when Strife, the strength of whose limbs has been restored during the period of rest, invades the Sphairos from without and destroys it. The period of rest, i.e. the life-span of the Sphairos, is characterized as having

been fixed “in exchange” by an oath sworn by Love and by Strife:

But after great strife had grown in its limbs

and risen to its honours, when the time was being completed

which they have defined in exchange by means of a broad oath, …

P. 26 : Both Love and Strife have sworn to each other to observe faithfully the timetable of their respective tetractys [...] Now on our Pythagorizing reconstruction of the timetable, the life time

of the Sphairos belongs to both the tetractys of Love and the tetractys of Strife, so that the Empedoclean oath implies, in particular, that Love and Strife have granted each other to cease fire during a common period of rest, i.e. during the life span of the Sphairos.

P. 27 : Love and Strife have defined the lifetime of the Sphairos “in exchange” [...]

[...] blood and muscles (1 part of earth, 1 part of fire, 1 part of water, 1 part of earth), bones (2 parts of earth, 2 parts of water, 4 parts of fire), and sinews (1 part of fire, 1 part of earth, 2 parts of water): all of these formulae remain within the compass of the Pythagorean tetractys.