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A few days after I read this book back in high school, I was cracking up just remembering it. The story is about the life of a square, who dreams of meeting lines and dots in other worlds, but has his own reality shaken up when a sphere lifts him into the sky and allows him to view the world in 3 dimensions. The square talks about his discovery, and is arrested and imprisoned for this dangerous knowledge.
Yes, the story and especially characters are absurd, but this is really a novel about ideas. It spends time worldbuilding, as our narrator, A. Square, explains how his world works. Rain comes from the north, so all houses are built with roofs facing north (wait - how are they built? Well, some questions are best left not trying to answer). Rank is determined entirely by number of sides on the shape. And circles as we here on Earth know them, don't technically exist - a "circle" is in fact a shape with so many sides that it's impossible to tell how round it is. That little tidbit actually got me thinking if our circles could in fact be described in a similar way.
Once we know how Flatland works, it's time to move on to other dimensions. Lineland has nothing but lines, who can only move in two directions - the directions they face. A. Square asks how a line could possibly be happy in such a state. The line, hearing A. Square's voice as though it were coming from inside his own body, states that it's simple - his family is safe and nothing is coming to harm, so he's satisfied. When A. Square presents himself, the line sees what appears to be an enemy line spawning into thin air, and promptly attempts to skewer A. Square.
Pointland is similar. With no-one else in existence, the dot is happy just to talk and think to himself.
It's the sphere that shakes things up a bit. He is to the square what the square is to the line - he appears to spawn from thin air, when in fact he merely just flew into the square's point of view. He introduces our hero not only to the third dimension, but even to the concept of more egalitarian gender roles. It's an interesting concept because it means more than one thing - not only the concept of other dimensions beyond what we know, but also, the idea that in a more complex society, gender roles may in fact be more equal.
There's not much story here, but plenty of food for thought.
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