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.

The intelligence raising drug, NEURO, began to change things a bit after it appeared in 1988. People's fantasies gradually became more sophisticated and philosophical, and their reality-tunnels accordingly adapted. With the publication of Sirag's General Field Theory in 1993, the smarter primates immediately realized what was really occurring on their planet and throughout the cosmos.

The first quote is from the present, non-fiction book about Ted Owens, whose purported contacts with Space Intelligences sound like the wildest science-fiction. The second quote is from a novel, whose very structure incorporates the many-worlds model of quantum mechanics. It is an amusing synchronicity that the paper "Consciousness: a Hyperspace View" (which could indeed be described as Sirag's General Field Theory) was published in 1993, as a 39-page appendix to the Second Edition of Jeffrey Mishlove's book Roots of Consciousness,.

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 (1920-1987), 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 four-dimensional (4-d) spacetime. Whatever doubts physicists had - and there were many - about the reality of the 4-dimensionality 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 (1831-1979), could be derived from the assumption that spacetime is actually a warped 5-dimensional geometric structure. With Einstein's help, Kaluza's 5-d 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 wave-particle 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 5-dimensional 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 5-d 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 4-d spacetime is replaced by a tiny circle whose radius is around 10-33 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 (10-13 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 Planck-length circle, as a candidate for the 5th dimension, entailed both Einstein's general relativity (applied to 5-d 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 5-d theory called Kaluza-Klein 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 (1879-1955) 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 holy-grail 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 10-dimensions of spacetime! Physicists suddenly began to read the old 5-d Kaluza-Klein 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 celebration-year 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 self-consistent theory of quantum gravity, which includes General Relativity and Quantum Mechanics as sub-theories. 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 (427-347 B.C.), who suggested in his Cave allegory, that we are like prisoners of the 3-d world, identifying ourselves with our 3-d shadows, rather than the hyper-dimensional creatures we really are. Plato never used the word hyper-dimensional, but the idea is clearly in his story of the projection of the prisoner's shadows (a 2-d 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 3-d world. He can now really interact with the other 3-d 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 shadow-world 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 modern-day 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 (1614-1687), 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 (1790-1868) is most famous for his discovery of the Moebius strip, a surface that has only one side. But in 1827 he described how a 3-d object (such as a right handed glove) could be turned into its mirror image (a left-handed glove) by rotating it through 4-dimensional 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 (1834-1882), an astronomer at the University of Leipzig (where Moebius taught), tried to prove that the spiritual realm was 4-dimensional 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 (1826-1866) which were not only non-Euclidean (with any degree of warping--called "curvature"), but also were spaces of any number of dimensions. Riemann, himself, even proposed that curved (non-Euclidean) 3-d space might account for gravity. He was almost right. Einstein in 1915 showed that gravity could be accounted for by a curved 4-d spacetime.

Now physics is in the (embarrassing) situation of having 10-dimensional 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 anti-particle partners for all the ordinary particles. The anti-electron (the positron) was quickly discovered in 1932; but the next antiparticle, the anti-proton, was not discovered until 1955. Only then did physicists agree that the anti-matter 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 sub-theories of a larger theory physicists have envisaged many new consequences, chief among them being the hyperdimensional (10-d) 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 A-D-E 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 A-D-E 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 sub-algebra 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 E-type petlytopes. This has everything to do with the 10-dimensionality 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 7-d 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 133-dimensional subalgebra of an infinite dimensional algebra, which is a kind of supermind to the E7 mind-at-large.

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 1-d membrane; an ordinary membrane is a 2-brane; and there are n-dimensional membranes going all the way up to 9-branes in 10-d 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 11-dimensional supergravity theory with 7 (= 11 - 4) hidden dimensions. These 7 dimensions are identical to the 7-d 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 lower-dimensional polytopes required for unified field theory), it must be that all the A-D-E 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 A-D-E hierarchy of hyperdimensional mathematical objects. Weather modification entails the control of catastrophic structures. It has been shown mathematically that the A-D-E hierarchy classifies the control parameters for all "simple" catastrophes. It may be necessary to go beyond the A-D-E hierarchy to a larger hierarchy to describe the control structures for the non-simple "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 hyper-reality must be the vast underlying mathematical object described by the entire A-D-E 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; error-correcting codes; analog-to-digital (and vice-versa) 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 A-D-E 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 A-D-E world. If so, the strange life of Ted Owens (presumably modelled in part by the A-D-E hierarchy itself) might provide some insight into the vast world beyond.
 
 
 

Biography of Saul-Paul Sirag
 

Saul-Paul 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.
 

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