Flatland

Flatland: A Romance of Many Dimensions was published in 1884 by Seeley and Co. of London, under the pseudonym "A Square". Its narrator is a Square, a respectable lawyer in a two-dimensional plane world where a citizen's number of sides fixes his station: Isosceles Triangles at the bottom, Squares and Pentagons in the professional middle, and many-sided Circles as the priestly class at the top. Women are simple Lines. The first half of the book is the Square's patient account of how such a world works — how its inhabitants recognise one another by sight and by feel, how its houses are built, and how its rulers suppress any suggestion that things might be otherwise.

The second half is a journey. The Square dreams his way into Lineland, a one-dimensional world whose Monarch cannot conceive of a direction called sideways, and finds him maddeningly obtuse. Then a Sphere from three-dimensional Spaceland arrives in his own study, appears to him first as a circle that grows and shrinks, and finally lifts him clear of his plane so that he can look down on Flatland entire. Converted, the Square presses his teacher on whether a fourth dimension might stand in the same relation to Spaceland — and discovers that his guide's tolerance for the argument stops exactly where his own world ends.

Abbott, a London headmaster and classical scholar, used the conceit to do two things at once. Flatland remains one of the clearest introductions ever written to reasoning about dimensions by analogy, which is why it has stayed on mathematics and physics reading lists for well over a century. It is also a satire of the Victorian social order it describes so calmly, and of the confidence with which any settled society mistakes the limits of its own experience for the limits of what is possible.