You have almost certainly never read a novel like Flatland: A Romance of Many Dimensions by Edwin A. Abbott (under the name ‘A. Square’). It depicts a two-dimensional world, and the narrator’s experience of being granted visions of other dimensions.

About two-thirds of the book consists in simply describing the nature and some of the history of Flatland. There all the people and objects are simple, flat shapes moving on a plane. But, since they are themselves flat, they don’t see the shapes, but perceive the world as nothing but lines of varying brightness. They infer the shapes through touch and the way the brightness of the lines differs. Women are straight lines, lower orders are isosceles triangles, tradesmen are equilateral triangles, lawyers and clerks and the like are squares, and the aristocracy and priestly classes are circles or many-sided polygons. Intelligence is linked to the evenness of their angles (though there are suggestions that this might be more assumption than fact), and sharp-angled shapes can easily transect and destroy other shapes, hence why sharp isosceles triangles serve as soldiers.

Women, being straight lines, have almost no higher intelligence and can easily kill their husbands whether accidentally or intentionally, so that there are strict laws governing their behavior to minimize the homicides, though again it’s implied that the situation isn’t quite as simple as it appears (this is not a feminist narrative, in case you were wondering, though the Square protests against being called a woman hater. In any case it ought to be a moot point, since Flatland rules hardly apply to us in Spaceland).

As I say, most of the book is spent explaining Flatland, it’s laws and customs, and how its inhabitants perceive the world. That alone makes this a pretty mind-bending book as the reader tries to force his brain into the experience of a two-dimensional world.

Then we take the next step and the narrator describes a vision of one-dimensional Lineland, where the inhabitants are lines of various shapes and distances, who perceive and interact with the world almost entirely through sound, since of course they can never move parallel to one another and so cannot shift positions along their line or come into contact without destroying each other. The Square tries in vain to convey a sense of two-dimensional space to the king of Lineland, who proves incapable of understanding.

Following this, the Square receives a visitation by a Sphere from Spaceland, who has selected him as the herald of the Gospel of Three Dimensions. This is where the plot, such as it is, kicks off as the Square tries first to grasp the experience, and then to convey it to others in the face of a strict law against preaching any such doctrine.

Again, the plot doesn’t take up much time, and the characters don’t really get much development or interactions, but even so they’re nicely, well, three-dimensional. The Square’s progress from completely rejecting the idea of a third dimension whatever proofs are offered to believing he can easily convince others of what is so patently glorious and rational is very believable, as is the fact that the Sphere is not quite above the same petty narrowness as the flat shapes exhibit. Even the Square’s wife gets some dimensions during her brief role.

Flatland was originally intended as a satire of hierarchical Victorian society. The satire has generally lost its relevance, for better or for worse (though from another perspective you could argue it’s more relevant today than it was then), but the imagery and ideas remain as potent as ever. This is a deep, mind-bending book, both in the world it presents and the concepts it explores. Through the analogy of a three-dimensional world making contact with a two-dimensional one, we can just grasp the idea of what a higher dimension to our own might be like.

This naturally suggests a framework for understanding an eternal or heavenly perspective (C.S. Lewis was fond of citing this book as an illustration). The Sphere can move freely through and around Flatland, enter locked chambers with no trouble, see everything happening at once, and is totally invulnerable to the Flatlanders, because he exists on a higher dimension, one to which all of Flatland seems but a small, trivial matter. It is only by a special act of his – a grace – that the Square is able to have his vision of the three dimensions and comprehend somewhat the idea of ‘upward, but not northward’.

It is not quite a religious book. It’s point is more a need for open-mindedness and continual exploration than the idea of their being an Infinite Absolute at the core of reality. Indeed, an encounter with a Point suggests that the author thinks such a being would be rather pathetic than glorious. And of course the Circular hierarchy are the antagonists. But again, it’s a very applicable analogy and certainly goes beyond the original intention of the author. In any case, it’s intelligent, nuanced, and original enough to be worth experiencing, whatever you come to think of it’s point.

This is the kind of book that I think most everyone should read at least once, just for the fascinating ideas and perspectives it offers.