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NEW YEAR’S EVE, just before midnight. You’re sitting at home, preparing to
welcome the coming year when suddenly a chilling voice comes from nowhere. You
sense a Presence, but there’s no one else in the room. Your blood seems to
freeze as an unearthly being materialises out of thin air: at first it is just a
tiny speck, but it grows with astonishing speed until it nearly fills the room . . .

What do you do? Well, if you are the protagonist of Edwin Abbott Abbott’s
Flatland, you mistake it for a woman. In Abbott’s fable, the hero is a
square—indeed, A. Square. His world is a two-dimensional plane, and its
inhabitants are straight out of the geometry book. The women are simply
one-dimensional—they are lines. The men are two-dimensional shapes:
triangles, squares, hexagons all the way up to the peerless circle. The Presence
is a sphere, a visitor from the mysterious third dimension. His intersection
with the planar world of Flatland is a circular slice which mysteriously changes
in size as the sphere moves.

Flatland, which appeared at the end of 1884, satirised the rigid
hierarchies of Victorian society, especially the subservient role of women. But
it also introduced its readers to the fourth dimension. A decade later, in 1895,
H. G. Wells’s The Time Machine appeared in The New Review,
setting out the possibility of time travel through the idea of time as a fourth
dimension.

Extra dimensions are now a standard feature of modern physics and
mathematics. But they remain just as difficult to comprehend as they were when
they began to fascinate Victorian society—which is why Abbott and Wells
have received such acclaim for their skill in explaining them.

Yet that acclaim may be somewhat misplaced. It seems that the real hero of
Victorian science writing—the inspiration for both Abbott and
Wells—was a mathematician and writer called Charles Howard Hinton. The
story linking Hinton, Wells and Abbott is a tangled one, but it provides a
beautiful illustration of how strangely science can interact with the rest of
human culture.

Hinton was a talented mathematician, in touch with the latest developments in
geometry. By the 1840s, mathematicians were beginning to move beyond the three
spatial dimensions we are familiar with, and into multidimensional space. Hinton
wrote for the public, popularising these complex ideas. In an 1880 issue of the
Dublin University Magazine he published an article entitled “What is
the Fourth Dimension?”. His canny publisher later reissued it as a pamphlet with
the subtitle “Ghosts explained”.

The Victorian public was not interested in the fourth dimension in a
scientific sense. The driving force for them was spiritualism, the belief that
the dead can communicate with the living, usually via a medium in a state of
trance. The fourth dimension is an ideal place to put the spirit world: in
contact with our world at every point, yet not part of it. Just as Abbott’s
sphere can manifest itself from the third dimension, spirits can materialise
from the fourth to remove the contents of sealed vessels, untie knots, or do
anything else you might care to imagine.

Highlighting a parallel between multidimensional mathematics and explanations
of the paranormal was—if not strictly accurate—a master stroke of
marketing. And Hinton’s writing was certainly inspirational to Abbott: the
similarities between Hinton’s 1880 article and Abbott’s 1884 book are too great
to be coincidence.

There is no record that the two men ever met, but it seems more than likely
that they did. Abbott’s desire to improve women’s education frequently led him
into the company of Dorothea Buss, Headmistress of Cheltenham Ladies’ College.
Hinton taught at Cheltenham from 1875 until the early 1880s. Abbott would almost
certainly have met Hinton there.

Even if they’d never met, Abbott could easily have come across Hinton’s essay
on the fourth dimension, which was reprinted in the college magazine in 1881.
And another opportunity for Hinton’s influence to reach Abbott arose when Hinton
moved from Cheltenham to become science master at Uppingham School. Flatland is
dedicated to Howard Candler, the mathematics master at Uppingham, who was
Abbott’s best friend. Abbott and his wife often visited Uppingham to meet the
Candlers.

The link with The Time Machine is just as hard to establish
concretely, even though the novel does bear traces of Hinton’s inspirational
fingerprints. Wells has said that he got the idea for from student discussions
in the Royal College of Science. At first sight that seems to rule out Hinton as
the inspiration, but it’s likely that things weren’t that straightforward.

Wells was a regular reader of Nature, which reviewed Hinton’s first
collection of “Scientific romances” in 1885. The review summarised his
explanations of the fourth dimension. Shortly afterwards Nature
published a reader’s response to the review that proposed considering time as
the fourth dimension—signed, enigmatically, “S”. The writer was almost
certainly the mathematician James Joseph Sylvester, who habitually signed
personal letters that way. Sylvester explained to friends as early as 1870 that
he and other mathematicians viewed time as a fourth dimension of space.

And there’s another link to Sylvester. In the introduction to The Time
Machine, the Time Traveller mentions a talk on four-dimensional
geometry given to the New York Mathematical Society by a Simon Newcomb. This was
a real-life event: Newcomb was a mathematician who was influenced by Sylvester
and his student William Kingdon Clifford. Newcomb published papers on
four-dimensional space from 1877 onwards, and he spoke to the society in
1893—obviously causing a big enough stir to be discussed back in London.
Wells’s book appeared just two years later.

Though Sylvester obviously played a larger part in inspiring Wells, it’s
likely that Hinton’s work, reported and discussed in Nature, had
sparked Wells’s interest.

Hinton’s influence and insight remain relevant today. In his 1880 essay, he
addressed the issue of why, supposing that space really has four dimensions, we
don’t notice the other one. His answer is: “our proportions in [a fourth
dimension] must be infinitely minute. It would probably be in the ultimate
particles of matter, that we should discover the fourth dimension.”

Modern physicists seeking a unified “theory of everything” have focused on
superstrings, in which space-time has six extra dimensions. And they give the
identical explanation for why we don’t notice them. Spooky, huh?