“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 [the poor sap].
“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.”
Aha! The fourth dimension. A few clever Continental mathematicians were already talking as though Euclid’s three dimensions were not the be-all and end-all. There was August Möbius, whose famous “strip” was a two-dimensional surface making a twist through the third dimension, and Felix Klein, whose loopy “bottle” implied a fourth; there were Gauss and Riemann and Lobachevsky, all thinking, as it were, outside the box. For geometers the fourth dimension was an unknown direction at right angles to all our known directions. Can anyone visualize that? What direction is it? Even in the seventeenth century, the English mathematician John Wallis, recognizing the algebraic possibility of higher dimensions, called them “a Monster in Nature, less possible than a Chimaera or Centaure.” More and more, though, mathematics found use for concepts that lacked physical meaning. They could play their parts in an abstract world without necessarily describing features of reality.
Under the influence of these geometers, a schoolmaster named Edwin Abbott Abbott published his whimsical little novel Flatland: A Romance of Many Dimensions in 1884, in which two-dimensional creatures try to wrap their minds around the possibility of a third; and in 1888 Charles Howard Hinton, a son-in-law of the logician George Boole, invented the word tesseract for the four-dimensional analogue of the cube. The four-dimensional space this object encloses he called hypervolume. He populated it with hypercones, hyperpyramids, and hyperspheres. Hinton titled his book, not very modestly, A New Era of Thought. He suggested that this mysterious, not-quite-visible fourth dimension might provide an answer to the mystery of consciousness. “We must be really four-dimensional creatures, or we could not think about four dimensions,” he reasoned. To make mental models of the world and of ourselves, we must have special brain molecules: “It may be that these brain molecules have the power of four-dimensional movement, and that they can go through four-dimensional movements and form four-dimensional structures.”
For a while in Victorian England the fourth dimension served as a catchall, a hideaway for the mysterious, the unseen, the spiritual—anything that seemed to be lurking just out of sight. Heaven might be in the fourth dimension; after all, astronomers with their telescopes were not finding it overhead. The fourth dimension was a secret compartment for fantasists and occultists. “We are on the eve of the Fourth Dimension; that is what it is!” declared William T. Stead, a muckraking journalist who had been editor of the Pall Mall Gazette, in 1893. He explained that this could be expressed by mathematical formulas and could be imagined (“if you have a vivid imagination”) but could not actually be seen—anyway not “by mortal man.” It was a place “of which we catch glimpses now and then in those phenomena which are entirely unaccountable for by any law of three-dimensional space.” For example, clairvoyance. Also telepathy. He submitted his report to the Psychical Research Society for their further investigation. Nineteen years later he embarked on the Titanic and drowned at sea.
By comparison Wells is so sober, so simple. No mysticism for him—the fourth dimension is not a ghost world. It is not heaven, nor is it hell. It is time.
What is time? Time is nothing but one more direction, orthogonal to the rest. As simple as that. It’s just that no one has been able to see it till now—till the Time Traveller. “Through a natural infirmity of the flesh…we incline to overlook this fact,” he coolly explains. “There is no difference between Time and any of the three dimensions of Space except that our consciousness moves along it.”
In surprisingly short order this notion would become part of the orthodoxy of theoretical physics.
—
WHERE DID THE IDEA come from? There was something in the air. Much later Wells tried to remember:
In the universe in which my brain was living in 1879, there was no nonsense about time being space or anything of that sort. There were three dimensions, up and down, fore and aft and right and left, and I never heard of a fourth dimension until 1884 or thereabout. Then I thought it was a witticism.
Very witty. People of the nineteenth century sometimes asked, as people will, “What is time?” The question arises in many different contexts. Say you want to explain the Bible to children. The Educational Magazine, 1835:
Ver. 1. In the beginning God created the heaven and the earth.
What do you mean by the beginning? The beginning of time.—What is time? A measured portion of eternity.
But everyone knows what time is. It was true then and it’s true now. Also no one knows what time is. Augustine stated this pseudoparadox in the fourth century and people have been quoting him, wittingly and unwittingly, ever since:
What then is time? If no one asks me, I know. If I wish to explain it to one that asks, I know not.*2
Isaac Newton said at the outset of the Principia that everyone knew what time was, but he proceeded to alter what everyone knew. Sean Carroll, a modern physicist, says (tongue in cheek), “Everybody knows what time is. It’s what you find out by looking at a clock.” He also says, “Time is the label we stick on different moments in the life of the world.” Physicists like this bumper-sticker game. John Archibald Wheeler is supposed to have said, “Time is nature’s way to keep everything from happening all at once,” but Woody Allen said that, too, and Wheeler admitted having found it scrawled in a Texas men’s room.*3
Richard Feynman said, “Time is what happens when nothing else happens,” which he knew was a wisecrack. “Maybe it is just as well if we face the fact that time is one of the things we probably cannot define (in the dictionary sense), and just say that it is what we already know it to be: it is how long we wait.”
When Augustine contemplated time, one thing he knew was that it was not space—“and yet, Lord, we perceive intervals of times, and compare them, and say some are shorter, and others longer.” We measure time, he said, though he had no clocks. “We measure times as they are passing, by perceiving them; but past, which now are not, or the future, which are not yet, who can measure?” You cannot measure what does not yet exist, Augustine felt, nor what has passed away.
In many cultures—but not all—people speak of the past as being behind them, while the future lies ahead. They visualize it that way, too. “Forgetting what is behind and straining toward what is ahead, I press on,” says Paul. To imagine the future or the past as a “place” is already to engage in analogy. Are there “places” in time, as there are in space? To say so is to assert that time is like space. The past is a foreign country: they do things differently there. The future, too. If time is a fourth dimension, that is because it is like the first three: visualizable as a line; measurable in extent. Still, in other ways time is unlike space. The fourth dimension differs from the other three. They do things differently there.
It seems natural to sense time as a spacelike thing. Accidents of language encourage that. We have only so many words; before and after have to do double duty as prepositions of space as well as time. “Time is a phantasm of motion,” said Thomas Hobbes in 1655. To count time, to compute time, “we make use of some motion or other, as of the sun, of a clock, of the sand in an hourglass.” Newton considered time to be absolutely different from space—after all, space remains always immovable, whereas time flows equably without regard to anything external, and by another name is called duration—but his mathematics created an inevitable analogy between time and space. You could plot them as axes on a graph. By the nineteenth century German philosophers in particular were groping toward some amalgam of time and space. Arthur Schopenhauer wrote in 1813, “In mere Time, all things follow one another, and in mere Space all things are side by side; it is accordingly only by the combination of Time and Space that the representation of coexistence arises.” Time as a dimension begins to emerge from the mists. Mathematicians could see it. Technology helped in another way. Time became vivid, concrete, and spatial to anyone who saw the railroad smashing across distances on a coordinated schedule—coordinated by the electric telegraph, which was pinning time to the mat. “It may seem strange to ‘fuse’ time and space,” explained the Dublin Review, but look—here is a “quite ordinary” space-time diagram: