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Flatland: A Romance of Many Dimensions

I recently bought the book: Flatland: A Romance of Many Dimensions1. While it wasn’t an enjoyable read, the main takeaway has started some pretty interesting conversations and for that I’m appreciative, as I’ll describe below.

Flatland was written by Edwin Abbot in 1884. It’s a short book, written from the perspective of a Square in Flatland, a two-dimensional “universe”. Flatland itself is an authoritarian world where any deviation from the norm or outside ideas are grounds for imprisonment or death. The book is commonly described as science fiction but it’s really more “mathematical fiction”. (If you haven’t stopped reading by now, I don’t know what’s wrong with you 😉.) It’s partly satire on the Victorian social hierarchy, but the most interesting parts are the discussions of dimensions.

Specifically, the book describes Flatland (for more than half the book, as this is the social commentary part), but also describes Lineland (1 dimensional), Spaceland (3 dimensional) and Pointland (no dimensions). As the protagonist visits these separate places in dreams and in reality and attempts to enlighten them to the other worlds, they are steadfast in their belief that no other dimensions exist. The Square himself resisted and attacked the Sphere that had come from Spaceland until the Sphere lifted the Square out of Flatland and into Spaceland to see for himself. The attempt to convince the “King of Pointland” is especially humorous as the point does not believe it’s possible for anything outside of itself to exist, and therefore believes it’s talking to itself when speaking with the Square.

That all sounds a bit weird, but I promise there’s a point.

The book attempts to prove the existence of additional dimensions using a simple mathematical proof. That is, that the progression from a point, to a line, to a square, to a cube does not have to end. Simple arithmetic would tell you that the sequence continues. The premise of the book is that even if additional dimensions do exist, it is impossible for us to comprehend them. Even the Sphere, aware of all the other lands, is angered by the Square who, in his excitement, begins to imagine what other dimensions lie beyond Spaceland.

The main takeaway I got from the book is that you don’t know, what you don’t know, and you possibly couldn’t understand if it were explained to you. This isn’t especially profound, but it’s intriguing to me.

It’s interesting that this was written 30 years or so before Einstein and his theory of relativity and space/time. Learning that the author was a theologian makes sense as well. A similar argument–the inability to comprehend–can be made for the existence of God2. That trying to understand God may not be possible because we don’t have the mental capacity to do so. An impactful point regardless of how you feel about spirituality or religion. On one hand it’s comforting to know that you wouldn’t ever know the answer, but on the other hand, knowing that it’s possible for that answer to be out there, and that you’re not capable of understanding it is frustrating and challenging.

All that from a mathematical essay.


  1. There is also a 2007 movie starring Martin Sheen, Kristen Bell and Tony Hale
  2. Or aliens, or quantum particles or…anything we have trouble imagining. 

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