Genesis of Flatland

 This is the account of Mankind and Mathematics: when they were created, and how they were destroyed again for ever by the folly of Woman.

In the beginning, when the first Man and the first Woman were naked in the garden, God took upon himself to teach them, for they were his children and he was responsible for their education. And so he began to teach them the holy forms of Geometries and of Algebras; yea, even Calculus did he teach them. Man and Woman were favored of God at this time, and so they readily understood what he taught them, even though their brains were fully developed and they lacked the plasticity of children.

One day, God said to Man, “Lo, behold this illustration. Seest thou how there is but a two-dimensional plane, upon which are figures such as you have become accustomed to regarding: the square, the triangle, the circle. Picture now how this figure might appear to them, for it is but a one-dimensional line, with line segments and points upon it.” And the Lord God did explain further the conceit of the two-dimensional land, until Man and Woman understood it.

“I see now how the point may no more easily turn and traverse in two dimensions than the square might lift himself from the plane and traverse in three,” declared Woman, and God approved, and it was good.

And the Lord God explained how his creations were in three dimensions, as limited as the two-dimensional beings in their own three dimensions. And the Woman saw that it was a pleasing analogy, and a desirable means of gathering wisdom. And the Man, too, saw the use of such an extension, and set about wondering what might be created in the fourth dimension, for he was of a practical nature, and longed to create something that would please his Father in Heaven.

The Woman preferred pure Mathematics to the more practical arts of Engineering, and she continued to extend the experiment in secret. Soon, she discovered that God dwelt in the highest dimension, the infinite dimension, where all things were known and knowable. And the Lord God was pleased, and it was good.

One afternoon, after the lesson had concluded, the Woman was sat beneath a tree when a serpent approached her. “Is infinity truly the highest sum?” he whispered to her. At first, she dismissed his words as nonsense. Of course Infinity was the highest number there was. Wasn’t that how Infinity was defined? Still, the serpent continued to whisper to her. “Imagine a table with infinite place settings. At each place setting, there is one knife and one fork. Therefore, there are infinite knives, and infinite forks, and exactly as many knives as forks. Those infinities are equal. But if you then place two ripe fruits onto each plate, is the infinity of fruits equal to the infinity of knives and forks?”

And the Woman wrestled with the question for a long day and a long night, and eventually she was forced to conclude that there were infinities that were greater than the Infinity she had been taught. And she wondered if there was a higher order of infinity than the Infinity of dimensions in which God resided.

Troubled, she called out to the Man, inviting him to partake of the thought experiment of the infinite fruit, but he could find no solution, and indeed, he too was troubled by the implications. For if there was infinity above Infinity, then was there a being of even a higher order than God himself?

The Lord God called to the Man, “Where are you?”

He answered, “I heard you in the garden, and I was afraid, so I hid.”

And the Lord God looked upon their scribblings on their clay tablets, and he recognized them, and he grew angry. “Who told you of transfinite cardinals and uncountable infinities?” he demanded.

The Man said, “The Woman was explaining it to me.”

And the Woman said, “The serpent enlightened me, and I learned.”

And thus it was that Man, Woman, and Serpent were expelled from the Garden of Knowledge, and since that day, all three have had to scrape together what bits of learning they can from the world around them.

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One Response to Genesis of Flatland

  1. Firedrake says:

    Learn from the world, or don’t learn at all. I know where I’m sitting.

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