The short story Flatland, which first appeared in 1882, is a memorable demonstration of the fictional potential of geometry. Some wanted to see in Abbott’s tale an astonishing anticipation of Einstein’s theory, and in fact the book has become fond reading for mathematicians and scientists alike. But Flatland is a fantastic, tiny and perfect universe and, as such, remains first and foremost an exercise of the imagination.
Page after page, the reader is transported into a two-dimensional world inhabited by segments, triangles, squares, various polygons and sublime circles.
In that world, hierarchies are immediately apparent: ranging from the vulgar and angular Triangles (the workers), to the more respectable Squares and Pentagons (the professionals) and the noble Polygons, which indefinitely approximate Circles (the priests), in which the brute angular nature is completely annulled. Women are Segments, and implicit in the form is their low and treacherous, yet supremely powerful and fearsome nature. A mechanism of concentric, incompatible and incommunicating worlds actually questions our own reference points, and the book closes with the unsettling hypothesis of a Fourth Dimension.