"Benford-FourthDimension" - читать интересную книгу автора (Benford Gregory)

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