imitate
art, it is nevertheless also true that art imitates life. One might
thus wonder whether the publication of Abbott’s Flatland within a decade following Maxwell’s
discovery about the nature of otherwise invisible electric and
magnetic fields and less than a decade before Michelson and Morley’s
experiments to probe the ether and Lorentz’s pioneering
speculations about the nature of space and time was purely a
coincidence. Was there something in the intellectual air at the
time that suggested something revolutionary was about to occur in
our understanding of nature?
In one sense the answer to this question is
clearly no. It was, after all, in 1900 that Lord Kelvin uttered his
famous remark that all laws of physics had already been discovered
and all that remained were more and more precise measurements. Yet
in spite of such hubris, scientific and mathematical puzzlement
about the nature of space and time had been spilling over to the
literary imagination for well over a century before Abbott wrote
his story. The notion that time might somehow be considered a
fourth dimension actually appeared in print as early as 1754, in an
article by Jean Le Rond d’Alembert on “Dimensions” in his Encyclopédie, although he attributed the idea to a
friend, possibly the French mathematician Joseph-Louise Lagrange. A
hundred years later German psychologist and spiritualist Gustav
Fechner wrote a satirical piece involving a “shadow man,” the
shadow projection of a three-dimensional image. Interestingly,
Fechner argued that such shadow figures would interpret the effects
of motion perpendicular to their plane of existence (which they, of
course, could not perceive as movement in space) as acting like
time. Fechner’s combined interest in extra dimensions and
spiritualism presaged, as we shall see, events that would unfold a
half a century later.
Ultimately the notion of time as a fourth
dimension was made famous within popular culture a full decade
before Einstein’s special relativity and thirteen years before
Minkowski clarified the dimensional relationship between space and
time by none other than H. G. Wells in his classic science fiction
epic, The Time Machine, published in 1895.
On the very first page of this novel, Wells’s hero, the Time
Traveller, has the following dialogue with an audience he has
invited for the occasion:
“You must follow me carefully. I shall have to
controvert one or two ideas that are almost universally accepted.
The geometry, for instance, they taught you at school is founded on
a misconception.”
“Is not that rather a large thing to expect us
to begin upon?” said Filby, an argumentative person with red
hair.
“I do not mean to ask you to accept anything
without reasonable ground for it. You will soon admit as much as I
need from you. You know of course that a mathematical line, a line
of thickness NIL, has no real existence. They taught you that?
Neither has a mathematical plane. These things are mere
abstractions.”
“That is all right,” said the Psychologist.
“Nor, having only length, breadth, and
thickness, can a cube have a real existence.”
“There I object,” said Filby. “Of course a
solid body may exist. All real things.”
“So most people think. But wait a moment. Can
an INSTANTANEOUS cube exist?”
“Don’t follow you,” said Filby.
“Can a cube that does not last for any time at
all, have a real existence?”
Filby became pensive. “Clearly,” the Time
Traveller proceeded, “any real body must have extension in FOUR
directions: it must have Length, Breadth, Thickness, and—Duration.
But through a natural infirmity of the flesh, which I will explain to
you in a moment, we incline to overlook this fact. There are really
four dimensions, three which we call the three planes of Space, and
a fourth, Time. There is, however, a tendency to draw an unreal
distinction between the former three dimensions and the latter,
because it happens
art, it is nevertheless also true that art imitates life. One might
thus wonder whether the publication of Abbott’s Flatland within a decade following Maxwell’s
discovery about the nature of otherwise invisible electric and
magnetic fields and less than a decade before Michelson and Morley’s
experiments to probe the ether and Lorentz’s pioneering
speculations about the nature of space and time was purely a
coincidence. Was there something in the intellectual air at the
time that suggested something revolutionary was about to occur in
our understanding of nature?
In one sense the answer to this question is
clearly no. It was, after all, in 1900 that Lord Kelvin uttered his
famous remark that all laws of physics had already been discovered
and all that remained were more and more precise measurements. Yet
in spite of such hubris, scientific and mathematical puzzlement
about the nature of space and time had been spilling over to the
literary imagination for well over a century before Abbott wrote
his story. The notion that time might somehow be considered a
fourth dimension actually appeared in print as early as 1754, in an
article by Jean Le Rond d’Alembert on “Dimensions” in his Encyclopédie, although he attributed the idea to a
friend, possibly the French mathematician Joseph-Louise Lagrange. A
hundred years later German psychologist and spiritualist Gustav
Fechner wrote a satirical piece involving a “shadow man,” the
shadow projection of a three-dimensional image. Interestingly,
Fechner argued that such shadow figures would interpret the effects
of motion perpendicular to their plane of existence (which they, of
course, could not perceive as movement in space) as acting like
time. Fechner’s combined interest in extra dimensions and
spiritualism presaged, as we shall see, events that would unfold a
half a century later.
Ultimately the notion of time as a fourth
dimension was made famous within popular culture a full decade
before Einstein’s special relativity and thirteen years before
Minkowski clarified the dimensional relationship between space and
time by none other than H. G. Wells in his classic science fiction
epic, The Time Machine, published in 1895.
On the very first page of this novel, Wells’s hero, the Time
Traveller, has the following dialogue with an audience he has
invited for the occasion:
“You must follow me carefully. I shall have to
controvert one or two ideas that are almost universally accepted.
The geometry, for instance, they taught you at school is founded on
a misconception.”
“Is not that rather a large thing to expect us
to begin upon?” said Filby, an argumentative person with red
hair.
“I do not mean to ask you to accept anything
without reasonable ground for it. You will soon admit as much as I
need from you. You know of course that a mathematical line, a line
of thickness NIL, has no real existence. They taught you that?
Neither has a mathematical plane. These things are mere
abstractions.”
“That is all right,” said the Psychologist.
“Nor, having only length, breadth, and
thickness, can a cube have a real existence.”
“There I object,” said Filby. “Of course a
solid body may exist. All real things.”
“So most people think. But wait a moment. Can
an INSTANTANEOUS cube exist?”
“Don’t follow you,” said Filby.
“Can a cube that does not last for any time at
all, have a real existence?”
Filby became pensive. “Clearly,” the Time
Traveller proceeded, “any real body must have extension in FOUR
directions: it must have Length, Breadth, Thickness, and—Duration.
But through a natural infirmity of the flesh, which I will explain to
you in a moment, we incline to overlook this fact. There are really
four dimensions, three which we call the three planes of Space, and
a fourth, Time. There is, however, a tendency to draw an unreal
distinction between the former three dimensions and the latter,
because it happens
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