The Analogy: Edwin Abbott’s Flatland: A Romance of Many Dimensions

At the outset of A Field Guide to Getting Lost, Rebecca Solnit explains how the book was inspired by a student bringing her an ancient koan: How will you go about finding that thing the nature of which is totally unknown to you? I don’t know that Solnit ever satisfactorily answers that question, unless the foggy, meandering book I discussed last week is itself her answer. (Which, appropriately, seems to be the author’s saying “get lost,” double entendre and all.) Unbeknownst to me, the other book I was reading contemporaneously to Solnit’s Guide was much more explicit in addressing the same question.

Edwin Abbott’s Flatland: A Romance of Many Dimensions is the story of a bunch of sentient, two-dimensional geometric shapes—weird, I know—and how one of them is finally enlightened to the existence of a third dimension, only to immediately be branded a lunatic by his society. And who can blame them? You wouldn’t believe someone who came up to you shouting about a literally trans-dimensional being who just revealed an entirely new aspect of reality.

aliens
Well, most people wouldn’t.

The revelation at the center of Flatland occurs after the two-dimensional protagonist does a Geometric Gulliver routine, meeting a one-dimensional being before meeting a three-dimensional one. In the former case, the protagonist is aware of a dimension that his companion can’t begin to fathom and so, in the latter case, he is able to extrapolate that initial experience out to understand that, just as the one-dimensional being’s blindness to the second dimension doesn’t preclude that dimension from existing, so too does his blindness to a third dimension not preclude such a dimension from being real.

It’s a clever combination of mathematics and storytelling and, more than the book’s satirical mockery of Victorian social norms, the lingering legacy of Abbott’s story is how it fosters critical thinking. And, as a writer, it tickles me that a book that is principally about math concludes that the true key to understanding is metaphor (or capital-A Analogy, in the book’s parlance) which is the tool of a writer, not a mathematician. Even in a land of talking triangles, a writer’s ability to communicate is central to an accurate understanding of the world.

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