A Square explains how willing he is to sacrifice his own safety and happiness to disseminate knowledge of the third dimension to the public. He uses an allusion and a simile to illustrate this for the reader:
[...] yet, like a second Prometheus, I will endure this and worse, if by any means I may arouse in the interiors of Plane and Solid Humanity a spirit of rebellion against the Conceit which would limit our Dimensions to Two or Three or any number short of Infinity.
The allusion A Square makes here is to Prometheus, a figure in Greek mythology who stole fire from the gods and gave it to humanity. Prometheus was punished for eternity for this thievery for the greater good: in legend, he was chained to a rock and forced to endure as an eagle arrived to eat his liver every day. It would then grow back overnight, the cycle repeating endlessly. His story is often used as an analogy to describe someone who sacrifices or endangers themselves for the sake of human advancement. By likening himself to Prometheus, A Square aligns his mission to this legacy of necessary sacrifice. Even though he knows it is dangerous to disseminate the knowledge of other dimensions, he feels he must bring the truth about Spaceland to Flatland.
A Square uses the Egyptian myth of the Sphinx to articulate his frustration at the difficulty of making the other Shapes believe his stories about Spaceland, employing both allusion and simile:
Heavily weighs on me at times the burdensome reflection that I cannot honestly say I am confident as to the exact shape of the once-seen, oft-regretted Cube; and in my nightly visions the mysterious precept, “Upward, not Northward,” haunts me like a soul-devouring Sphinx.
The Sphinx was a mythical creature from Ancient Egypt. It was known for posing impossible riddlers to the unlucky travelers who crossed its path, and devouring anyone who could not solve them. The simile A Square uses here refers to the difficulty of this riddle and the dangers the Sphinx posed to its victims.
The “mysterious precept” of moving in three dimensions haunts A Square. He knows he must find a way to tell people about his experiences with The Sphere, and to explain what the Cube looks like to the other polygons, but he fears the “soul-devouring” consequences of both doing so and failing to do so. The Sphinx would let people who could solve its riddle leave in peace, but the difficulty of answering its question accurately made it an almost impassable obstacle. Like the Sphinx, the obstacle of how to get his point across to the other denizens of Flatland blocks A Square at every turn, “haunting” him.
