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This is a weird book. It’s a novella, set in a two dimensional world, narrated by a square. In the first half of the book he explains how their world works, in the second he talks to both the king of Lineland (a one dimensional world) and a sphere from Space (the three dimensional world). Obscure enough for you yet? Well take all that, and then skew your head around it being written in 1884, Victorian times. Bizarre!

So in Flatland all people are shapes, which is how class is decided. The lowest class are triangles, and the more isosceles, the lower they are, all the way through to polygons with so many sides they appear to be circles, these are the highest class of people. All shapes beyond triangles must be regular, or else will likely be banished from society. But we must remember that this was written a very long time ago, and so the exception to the above is women; all women are single lines, which tells you a lot about how they’re talked about in this book eg “they are consequently wholly devoid of brain power”, though at times they are also referred to as “formidable”, and “by no means to be trifled with” thanks to the sharp end of their line, sharper than any man’s angles.

Now, since it’s two dimensional, all you can see is one dimension (in the same way that in our three dimensional world, we see two dimensions), and so all these different shapes, at first glance look like just lines. They identify each other either by feeling, or with a bit of depth perception since there is normally a slight fog or mist. This is all explained in the book in a LOT more detail! You may wonder why they can’t be identified by some colour change or design, well, they used to, but there were problems with people faking their colours, and so now all colours are banned.

You may be spotting many holes in how life might work in a two dimensional world, and handily, these are skipped right over as our narrator, the square, decides it’s high time he moves on to the next section of the book, and so says he won’t have time to cover “our method of propelling and stopping ourselves, although destitute of feet; the means by which we give fixity to structures of wood, stone or brick, although of course we have no hands, nor can we lay foundations as you can, nor avail ourselves of the lateral pressure of the earth; the manner in which the rain originates in the intervals between our various zones, so that the northern regions do not intercept the moisture from falling on the southern; the nature of our hills and mines, our trees and vegetables, our seasons and harvest; our Alphabet and method of writing, adapted to our linear tablets; these and a hundred other details of our physical existence I must pass over.”

So that’s the first half dealt with! In the second, he first meets the Monarch of Lineland, and tries to explain to him life in two dimensions, which he obviously cannot understand, any more than we could understand what a world with four dimensions might look like. In Lineland, they can’t pass each other to get anywhere, but he explains that they can communicate over thousands of miles by sound, even to the point of impregnating, which requires one man and two women, and will always produce three children in that same ratio to preserve how that society works.

Following this, a sphere intersects the plane of Flatland and tries to explain life in two dimensions to the square. The irony of the conversation being the same with the same frustrations at not being understood now the show is on the other foot, is quite funny, but eventually the sphere is able to bring square out of Flatland into Space, and show him!

Then comes his return to Flatland, and his attempts to convert folk to the Gospel of the Three Dimensions, but this is an imprisonable offence….

What did I tell you – weird! Just feels way too abstract for something of that era, though I guess it’s not far off Lewis Carroll, and he wrote some weird stuff too….