so that even those who adhere to scientific principles may ultimately find its view of reality lacking. For Zöllner and others, the fact that the possibility of the existence of extra dimensions was at least allowed by science—even if no direct evidence had been forthcoming—also meant it allowed a place for a world of purpose, the spiritual world, to exist. This deep yearning is undoubtedly associated with ubiquity of religion in the human experience, of which I spoke at the beginning of this book. The need for a hidden god to guide the universe of our experience while existing outside of that universe, and the hoped-for existence of a “better place” where we might go after we die, are part and parcel of the same sense of longing for something transcendent that is evident even in the fourteen-thousand-year-old cave paintings in France.
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.”
All of these diverse notions about a fourth dimension were widely debated and culminated in a 1909 essay contest sponsored by Scientific Ameri- can for the best “explanation of the Fourth Dimension.” Of particular interest today, because of their prescient resemblance to arguments that would later become part of modern lore, was the stated possibility, à la Hinton, of multiple three-dimensional universes existing within a fourdimensional framework. The development of special relativity ultimately did provide, in 1908, via Minkowski’s work, a scientific basis for a fourth dimension, but not the spatial fourth dimension so cherished by Hinton, Abbott, Wells, and others. Nevertheless, Einstein’s work did play at least an indirect role in rekindling a surge of cultural interest in extra spatial dimensions. One of the chief instigators of this was Henri Poincaré, the French mathematician whose own work on symmetries of space and time played a role in the development of relativity. The relativity of length and time measurements that were a hallmark of the special theory somehow implied to Poincaré that all our sense perceptions were relative, including even our perception of the number of dimensions.
In his book Science et Méthode (1908), Poincaré wrote: “So, the characteristic property of space, that of having three dimensions, is . . . an internal property of human intelligence, so to speak.” Like Hinton before him, Poincaré believed that the key to revealing the inner reality of extra dimensions involved breaking the bonds of our limited three-dimensional intuition. As he put it: “One who devoted his life to it could perhaps eventually be able to picture the fourth dimension.” He was a tremendously influential intellectual figure in early-twentieth-century France, and his extended notion of what one might call philosophical relativism and the associated idea that the four-dimensional world was accessible to us had wide impact.
The ways in which science has had an impact upon our culture are fascinating, and no doubt deserve more discussion than I can provide here. Yet what we see in the adoption of concepts like four dimensions and relativity as a framework for other philosophical purposes is, I suspect, more universal. People adapt what they perceive are scientific ideas and apply them with their own particular prejudices. They pick and choose what resonates, and the results may ultimately bear little resemblance to the actual underlying science.
Among those who helped further popularize the French fascination with four dimensions was the journalist, editor, theater critic, and science fiction writer, Gaston de Pawlowski, whose Journey to the Country of Four Dimensions (1912) was first seria
lized in installments on the front page of the literary journal Comoedia.
Pawlowski’s literary effort, like Wells’s Time Machine, involved a voyage to the future. But unlike Wells, he used the fourth dimension as a plot device to reflect a time when the tyranny of scientists, with their threedimensional science, would be replaced in a future Utopia, once the existence of four dimensions was revealed to the world. Whatever one may think of this premise, Pawlowski helped instill a notion that would be popular in France and elsewhere for generations: Namely, that a lack of the proper vocabulary, both visual and verbal, has hindered our ability to free our minds to fully appreciate the underlying reality of four dimensions. As he wrote:
The vocabulary of our language is in fact conceived according to the given facts of three-dimensional space. Words do not exist which are capable of defining exactly the strange, new sensations that are experienced when one raises himself forever above the vulgar world. The notion of the fourth dimension opens absolutely new horizons for us. It is precisely this excitement of freeing our minds, extending the range of our senses, and opening ourselves to new experiences that is so seductive.
Ultimately the growing call for a new vocabulary with which to explore our world resonated most strongly with visual artists, whose aesthetic is directly tied to pushing against the limits of our reality. I wrote earlier about Vincent Van Gogh freeing us in 1882 from the tyranny of color, and demonstrating exotica otherwise hidden in ordinary objects. But as strange and hauntingly pleasing as his images are to the modern eye, they nevertheless preserve the spatial relationships of all the objects they represent, which remain, in spite of their jarring colors, more or less instantly recognizable. This was not to be true of a school of artists that comprised perhaps the most influential painters and sculptors of the twentieth century who, starting about 1910, also began to transform the very definition of art. One merely has to glance at Picasso’s famous Man with Violin (1911–12) to realize that a new way of viewing the world was emerging. Even in his early Les Demoiselles d’Avignon (1907), one can see in the distorted faces the beginnings of what would become a characteristic trait of presenting different perspectives on parts of figure in the single plane of a painting.
Hiding in the Mirror: The Quest for Alternate Realities, From Plato to String Theory (By Way of Alicein Wonderland, Einstein, and the Twilight Zone) Page 9
