Flatland opens with the following paragraph:

Imagine a vast sheet of paper on which straight Lines, Triangles, Squares, Pentagons, Hexagons, and other figures, instead of remaining fixed in their places, move freely about, on or in the surface, but without the power of rising above or sinking below it, very much like shadows—only hard with luminous edges—and you will then have a pretty correct notion of my country and countrymen. Alas, a few years ago, I should have said "my universe:" but now my mind has been opened to higher views of things.

First, I must admit that I'm still early on in the book, but I couldn't help but notice the resemblance to Plato's Cave: first, the phrase "very much like shadows", then the fact that the narrator now has a "higher view." Am I understanding this correctly, or am I reading too much into it?

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    Probably overreading. Plato's ideal-transcendence can't be reduced to a quantifiable dimension. – CJ Sheu Nov 13 '17 at 18:04

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