Benford, Gregory - Fourth Dimension

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GREGORY BENFORD

THE FOURTH DIMENSION

Suppose that next to you, right now, a pale gray sphere appeared. It grew from

baseball-sized to a diameter as big as you -- grainy, gray, cool to the touch --

then shrank to a point . . . and disappeared.

You would probably interpret it as a balloon blown up, then deflated. But where

did the flat balloon go?

Or you could realize that you had been visited by a denizen of a higher

dimension -- a four dimensional sphere, or hypersphere. In three dimensions, it

looks like a sphere, the most perfect of figures, just as a sphere projected in

two dimensions makes a circle. The fact that this isn't an everyday occurrence

implies that travel between dimensions is uncommon, but not that it is

illogical.

Probably you would not have thought of such ideas before 1884. That is due to

the Reverend Edwin Abbott Abbott, M.A., D.D., headmaster of the City of London

School.

Respected, well liked, he led a strictly regular life, as proper as a

parallelogram. He had published quite a few conventional books with titles like

Through Nature to Christ, Parables for Children and How to Tell the Parts of

Speech. These did not prepare the world for his sudden excursion into the

fantastic, in 1884. Beneath his exterior he was a bit odd, and his short novel

Hatland has proved his only hedge against oblivion, an astonishingly prescient

fantasy of mathematics.

Abbott's oddity began with his repeated name, which a mathematical wit might see

as A times A or A Squared, A[sup 2]. Abbott's protagonist is A Square, a much

troubled spirit. Liberated into another character, Abbott seems to have broken

out of his cover as a prim reverend, and poured out his feelings.

The book has a curiously obsessive quality, which perhaps accounts for its

uneasy reception. Reviewers termed it "soporific," "prolix,"" mortally tedious,"

"desperately facetious, "while others found it "clever," "fascinating," "never

been equaled for clarity of thought," and "mind broadening," and they even

likened it to Gulliver's Travels. This last comparison is just, because beneath

the math drolleries lurks a penetrating satire of Victorian society.

A Square's society is as constrained as were the prim Victorians. Women are not

full figures but mere lines. Soldiers are triangles with sharp points, adept at

stabbing. The more sides, the higher the status, so hexagons outrank squares,

and the high priests are perfect circles.

In a delicious irony, the upper classes are polygons with equal sides --but

their views certainly do not embrace equality. Mathematicians term equal-sided

figures "regular," and in nineteenth century terms, proper upper class polygons

are of the regular sort.

A Square learns that his view of the world is too narrow. There is a third

dimension, grander and exciting. but his hidebound fellows cannot see it. This

opening-out is the central imaginative event of the novel, Abbott echoing an

emergent idea.

In the late nineteenth century higher dimensions were fashionable.

Mathematicians had laid the foundations for rigorous work in higher-dimensional

space, and physicists were about to begin using four-dimensional spacetime.

Twenty centuries after Euclid, the mathematician Bernhard Riemann took a great

leap in 1854, liberating the idea of dimensions from our spatial senses. He

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Benford, Gregory - Fourth Dimension

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