Friday, July 29, 2011

Greek Cave Finger Talk - Alchemy

When Theon had done, I think it was Eustrophus of Athens who addressed us: 'Do you see with what a will Theon backs Dialectic? He has only to put on the lion's skin! Now then for you who put down under number all things in one mass, all natures and principles divine as well as human, and take it to be leader and lord in all that is beautiful and honourable! It is n time for you to keep quiet; offer to the god a first-fruits of your dear Mathematics, if you think that "E" rises above the other letters, not in its own right by power or shape, or by its meaning as a word, but as the honoured symbol of an absolutely great and sovereign number, the "Pempad*", from which the Wise Men took their verb "to count".17 Eustrophus was not jesting when he said this to us; he said it because I was at the time passionately devoted to Mathematics, though soon to find the value of the maxim, 'NOTHING TOO MUCH', having joined the Academy. So I said that Eustrophus' solution of the problem by number was excellent. 'For since,' I continued, 'when all number is divided into even and odd, unity alone is in its effect common to both, and therefore, if added to an odd number makes it even, and vice versa; and since even numbers start with two, odd numbers with three, and five is produced by combination of these, it has rightly received honour as the product of first principles, and it has further been called "Marriage", because even resembles the female, odd the male. For when we divide the several numbers into equal segments, the even parts asunder perfectly, and leaves inside a sort of recipient principle or space; if the odd is treated the same way, a middle part is always left over, which is generative. Hence the odd is the more generative, and when brought into combination invariably prevails; in no combination does it give an even result, but in all cases an odd. Moreover, when each is applied to itself and added, the difference is shown. Even with even never gives odd, or passes out of its proper nature; it wants the strength to produce anything different. Odd numbers with odd yield even numbers in plenty because of their unfailing fertility. The other powers of numbers and their distinctions cannot be now pursued in detail. However, the Pythagoreans called five "Marriage", as produced by the union of the first male number and the first female. From another point of view it has been called "Nature", because when multiplied into itself it ends at last in itself. For as Nature takes a grain of wheat, and in the intermediate stages of growth gives forms and shapes in abundance, through which she brings her work to perfection, and, after them all, shows us again a grain of wheat, thus restoring the beginning in the end of the whole process, so it is with numbers. When other numbers are multiplied into themselves they end in different numbers after being squared; only those formed of five or six recover and preserve themselves every time. Thus six times six gives thirty-six, five times five twenty-five. And again, a number formed of six does this only once, in the single case of being squared. Five has the same property in multiplication, and also a special property of its own when added to itself; it produces alternately itself or ten, and that to infinity. For this number mimics the principle which orders all things. As Heraclitus tells us that Nature successively produces the universe out of herself and herself out of the universe, bartering "fire for things and things for fire, as goods for gold and gold for goods", even so it is with the Pempad*. In union with itself, it does not by its nature produce anything imperfect or foreign. All its changes are defined; it either produces itself or the Decad, either the homogeneous or the perfect.
- Plutarch, "On the E at Delphi"

*"...Under such conditions, we who repose in the Theory of Numbers all affairs together, natures and principles of things divine and human alike, and make this theory far above all else our guide and authority in all that is beautiful and valuable, should not be likely to hold our peace, but to offer the god our first fruits of our beloved mathematics, believing, as we do, that, taken by itself, E in not unlike all the Letters either in power or in form or as a spoken word, but it has come to be held in honor as a symbol of a great and sovereign number, the pempad, from which the wise gave the name 'pemapzein" to counting which is done in fives."

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