De E apud Delphos

I said, therefore, that Eustrophus solved the difficulty most excellently with his number. For since, I continued, every number may be classified as even or odd, and unity, by virtue of its potentiality, is common to both, for the reason that its addition makes the odd number even and the even number odd,[*](Cf. 429 a, infra.) and since twTo makes the first of the even numbers and three the first of the odd, and five is produced by the union of these numbers, very naturally five has come to be honoured as being the first number created out of the first numbers; and it has received the name of marriage[*](Cf.Moralia, 263 f, 1012 e, 1018 c, and Clement of Alexandria, Stromateis, v. chap. xiv. 93. 4 (p. 702 Potter).) because of the resemblance of the even number to the female and of the odd number to the male.[*](Cf.Moralia, 288 c-e.) For in the division of numbers into two equal factors, the even number separates completely and leaves a certain receptive opening and, as it were, a space within itself; but in the odd, when it undergoes this process, there is always left over from the division a generative middle part. Wherefore it is more generative than the other, and in combination it is always dominant and is never dominated.[*](Cf. Plutarch, Life and Poetry of Homer, 145 (Bernardakis, vol. vii. p. 416).) For in no combination of these two numbers (even and odd) is there produced from the two an even number,

but in all combinations an odd. Moreover, each when applied to itself and made composite with itself shows the difference. For no even number united with even gives an odd number, nor does it ever show any departure from its own distinctive nature, being impotent through its weakness to produce the other number, and having no power of accomplishment; but odd numbers combined with odd produce a numerous progeny of even numbers because of their omnipresent generative function. It would not be timely at this moment to enumerate the other potent properties and divergences of numbers; let it suffice to say that the Pythagoreans called Five a Marriage on the ground that it was produced by the association of the first male number and the first female number.

There is also a sense in which it has been called Nature, since by being multiplied into itself it ends in itself again. For even as Nature receives wheat in the form of seed and puts it to its use, and creates in the interim many shapes and forms through which she carries out the process of growth to its end, but, to crown all, displays wheat again, and thus presents as her result the beginning at the end of the whole, so in like manner, while the other numbers when raised to a power end in different numbers as the result of the increase, only the numbers five and six, when multiplied by themselves, repeat themselves and preserve their identity. Thus six times six is thirty-six, and five times five is twenty-five; and furthermore, the number six does this but once, and the single instance is when it is squared; but with five this result is obtained in raising it to any power, and it has a unique characteristic, when added to

itself, of producing either itself or ten alternately[*](That is, a number ending in 5 or 0. Cf. 429 d, infra.) as the addition progresses, and of doing this to infinity, since this number takes its pattern from the primal principle which orders the whole. For as that principle by changes creates a complete universe out of itself, and then in turn out of the universe creates itself again, as Heracleitus[*](Diels, Frag. der Vorsokratiker, i. p. 95, Heracleitus, no. b 90.) says, and exchanges fire for all and all for fire, as gold for goods and goods for gold, so, in like manner, the conjunction of five with itself is determined by Nature’s law to produce nothing incomplete or foreign, but it has strictly limited changes; it produces either itself or ten, that is to say, either its own characteristic or the perfect whole.

If, then, anyone ask, What has this to do with Apollo?, we shall say that it concerns not only him, but also Dionysus, whose share in Delphi is no less than that of Apollo.[*](Cf. 365 a, supra, and Lucan, v. 73-74; and for the proverb Cf.Moralia, 280 d and the note.) Now we hear the theologians affirming and reciting, sometimes in verse and sometimes in prose, that the god is deathless and eternal in his nature,[*](Cf. Clement of Alexandria, Stromateis, v. 14 (p. 711 Potter).) but, owing forsooth to some predestined design and reason, he undergoes transformations of his person, and at one time enkindles his nature into fire and makes it altogether like all else, and at another time he undergoes all sorts of changes in his form, his emotions and his powers, even as the

universe does to-day; but he is called by the best known of his names.[*](Cf. Stobaeus, Eclogae Phys. et Ethic. i. 21. 5 (i. p. 184. 11 ed. Wachsmuth).) The more enlightened, however, concealing from the masses the transformation into fire, call him Apollo because of his solitary state,[*](Cf. 354 b, 381 f, supra, and 393 b, infra.) and Phoebus because of his purity and stainlessness.[*](Cf. 393 c, infra.) And as for his turning into winds and water, earth and stars, and into the generations of plants and animals, and his adoption of such guises, they speak in a deceptive way of what he undergoes in his transformation as a tearing apart, as it were, and a dismemberment. They give him the names of Dionysus, Zagreus, Nyctelius, and Isodaetes; they construct destructions and disappearances, followed by returns to life and regenerations — riddles and fabulous tales quite in keeping with the aforesaid transformations. To this god they also sing the dithyrambic strains laden with emotion and with a transformation that includes a certain wandering and dispersion. Aeschylus,[*](Nauck, Trag. Graec. Frag., Aeschylus, no. 355.) in fact, says

1. Fitting it is that the dithyramb
2. With its fitful notes should attend
3. Dionysus in revel rout.

But to Apollo they sing the paean, music regulated and chaste.

Apollo the artists represent in paintings and sculpture as ever ageless and young, but Dionysus they depict in many guises and forms; and they attribute to Apollo in general a uniformity, orderliness, and unadulterated seriousness, but to Dionysus a certain

variability combined with playfulness, wantonness, seriousness, and frenzy. They call upon him[*](Cf. Bergk, Poet. Lyr. Graec. iii. p. 730, Adespota, no. 131; quoted by Plutarch in Moralia, 607 c and 671 c also.):

1. Euoe Bacchus who incites
2. Womankind, Dionysus who delights
3. ’Mid his honours fraught with frenzy,

not inappositely apprehending the peculiar character of each transformation.

But since the time of the cycles in these transformations is not equal, but that of the one which they call Satiety,[*](Cf. von Arnim, Stoicorum Veterum Fragmenta, ii. 616 (p. 186); Philo, De Spec. Leg. i. 208.) is longer, and that of Dearth shorter, they observe the ratio, and use the paean at their sacrifices for a large part of the year; but at the beginning of winter they awake the dithyramb and, laying to rest the paean, they use the dithyramb instead of it in their invocations of the god; for they believe that, as three is to one, so is the relation of the creation to the conflagration.