Engines of Our Ingenuity

No. 783: FLATLAND

by John H. Lienhard

Click here for audio of Episode 783.

Today, we wonder if a book is on the wrong shelf. The University of Houston's College of Engineering presents this series about the machines that make our civilization run, and the people whose ingenuity created them.

I'm in the library stacks. I'm in the section on very pure mathematics. Here's one on the geometry of higher dimensions: "Spectral Theory in the Hilbert Space." Next to it is an old book of a very different kind. The title is Flatland.

This is an odd pairing indeed -- one more way the Library of Congress classification drives the sober to drink. You see, on the one hand, Flatland did anticipate the mathematics of relativistic space. On the other hand, the book is pure social satire.

Flatland came out in 1884. The author was Edwin Abbott, a progressive Anglican clergyman. He believed we should use our minds to sort out the rising debate between science and religion.

His allegorical world of Flatland is, literally, a 2-dimensional world, Its citizens are flat triangles, squares, higher polygons, and finally perfect circles. They live and move in a planar landscape -- with no up or down.

The more sides you have, the higher your social standing. At the bottom are triangular laborers. At the top are priestly circles. Abbott writes under the name of A. Square. He's a respectable member of the middle class. Mr. A. Square parodies Victorian social and sexual inequality with chilling accuracy.

Then, one day, a sphere moves through the planar world of Flatland. A. Square sees it as a dot widening into a circle that then shrinks back to a dot and disappears. The sphere takes A. Square into the world of 3 dimensions and opens his eyes to things beyond his imagining.

Back in Flatland, A. Square tells his vision of the third dimension. He is ridiculed, ignored, and finally haled into prison where he writes his book. Indeed, he was already in trouble during his visit with the sphere. As the world of 3 dimensions opened up, he wondered if a fourth dimension might lie beyond the sphere's comprehension. The sphere scolded him for his foolish speculation.

Abbott's message to the conservative church was, "Be more cautious about the reach of your understanding. Honor your own limitations." Then, just a few years later, Einstein made time into a fourth dimension. What Relativity Theory said about 4-dimensional reality was no less stunning to us than A. Square's trip through 3-dimensional space had been for him.

So I look at those two books: Relativistic geometry next to Flatland. Did some library cataloger have a bent sense of humor? Maybe pigeon-holing knowledge is a fool's game to begin with. Either way, Abbott's moral fable warns that the world holds huge surprises -- but only if we're ready to see them.

I'm John Lienhard, at the University of Houston, where we're interested in the way inventive minds work.

(Theme music)


Abbott, E. A., Flatland, A Romance of Many Dimensions. Cutchogue, NY: Buccaneer Books, 1976 (This is one of many reprints of the 1884 second edition. It appears that the first edition had come out earlier that same year.)

My good listeners, you are in luck here! You may find the complete text of Abbott's Flatland at the following website:

http://www.alcyone.com/max/lit/flatland/


The Engines of Our Ingenuity is Copyright © 1988-1997 by John H. Lienhard.

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