By Edwin A. Abbott (originally pseudonymously as “A. Square”)

This is not what I expected! I don’t honestly know WHAT I expected, but it wasn’t this. For a start, it is way older than I had thought – 1884! And for another, there is almost no plot. It’s sort of a memoir, sort of a philosophical treatise, about Flatland: a land that exists in only two dimensions. Our interlocutor is a Square – in Flatland’s hierarchy, solidly middle class (Isosceles Triangles are working class, the most-sided Polygons the highest class. Women are Straight Lines). The first chunk is Square explaining how life and society can function in just two dimensions, with a great discussion about how you can tell the difference between triangles and polygons either thanks to their voices (a method only for the lower classes), feeling (slightly more respectable) or sigh (only for the upper classes because it takes years to perfect). After all of that he comes to the point (heh), which is experience of meeting a Solid – a Sphere – who informs him that there is <i>another dimension</i>, and proceeds to prove it. Sadly, this is heresy in Flatland…

This little book – 82 pages! – operates on many levels. On one, it’s an amusing intellectual conceit, to consider how life would be different in two dimensions (there’s also brief discussion of Lineland and Points). Thanks to this, it’s also an intellectual challenge, because as Square himself says to Sphere: if you’re telling me there’s another dimension that I can’t perceive but need to accept basically on faith, is there then a fourth…? Quite apart from the mathematical side, this is a biting satire of Victorian society and manner, in the way that undesirable elements amongst the lower (Isosceles) triangles are described and in how manners and attitudes of exalted Polygons are portrayed.

The question of the women is one I haven’t quite worked out for myself. If I can accept that Abbott is being satirical about the lower classes then I am hoping that he is being satirical about the women, too, because they really don’t come off very well. They are Straight Lines, therefore no angles, therefore… no brains? They’re certainly treated as emotional not rational, to the point of there being basically two languages – how men speak to themselves and how they speak to their wives. I suspect he may indeed be ironic, because in the introduction to the 1884 edition (reprinted here) “Square” responds to some alleged criticism from Spaceland, about being a woman-hater, in which he admits that he is similar to our Historians, to whom until recently “the destinies of Women and of the masses of mankind have seldom been deemed worthy of mention and never of careful consideration.”

An amusing book, and a quick read.