If It's a Red Apricot, It Must Climb Over the Wall—An Apricot That Doesn't Is Imperfect!

2006/4/5 17:00:52

What is mathematics? Mathematics is beauty, mathematics is music, mathematics is the expanse of azure sky one beholds when one "walks to where the water ends and sits watching the clouds rise." Those who take numbers, axioms, sets, and roots of equations to be mathematics are boors who want the box but not the pearl—how are they fit to discuss mathematics? Those who treat mathematics merely as a tool are like those foul ape-men who treat women merely as tools—with their crude taste, how could they distinguish a wildflower from a peony? Mathematics is the Queen of the Sciences; all sciences bow before her scepter:

A: So, is mathematics philosophy, or Being, or something like that?
B: Philosophy is nothing but the helpless groaning of decrepit old men reminiscing about their youth. Being is merely a series of ornate dreams conjured by beings gazing into the empty mirror of non-being. Mathematics is the philosophy of philosophy, the Being of Being, the everything of everything. Mathematics is ineffable.
A: So, is mathematics the Dao of that old man who rode off on a green ox? The carefree wandering of that petty official of the lacquer garden who couldn't tell himself apart from a butterfly? Or—?
B: How can you equate mathematics with these trivial things! Mathematics is ineffable, mathematics speaks in all things, mathematics is neither mind nor matter, mathematics is both mind and matter, mathematics—
A: Alright, alright, stop talking. I'm dizzy. I'm most afraid of chattering women, even the celestial kind.
B: Beauty is not always beautiful because of beauty. Mathematics speaks in all things, so let this woman use the example of mathematics to demonstrate to all beings in the universe such as Mr. A that an apricot that doesn't climb over the wall is impossible—so that all thieving courage can find no thieving heart, and all thieving hearts can find no thieving courage.
A: ——
B: If the red apricot represents perfection and the wall represents completeness, then any apricot that is truly an apricot must climb over the wall; an apricot that stays inside is impossible. In mathematics, this idea is called Godel's Incompleteness Theorem. If a red apricot is simply a red apricot and a wall is simply a wall, then an equivalent statement is: an apricot inside the wall is always imperfect; to make the apricot perfect, you must let her climb over the wall. The perfection of the red apricot lies in her climbing over the wall.
A: Ah, mathematics can actually be this accessible—she rips open the scars of every man in the universe, filling the cosmos with men's wails.
B: All women will fall in love with mathematics because of Godel's theorem.
A: All men will despise mathematics because of Godel's theorem.
B: Mathematics pays no heed to love and hate and such trifles, because she is love and hate; mathematics has no fantasies, because she is fantasy; mathematics has no truth, because she is truth. Mathematics—it is not mathematics, which is why it is called mathematics.
A: Alright, alright, stop. Mathematics is about to become a woman's toy. I'm out—is that acceptable?

The above dialogue is entirely fictional. Any resemblance is purely coincidental.