Deflating Hyperspace

[Dave Monroe]

"Deflating Hyperspace" by: David Pacchioli (Research/Penn State, Vol.
16, no. 4 (December, 1995))

Where exactly is hyperspace?

[...]

It's all in your head, of course.

In which case, well, what is it doing there? And, um . . . why is it
taking up so much . . . space?

Or, as Jason Chernosky more decorously puts it: "What cultural work is
getting done by this curiously protean word?"

For Chernosky, a Ph.D. candidate in English literature, this isn't
exactly the same thing as asking what hyperspace means. Hyperspace
seems to mean a lot of things, and then again not to mean much at all;
its meaning shifts with the user, if not with the wind. It is,
Charnesky writes, "an almost empty signifier capable of almost
limitless application."

"This fuzziness," he adds in person, "is its power." It is also a
quality that puts hyperspace in rather crowded company. Our language
is loaded with terms appropriated from science for use in popular
discourse. Along the way, the borrowed word's highly technical,
narrowly precise -- not to say arcane -- meaning is typically
transformed. What emerges is a fluttering, eye-catching, all-purpose
concept that can be used interchangeably for explaining the weather or
selling toothpaste.

[...]

"Hyperspace" is now enjoying a similar vogue. The difference, says
Chernosky, is that in this case it's the second time around.
Hyperspace, it turns out, is a concept with a history.

"We were doing the same thing 100 years ago with the very same word."

The term hyperspace emerged, for the first time, out of the very
specialized context of mid-19th-century analytical geometry.

Geometry had, for 2,000 years, been the province of Euclid. The Greek
master's three-dimensional arsenal of spheres and triangles "were
believed to be truly existing aspects of the real earth, clearly
evident in real space," as Chernosky writes. This concreteness matched
well with Victorian scientific rationalism; classical geometry was
regarded by educators as science's apogee. But by mid-century a
revolution had taken place in mathematics -- one whose repercussions
continue to be felt. For at about that time, two new geometries arose
to change the way we see the world.

The first of these geometries, called simply non-Euclidean,
successfully presented a three-dimensional space in which Euclid's
parallel postulate (which states that through a point outside a line
only one line can be drawn parallel to the given line) is violated,
without contradictions.

The second, less remembered today, is known as n-dimensional geometry.

"Since Descartes," Chernosky explains, "analytical geometry
represented spatial dimensions with algebraic variables, x, y, and z.
Theoretically, there was no reason why a fourth variable could not be
added. Algebraically, such four-dimensional geometries are perfectly
self-consistent." Nineteenth-century geometers began exploring the
meaning of this truth.

To discuss new parameters they needed a new word. The term designated
to refer to space other than the Euclidean, i.e., space of more than
three dimensions, was "hyperspace."

The ripple effect occasioned by the fourth dimension's arrival was
swift. "A change in geometrical theory which carried with it such
important philosophical ramifications," Chernosky writes, "gave
writers and thinkers a new metaphor."

By 1884, hyperspace had made its debut in fiction, in a novel by the
Anglican clergyman Edwin Abbott Abbott. In Abbott's charming Flatland:
A Romance of Many Dimensions by A Square, a Square, inhabiting the
world of two dimensions, is visited by a Sphere. Made thus aware of
the existence of a third dimension, Square wonders aloud about the
possibility of four dimensions, or five, or more . . . and is
imprisoned for this heresy. (The book is still prized by
science-fiction aficionados.) Ten years later, H. G. Wells wrote The
Time Machine, for the first time treating time itself as the fourth
dimension.

Many geometers, for their part, were quick to issue disclaimers. E. H.
Neville, in his book, The Fourth Dimension, attempted to stem the
popular tide:

"The pure mathematician," he wrote, "makes no attempt to imagine a
space of four dimensions; he lays no claim to visualizing a world that
is inconceivable to other men. . . . Now it has happened that the talk
of a few mathematicians has suddenly become of universal and absorbing
interest. . . . [Mathematicians are not talking] about a new heaven
and a new earth but about linear algebraic equations."

But such protestations were no use. Hyperspace continued to show up in
science fiction and popular philosophy. Spiritual and mystical tracts
were published in Europe and the United States, with titles like The
Unseen Universe, An Experiment with Time, and Little Journeys into the
Invisible: A woman's actual experiences in the fourth dimension. At
the same time, the Theosophists, proponents of a mystical,
Buddhist-influenced religious philosophy in which reincarnation played
a central role, latched on to hyperspace as a way of explaining their
concept of higher planes.

Attempts to represent hyperspace in visual terms were equally popular.
British mathematician Charles Hinton devised a system involving a set
of multi-colored cubes that would help a viewer visualize a
four-dimensional hypercube.

Perhaps the foremost American proponent of the fourth dimension was
the architect and theosophist Claude Bragdon. Bragdon published
numerous books on the subject through his Manas Press, including his
own English translation (the first) of the Russian spiritualist P. D.
Ouspensky's Tertium Organum, probably the most widely read book ever
written on the fourth dimension. Bragdon also developed an
architectural style which, as Chernosky writes, "employed three
dimensional sections of four dimensional hyper-shapes as the unifying
motifs and structural elements of his buildings. These 'shadows of the
fourth dimension' were meant to serve as embodied reminders . . . of a
higher spiritual reality which, Bragdon feared, America was quickly
forgetting."

In invoking hyperspace, Charnesky says, all of these disparate
popularizers had one aim. "They were using the new geometries to make
scientific their spiritual yearnings." By grounding their beliefs and
speculations in the hard rock of science they were giving them a
legitimacy they otherwise lacked.

Chernosky's first encounter with the early popularization of
hyperspace came via the poet W. B. Yeats. Yeats was an artist with
considerable interest and involvement in the occult. For a time he was
a theosophist, and later he joined the secret London society known as
the Golden Dawn. One of the knottier problems for Yeats scholars has
been a slim volume called A Vision, authored by the poet with his
wife. This peculiar book purports to explain in scientific fashion the
source of the artist's creative power. The "vision" of the book's
title was a manifestation of the spirit world which "dictated" Yeats'
poems, so he wrote, through the medium of his wife. This transmission
centered around a complicated -- indeed, heretofore unintelligible --
system of geometry.

"Yeats' system features a pair of interlocking cones," Chernosky says.
He seizes pen and paper and draws them.

At the time Chernosky was struggling to understand A Vision, he was
also reading some of the occult stuff -- "the 19th-century New Age" --
that had influenced Yeats. When he saw the cones, they immediately
looked familiar.

"I thought, 'Ouspensky has a diagram of a hypersphere,' " he
remembers, " 'and damn if it doesn't look like this.' I saw it and I
knew." The cones represented -- in two dimensions -- what a
hypersphere would look like if it were transported into
three-dimensional space.

Chernosky, excited, believed he had found a topic for a doctoral
dissertation. "I thought I was going to make some sense of Yeats for
the world," he says. This new connection would give A Vision the
historical context it had always lacked. "The reason Yeats used
geometry was that they were using geometry. There was this whole
culture out there."

The Yeats connection led him smack into the middle of this culture,
and soon enough to art historian Linda Dalrymple Henderson, who in a
1984 book traced the influence of the fourth dimension -- and
hyperspatial philosophy -- on modern art, and in particular on the
Cubist movement. "Duchamp's 'Nude descending a staircase,' " Chernosky
says, "is a vision of hyperspace." The influence extends in
literature, Henderson shows, to Gertrude Stein.

"Stein said 'What Picasso is doing with paint, I do with words,' "
Chernosky says. "Her work is called Cubist literature, but nobody
really knows what that means. I hope to place her in this tradition."

Nor did the spread of hyperspace end with Stein. "There was this whole
industry of writing these fourth-dimension books right up until the
1930s," Chernosky says, "and then it dies out.

"What happens is a new metaphor takes over -- relativity. Einstein
becomes the paradigm of scientific genius."

As this broader picture emerged, Chernosky's interest shifted from
Yeats to a larger, theoretical, question. Why? Why did the concept of
hyperspace become so popular? Or, as he puts it, why this concept and
not some other?

And how does the answer to this question relate to the current,
second, round of hyperspace's popularity?

The fourth dimension resurfaced in popular culture earlier than a
casual observer might think. "It had been there all along in science
fiction," Chernosky notes, "in that sub-genre known as space opera."
The real rebirth, however, came with the rise of computer networks in
the early 1980s. "A technology gets invented that needs a word,"
Chernosky says. "It's hard to trace exactly where a usage begins, but
very quickly the word becomes popularized."

Within a few years the concept had spread far beyond the Internet. So
Sports Illustrated in 1993 refers to the salaries of professional
athletes as having rocketed "into hyperspace." The Wall Street Journal
talks about hyperspace as the place where international finance is
transacted. And the variant term, "cyberspace," coined by
science-fiction writer William Gibson in the early 1980s to stress the
close connection to information technology, is simply ubiquitous.

"It's very similar to what was happening in the 19th century," Charnesky says.

"What's different," he adds, "is that before, all they had as examples
of hyperspace was this idea from mathematics, and the metaphors it
engendered. Hyperspace is like ghosts, like spirits, like God. Whereas
we have computers -- this magnificent technology. The spatial
metaphors from this technology are already part of the popular
culture."

What's the same as 100 years ago, Chernosky argues, is the value being
granted the term. "There's an assigning of importance," he says, "that
goes above and beyond the meaning of the word itself."

Anything affiliated with computers has instant cachet, the argument
runs, so we invoke its terms in all kinds of contexts, appropriating
their legitimacy. "We use them to win arguments which we wouldn't win
on their own merits."

But why does hyperspace have this power? What does it mean to us, that
we invoke it? It means a lot of things, but what it stands for,
Chernosky suggests, is transcendence -- the world beyond immediate
sensory experience. Linked to geometry -- queen of the queen of the
sciences -- in the 19th century, the concept of hyperspace gave
popular culture an acceptable way to talk about transcendence at a
time when traditional religious concepts were falling before the
onslaught of modernism. Linked to our supreme technology of today, it
again provides a bridge between seen and unseen, the rational and the
super-rational. The concept of hyperspace allows us to think about
transcendence in terms we can accept and understand -- or think we
understand.

[...]

"This is my claim -- that the 19th- and 20th- century uses of
hyperspace involve the same abstract machine."

In both cases, he contends, hyperspace mediates between realms of
discourse that otherwise would not communicate. And in both cases,
hyperspace is used as a "sign" for transcendence. What we gain by
noticing this similarity is the insight that "lots of people are using
this new idea to bolster the same old arguments."

Back in the 19th century, Charnesky relates, "after the theosophists
had used hyperspace to establish a bridge between their idea of higher
planes and the geometrical concept of mirror images, the spiritualists
moved in.

[...]

http://www.rps.psu.edu/dec95/hyper.html