10/7/21

Zeno’s Paradox: Red Scharlach’s Labyrinth as a Geometric Series

We discussed in class how Jorge Luis Borges embodies philosophical theories through his literature and often converges them with mathematical motifs (i.e. symmetry, geometry, etc). In Borges’s story “Death and the Compass,” Red Scharlach’s premeditated murder of his arch-nemisis, Lonnrot, draws inspiration from Zeno’s paradox: “I know of a Greek labyrinth that is but one straight line” (pg. 156). Zeno’s paradoxes were the basis of all theories related to space, time and infinity. One of them, Achilles and the tortoise, tells the story of the Greek hero, Achilles, being challenged to a race by a tortoise who claims he can beat Achilles if he’s given a head start. When the race starts, the tortoise is ahead and Achilles begins to make up ground on the slow moving tortoise. But by the time Achilles reaches the tortoise’s starting point, the tortoise had moved forward by one meter. When he makes up ground on the new gap, the tortoise had moved again creating a new but smaller gap. At every point where Achilles reaches the tortoise’s last point, the tortoise is still ahead by incrementally smaller distances. This situation can therefore be expressed as an infinite geometric series. Just as Achilles cannot overtake the fleeing tortoise, Red Scharlach is always ahead of Lonnrot which would ultimately leads him to his demise. While Scharlach did have personal history with Lonnrot, what ultimately got him ahead was the coincidental murder of the rabbi which was published in the newspaper. Knowing Lonnrot had much knowledge in religious scriptures and text, Scharlach concocted a plot that he knew only Lonnrot would be able to solve. Lonnrot of course was too transfixed on solving the mystery that he was unsuspecting of Scharlach’s mischief. Although the “labyrinth” was technically a rhombus, Lonnrot critiques Scharlach saying his elaborate plot could’ve been better if he had mapped it out exactly like Zeno’s paradox: “So many philosophers have been lost upon that line that a mere detective might be pardoned if he became lost as well” (pg. 156). Scharlach then promises the labyrinth would be a straight line in his next life before he shoots him.