that our consciousness moves intermittently in
one direction along the latter from the beginning to the end of our
lives.”
“That,” said a very young man, making spasmodic
efforts to relight his cigar over the lamp, “that . . . very clear
indeed.”
“Now, it is very remarkable that this is so
extensively overlooked,” continued the Time Traveller, with a
slight accession of cheerfulness. “Really this is what is meant by
the Fourth Dimension, though some people who talk about the Fourth
Dimension do not know they mean it. It is only another way of
looking at Time. THERE IS NO DIFFERENCE BETWEEN TIME AND ANY OF THE
THREE DIMENSIONS OF SPACE EXCEPT THAT OUR CONSCIOUSNESS MOVES ALONG
IT. But some foolish people have got hold of the wrong side of that
idea. You have all heard what they have to say about this Fourth
Dimension?”
“I have not,” said the Provincial Mayor.
“It is simply this. That Space, as our
mathematicians have it, is spoken of as having three dimensions,
which one may call Length, Breadth, and Thickness, and is always
definable by reference to three planes, each at right angles to the
others. But some philosophical people have been asking why THREE
dimensions particularly—why not another direction at right angles
to the other three?—and have even tried to construct a
FourDimension geometry. Professor Simon Newcomb was expounding this
to the New York Mathematical Society only a month or so ago. You
know how on a flat surface, which has only two dimensions, we can
represent a figure of a three-dimensional solid, and similarly they
think that by models of three dimensions they could represent one
of four—if they could master the perspective of the thing.
See?”
This passage is remarkable not merely because
of Wells’s anticipation of a connection between space and time in a
four-dimensional framework, but because he correctly recognized
that what fascinated writers and the public alike was not a temporal fourth dimension but a spatial
one. Wells also wrote several stories reminiscent of Flatland, in which he utilized four spatial
dimensions as plot devices. In no fewer than four tales Wells
exploited different manifestations of extra dimensions that would
be borrowed by a host of future science fiction writers. These
included a story involving a person being turned into his mirror
image through a four-dimensional rotation, the possibility of
connecting otherwise distant locations in three-dimensional space
via a four-dimensional portal, the mysterious appearance and
disappearance of a four-dimensional being (an angel, as it happens)
traveling through our three-dimensional plane of existence, and
finally an object achieving invisibility by sliding into the fourth
dimension.
About 150 years earlier, around the same time
as d’Alembert was writing, none other than Immanuel Kant was
pondering the possibilities of extra spatial dimensions. While he
may have felt that Euclidean geometry was an essential part of
existence, he was much more sanguine about variations beyond our
three-dimensional space, although he felt that while they could
exist, they must be separate from ourselves. He discussed this
possibility in his very first published work, Thoughts on the True Estimation of Living Forces, concluding: “Spaces of this kind,
however, can not stand in connection with those of a quite
different constitution. Accordingly such spaces would not belong to
our world, but must form separate worlds.”
The German physicist and mathematician August
Möbius, father of the famous one-sided Möbius strip, followed up on
Kant’s earlier musings from the 1700s and came up with an
interesting suggestion. He argued in 1827 that a fourth dimension
would allow otherwise distinct threedimensional figures—such as a
right hand and a left hand—to coincide. Namely, just as a mirror
flips left and right, one could turn a right hand into a left hand
by twisting it into a fourth dimension and back
one direction along the latter from the beginning to the end of our
lives.”
“That,” said a very young man, making spasmodic
efforts to relight his cigar over the lamp, “that . . . very clear
indeed.”
“Now, it is very remarkable that this is so
extensively overlooked,” continued the Time Traveller, with a
slight accession of cheerfulness. “Really this is what is meant by
the Fourth Dimension, though some people who talk about the Fourth
Dimension do not know they mean it. It is only another way of
looking at Time. THERE IS NO DIFFERENCE BETWEEN TIME AND ANY OF THE
THREE DIMENSIONS OF SPACE EXCEPT THAT OUR CONSCIOUSNESS MOVES ALONG
IT. But some foolish people have got hold of the wrong side of that
idea. You have all heard what they have to say about this Fourth
Dimension?”
“I have not,” said the Provincial Mayor.
“It is simply this. That Space, as our
mathematicians have it, is spoken of as having three dimensions,
which one may call Length, Breadth, and Thickness, and is always
definable by reference to three planes, each at right angles to the
others. But some philosophical people have been asking why THREE
dimensions particularly—why not another direction at right angles
to the other three?—and have even tried to construct a
FourDimension geometry. Professor Simon Newcomb was expounding this
to the New York Mathematical Society only a month or so ago. You
know how on a flat surface, which has only two dimensions, we can
represent a figure of a three-dimensional solid, and similarly they
think that by models of three dimensions they could represent one
of four—if they could master the perspective of the thing.
See?”
This passage is remarkable not merely because
of Wells’s anticipation of a connection between space and time in a
four-dimensional framework, but because he correctly recognized
that what fascinated writers and the public alike was not a temporal fourth dimension but a spatial
one. Wells also wrote several stories reminiscent of Flatland, in which he utilized four spatial
dimensions as plot devices. In no fewer than four tales Wells
exploited different manifestations of extra dimensions that would
be borrowed by a host of future science fiction writers. These
included a story involving a person being turned into his mirror
image through a four-dimensional rotation, the possibility of
connecting otherwise distant locations in three-dimensional space
via a four-dimensional portal, the mysterious appearance and
disappearance of a four-dimensional being (an angel, as it happens)
traveling through our three-dimensional plane of existence, and
finally an object achieving invisibility by sliding into the fourth
dimension.
About 150 years earlier, around the same time
as d’Alembert was writing, none other than Immanuel Kant was
pondering the possibilities of extra spatial dimensions. While he
may have felt that Euclidean geometry was an essential part of
existence, he was much more sanguine about variations beyond our
three-dimensional space, although he felt that while they could
exist, they must be separate from ourselves. He discussed this
possibility in his very first published work, Thoughts on the True Estimation of Living Forces, concluding: “Spaces of this kind,
however, can not stand in connection with those of a quite
different constitution. Accordingly such spaces would not belong to
our world, but must form separate worlds.”
The German physicist and mathematician August
Möbius, father of the famous one-sided Möbius strip, followed up on
Kant’s earlier musings from the 1700s and came up with an
interesting suggestion. He argued in 1827 that a fourth dimension
would allow otherwise distinct threedimensional figures—such as a
right hand and a left hand—to coincide. Namely, just as a mirror
flips left and right, one could turn a right hand into a left hand
by twisting it into a fourth dimension and back
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