Cute satire. Narrator, square, attorney, describes his 2D setting, visits 0D, 1D, & 3D settings, and dreams of 4D, 5D, &c.
We find that the 2D world has a "remote and backward agricultural district [wherein] an antiquarian may still discover a square house," which is perfectly suggestive that, even in 2D worlds, progressive economic development causes all that is solid to melt into air.
Transition of lowly triangles into other polygon forms "is welcomed, not only by the poor serfs themselves, as a gleam of light and hope shed upon the monotonous squalor of their existence, but also by the Aristocracy at large; for all the higher classes are well aware that these rare phenomena, while they do little or nothing to vulgarize their own privileges, serve as a most useful barrier against revolution from below." So, class mobility as wealth insurance. Sounds familiar enough!
Lotsa cool little gems, like a proto-futurism in "How great and glorious the sensuous development of these days must have been is in part indicated by the very language and vocabulary of the period," in describing war. Or how egalitarian doctrine is held up as virtue, but its proponents are destroyed, because "political power would be in the hands of the greatest number, that is to say the Criminal Classes, who were already more numerous than the Workmen." The gender politics of the text are of course abysmal, arising during the time of coverture--females are reduced to mere lines with no function other than breeding, apparently.
Cool bit regarding the priest class, which are designated circles, but are merely polygons with many sides, and "as the number of sides increases, a Polygon approximates to a Circle." Though "popularly everyone called a Circle is deemed a Circle, yet among the better educated Classes it is known that no Circle is really a Circle." So, pretty obvious false consciousness as part of class-based authority. That the false consciousness is rooted in the geometer's truths is just badass.
Recommended for those who move to and fro with a rhythmic motion of more than usual violence, readers with some more dimensionable dimensionality, and promulgators of paradoxes who maintain that there is no necessary connection between geometrical and moral irregularity.