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.

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