Abbott's Flatland: Imagining the spatial dimensions

Edwin Abbott Abbott (1838-1926), English schoolmaster and theologian, is best known as the author of the mathematical satire and religious allegory Flatland: A Romance of Many Dimensions (1884).

Here's the gist of the Flatland story, from PBS Nova's Imagining Other Dimensions:

"The square [the unnamed narrator in the story] describes his world as a plane populated by lines, circles, squares, triangles, and pentagons. Being two-dimensional, the inhabitants of Flatland appear as lines to one another. They discern one another's shape both by touching and by seeing how the lines appear to change in length as the inhabitants move around one another.

"One day, a sphere appears before the square. To the square, which can see only a slice of the sphere, the shape before him is that of a two-dimensional circle. The sphere has visited the square intent on making the square understand the three-dimensional world [Spaceland] that he, the sphere, belongs to. He explains the notions of "above" and "below," which the square confuses with "forward" and "back." When the sphere passes through the plane of Flatland to show how he can move in three dimensions, the square sees only that the line he'd been observing gets shorter and shorter and then disappears. No matter what the sphere says or does, the square cannot comprehend a space other than the two-dimensional world that he knows.

"Only after the sphere pulls the square out of his two-dimensional world and into the world of Spaceland does he finally understand the concept of three dimensions. From this new perspective, the square has a bird's-eye view of Flatland and is able to see the shapes of his fellow inhabitants (including, for the first time, their insides)."

Flatland is also a satire on the social hierarchy of Victorian society. But even today, Flatland continues to be popular, especially among mathematicians and computer science students. It's because Flatland provides a visualization of how the spatial dimensions interact.

[Image: Wikipedia]

Related post: Fred Alan Wolf and Flatland
Related post: Flatland on films

2D, 3D, 3rd dimension, Edwin Abbott Abbott, Flatland, spatial dimensions

Comments

[Jerry Thornton]

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