Flatland

A respectable lawyer who is himself a Square lives on a flat plane where rank depends on the number of sides. Isosceles Triangles sit at the bottom, Squares and Pentagons make up the professional middle, and many-sided Circles form the priestly class. Women are Lines. He narrates this world in his own voice, as a patient and sober citizen.

The first half works as a guided tour of Flatland. The Square describes how its people tell one another apart by sight and by touch, how houses are built, and how the authorities put down any hint that life could be arranged differently.

The second half turns into a journey of ideas. In a dream the Square visits Lineland, a one-dimensional realm whose Monarch cannot grasp the idea of sideways.

Then a Sphere from three-dimensional Spaceland appears in his study, first as a circle that swells and shrinks, and lifts him out of his plane to see his whole country from above. Won over, he asks whether a fourth dimension might relate to Spaceland as Spaceland relates to Flatland, and his teacher will not hear it.

The book is a short Victorian romance in the old sense, written in 1884 under the pseudonym A Square. It reads as calm, dry and often funny, a satire of class and of the habit of treating what a society knows as the limit of what exists. It is also a clear introduction to thinking about dimensions by analogy, long used on mathematics and physics reading lists.