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

Cutting a hypercube in the right way allows one to unfold it and reform it into
a 3D pattern of eight cubes, just as a 3D cube can be made up of six squares.
One choice looks like a sort of 3D cross. Salvador Dali used this as a crucifix
in his 1954 painting Christus Hypercubus. Not only does the hypercube suggest
the presence of a higher reality; Dali deals with the problem of projecting into
lower dimensions. On the floor beneath the suspended hypercube, and the
crucified Christ, is a checkerboard pattern -- except directly below the
hypercube. There, the hypercube's shadow forms a square cross. (Shadows are the
only 2D things in our world; they have no thickness.) Comparing this simple
cross with the reality of the hypercube which casts the shadow, we contemplate
that our world is perhaps a pallid shadow of a higher reality, an implicit
mystical message.

Robert Heinlein gave this a twist with "And He Built a Crooked House," in which
a house built to this pattern folds back up, during an earthquake, into a true
hypercube, trapping the inhabitants in four dimensions. Much panic ensues.

Rudy Rucker, mathematician and science fiction author, has taken A Square and
Flatland into myriad fresh adventures. I met Rucker in the 1980s and found him
much like his fictional narrators, inventive and wild, with a cerebral spin on
the world, a place he found only apparently commonplace. His The Sex Sphere
(1983) satirizes dimensional intrusions, many short stories develop ideas only
latent in Flatland, and his short story "Message Found in a Copy of Flatland"
details how a figure much like Rucker himself returns to Abbott's old haunts and
finds the actual portal into that world in the basement of a Pakistani
restaurant. He finds that the triangular soldiers can indeed cut intruders from
higher dimensions, and flatlanders are tasty when he gets hungry. As a sendup of
the original it is pointed and funny.

In science fiction there have been many stories about creatures from the fourth
dimension invading ours, generally with horrific results. Greg Bear's "Tangents"
describes luring 4D beings into our space using sound. While we puzzle over
whether an unseen fourth dimension exists, modem physics has used the idea in
the Riemannian manner, to expand our conceptual underpinnings. Riemann saw a
mathematical theme of conceptual spaces, not merely geometrical ones. Physics
has taken this idea and run with it.

Abbott's solving the problem of flatlander physical reality by adding a tiny
height to them was strikingly prescient. Some of the latest quantum field
theories of cosmology begin with extra dimensions beyond three, and then "roll
up" the extras so that they are unobservably small --perhaps a billion billion
billion times more tiny than an atom. Thus we are living in a universe only
apparently spatially three-dimensional; infinitesimal but real dimensions lurk
all about us. In some models there actually are eighteen dimensions in all!

Even worse, this rolling up occurs by what I call "wantum mechanics" --we want
it, so it must happen. We know no mechanism which could achieve this, but
without it we would end up with unworkable universes which could not support
life. For example, in such field theories with more than three dimensions, which