[8] 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,
1
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
2
because of the resemblance of the even number to the female and of the odd number to the male.
3
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.
4
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
5
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
6
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.
De E apud Delphos. Plutarch. Frank Cole Babbitt (Translator). Cambridge, MA. 1936.
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