How would a creature limited to two dimensions be able to grasp the possibility of a third? Edwin A. Abbott's droll and delightful "romance of many dimensions" explores this conundrum in the experiences of his protagonist, A Square, whose linear world is invaded by an emissary Sphere bringing the gospel of the third dimension. Part geometry lesson, part social satire, this classic work of science fiction brilliantly succeeds in enlarging all readers' imaginations beyond the limits of their "respective dimensional prejudices." Unless you're a mathematician, the chances of you reading any novels about geometry are probably slender. But if you read only one in your life, this should be at the top of your list. Flatland imagines a two-dimensional world inhabited by sentient geometric shapes who think their planar world is all there is. But one Flatlander, a Square, discovers the existence of a third dimension and the limits of his world's assumptions about reality and comes to understand the confusing problem of higher dimensions. The book is also quite a funny satire on society and class distinctions of Victorian England.
I call our world Flatland, not because we call it so, but to make its nature clearer to you, my happy readers, who are privileged to live in Space. Imagine a vast sheet of paper on which straight Lines, Triangles, Squares, Pentagons, Hexagons, and other figures, instead of remaining fixed in their places, move freely about, on or in the surface, but without the power of rising above or sinking below it, very much like shadows—only hard and with luminous edges—and you will then have a pretty correct notion of my country and countrymen. Alas, a few years ago, I should have said "my universe": but now my mind has been opened to higher views of things. In such a country, you will perceive at once that it is impossible that there should be anything of what you call a "solid" kind; but I dare say you will suppose that we could at least distinguish by sight the Triangles, Squares, and other figures, moving about as I have described them. On the contrary, we could see nothing of the kind, not at least so as to distinguish one figure from another. Nothing was visible, nor could be visible, to us, except Straight Lines; and the necessity of this I will speedily demonstrate.