a Euclidean horror story
You must not attempt this approach to parallels. I know this way to the very end. I have traversed this bottomless night, which extinguished all light and joy in my life. I entreat you, leave the science of parallels alone… Learn from my example.
Farkas Bolyai, 1820
I came over the dunes a little before dawn. Already waiting for me were three Examiners: robed, masked, inhumanly tall. Their silhouettes loomed against the dark ocean; their silence loomed, too, against the dull grinding of the waves.
“I’m ready for the final test,” I told them. I wasn’t sure I wanted to pass, but I knew I didn’t want to fail.
The first Examiner spoke in a thunderous rasp: “Then your task is simple.”
The second Examiner explained: “Draw two parallel lines in the sand.”
I looked to the third Examiner, who said nothing. No further instructions came.
Was that all, then?
I grabbed a dry stick of driftwood, and scraped two parallels, a few feet in length, into the damp earth.
“Longer,” said the first Examiner.
I extended the lines.
“Longer,” said the second Examiner.
I did it again.
The third Examiner shook its head, and I began to sense the nature of the task.
It was arbitrary, a measure only of blind obedience.
(Maybe all tests are, in the end.)
I fetched a second stick, similar in length to the first. Then I walked backwards along the beach, dragging the two sticks behind me, one in each hand. The Examiners followed, seeming to glide, leaving no footprints. I extended the parallel lines until they were a quarter-mile, a half-mile, a full mile long.
“How much further?” I asked, perhaps an hour after sunrise.
No one spoke. I counted a dozen waves before the first Examiner replied: “Do you know the meaning of ‘parallel’?”
“It means the lines never meet,” I said.
The second Examiner nodded. “Prove that you know what this signifies.”
I shivered, despite the building heat of day. “Why? I know what ‘never’ is.”
“Do you?” the first Examiner asked. “You scratch symbols, but symbols of what? You mutter sounds, but are there thoughts behind them? A mortal mouth can mimic immortal speech. It does not mean you understand.”
Ah. So this was the test.
I picked up the sticks and began to scrape again. The sun continued to climb. I watched my shadow shorten, and couldn’t help noticing that the Examiners cast no shadows of their own.
By the early afternoon, I was sweating, stumbling, panting with thirst. I stopped to rest, though I knew this displeased the Examiners.
“I know what parallel lines are,” I told them again.
“Do you?” the second Examiner asked. “You watched the Archer of Time notch his first arrow? You observed the Sculptor of Space, when this universe was mere potter’s clay on a spinning wheel? You, a mortal creature, flinching at pain—you claim to know eternity?”
There was nothing to say to that.
I continued to scratch lines in the wet sand, step by backwards step, my body fraying with thirst, my worthless work trailing into the distance.
Hours later, as the sun set over the dunes, I fell to my knees. “I can’t go on,” I told them. My hoarse voice scarcely sounded like my own.
“Then you don’t understand,” concluded the first Examiner.
“Parallel lines never meet,” whispered the second. “Never, never, never.”
The third Examiner said nothing.
What, I wondered, was the purpose of this test? Did it sift the wise from the rash, the patient from the arrogant? Or did it exist only to separate test-givers from test-takers? Did it merely flaunt their power to demand—and my powerlessness to refuse?
I felt a surge of impotent anger, and lashed out the only way I could: I drew the two sticks together, crossing the lines in the sand. “There,” I said. “There are your parallel lines—at least, the closest you’ll have from my hands.”
I braced myself for their final judgment, for the fatal pressure on the back of my neck.
But when I looked up, two of the Examiners had vanished. Only the third remained. I saw its outstretched fingers, elongated and skeletal, and I sensed that it was smiling behind its mask.
“Congratulations,” the Examiner said, with a sinister calm. “You do understand.”