THE PEARLY GATES OF CYBERSPACE

Margaret Wertheim

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HYPERSPACE.

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place of liberation and redemption, one with distinctly heavenly overtones. Such was the vision of Wells' French disciple Gaston de Pawlowski. In Pawlowski's Voyage to the Country of the Fourth Dimension (1912), he served up a ringing moral tale in which the ability to see and comprehend a fourth dimension saves mankind from scientistic hubris. Within the novel, history was divided into three eras. Beginning in the early twentieth century was what Pawlowski called the "Epoch of Leviathan," an age of rampant materialism and positivism. According to the author this era would culminate during the late twentieth century with a "scientific period" full of nameless horrors. Finally, salvation would come when the fourth dimension was revealed, initiating the "epoch of the Golden Bird." In this "idealist renaissance" man would apparently "raise himself forever above the vulgar world" of three dimensions and find himself in a "higher" realm of wisdom and cosmic unity. As Pawlowski explained: "The notion of the fourth dimension opens absolutely new horizons for us. It completes our comprehension of the world; it allows the definitive synthesis of our knowledge to be realized. . . . When one reaches the country of the fourth dimension. . . one finds [one ]self blended with the entire universe."8
Pawlowski's heavenly vision of the fourth dimension and his belief in its salvific properties would be widely reflected by others in the first decades of our century. A whole brand of what Henderson terms "hyperspace philosophy" would spring up, giv-ing rise to all manner of curious blendings of science and spiritu- ality. Ironically, the same kind of mathematics that Einstein would later use in the general theory of relativity has also served as a foundation for some of the most bizarre pseudoscientific specula-tions of our age.
Foremost among the new hyperspace philosophers was Englishman Charles Hinton. As a professional mathematician, Hinton taught at Princeton University and later worked for the / Page 193 / United States Naval Observatory and the U.S. Patent Office, but parallel to this orthodox professional life was a mystical under-belly in which he pursued a spiritual approach to the fourth di- mension. In A New Era of Thought (1888) Hinton outlined a system by which people could supposedly train themselves to be- come aware of the true four-dimensional nature of space. At the core of this system was a set of special colored blocks, the con- templation of which would supposedly break down restricting "self-elements" within the mind, thereby opening the doors of
perception to the fourth dimension.
Hinton dreamed of bringing forth "a complete system of four-dimensional thought-mechanics, science and art,"9 but in truth he was interested less in the practical applications of the fourth dimension than in its spiritual and philosophical ramifica- tions. Here he was inspired by Plato's analogy of prisoners chained in a cave, doomed forever to see only the shadows of the "real" world outside.
For Hinton, our normal experience of three-dimensional space doomed us to see only the "shadows" of the "rea1" reality, which is four-dimensional. By becoming aware of this extra di-mension, he believed that Plato's realm of the ideal would be re-vealed. As the realm of the noumenon, the fourth dimension could also be seen, in Hintons view, as Kant's "thing-in-itself"
Hinton never realized his "complete system" of four-dimensional thought, but his philosophical interpretation of the fourth dimension would greatly influence later hyperspace thinkers. Among them was the Russian mystic Peter Demianovich Ouspensky. "In the idea of a spatial fourth dimension," says Henderson, "Ouspensky believed he had found an explanation for the 'enigmas of the world,' and with this knowledge he could offer mankind a new truth that would, like the gift of Prometheus, transform human existence."¹⁰
For Ouspensky, the fourth dimension was none other than / Page 194 / time. But according to him, in our everyday experience of this di-mension we are deceived. In truth, Ouspensky declared, time is just another dimension of space, and thus all motion is an illusion. According to Ousp~nsky, the real reality is a changeless four- dimensional stasis. Not just time and motion, but matter also is an illusion that people must overcome by learning to "see" anew. Not everyone, however, wa; mentally equipped for Ouspensky's four-dimensional vision. Those who are so gifted constitute a race of "supermen" with the power to realize what Ouspensky called "cosmic consciousness." In this final state of evolution, the new "supermen" will find themselves graced with "higher emotion, higher intellect, intuition, and mystical wisdom."¹¹ In this realm, ordinary laws of mathematics and logic will be superseded by a new "logic of ecstasy." It was through just such an "intuitive logic" that Ouspensky proposed to prepare future supermen for the mys-tical revelation of the fourth dimension.
In Ouspensky's vision of the fourth dimension de we not detect distinct echoes of the medieval Christian Heaven? Just as in the Empyrean time was negated, subsumed into an eternal bliss- ful stasis, so also in Ouspensky's hyperspace realm we find our-selves in a state of ecstatic stasis. Here too in the fourth dimension, we are promised "higher emotion," "higher intellect," even "mys- tical wisdom." In such early twentieth-century visions of a fourth dimension we witness a recasting into scientific terms the old idea of a transcendent, heavenly domain.
Another hyperspace philosopher with even more overtly Christian leanings was the Rochester, New York, architect Claude Bragdon. It was Bragdon who organized the English translation of Ouspensky's work, and the two men immediately recognized kin- dred spirits in one another. In addition to Bragdon's more philo- sophical works, his oeuvre also included a curious littte religious title called Man the Square: A Higher Space Parable. Here, Brag-don used the analogy of a two-dimensional world (rather like / Page 195 / Abbott's Flatland), "to convey a message of love and harmony."¹² As in Flatland, Bragdon's characters are also simple geo-
metric figures living on a flat surface (see Figure 5.1).As the story unfolds, however, we learn that all these figures are really cross sec-tions of cubes, tilted at different angles to their two-dimensional planar world (See Figure 5.2). Seen from the "higher" reality of three dimensions, the beings are not flat figures but hearty, solid cubes. At the end of the story, this higher-dimensional reality is demonstrated to the flatlanders by a "Christos cube," which reveals its true cubic nature by folding down its six sides to form the shape of a cross. In the logic of the story, what brings about disharmony in the two-dimensional world is that the cubes of the flatlanders are all tilted at odd angles to their plane. To reinstate harmony, the cubes need to be aligned upright so they are all "square" with their plane. The moral of the tale (of course) was that we too need to get ourselves properly aligned in our own higher space dimen-sion-i.e., the fourth.
Along with the supposedly philosophical and moral impli-cations of the fourth dimension, Bragdon was also interested in its aesthetic possibilities. "Consciousness is moving towards the con-quest of a new space," he wrote. "Ornament must indicate this movement of consciousness."13 To this end, Bragdon produced Projective Ornament, a book of images created by projecting four-dimensional figures onto two-dimensional surfaces. The result, as in Figures 5.3 and 5.4, was a kind of geometric Art Deco that was in truth, rather banal. Bragdon's imagery failed to precipitate the aesthetic revolution he was hoping for, but elsewhere real art- world heavyweights were looking to the fourth dimension for in-spiration. And some may even have taken cues from Bragdon's work..."

HYPERSPACE

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..."That Cubists and other modernist artists should be inter-ested in higher-dimensional space is hardly surprising, for a pri- mary thrust of early twentieth-century art was to break with the tradition of perspective. If it turned out that physical space was not in fact three-dimensional, then the rules of linear perspective would simply be arbitrary. The possibility of higher-dimensional space thus served a powerful rhetorical function for the nascent modems. Recognizing this explicitly, Gleizes and Metzinger stated in Du Cubism that "If we wished to tie the painter's space to a particular geometry, we should have to refer it to the non- Euclidean scholars."17
The painter who most seriously took up this challenge was Marcel Duchamp. Originally associated with the Cubists, Duchamp soon spun off onto his own peripatetic paths. Like Malevich, his most famous work was also inspired by the fourth di-
mension. The Bride Stripped Bare by Her Bachelors, Even, often known as TheLarge Glass, is surely one of the most pondered-over
works in the modem canon; and this time we have extensive notes by the artist detailing the process of genesis. Specifically, we know that in preparing for this work Duchamp embarked on a study of non-Euclidian and higher-dimensional geometries. The end result of these efforts was a complex work divided into two distinct halves: in the top half is the "Bride," and in the bottom half the "Bachelor Apparatus." According to Duchamp's notes the Bride is supposed to be a four-dimensional entity, while the bachelors are three- dimensional. Floating above her retinue, this higher-space spouse hovers enigmatically in a world of her own.

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With all this artistic, literary, and mystical speculation about a fourth dimension, what delicious synchronicity when the theory of relativity suddenly;enshrined the concept in physical reality. Einstein's revelation of the fourth dimension seemed to many hy-perspace enthusiasts a confirmation of what they had known all along. The common thread running between the worlds of rela-tivistic physics and that of the writers and artists was of course the new mathematics of non-Euclidian geometry. Ironically, many of the new-math pioneers had themselves been driven to their radi-cal geometries by a scientific interest in the structure of physical space. To these men, Gauss included, their fantastical new geo-metries had originally evolved as tools for helping them to better understand the nature of the concrete physical world. Thus while they are generally remembered today as mathematicians, along with Einstein these men ought also to be recognized as pioneers in the physics of space.
In fact, the whole development of non-Euclidian geometry that Gauss initiated emerged out of his work on the measurement of the earth. Given that the literal meaning of the word "geome-try" is "earth measurement," this was particularly apt. In its origi-nal incarnation, the science of geometry had emerged from ancient Egyptian surveying of the Nile Delta. This ancient (i.e., Euclidian) geometry had only dealt with flat space, such as the surface of this page. On a large scale, however, the surface of the earth is spherical, and hence curved. Thus a study of the earth's surface ultimately requires a geometry of curved surfaces. Gauss' seminal papers on curved-space geometry were inspired by his stint as scientific advisor to a geodetic survey of the region of Hanover. "Once again," says Max Jammer, "we see that histori-cally viewed, abstract theories of space owe their existence to the practice of geodetic work."18
Humans had long known that the surface of our planet is curved, but what about the space in which our globe is embedded? / Page 202 / Might space itself be curved? For Newton and his contemporaries there had been no mathematical alternatives to Euclidian space so they had simply assumed that this was-the correct model for phys-ical space. But after Gauss' work on curved surfaces, he began to wonder if the assumption of a Euclidian universe was justified. In the early nineteenth century -long before Einstein was born- Gauss actually tried to measure the curvature of physical space. He did this by the ingenious method of surveying a triangle formed by three mountaintops. In Euclidian, or flat space, three angles of a triangle must add up to 180 degrees, but if the space is curved the angles will add up to something else. (To more than 180 if the space is "positively" curved, like a sphere, and less than 180 if it is "negatively" curved, like a saddle.) Since Gauss failed to find any deviation from 180 degrees, he concluded that at least in the vicin- ity of the earth, space must be Euclidian.
The later Russian mathematician, Nikolai Ivanovich Lobachevsky, would try a similar experiment but on a much larger scale. Instead of mountains, Lobachevsky used distant stars, yet still he found no deviation from flat space. Both Gauss and Lobachevsky concluded, based on the evidence available to them, that our local area of the universe was Euclidian, but both realized there was no reason why this must be the case. As Gauss pre-sciently put it: "In some future life, perhaps, we may have other ideas about space which, at present, are inaccessible to us "19
While Gauss and Lobachevsky pioneered the idea of curved space, later in the nineteenth century a brilliant young mathe-matician named Bernhard Riemann even considered the pos- sibility that gravity was a by-product of curvature in higher- dimensional space. While there is no doubt that Einstein thought up this concept for himself, it is worth noting that the idea had already been imagined more than half a century before. The young man responsible for this astonishing insight was a disciple of Gauss, and he remains one of the most underrated / Page 203 / visionaries in modern science. Today Riemann is generally re-membered as a pure mathematician, but what really interested this pathologically shy Austrian was the problem of how physical forces arise. Decades before Einstein's birth, Riemann became convinced that the explanation for gravity must lie in the geometry of space.
Thinking about the problem of physical forces, Riemann imagined a world not unlike Abbott's Flatland, in which a race of two-dimensional creatures were living on a flat sheet of paper. Now what would happen, Riemann asked, if we crumpled the paper? Because the creatures' bodies are embedded in the paper, they would not be able to see the wrinkles - to them their world would still look perfectly flat. Yet Riemann realized that even if the space looked flat, it would no longer behave as if it were flat. He ar-gued that when the creatures tried to move about in their two - dimensional world they would feel a mysterious unseen "force" whenever they hit one of the wrinkles, and they would no longer be able to move in straight lines.
Extrapolating this idea to our three-dimensional universe, Riemann imagined that our three-dimensional space was also "crumpled" in an unseen fourth dimension. Like the two-dimensional beings of the paper universe, he reasoned that al-though we could not see such "wrinkles" in the space around us, we too would experience them as invisible forces. From this bril-liant insight, Riemann concluded that gravity was "caused by the crumpling of our three-dimensional universe in the unseen fourth dimension."20 Having outlined his basic theme, this shy genius set about developing a mathematical language in which to express these ideas. The result of his labors was the new geometry that Ein- stein would eventually use in his general theory of relativity. "In retrospect," says physicist Michio Kaku, "we now see how close Riemann came to discovering the theory of gravity 60 years before Einstein."2l In one way or other, speculations about the physics of Flatland have had profound consequences for us all.

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Einstein's "discovery"-of a fourth dimension must surely rate as one of modem science's most amazing findings. With this dis-covery, man was now in a position (like the Square in Abbott's tale) to see his world from a new perspective. But as the Square said to Lord Sphere, why stop at four dimensions? With our vision thus expanded, might we too not "resolve that our ambition [should] soar" onward and upward to higher dimensions still? And since human beings are as naturally curious as Squares, indeed it was not long before someone began to dream about a fifth dimension. In the 1920s, a young Polish mathematician had the bright idea that if the force of gravity could be explained by the geometry of four-dimensional space, then perhaps he might be able to explain the electromagnetic force by the geometry of five- dimensional space. With this seeming science fiction fantasy begins one of the most curious episodes in the history of space.
If Riemann was a maverick in the history of science, Theodr Kaluza was decidedly an oddity. An obscure mathematician at the University of Konigsberg (in what is now Kaliningrad in the former Soviet Union), Kaluza was convinced that Einstein's approach to gravity could be expanded and enhanced. In particular, he wanted to apply Einstein's approach to the electromagnetic force-the force responsible for electricity, magnetism, and, light. Along with Riemann, in fact, Kaluza believed that electromagnetism must also be the result of curvature (or ripples) in a higher-dimensional space. But the problem Kaluza faced was that there did not seem to be any more dimensions left. With three of space and one of time, nature's stock seemed to be exhausted.
Yet Kaluza was not a man to be deterred by such prosaic objections. In an audacious move he simply rewrote Einstein's equations of general relativity in five dimensions. Lo and behold, when he did so it turned out that these five-dimensional equations contained within them the regular four-dimensional equations of relativity, plus an extra bit which turned out to be / Page 205 / precisely the equations of electromagnetism. In effect, Kaluza's five-dimensional theory consisted of two separate pieces that fit- ted together like a jigsaw puzzle-Einstein's theory of gravity and Maxwell's theory of.-.electromagnetism (the field equations of light).
Another way of understanding this "mathematical miracle," says physicist Paul Davies, is that "Kaluza showed that electro-magnetism is actually a form of gravity." Not the regular gravity of everyday physics, but "the gravity of an unseen [fifth] dimension of space."22 In 1919 Kaluza sent a paper on all this to Einstein. So stunned was the great physicist by the young Pole's radical addition of an extra dimension that like Lord Sphere in Abbott's Flatland, he was appalled. For two years Einstein apparently refused to an- swer Kaluza's letter. But the whole construction was so mathe-matically elegant he could not get it out of his mind, and finally in 1921 he became convinced of the importance of Kaluza's ideas and submitted the paper to a scientific journal.
Ironically, it was the very beauty of Kaluza's construction that so shook Einstein, and many other physicists. Was this five- dimensional space of Kaluza's "just a parlor trick? Or numerology? Or black magic?"23 It was all very well to propose that time was a fourth dimension (for that, after all, is a real aspect of our physical experience), but what on earth was this supposed fifth dimension? If Kaluza's equations were to be taken seriously-and not just as mathematical chicanery-then the awkward question arose: Where is this extra dimension? Why don't we see it?
To this query Kaluza had a disarmingly simple answer. He declared that the extra dimension is so small it escapes our normal attention. The reason we don't see, he said, it is because it is mi- croscopic. To understand this proposal, again it is helpful to resort to a lower-dimensional analogy. Imagine this time that you live on a line, what we might call Lineland, the one-dimensional sibling of Flatland. As a dot in this linear universe, you can travel up and / Page 206 / down your line, always remaining in a single dimension. Now suppose that one day a scientist in your Lineland announces she has discovered an extra dimension and that your universe is really two-dimensional. At first you think she is mad. Where is this other dimension? you ask. Why can't we see it? But then the scientist ex-plains that in fact you don't live on a line, but on a very thin hose. Each point of your line universe is not really a point, but a tiny circle, one so small that you never notited it. Taking this extra microscopic dimension into account, your world is not a line, but really a two-dimensional cylindrical surface.
This was the essence of Kaluza's explanation for his fifth di-mension. According to him, every point in our three dimensions of space is actually a tiny circle, so that in reality there are four di-mensions of space, plus one of time, making a total of five. In 1926 the Swedish physicist Oskar Klein made improvements to Kaluza's theory which enabled him to calculate the size of this tiny hidden dimension. According to Klein's calculations, it was no wonder we had not observed the extra direction because it is ab-solutely minute. Its circumference was just 10-32 centimeters-a hundred billion billion (102°) times smaller than the nucleus of an atom!
So small was Kaluza's dimension that even if we ourselves were the size of atoms we would still not notice it. Yet this tiny di-mension could be responsible for all electromagnetic radiation: light, radio waves, X rays, microwaves, infrared, and ultraviolet. A powerful punch indeed for something so small. Unfortunately, the Kaluza-Klein dimension was so small there was no way of measuring it directly. Even our largest accelerators today still cannot measure things on such a minute scale. So what then are
we to make of Kaluza's vision? Is this fifth dimension physically real? Or is it just an elegant mathematical fiction?
Kaluza himself insisted that the beauty of his theory could not "amount to the mere alluring play of a capricious accident."24

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He firmly believed in the reality of his fourth spatial dimension. He knew his tiny dimension could not be tested directly, so he de-cided instead to conduct an experiment of his own to test the gen-eral correspondence between theory and reality. The test case he chose was not anything from the realm of physics, but the art of swimming. As someone who could not swim, Kaluza decided he would learn all he could about the theory of swimming and when he had mastered that then he would test this theoretical framework against the reality of the sea. Giving himself over to the,project, he diligently studied all aspects of the aquatic art until finally he felt he was ready. Now, trunks in hand, the young Pole escorted his family to the seaside for the crucial test. With no prior experience, in front of the assembled Kaluza clan, Theodr hurled himself into the waves. . . and 10 and behold he could swim! Theory had been born out by practice in the real world. Could the tiny dimension also be there in the real world?
Unfortunately, if in Kaluza's own mind the swimming ex-periment supported a general correspondence between theory and reality, few others were willing to embrace the idea of an unseen and unmeasurable fifth dimension. Sadly, after an initial flurry of interest, the physics community turned away. Yet the startling el-egance of Kaluza's equations raised an uneasy question: How many dimensions of space are there really in the world around us?
As happens so often in the history of science, it was not in fact a new question. As long ago as the second century, Ptolemy had considered the matter and had argued that no more than three di-mensions are permitted in nature. Kant also had argued that three dimensions are inevitable. In this he could call upon the support a good deal of hard science. For instance it is well known that gravity and the electromagnetic force both obey "inverse square laws" - the strength of the force drops off according to the square of the distance. As early as 1747, "Kant recognized the deep con-nection between this law and the three-dimensionality of space."25

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" It turns out that in anything other than three dimensions, problems quickly arise with inverse square forces. For example, in four or more spatial dimensions, gravity would be so strong that planets would spiral into the sun; they would not be able to form stable orbits. Similarly, electrons would not be able to form stable orbits around nuclei.26 Hence atoms could not form. It can also be shown that in four spatial dimensions, waves cannot propagate cleanly. From these physical facts, Kant and others had concluded that we must live in a universe with just three spatial dimensions.
But all these arguments had assumed that any extra dimen- sions would be fully extended like the regular three. If an addi- tional dimension was tiny, however, it would not affect the regular functioning of gravity, electricity, and wave propagation. On the large scale, such a universe would operate as if there were just three dimensions; only on the microscopic scale would the extra one reveal itself. In other words, our universe could function prop-erly with five dimensions.
If Kaluza was right, and such a thing did exist, it would pack a very potent punch. "Viewed this way, there [would be] no forces at all, only warped five-dimensional geometry, with particles me-andering freely in a landscape of structured nothingness."27 It was a very beautiful idea, but for over half a century most physicists paid no more attention to Kaluza than to Hinton or Ouspensky, and the fifth dimension seemed little less than an oddity of math-ematical mysticism. Then suddenly in the 1980s that began to change when new developments in particle physics began to sug- gest that Kaluza might just be onto something.
By the 1 980s, two new forces of nature had been discovered. In addition to gravity and electromagnetism, there was now the weak nuclear force and the strong nuclear force. These forces are what holds atomic nucleirogether, hence they are responsible for keeping matter stable. With these nuclear powers, the basic "forces of nature" had expanded in number from two to four. Today physi-/ Page 209 / cists feel confident that this set-gravity, electromagnetism, the weak force, and the strong force - represent the full complement of our physical universe. But what really began to excite them was the idea that all four might be just different aspects of a single overarching force-a kind of unifying super-force.
The idea of an underlying unity among all four forces of na-ture was so thrilling to many theoretical and particle physicists they were prepared to try anything to realize this vision. Many at-tempts were made to find a unifying theory, but after a decade of failure, they began to realize that desperate measures might be called for. At this point they began to look again at Kaluza. After all, he had been able to unify gravity and the electromagnetic force; perhaps his approach might be able to unify all four forces? Now, the idea of unseen hidden dimensions reared its head with a vengeance, for while Kaluza had been able to explain electro-magnetism by adding just one more dimension to Einstein's equa-tions, physicists found that in order to accommodate the weak and strong forces they had to add another six dimensions of space- bringing the total number of dimensions to eleven! As before, all these extra dimensions are microscopic-tiny little curled-up di-rections in space that can never be detected by human senses.
The picture that has emerged over the past decade is thus of an eleven-dimensional universe, with four extant, or large, di-mensions (three of space and one of time), and seven microscopic space dimensions all rolled up into some tiny complex geometric form. On the scale that we humans experience, the world is four-dimensional, but underneath, say these new "hyperspace" physi-cists, the "true" reality is eleven-dimensional. (Or, according to some of the latest theories, maybe ten-dimensional.)
Perhaps the most radical feature of this eleven-dimensional vision is the fact that it explains not only all the forces, but matter also, as a by-product of the geometry of space. In these extended Kaluza-Klein theories, matter too becomes nothing but ripples in / Page 210 / he fabric of hyperspace. Here, subatomic particles are also ex-plained by the properties of the seven curled-up dimensions. One of the major projects of theoretical physics over the past two decades has been to articulate precisely how the curling up of these extra spatial dimen~ions. occurs. Unfortunately there are an enormous number of possible topologies for a seven-dimensional space, and so far it has proved impossible to tease out which ones (if any) correspond to the real world we live in. Part of the prob- lem, again, is that all these dimensions are too tiny to be measured directly, so any such theories can only be tested indirectly-if at all. Nonetheless, hyperspace physicists are confident that they will find the correct one.
We have looked at how the curvature of space can produce the effect of physical forces such as gravity; let us consider now the even more radicatidea that the curvature of space may also be re- sponsible for matter. Forces such as gravity and magnetism (which travel through thin air) have always, in a sense, been closely allied with space, but how could matter - the concrete stuff of our flesh and bones-arise from the non-substance of space?
At first glance the whole notion seems absurd, but once again the idea of matter as ripples in space is actually quite old. As early as the 1870s Riemann's English disciple William Clifford de-livered an address to the Cambridge Philosophical Society "On the Space Theory of Matter."28 Taking Riemann's ideas further even than the master himself, Clifford put forward the view that particles of matter were just tiny kinks in the "fabric" of space. A more sophisticated version of the same idea arose early in our own century when physicists began to think about wormholes. Original interest in wormholes was not in the large-scale ones that would so excite science fiction writers, but in microscopic wormholes that might be associated with subatomic particles. A host of physics luminaries from Einstein to Hermann Weyl "wondered whether all fundamental particles might not actually be microscopic worm-/ Page 211 / holes."z9 In other words, just "the products of warped spacetime." Einstein in particular became obsessed with the notion that matter might be ripples in space, and he spent the last thirty years of his life trying to extend the equations of general relativity in this direction. He called this dream a "unified field theory" and his fail-ure to find such a theory was the greatest disappointment of his life. According to Kaku, "to Einstein the curvature of spacetime was like the epitome of Greek architecture, beautiful and serene."30 But he regarded matter as messy and ugly. He likened space to "marble" and matter to "wood," and he desperately wanted a theory that could transform ugly "wood" into beautiful "marble."
Neither Clifford nor Einstein had the mathematical tools to achieve the difficult synthesis of matter and space-above all they were trying to work with just four dimensions. Today physicists know that if matter is to be incorporated into the structure of space, it must be achieved with a higher-dimensional theory. In such a theory, matter, like force, would not be an independent en- tity, but a secondary by-product of the totalizing substrate of space. Here, everything that exists would be enfolded into the bosom of hyperspace. Theories that attempt to do this are sometimes known by the modest nickname "theories of everything," commonly re- ferred to as TOEs. In a successful TOE, every particle that exists would be described as a vibration in the microscopic manifold of the extra hidden dimensions. Objects would not be in space, they
would be space. Protons, petunias, and people - we would all be- come patterns in a multidimensional hyperspace we cannot even see. According to this conception of reality, our very existence as material beings would be an illusion, for in the final analysis there would be nothing but "structured nothingness."
With a hyperspatial "theory of everything" we thus reach the apogee of a movement that began in the late Middle Ages: The el-evation of space as an ontological category is now complete. As we / Page 212 / have seen, in the Aristotelian world picture, space was a very minor and unimportant category of reality-so unimportant that Aristo- tle didn't really have a theory of "space" per se but strictly speak-ing only a theory of "place." With the emergence of Newtonian physics in the seventeenth century, the status of space was raised so that along with matter and force it became one of three major categories of reality. Now, at the close of the twentieth century, space is becoming the only primary category of the scientific world picture. Matter and force, which in Newtonian physics were really above space in ontological status, have now been relegated to sec-ondary status, with space alone occupying the primary rung of the real. It is a little-remarked-upon feature of modem Western physics that one way of characterizing the enterprise is by the gradual as-cent of space in our existential scheme. The final triumph of this invisible, intangible entity to the ultimate essence of existence is surely one of the more curious features of any world picture.
Hyperspace physicists' intensely geometric vision of reality also marks the final chapter of the saga begun by Giotto and the geometer-painters of the Renaissance. Here in TOE physicists' equations would be the ultimate "perspective" picture of the world, a vision in which everything is refracted through the clari-fying prism of geometry. If, as Plato famously declared, "God ever geometrizes," here would be the last word on divine action. As the apotheosis of Roger Bacon's "geometric figuring," a hyper-spatial "theory of everything" would be, quite simply, a twenty- first-cen~ry realization of a thirteenth-century dream.
In another way also a "theory of everything" would be the ul-timate perspective picture of our universe, for this picture too has a single point from which the whole world-image originates. Physi- cists call it the big bang. According to hyperspace physics, at the initial split second of creation the entire universe was condensed into a microscopic point containing all matter, force, energy, and space. At this quintessential point, however, matter, force, energy, / Page 207 / have seen, in the Aristotelian world picture, space was a very minor and unimportant category of reality-so unimportant that Aristo-tle didn't really have a theory of "space" per se but strictly speak- ing only a theory of "place." With the emergence of Newtonian physics in the seventeenth century, the status of space was raised so that along with matter and force it became one of three major categories of reality. Now, at the close of the twentieth century, space is becoming the only primary category of the scientific world picture. Matter and force, which in Newtonian physics were really above space in ontological status, have now been relegated to sec- ondary status, with space alone occupying the primary rung of the real. It is a little-remarked-upon feature of modem Western physics that one way of characterizing the enterprise is by the gradual as- cent of space in our existential scheme. The final triumph of this invisible, intangible entity to the ultimate essence of existence is surely one of the more curious features of any world picture.
Hyperspace physicists' intensely geometric vision of reality also marks the final chapter of the saga begun by Giotto and the geometer-painters of the Renaissance. Here in TOE physicists' equations would be the ultimate "perspective" picture of the world, a vision in which everything is refracted through the clari-fying prism of geometry. If, as Plato famously declared, "God ever geometrizes," here would be the last word on divine action. As the apotheosis of Roger Bacon's "geometric figuring," a hyper- spatial "theory of everything" would be, quite simply, a twenty- first-cen~ry realization of a thirteenth-century dream.
In another way also a "theory of everything" would be the ul- timate perspective picture of our universe, for this picture too has a single point from which the whole world-image originates. Physi- cists call it the big bang. According to hyperspace physics, at the initial split second of creation the entire universe was condensed into a microscopic point containing all matter, force, energy, and space. At this quintessential point, however, matter, force, energy, / Page 213 / nd space were not yet separated from one another, but were united in a single hyperspace substrate. In other words, at the split second of creation everything was folded within the all-embracing oneness of "pure" eleven-dimensional space. From this point of hyperspatial unity, the universe then unfolded.
As the single point from which the physicists' world picture originates, the big bang is a scientific equivalent of the perspective painters' "center of projection." It is the point at which all "lines" in the hyperspace universe converge. This is the place, then, where TOE physicists would dearly like to "stand." Just as the viewer of a perspective painting gets the most dramatic effect when standing in the place from which the artist constructed the image, so a hyperspace physicist could see his world picture most clearly if he "stood" at the cosmic center of projection-the big bang.
It is in search of this particular "point of view" that physicists build ever larger particle accelerators. The higher the energy one can generate in an accelerator, the closer one gets to "melting" to-gether the four separate forces, and thus the more one can see of the underlying hyperspatial unity. In a very real sense, particle ac-celerators are tools for exploring higher-dimensional space, and the final goal with such machines is to glimpse once more the ini-tial point of "pure" eleven-dimensional hyperspace. Physicists speak about this initial period of hyperspace unity as the time when there was "perfect symmetry" between all eleven dimen- sions. What they want to do is to glimpse for themselves this orig- inal perfect symmetry. Ironically, while artists long ago abandoned Renaissance aesthetics, those classical ideals of beauty live on in physicists' dream of a "theory of everything." Like the Renaissance painters, TOE physicists also hold mathematical symmetry as the highest aesthetic ideal. It is their dream, their goal, and, it has even been said, their "Holy Grail."..."

MEPHISTOPHELES

(to Faust):

THE JUPITER EFFECT
John Gribbin and Stephen Plagemann
1977
Page 122
"Seventeen 'major historical earthquakes' are referred to in the report all of which occurred since
1836"

THE
LIGHT OF ASIA
Sir Edward Arnold
1909