The Cult of Infinite Hermaphrodites
When neophytes enter the Cult of Infinite Hermaphrodites at Xidar, they are taught, amidst their initial duties of sweeping and service, the operations of simple arithmetic. Then, at the end of their first year, now most practised in this arithmetic, they are asked to say which number it is that, self-mated, beareth 4. And they reply, of course, that 4 is born of self-mated 2. And asked the same of 9, they reply 3; and of 16, they reply 4. Thus it is (they now learn) that 2 is called by the Cult the hermaphrodite of 4, as 3 is the hermaphrodite of 9, and 4 of 16. Then the neophytes are asked to say which number it is that, self-mated, beareth 1: which is to say, what is the hermaphrodite of 1? And they reply, of course, that 1 is auto-hermaphroditic, self-mating to bear itself. And then, in mildest, most deceptive tones, they are asked to name the hermaphrodite of 2. And here, in this simplest of questions, they stand (tho’ they know it not) on the brink of a Mysterium Magnissimum et Tremendissimum, a Riddle Most Mighty and Awesome.
Now, ’tis evident that the hermaphrodite of 2 falleth betwixt 1 and 2, for 1 is the Auto-Hermaphrodite, self-mating to bear itself, and self-mated 2 beareth 4, as remarked above. But where-betwixt doth the requested hermaphrodite fall? The neophytes know not. So they are told: test the mid of 1 and 2, which is 1½, or 3/2. Self-mated, this bears 9/4, or 2¼. And this falls too high. So, subtract a ½ of a ½ from 1½, for 1¼, or 5/4. Self-mated, this bears 25/16, or 1 and 9/16. And this falls too low. So, add a ½ of a ¼ to 1¼, for 1⅜, or 11/8. Self-mated, this bears 121/64, or 1 and 57/64. Again, too low. So, add a ½ of an ⅛ to 1⅜, for 23/16, or 1 and 7/16. Self-mated, this bears 529/256, or 2 and 17/256. Too high. And thus the neophytes proceed for a day, dividing and subtracting, dividing and adding, ever approximating the hermaphrodite of 2.
But do they ever reach it? Could they ever reach it, by this or any other mode of rational approximation? And here is the Mighty Mystery, the Riddle that Wrencheth the Brain, for the Cult replieth: Nay, Nay, Never! For It hath an incontrovertible proof that demonstrateth, by easy steps of simple logic, that the hermaphrodite of 2 is impossibly a ratio of finite integer to finite integer: which is to say, it must be infinite. Were the sky all parchment, the seas all ink, and gulls all plucked for quills, the hermaphrodite of 2 remained irrecordable. And more than this: the Cult can prove, by adaptation of the aforementioned logic, that the hermaphrodites of all integers, save the perfect squares, are similarly infinite and irrecordable, eternally elusive of finite man, yet definable even in their boundless nature by his skull-boxed brain-speck. And this truth the Cult flaunteth to the profane in its very name, which titillateth and tempteth, yet yieldeth not the guessed-at, the hoped-for fruit.
All hail, O World, the lowly Worm,
Which, same to same, exchangeth sperm!
And twines its twin, beneath the moon,
To grant itself renewal’s boon!
Next bow, yea bow, and loudly hail
The spiral-foot, the crawling Snail!
That twines its twin, ’midst nuptial slime,
To slay the slayer, scything Time!
From The Hymn to Hermaphroditi.