Hiding in the Mirror (9 page)

Actually, an explicit connection between the
spiritual realm and something akin to extra dimensions predates
Zöllner by at least two centuries. In 1671 the Cambridge
philosopher Henry More proposed that spirits were four-dimensional.
He even framed a pseudoscientific quantity, which he called
“spissitude,” which differentiated between identical bodies of
living and dead persons. Living ones had more spissitude, which was
nevertheless unobservable because it had thickness in the fourth
dimension. A variation on this theme was taken up a century later
by the Swedish scientist, linguist, theologian, and mystic Emanuel
von Swedenborg. Swedenborg wrote over fifty works on science,
chemistry, and theology and was fluent in eleven languages. His
remarkable combination of brilliance, spiritual flights of fancy,
and mystical visions (which may have been a symptom of underlying
schizophrenia) had a huge impact on generations of writers from
Goethe to Henry James. In midlife, inspired by a series of
visionary experiences, he abandoned his scientific investigations
and devoted himself to prophecy and spirituality. Perhaps because
of his scientific background, however, we find in Swedenborg an
explicit turning to science as an explanation of the spirit world.
In particular, he argued that humankind existed simultaneously in
two parallel worlds, the material and the spiritual, the latter of
which is populated by angels and also humans after they die. Among
his other postvisionary writings is the book
Earths in the
Universe,
in
which he claimed that the moon was populated by aliens who speak
through their stomachs with a language that sounds like
belching!

By the time of
Flatland
many English clergy had taken up with renewed fervor the notion
that the fourth dimension was associated with spritual phenomena.
Their viewpoint was presented by A. T. Schofield in his book,
Another World
(1888), in which he wrote:
“We conclude, therefore, that a higher world than ours is not only
conceivably possible, but probable: secondly, that such a world may
be considered a world of four dimensions, and thirdly, that the
spiritual world agrees largely in its mysterious laws . . . in its
miraculous appearances . . . with what would be the laws, language,
and claims of a fourth dimension.”

An interesting and similar view is expressed in
a piece by N. A. Morosoff, “Letter to my Fellow-Prisoners in the
Fortress of Schlusselburg” (1891), where he muses about how he and
his three-dimensional friends might appear if they managed to
escape and visit a nearby lake to twodimensional beings who were
confined to the surface of the lake: “In their eyes you would be an
all-powerful being—an inhabitant of a higher world, similar to
those supernatural beings about whom theologians and metaphysicians
tell us.”

A fourth spatial dimension was not just exotic
but offered many possibilities that obviated the constraints of our
existence, and in so doing promised to free our minds from the
vicissitudes of our own tedious three dimensional lives. What if
traveling into another dimension allowed one to touch back down
into our three dimensions of space, but at a different time? Would
time travel then be possible? What about ESP or remote sensing?
Could one somehow “sense” phenomena through perceptions into
another dimension that one could not perceive otherwise? What about
God, the spirit world, or even aliens? How many angels in the
fourth dimension could dance on the head of a pin? As we shall
later see, all of these issues have been the fodder for fiction,
speculation, and belief in the twentieth century.

Abbott himself clearly viewed the fourth
dimension as providing possibilities for performing precisely the
kind of magic of which Zöllner believed Slade was capable. Witness
his 2D hero’s dialogue with his 3D spherical guide, who visited him
coincidentally at midnight on the last day of 1999, which even in
Flatland
they incorrectly referred to as
the end of the second millennium:

“Pardon me. O Thou Whom I must no longer
address as the Perfection of all Beauty; but let me beg thee to
vouchsafe thy servant a sight of thine interior.”

“My what?”

“Thine interior: thy stomach, thy
intestines.”

“Whence this ill-timed impertinent request? And
what mean you by saying that I am no longer the Perfection of all
Beauty?”

“My Lord, your own wisdom has taught me to
aspire to One even more great, more beautiful, and more closely
approximate to Perfection than yourself. As you yourself, superior
to all
Flatland
forms, combine many Circles
in One, so doubtless there is one above you who combines many
Spheres in One Supreme Existence, surpassing even the Solids of
Spaceland. And even as we, who are now in Space, look down on
Flatland
and see the insides of all things,
so of a certainty there is yet above us some higher, purer region,
wither thou dost surely purpose to lead me. . . . Some yet more
spacious Space, some more dimensionable Dimensionality, from the
vantage-ground of which we shall look down together upon the
revealed insides of Solid things, and where thine own intestines,
and those of thy kindred Spheres, will lie exposed to the view of
the poor wandering exile from
Flatland,
to
whom so much has already been vouchsafed. . . . What therefore more
easy than now to take his servant on a second journey into the
blessed region of the Fourth Dimension, where I shall look down
with him once more upon this land of Three Dimensions, and see the
inside of every three-dimensioned house, the secrets of the solid
earth, the treasures of the mines of Spaceland, and the intestines
of every solid living creature, even of the noble and adorable
Spheres. . . . I ask therefore, is it, or is it not, the fact, that
ere now your countrymen also have witnessed the descent of Beings
of a higher order than their own, entering closed rooms, even as
your Lordship entered mine, without the opening of doors or
windows, and appearing and vanishing at will?”

Magic tricks aside, Abbott’s tongue-in-cheek
handling of A. Square’s path to enlightenment through successively
higher dimensions is typical of another, perhaps more profound,
aspect of the literary tradition associated with the explorations
of other dimensions. This is its use in fiction as a medium of
social criticism. As we have seen, Carroll may have used Alice’s
experiences in the looking glass house to poke fun at British
idiosyncrasies, but Abbott’s story is rife with implicit satire
regarding racism, sexism, and even some aspects of religion. In
Flatland, women are Lines, essentially the lowest form of being,
who, because of the fact that they might accidentally pierce
unsuspecting males, must make a special cry in all public places to
make people aware of their location, and they have segregated
entrances in all buildings. Triangles are the next lowest class,
with very limited rights. Among them, Triangles with unequal sides
are workmen, who live lives of servitude. If, by chance or careful
arrangement, an Isosceles Triangle gives birth to a more
prestigious Equilateral Triangle, the child is removed and sent to
Equilateral parents, and forbidden from ever seeing its original
parents again. Squares are a bit higher in status, and so on, all
the way up to Spheres, who are priests and the most exalted of all.
It is heresy in Flatland to speak of higher dimensions, and one can
be jailed for life for thinking or suggesting a better possible
existence in three dimensions.

In
The Time Machine
H.
G. Wells employed temporal travel as a means of using the future as
a mirror for the present. The destruction of society by misuse of
technology, which gave rise to a caste system populated by widely
divergent biological descendants of present-day humans, allowed
Wells, in a manner that has been a characteristic of much of
science fiction, to explore issues that would have been more
contentious if framed purely in the here and now.

Yet another aspect of the use of higher
dimensions in nineteenth-and twentieth-century literature was as an
impetus to free up the mind for speculation about the universe.
Charles Hinton, a British mathematician and physicist who
essentially devoted his life to writing about the fourth dimension,
took this approach. He felt that if we could improve our intuition
to comprehend the nature of four-dimensional objects, our minds
would be liberated to better appreciate all aspects of the world
around us. To this end he wrote innumerable stories and books
outlining precise methods by which he felt one could visualize
objects such as the four-dimensional extension of a cube, which he
called a tesseract, by picturing different threedimensional cubes
that would provide its faces, just as two-dimensional squares
provide the faces of a three-dimensional cube, or by imagining how
the image of such an object might be projected onto three
dimensions, just as one might project the image of a
three-dimensional cube onto the surface of a page.

I recommend trying the latter if you truly want
to get an appreciation for how hard it must have been for A. Square
to attempt to visualize a sphere. Incidentally, it was none other
than Abbott’s Square who presented a simple mathematical algorithm
to help out. How many end points in a line? Two. How many end
points in a square? Four. How many end points in a cube? Eight. It
does not take a rocket scientist to extend the sequence 2,4,8, to
imagine that a tesseract must have sixteen end points. Similarly,
if a line is obtained by joining two points, and a square can be
obtained by joining together four lines, and a cube six squares,
one should be able to construct a tesseract by appropriately
connecting eight cubes. Because Hinton believed the world was, in
actuality, fourdimensional—as he put it, “We must really be
four-dimensional creatures or we could not think about four
dimensions”—he considered how a true four-dimensional understanding
might alter our scientific worldview. In this respect Hinton appears
strikingly modern, and some of his ideas bear at least a
resemblance to current proposals I shall later describe, even if
Hinton himself had no appropriate underlying theoretical basis for
his contentions. Among his proposals were the suggestion that the
existence of higher dimensions might help in our understanding of
minute elementary particles, whose physical extension might be as
large in a fourth dimension as it is in the other three. He also
wondered whether the existence of positive and negative electric
charges might somehow be a reflection of some underlying
four-dimensional phenomena. Finally, he considered whether the very
space in which we live, which was then thought to be permeated by
an invisible ether (which, as we have seen, Albert A. Michelson, a
student at the Naval Academy, where Hinton taught for awhile, would
soon demonstrate did not exist), might have been formed as the
common boundary of two adjacent four-dimensional spaces, just as a
line can form the common surface of two adjacent squares, and a
plane the common surface of two adjacent cubes. Actually a
connection between the long-sought ether and a fourth dimension had
another, somewhat weirder manifestation. In the 1860s William
Thomson, better known as the famous physicist Lord Kelvin, proposed
the interesting idea that matter is made up at a fundamental level
of three-dimensional “vortex rings” in the ether. Vortex rings are
like smoke rings that swirl around and around on themselves,
decoupled from the air around them.

Thomson’s notion was actually reasonably well
founded, and, as we shall again see, seems strikingly modern. It
explained, for example, why atoms would have a finite size but would
nonetheless be indivisible. (If you cut a smoke ring in half, it
just dissipates in the air.) While Thomson’s proposal eventually
died as atoms became better understood, it did spawn a far wilder
concept, which appeared in a book entitled
The
Unseen Universe
(1875) by B. Steward and P. G. Tait. The latter
was a very highly regarded mathematician and also a former
collaborator of Kelvin. These authors, returning once again to a
connection between spirits and extra dimensions, suggested that our
very souls existed as knotted vortex rings in the ether. These
knots, created by God, could of course only be unknotted by moving
into a higher dimension. (Thomson’s notions of vortices and the
ether also inspired the French writer Alfred Jarry, who was
connected with the cubist artists as I shall soon discuss, to write
a “Commentary” on four dimensions and possible time machines.)
Steward and Tait’s idea might not be worth mentioning, except for
the fact that none other than James Clerk Maxwell wrote about it in
his famous 1876
Britannica
encyclopedia
article on the ether. He was apparently so amused by it that he
also wrote a poem about unknotting his soul in four dimensions,
which you can find quoted later in this book. Following yet further
on the possibility of the ether as a portal into higher dimensions,
Karl Pearson proposed in 1892 that atoms are not vortex rings, but
rather merely points where an underlying four-dimensional etherlike
field literally leaked out into our three-dimensional space. This
“aether squirt” theory became quite popular for some time. Hinton’s
oft-stated, utter conviction that a fourth dimension was an
essential part of our being was not unique. The Russian self-taught
journalist, philosopher, and mystic Peter Ouspensky wrote an opus
entitled
Tertium Organum
(1912) in which he
stated this premise even more strongly:

“And when we shall see or feel ourselves in the
world of four dimensions we shall see that the world of three
dimensions does not really exist, and has never existed; that it
was the creation of our own fantasy, a phantom host, an optical
illusion, a delusion—anything one pleases excepting only
reality.”