TWM 

Hyperspace Reality 
by SaulPaul Sirag 
Despite
the fact
that the 'new' physics,
a godchild of the Einsteinian revolution has taught us that the
Universe
we perceive is a mere shadow of a vastly more unpredictable one, most
of
us still view the world in a distinctly materialistic way. A world
where
mind and matter exist independently, neatly bordered by a strong and
infinite
boundary.
D. Scott Rogo
and Jeffrey
Mishlove
(1979: the 100th anniversary of Einstein's birth) Original manuscript of Earth's Ambassador. Robert Anton
Wilson
(1981) p. 248 of Schroedinger's
Cat II:
The
Trick Top Hat.
A preliminary version of this paper was presented on September 28, 1987 at the University of California at Berkeley, in a meeting sponsored by the California Society for Psychical Study. Jeffrey Mishlove, who was the president that year, persuaded me to give that talk: "The Cosmology of Consciousness." Ted Owens, who died in 1987, the year in which that paper was given, always referred to the Space intelligences (SIs) as coming from a higher dimensional realm and not from some distant planet. Whether Ted knew it or not, all during his lifetime (19201987), the world of physics underwent radical changes in its view of reality, that I will review here. These changes lend support to Owens' claims and his vision: A Brief History of Hyperspace Albert Einstein in 1915 introduced the idea that gravity is to be explained as the warping of fourdimensional (4d) spacetime. Whatever doubts physicists had  and there were many  about the reality of the 4dimensionality of spacetime (as a unified geometrical whole which could be warped) were erased by the dramatic verification of Einstein's gravity theory (called the General Theory of Relativity) in 1919, when a group of British astronomers led by Arthur Eddington measured the bending of starlight grazing the sun during a solar eclipse. That same year, Theodore Kaluza, a Polish physicist, came up with the idea that not only the Einstein gravity theory but also electromagnetism, including the electromagnetic theory of light due to James Clerk Maxwell (18311979), could be derived from the assumption that spacetime is actually a warped 5dimensional geometric structure. With Einstein's help, Kaluza's 5d theory was published in 1921. The decade of the 1920s was the most revolutionary decade in physics and astronomy. I will mention only the highlights. In quantum physics: deBroglie's waveparticle duality; Heisenberg's matrix mechanics, and the uncertainty principle; Bohr's complementarity principle; Pauli's exclusion principle; Schroedinger's wave function equation; Dirac's antimatter equation (which unified quantum theory and Einstein's special relativity). In astronomy: Eddington's theory of the internal constitution stars (including the sun); the discovery of galaxies beyond the Milky Way galaxy; Friedmann & Lemaitre's theory of the expansion of the universe; Hubble's observations verifying the expansion of the universe. In the midst of this revolution, Einstein contributed seminal papers on the statistics of quantum theory and the stimulated emission of photons from atoms. These papers led to many later developments including the laser. But Einstein was primarily interested in what he called "Unified field theory," which meant the unification of gravity with electromagnetism. Kaluza's 5dimensional version of such a unified theory was an amazing achievement, but it had the major flaw that it could not explain why we don't see the 5th dimension (which is supposed to be spatial). Another flaw was that it said nothing about the new quantum mechanics which was exploding throughout the 1920s. The Swedish physicist Oscar Klein in 1926 spoke to both these questions by publishing his version of the 5d theory, in which the 5th dimension is not visible to us because it is an extremely small compact dimension; in other words, each point of 4d spacetime is replaced by a tiny circle whose radius is around 1033 cm. This is the Planck length, which is named for Max Planck who defined this size as the basic unit of size in the quantum world. The Planck length is 20 orders of magnitude smaller than a proton (1013 cm): so if the 5th dimension is. a Planck length circle, it is no wonder we can't walk around in it; not even a proton could do that! Klein's Plancklength circle, as a candidate for the 5th dimension, entailed both Einstein's general relativity (applied to 5d spacetime) and quantum theory to provide the smallness of the extra dimension. As a bonus, the theory provides a geometric explanation for the quantization of electric charge; that is why every electron carries the same charge. This 5d theory called KaluzaKlein theory was forgotten in the world of physics for several decades during which the frontier of physics became the exploration of the nucleus of the atom, where two new forces were discovered: the strong and weak nuclear forces. The strong force holds the nucleus together against the electrical repulsion of the constituent protons, all carrying an identical positive charge (remember: like charges repel). The weak force causes the most common type of nuclear decay  changing one type of atom into another in a kind of 20th century alchemy. These forces were exciting things to explore, and it was obvious that any proposed "unified field theory" would be incomplete without taking them into account. In his last two decades, Einstein (18791955) was a revered grandfather figure, who was widely believed to be out of touch with the frontiers of physics  persisting in his doubts about the fundamental nature of quantum mechanics, and his fervent pursuit of the holygrail of physics "the unified field theory." It was quite a surprise to physics that by the 100th anniversary celebrations of Einstein's birth, a truly unified theory had arisen: superstring theory. Discovered in 1971 (by Raymond, Neveu and Schwarz), it required 10dimensions of spacetime! Physicists suddenly began to read the old 5d KaluzaKlein theory papers (and translated them into English). In 1975, Sherk and Schwarz showed that superstring theory unifies both Einstein's theory of gravity and quantum mechanics, and also provides for the unification of all the forces: gravity, electromagnetism, and the strong and weak nuclear forces. During the Einstein celebrationyear 1979, John Schwarz teamed up with Michael Green  the black and green team!  and together (over several years,) they proved that superstring theory is a selfconsistent theory of quantum gravity, which includes General Relativity and Quantum Mechanics as subtheories. This was published in 1984 and created a sensation in the world of physics. Many (especially younger) physicists immediately jumped on this "bandwagon," so that today unified field theory  the gleam in Einstein's eye  is a vast industry in physics. This is why physicists take the notion of hyperspace (10 dimensions of spacetime) seriously. Of course, the idea of hyperspace goes way back to Plato (427347 B.C.), who suggested in his Cave allegory, that we are like prisoners of the 3d world, identifying ourselves with our 3d shadows, rather than the hyperdimensional creatures we really are. Plato never used the word hyperdimensional, but the idea is clearly in his story of the projection of the prisoner's shadows (a 2d projection) on the cave wall. The prisoners because they are so securely chained, come to identify themselves with their shadows cast by a fire behind them; and they believe they, as shadows, are interacting with the shadows cast by people walking behind them. One of the prisoners breaks free of his chains and escapes to the world outside the cave, where he sees the full 3d world. He can now really interact with the other 3d people and objects. However, he goes back to try to rescue his former fellow prisoners. They mock him and challenge him to tell them what he thinks he sees in their shadow world. Because he has been in the bright sunlight outside the cave, his eyes are not as keenly. adjusted to the dark shadowworld in which his fellow prisoners live. They can make out the details of the shadows better than he can. This proves to them that he is merely mad. It is worth considering that the bizarreness of the Ted Owens story is a modernday version of Plato's Cave allegory. Even though Plato had said of his Academy: "Let no one enter here without geometry," it took many centuries for geometry to extend to the 4th dimension. It was the 4th dimension as a doorway to the spiritual realm that inspired this geometric foray. The philosopher who attempted to geometrize the Platonic realm was Henry More (16141687), an influential colleague of Isaac Newton at Cambridge University. He taught that the spiritual realm extended into a 4th dimension, which he called "spissitude." But this sort of thinking caught on only when mathematicians began exploring the geometry of higher dimensional spaces. August Moebius (17901868) is most famous for his discovery of the Moebius strip, a surface that has only one side. But in 1827 he described how a 3d object (such as a right handed glove) could be turned into its mirror image (a lefthanded glove) by rotating it through 4dimensional space. Such a rotation could also be used to tie or untie a knot (whose ends are connected as in the mathematical definition of a knot); and link or unlink a chain. Johann Carl Friedrick Zoellner (18341882), an astronomer at the University of Leipzig (where Moebius taught), tried to prove that the spiritual realm was 4dimensional by having mediums such as Henry Slade link two wooden rings (one of oak and one of alder). Slade never did this, but succeeded in convincing Zoellner that he could move things through the 4th dimension by (among other things) tying four trefoil knots in a loop of string whose ends were sealed together. Zoellner wrote about these ideas in the book, Trancendental Physics, which made the notion of the 4th dimension abhorrent among scientists. Mathematicians, largely unconcerned with the application of their discoveries, continued to explore geometries well beyond the 4th dimension. They were interested in the most general case  any number of dimensions. Hyperspace as a word meaning a space of more than three dimensions was coined in the 1890s by mathematicians, who were exploring the geometries defined by Bernhard Riemann (18261866) which were not only nonEuclidean (with any degree of warpingcalled "curvature"), but also were spaces of any number of dimensions. Riemann, himself, even proposed that curved (nonEuclidean) 3d space might account for gravity. He was almost right. Einstein in 1915 showed that gravity could be accounted for by a curved 4d spacetime. Now physics is in the (embarrassing) situation of having 10dimensional spacetime forced on it (at least in theory) if we wish to unify general relativity with quantum theory. The major experimental test of this theory is the search for supersymmetry partners for all of the ordinary fundamental particles. Ironically, this seems to be a replay of Dirac's 1929 unification of quantum theory and special relativity, which required the introduction of antiparticle partners for all the ordinary particles. The antielectron (the positron) was quickly discovered in 1932; but the next antiparticle, the antiproton, was not discovered until 1955. Only then did physicists agree that the antimatter idea must be true for all particles. Since general relativity and quantum theory are gigantic worlds unto themselves (and hardly on speaking terms with each other), it is not surprising that in order to unify these two theories as subtheories of a larger theory physicists have envisaged many new consequences, chief among them being the hyperdimensional (10d) spacetime. The Mathematics of Higher Dimensions In order to describe this hyperspacetime as well as other spaces that must interact with it, some of the most arcane (and beautiful) discoveries in recent mathematics must be utilized by the physicists. It has been my contention that the powerful unification of mathematical categories afforded by the ADE Coxeter graphs is the most appropriate tool to use in the modeling of unified field theory that is, the truly unified theory afforded by superstrings, and their recent generalization to membrane theory. An ADE Coxeter graph (named for the Canadian mathematician H.S.M. Coxeter (1907 ) is a set of nodes joined by lines in one of three patterns: [Illustration not included] Thus there are an infinite number of A's and an infinite number of D's, but only three E's. These graphs, simple as they seem, are the most powerful tools to explore hyperspace. The number of nodes in a diagram is the number of dimensions in a kind of space, which I call a reflection space, and Coxeter calls a kaleidoscope, but which most mathematicians call "the dual space of a Cartan subalgebra of a Lie algebra." In 1935, Coxeter devised these diagrams to describe hyperdimensional generalizations of the Platonic solids (tetrahedron, cube, octahedron, dodecahedron, and icosahedron) and other highly symmetric geometrical objects, which he called "polytopes." It is reflections in hyperspace mirrors that transform these polytopes into themselves. But lower dimensional polytopes are substructures in higher dimensional polytopes, and the Coxeter graphs, which generate the mirrors for these reflections, control, by their hierarchical structure, the embedding of lower dimensional polytopes in the higher dimensional polytopes. This implies also that the lower dimensional objects are projections of the higher dimensional objects. Physicists became interested in these graphs when they discovered that the observable charges (electrical, weak, and strong) associated with particles  and thus defining the particles  correspond to the vertices of polytopes described by these Coxeter graphs. Moreover, in superstring theory, which brings gravity into the unification picture, it is necessary to embed the polytopes describing the particle charges (A4 and D5 for exarnple) in the Etype petlytopes. This has everything to do with the 10dimensionality of spacetime in superstring theory. In fact in the E8 version of superstring theory, the 8 nodes of the E8 graph correspond to the 8 vibrational degrees of freedom of the "worldsheet" swept out by the vibrating superstrings  analogous to the worldline traced out by a point particle. Thus the 2 dimensions of the worldsheet itself, plus the 8 dimensions of worldsheet vibrations (whose harmonics are particle states), add up to the 10 dimensions of spacetime. As readers of my (1993) appendix paper in Roots of Consciousness know, I have been partial to E7 as the basic descriptor of the hyperworld. In this theory, I identify the E7 reflection space (a 7d complex space) with universal consciousness. The E7 Lie algebra (whose largest commutative subalgebra can be identified with the reflection space) corresponds to a mind at large (both conscious and subconscious). In turn, this E7 Lie algebra is a 133dimensional subalgebra of an infinite dimensional algebra, which is a kind of supermind to the E7 mindatlarge. Since E7 has been largely neglected by the superstring theorists, it is gratifying to learn that the recent generalization of superstring theory to membrane theory makes the E7 theory a kind of master theory. In membrane theory a string is a 1d membrane; an ordinary membrane is a 2brane; and there are ndimensional membranes going all the way up to 9branes in 10d spacetime. The great excitement in this theory is that membrane theory unifies all five competing versions of superstring theory. Moreover, as a master theory there is an 11dimensional supergravity theory with 7 (= 11  4) hidden dimensions. These 7 dimensions are identical to the 7d Cartan subgroup of the E7 Lie group; and thus correspond exactly to the 7 nodes of the E7 Coxeter graph. So the master theory is the E7 theory. By the very nature, however, of the unification of the competing superstring theories (and by the embedding of the lowerdimensional polytopes required for unified field theory), it must be that all the ADE graphs are implicit in some vast unification which entails consciousness in a universal sense. To me the hierarchy of the embedding structures suggests a hierarchy of realms of consciousness  or realities, for short. If we attempt to model the events which Ted Owens seemed to trigger (drastic weather modifications and UFO sightings) I believe we must employ models afforded by the ADE hierarchy of hyperdimensional mathematical objects. Weather modification entails the control of catastrophic structures. It has been shown mathematically that the ADE hierarchy classifies the control parameters for all "simple" catastrophes. It may be necessary to go beyond the ADE hierarchy to a larger hierarchy to describe the control structures for the nonsimple "chaotic" catastrophes. In this case the three E graphs form the gateways into the higher catastrophes [Arnold, Gilmore]. Closely related to catastrophes are "caustic" structures. Russian mathematicians have labeled one of these the "flying saucer" caustic. And it looks like a flying saucer. As they describe it: "for positive time the caustic is absent but...for negative time it exists. According to V.M. Zakalykin this reconstruction, possibly, illustrates the phenomenon of the disappearance of 'flying saucers'" [p. 176 in Singularities of Differentiable Maps, Vol II, Arnold et al,1988] In fact, the model for hyperreality must be the vast underlying mathematical object described by the entire ADE series itself. Each category of mathematical object described by these graphs is merely another window into this underlying object. There are by now more than twenty such mathematical windows. I will name only those few whose relevance for physics and consciousness are obvious: reflection groups.; Lie algebras (and groups); Heisenberg algebras; gravitational instantons; catastrophe structures; errorcorrecting codes; analogtodigital (and viceversa) coding; conformal field theories; McKay groups  such as tetrahedral double (E6), octahedral double (E7), and icosahedral double (E8) groups. These latter groups hearken back to Plato's dialogue the "Timaeus," where the regular (Platonic) solids discovered by the Pythagoreans are discussed. For this reason, the Russian mathematician V.I. Arnold, who has most vigorously led the exploration of the ADE hierarchy, calls this study "Platonics." The three exceptional graphs (E6, E7, and E8) are the three doorways into an even larger, much more complicated hierarchy of mathematical objects. It is just possible that these doorways allow really spooky things to project down into the "ordinary" superstring realms of the ADE world. If so, the strange life of Ted Owens (presumably modelled in part by the ADE hierarchy itself) might provide some insight into the vast world beyond. Biography of SaulPaul Sirag SaulPaul Sirag is a theoretical physicist whose theories encompass the age and size of the universe as well as the number and nature of all subatomic particles. Return to essay menu. Return to William James Bookstore 
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