**Saul-Paul Sirag**

**March 29, 1999**

JEFFREY MISHLOVE: Welcome to Virtual U, all of you out there in Wisdomland. This is the first evening of our new program, with our new music, which has been custom-prepared, created and composed for Virtual U by Gary Takesian, Music Director Lars Spivock.

We have an interesting program for you tonight. My guest is Saul-Paul
Sirag. Saul-Paul and I have been affiliated with each other for well over
twenty years. He wrote the section in my book, *The Roots of Consciousness*,
in the new revised edition, the Appendix called "Consciousness: a Hyperspace
View." I regard it as the most advanced attempt yet to integrate our understanding
of consciousness with what we know today about physics and cosmology.

Saul-Paul has approached this by attempting to develop a grand unified theory in cosmology, that is, a theory that can integrate in one mathematical structure, the size and the age of the universe, as well as all of the subatomic particles and the subatomic forces known in physics. And he discovered, during this great quest, that the mathematical structure he encountered, a "hyperspace" mathematical structure, which we'll talk about more, also provides many insights into the nature of consciousness, waking consciousness, but more than that, mystical states of consciousness: dream states of consciousness.

Saul-Paul is an expert when it comes to science and he's an expert when it comes to mystical, theological and spiritual traditions as well, so it's my great pleasure to welcome you tonight, Saul-Paul, to the first program of Virtual U.

SAUL-PAUL SIRAG: Hi, Jeffrey, I'm here!

MISHLOVE: I'm glad. I'm glad to be with you once again, Saul-Paul. Now, your theories are very complex, they've been published in scientific journals like Nature,

SIRAG: And The International Journal of Theoretical Physics, for one thing. That's my Cosmology paper, it was published there. And some of my Unified Field Theory work was published in The Bulletin of the American Physical Society, and the most recent publication of mine actually is a book review, which relates to my work. It's in The Journal of Consciousness Studies, the issue that just came out last December,1998. It would be Volume 5, numbers 5 and 6, 1998, and it's a review of the work of H. H. Price, a British philosopher who was very interested in the mind-body problem. He didn't write a whole book on the topic, but he wrote many, many papers; and some of these papers have finally been collected in a book published in 1995 with an Introduction by Frank B. Dilly, who's a philosopher at the University of Delaware.

I wrote a review of this, and the interesting thing about H. H. Price's
point of view is that as long ago as the thirties and forties, he was talking
about a hyperspace view of consciousness. Now of course the idea of hyperspace
and the spiritual realm goes back, really, to the nineteenth century, to
a work by Edwin A. Abbott, who wrote *Flatland*.

He was actually a minister who was trying to make the spiritual realm more palatable, more understandable, by appealing to the idea that if we were like flatworms, if we were two-dimensional beings, and something from the three-dimensional world entered our world, we would consider it a miracle and that was kind of the first quasi-science fiction story involving hyperspace, you might say, because obviously his idea was that we three-dimensional beings are really just a substructure of a higher-dimensional realm in which all kinds of things were going on which we couldn't understand without a mathematical or physical model of the hyperdimensonal realm.

MISHLOVE: Flatland was a way for us to imagine what it's like for us, by assuming that if we lived on a plane, like on a sheet of paper, then the three-dimensional world would seem mysterious and foreign to us.

SIRAG: Yes, and miraculous, even. And from the point of view of the three-dimensional realm, things would be completely obvious and open to us. For instance, there wouldn't be any barriers between the inside and the outside of a two-dimensional house or a two-dimensional being, for that matter. And of course, the same would be true of us, from a four-dimensional point of view.

There wouldn't be any barrier between what we regard as inside our skin, say, or outside our skin, or inside our house and outside our house. It would all be open to a larger realm and so there could be connections between things that would be very mysterious, from let's say, a three-dimensional point of view that we're familiar with.

And it's intuitively obvious to us that the world simply is three-dimensional. We generally don't have to think of the questions: is it really is three-dimensional; and why is it three-dimensional? These are the kinds of questions that we are trying to answer now in physics, and the interesting thing is that physics in the form of Unified Field Theory, has come up with the notion very strongly held now, among Unified Field Theorists, that the world is actually ten-dimensional!

And we say that space-time is ten-dimensional. And that there are hidden dimensions. There are at least ten dimensions. There are aspects of space-time that are even larger, but minimally, a ten-dimensional world. So there'd be minimally, six hidden dimensions.

But they're very tiny dimensions. They're inside of everything. Which is why we weren't aware of them until we developed these Unified Field Theory and String Theory descriptions of how the forces relate to each other. That's the context in which String Theory evolved -- starting in 1970, by the way, so it's been around for a long time.

MISHLOVE: How widely accepted would you say that idea is today?

SIRAG: Well, it's a controversial idea in the sense that the claim is frequently made, especially by experimental physicists, that there's no experimental evidence for the truth of this Theory. Among theoreticians who are actually working on the Theory, it's very, very popular. In the whole history of physics, there's always a kind of tug of war going on between the theoreticians, especially the theoreticians at the cutting edge, and the experimentalists, because they have different jobs to do, in effect.

The job of an experimentalist, say, is looking for particles or some kind of phenomenon that we haven't heard of before. Their job--what makes their day--is to find something that no theoretician has yet thought of. That's understandable.

And the other thing they can do is simply to verify what theoreticians have claimed must exist. An example of that would be the top quark, which was just discovered by experimentalists a couple of years ago, but it was predicted as long ago as 1970. And it took a long time for the experimentalists to verify that any quarks existed. That wasn't experimentally verified till about 1977. And it took even longer to verify that six different types of quarks, including the most difficult to find, called the "top quark," which wasn't discovered until a couple of years ago.

But those experimentalists who discovered that quark, they'll probably get the Nobel Prize and everything, but on the other hand, they will feel as if they're just verifying what theoreticians told them must be there. What they'd be much happier about would be to discover something really oddball that the theoreticians can't explain yet, so that the theoreticians would have to go back to square one and try to figure it out.

That's the kind of game that goes on.

With that perspective on how the game is played, you can see that the experimentalists are saying things like, "Well, you know, it's going to take a very long time for us to verify Superstring Theory because the kind of energies involved are so immense that we can't really build accelerators remotely big enough to test this Theory. That's what some of them are saying. It's really just a kind of a metaphysical theory, then, if it's untestable.

But the theoreticians argue back that actually before a theory is tested experimentally, by looking for new particles that are predicted, which is a kind of standard way -- and these theories do predict new particles -- what any Theory has to do is to pass all kinds of consistency tests that are purely mathematical, really.

From that point of view, Superstring Theory does very well, which is why it's popular. You see, Superstring Theory is an attempt to do something that by many physicists was considered impossible. And that is to unify the General Theory of Relativity, which is Einstein's Theory of Gravity, with quantum mechanics.

In other words, to construct a quantum mechanically correct theory of gravity; and there are many problems, but the main problem is really that these two theories are conceptually so different from one another that they're hardly on speaking terms with one another. But still, Superstring Theory is the only known theory that does this virtually impossible task, which is to construct a consistent Theory that obeys both the rules of General Relativity and quantum mechanics -- as special cases of an over-arching, bigger Theory. And, in addition to that, it brings in all the other forces, not just gravity, but the strong, weak, and the electromagnetic. The strong and the weak forces are the forces that we call "nuclear" forces, they act over very short ranges.

MISHLOVE: Saul-Paul, we'll come back and we'll talk more about Superstring Theory and how it relates to hyperspace, and cosmology and consciousness and subatomic physics, after a few messages from WisdomRadio. I'm Jeffrey Mishlove, host of Virtual U.

[Break]

MISHLOVE: You're listening to Virtual U on WisdomRadio, and my guest today, Saul-Paul Sirag, is a theoretical physicist who is working on the frontiers of cosmology, quantum theory, and consciousness, and we're exploring how the notion of "hyperspace" that space itself is more than just the three dimensions that we receive with our senses is well established in a branch of theoretical physics known as "Superstring Theory" which has come to be a very popular and widely accepted branch, although it still lacks experimental verification.

But, Saul-Paul, as you were explaining, from the time the idea of the quark was first theorized, until we developed experimental proof, it took many decades.

SIRAG: Well, about a decade until the existence of quarks per se was first proved, but you see, beyond the bare existence of quarks, what our best theories told us was that there were three "families" of quarks. It's kind of mysterious that there would be three families, but theoreticians could show that they were necessary in order to explain certain facts that were well known in particle physics.

But simply saying we need three families of quarks in order to make the math come out right, which is what the argument boils down to, in a sense, is one thing, but it's another thing to really verify the existence of these three families of quarks, two quarks in each family! For instance, the first family consists of quarks called the "up" and "down" quarks, and the second family is the "strange" and "charmed" quarks, and the third family is the "bottom" and "top" quarks. The charm quark was discovered in 1974, for instance, before the evidence for the existence of quarks was really in hand -- before physicists were really convinced that experimentally we knew for sure there were quarks.

So these things overlap each other. But the top and bottom quarks, because they're very heavy, took a lot longer to find. The top quark is extremely heavy, and wasn't found, until big enough accelerators were built. In other words, the heavier the particle, the bigger the accelerator you have to have in order to create it. We find these things by creating them, in effect, by very high-energy interactions. It wasn't found until a couple of years ago -- the top quark.

MISHLOVE: How heavy is it, let's say compared to a proton?

SIRAG: It's on the order of, if I remember right, it's on the order of much more than a proton. It's of hundreds of protons. It'd be like the mass of a heavy atom, maybe something like an iron atom, or even something heavier. Actually, heavier than an iron atom. [Note: about as heavy as a gold atom.]

MISHLOVE: Now this is quite remarkable, because a quark is a particle that is supposedly one of the constituents of a proton, or of an electron.

SIRAG: Right.

MISHLOVE: Or a neutron.

SIRAG: The protons and electrons are made up of really light quarks. They're made up of up and down quarks. A proton consists of two up quarks and one down quark; and if you change one of those up quarks into a down quark so that you have one up quark and two down quarks, then you'd have a neutron.

What we claim is going on in the nucleus of an atom is continual exchange between protons and neutrons; in other words, neutrons changing into protons, and protons changing into neutrons, by these quarks changing into each other by way of certain interactions called the strong interaction.

MISHLOVE: All of this is quite different than the physics that I was taught twenty or thirty years ago,

SIRAG: That's what glues the nucleus together because, you see, in the nucleus, you have a problem, explaining how you can have all these positive charges sitting right next to each other without the thing blowing apart, because like charges repel, after all, electrically. So that's how the strong force was first invented, to simply answer the question how these positive charges hang out together. Well, there must be a force that holds them together, some sort of "glue", that is stronger than the electrical force. And we called it the "strong force" and we didn't know much about it till the quark model came along, actually.

MISHLOVE: These are the forces that are involved, in effect, in nuclear weapons.

SIRAG: Yes. Fission has to do with overcoming this force that holds the nucleus together; and in a heavy atom, like a Uranium atom, it's the electrical force that pushes the two pieces of a Uranium nucleus apart, in fission. The electrical force that's there all the time, because like charges repel, after all. So it's sort of like a dam that you break, and once the dam is broken, then the water comes rushing out.

MISHLOVE: A lot of people would think, and I think, for a long time, that physics is totally unrelated to the question of consciousness. Physics is about matter, inert, there's nothing conscious in physics per se, but you maintain that the theories of physics tell us many, many things very intimate, about the nature of consciousness.

SIRAG: Yes, there are many different aspects of physics that one has to think about in order to deal with very deep problems such as the nature of consciousness, but in a larger sense, we're really dealing with the question of the nature of reality as well as the nature of consciousness.

The old conundrums of the mind-body problem that philosophers talk about.

MISHLOVE: We have just a few more seconds and you've raised the old conundrum, how is it that inert matter, that consciousness can arise from the matter of physics? And we'll come back to that after the break.

[Break]

MISHLOVE: I'm Jeffrey Mishlove, host of Virtual U, and we're discussing some of the ancient conundrums of consciousness with a modern physicist and consciousness researcher, Saul-Paul Sirag. We've been talking about hyperspace, and we're getting right down to one of the fundamental questions, and it's one that you have an answer for, Saul-Paul. It has to do with how is it that reality has consciousness and it includes the physical sciences that seem to have no room at all for consciousness.

SIRAG: Yes, there have been, historically, many approaches to the mind-body problem; and the idea of hyperspace being one possible approach is really old-hat, although the people like H. H. Price, I mentioned earlier, weren't saying it from the point of view of modern physics, they were just saying it from the point of view of just thinking abstractly, mathematically, about it.

Bertrand Russell had very similar ideas that he actually developed from ideas of Leibniz; but I'm not going to go into those approaches because I go directly to what physics says about the nature of reality. It says, other than the hyperspace aspect that I've been discussing, there are other aspects of physics that have to be taken into account, that definitely seem to relate to consciousness. For one thing, quantum mechanics itself has been discussed by many physicists, most notably the mathematician Von Neuman, and the physicist Wigner.

MISHLOVE: Nobel Laureate Wigner,

SIRAG: Wigner is a Nobel Laureate, right; and Von Neumann would have been if there'd been such a thing in mathematics; and he was a very, very great mathematician, but also was interested in physics and the foundations of quantum mechanics; and he wrote a book that's considered kind of a bible of quantum mechanics, called Mathematical Foundations of Quantum Mechanics, and in that book he proposes the idea that -- and I'll have to explain the terms -- but what he basically suggests is that consciousness is involved in every quantum mechanical observational process, you might say.

You see, quantum mechanics is very peculiar in the sense that it has two very different kinds of operations, you might say. It has an operation that just smoothly -- deterministically, actually -- changes the system, any system that we apply quantum mechanics to. And that's called The Schroedinger Equation evolution of the system.

But there's another thing that happens; and really here's the interesting thing: whenever anything happens, the smooth Schroedinger Equation evolution is in effect set aside and what we call the "collapse of the wave function" or "the projection of the state vector" (those are different mathematical terms, or different mathematical ways, of describing really the same thing) occurs; and what happens in that case is that from a large number of possible things that could happen, one thing does happen.

MISHLOVE: In other words, the Schroedinger Wave Function describes what is sometimes thought of as a probability cloud, an amorphous number of many, many different possibilities any one of which could happen, or in some views, all of which are simultaneously happening in multiple realities, but when an observation is made, we see just one possibility.

SIRAG: Yeah. You might ask, what is happening as your Schroedinger Equation evolves -- what is changing? Well, what is changing is the probabilities themselves. But just because the probabilities are changing as time goes on, say in a system, we still don't know -- the equation doesn't tell us -- what actually does happen.

When something actually happens, like, typically, an electron interacts with another particle, another electron or whatever, that interaction -- any interaction -- entails what has been called the collapse of the wave function. In other words, the projection of one possible state from many, many possible states into a single state; and associated with that state, which we call an "eigenstate," is a quantity which we call an "eigenvalue."

Now, from my point of view, the eigenvalues are what's actually observed in an observation.

MISHLOVE: Theoretically speaking, quantum physics suggests that we might be in all possible worlds simultaneously, but any time we look, we find ourselves in just one reality.

SIRAG: That's correct. That's one way of putting it, yes. And of course looking is, in a way, what's involved in consciousness. Consciousness is the looking, so to speak. If you're not looking, you're not conscious. And I'm using the word "look" in the broadest possible sense. It involves much more than the visual sense. "Sensing" would be the broader term.

What this suggests is that any time we look at a scene, we're actually experiencing a lot of tiny little looks at once, and how do we do that? Well, we do that with the very complex mechanism of our nervous system in our very complex, evolved brain.

MISHLOVE: Saul-Paul, we're about to take another break.

SIRAG: OK.

MISHLOVE: WisdomRadio has some messages, and we'll be back again, after them!

[Break]

MISHLOVE: I've been talking with Saul-Paul Sirag, theoretical physicist; and we're exploring the relationship between consciousness and hyperspace in physics; and we're coming now to a very interesting point, which is the relationship between the nervous system itself and consciousness, and then the quantum physical ideas about consciousness involving the observations that are made, in physics.

Physics, it seems to me, is quite paradoxical, because it is a science that has been produced by human consciousness, but it on some level, in its most materialistic interpretations, it posits a universe in which consciousness is not even necessary.

Saul-Paul is providing us with another view, which suggests that consciousness is intimately involved in every physical observation, so intimately, that it must be viewed as prior to space, time, matter, and energy, rather than merely an epiphenomenon, a product of the nervous system!

SIRAG: Yes. What is the product of the nervous system is the very rich field of consciousness, you might say, that we enjoy, but if we think of entities that don't have such a rich nervous system, like maybe a slug or a carrot or something, these entities still sense the world around them, but not, we would guess, from the lack of a complex nervous system, that it wouldn't be as rich.

But we can take this argument all the way down to atoms and particles, and from the point of view of quantum mechanics, each little particle interaction could be viewed as a little blip of awareness, not the kind of awareness that you and I enjoy, because we enjoy such a complex of blips, in other words, it's the difference between a few grains of sand and a lovely beach.

We enjoy the beach, but the beach is made up of jillions of little grains of sand. It's a little bit like the dots that make up -- this is just an analogy, of course -- the dots that make up the image that you see on your TV screen. Each little dot you can think of as a little blip of awareness, of whatever color is there; it wouldn't be any big deal without all the other dots being part of the same picture, and it takes a complex nervous system to take in all those dots at once, and process them.

MISHLOVE: In other words, our nervous system might be acting more like a television receiver receiving consciousness than some kind of an organ that produces consciousness.

SIRAG: Yes, that's a good way of putting it. Our bodies -- as far as physics is concerned -- our bodies are made up of molecules; and the molecules are made up of atoms; and the atoms are made up of particles. Ultimately we're quantum mechanical entities and there are probably even very special -- I would guess, very specia-- quantum mechanical states that are peculiar to such a specialized organ as a human brain.

Other people have speculated about this and possibly we will find evidence for this in the future. This is a scenario that's actively being looked at in brain physiology. What I mean by that is special coherence states. Most quantum mechanical states are just tiny little blips that aren't necessarily connected with other blips that are far away, but there are what we call macroscopic states such as a "superfluid". If you cool a fluid down very close to absolute zero, it will become superflowing and it will act as if it's all one entity.

MISHLOVE: I think we're talking about the difference, if we use the television set as an analogy, between just static on the TV set, or snow, as it's sometimes called, and actually having a picture.

SIRAG: Yes. Having a picture where one part of the picture relates to the other part of the picture in a meaningful way, yes. And these are called Bose- Einstein condensations of particles.

MISHLOVE: These coherent particles,

SIRAG: These coherent states. A coherent state, the kind I'm talking about, is called a Bose-Einstein condensation. But we don't have to go into that which, in essence, is a complex term.

MISHLOVE: But one point I do want to make, to come back to where we started at the beginning of the hour, is that all of these particles, these dots on the TV screen of our mind, so to speak, are interacting and dancing not just on a two-dimensional surface, like a TV screen, but you're suggesting, in at least ten dimensions!

SIRAG: Yeah. Let me get into that a bit. Remember, I said earlier that the quality that is associated with a happening, with an event, the event state itself is called an eigenstate, but the quality that identifies it is called an eigenvalue. Now, one of the things that's very interesting in Unified Field Theory is that the eigenvalues of all the subatomic particles that we are unifying in Unified Field Theory, and there are many, many of them, but the thing that makes the Theories work is the fact that these eigenvalues exist as beautiful, symmetrical, crystallographic objects in a hyperspace, which is different from space-time.

MISHLOVE: Now you're creating a very beautiful structure, Saul-Paul, but we're about to hear some more messages from WisdomRadio, so we'll be back again after them.

{Break]

MISHLOVE: You've been listening to Virtual College on WisdomRadio; and I'm your host, Jeffrey Mishlove. For the past hour I've been interviewing Saul-Paul Sirag, a theoretical physicist whose work specializes in the area of hyperspace as a tool for integrating consciousness with cosmology and with particle physics.

We'll be back again at six and a half minutes after the hour and we'll continue for another hour with our discussion. Right now I'd like to let you know that we can be reached.

Are there some final thoughts you'd like to share with our listeners before we take our break at the top of the hour?

SIRAG: I'd just like to have them focus on what I'm going to return to after the break, which is this hyperspace crystallographic structure, because that's really the key idea. It's something that mathematicians figured out a long time ago, but it's only been applied to physics recently. The mathematicians call it "hyperspace crystallography" or they refer to it as being a "hyperkaleidoscope".

MISHLOVE: We'll be back at six and a half minutes after the hour. Thanks, Saul-Paul.

[Break]

MISHLOVE: One thing I forgot to mention earlier, when I talked about Saul-Paul Sirag, my guest tonight, in his qualifications, is that he is one of the moderators of the Quantum Mind E-mail Discussion List, which is co-sponsored by the Department of Consciousness Studies at the University of Arizona and the Intuition Network, a nonprofit organization of which I am the President.

For those of you who have a serious interest in pursuing the details of the fascinating debates that take place among scientists probing the relationship between physics and consciousness, the best way to subscribe to that List is to link to it through the "mishlove.com" website that I announced earlier.

Well, Saul-Paul, before the break, you were describing what you called "hyperspace crystallography" and I guess from the point of view of the layman, what it suggests to me is, when we think of these higher dimensions of space, let's say a ten-dimensional space-time matrix that is postulated in Superstring Theory, we're looking at not just something that's mysterious and random, but something that has a very definite structure. That hyperspace itself is perhaps crystalline in nature.

SIRAG: There's something to that. It's actually the mathematical, geometrical structure of the spaces that is the basis of the theories that we talk about in Superstring Theory. In fact, as I said before the break, it's the eigenvalues -- in other words, the qualities -- that are associated with particle interactions that identify the particles in the interaction. In the context of Unified Field Theory, all those eigenvalues correspond to the vertices of crystallographic structures.

OK. And because the mathematics of these crystallographic structures has long since been worked out by mathematicians, this is simply using what is already there, as far as the mathematicians are concerned.

Now, there are a number of things about these structures that are suggestive to me of consciousness, starting, of course, with the fact that the vertices themselves are actually eigenvalue vertices. Yes?

MISHLOVE: I think we'd better define the term "vertices".

SIRAG: OK. If you have a snowflake, that's a six-sided figure, each of the six points on this six-pointed snowflake is a vertex, we say; and the plural would be "vertices." There are six vertices. In fact, the snowflake form, the hexagonal form, actually, is exactly one of the eigenvalue structures for particles. It's exactly the eigenvalue structure for the strong nuclear force.

It corresponds to three colors and three anti-colors. In other words, if you think of two triangles intersecting in the form of the Star of David, say, -- that's the hexagonal form made up of two intersecting triangles -- then the vertices of one triangle would correspond to quarks of three different colors, and the other, the opposite triangle would correspond to the anti-colors.

And that's a two-dimensional crystallographic structure. But that is simply the sub-structure of a three-dimensional crystallographic structure which would actually also include not just the strong force eigenvalues but electrical force eigenvalues and then we would have the quarks having just the right electrical values of one-third or two-thirds, which was very peculiar when the quark model was first proposed -- in fact, it was very controversial.

Because people thought, "Oh, you can't have fractional charges!" Well, quarks do have fractional charges, according to our theories; and it's beautifully depicted by these crystallographic structures.

In this case, you'd have two intersecting tetrahedra, actually, which would project down to the two triangles in two-dimensional space. The tetrahedra would be sitting in a three-dimensional space. I proposed a name for these kinds of spaces, since there isn't a name already in existence. I call them "reflection spaces," because it's a kind of mathematical reflection that changes one of these vertices into another vertex. It's very much like the way a kaleidoscope works, which is why mathematicians call these structures "kaleidoscopic".

And in turn, the three-dimensional reflection space -- three-dimensional crystallographic reflection space -- is embedded in even higher-dimensional spaces which are necessary in order to include the weak force, and even higher-dimensional structures to include gravity.

In Superstring Theory, we go to much larger reflection spaces all the way up to sixteen-dimensional reflection spaces. OK?

MISHLOVE: Saul-Paul, what this reminds me of is sort of the medieval view of the universe, where we had the "celestial spheres." Each sphere was embedded within a larger sphere, and they were constantly rotating and I believe the medieval researchers felt that the friction between the celestial spheres created music!

It's as if these crystalline structures embedded within each other are analogous to that, but instead of spheres reaching out to the stars, you're reaching up into higher and higher dimensions of space!

SIRAG: Yeah, and this isn't yet space-time. We're going to get to space-time. We're going to get space-time out of this, in a way. What we're really going to get are the hidden dimensions -- the dimensions that we don't see, that are called extra space-time dimensions.

The way you get those dimensions from those crystallographic structures is in a way that is very understandable to mathematicians but difficult to describe, especially without pictures, a blackboard and so on. But even that doesn't help very much.

The thing is, that these crystallographic structures form lattices like -- you can think, you can see in your mind's eye the hexagonal lattice, certainly -- just a bunch of hexagons that are...

MISHLOVE: Like a honeycomb.

SIRAG: Like a honeycomb; and the hexagons would be made up of triangles, six triangles, right?

MISHLOVE: Mm.

SIRAG: Six equilateral triangles around a point make a hexagon. So you can imagine a lattice of triangles that contain all these hexagons. OK. Each point, each vertex within the lattice, is actually an active point in the sense that it can act on the space that it's sitting in -- mathematically it can act on it. We can think of the entire lattice as acting on the space and creating a new space. And that new space is a toroidal space.

MISHLOVE: A toroid is like a donut shape,

SIRAG: Like a donut shape, except in this case it might be a higher-dimensional donut. The two-dimensional analog is easy enough to view in your mind's eye. To make it really easy, just have a square-lattice and let's just take one cell of this square lattice, one square, in other words, and hook up opposite sides -- you get a donut, right?

MISHLOVE: Right. Or a ring of some kind.

SIRAG: Well, you'd get a ring if you just hook up two sides, but if you then hook up the two remaining sides, you'd have a donut. As you say, it would look like a ring, an anchor-ring or something.

MISHLOVE: Mm-hmm.

SIRAG: Well, you see, you could have done that with the whole lattice. The whole square lattice. You would just roll the whole thing together in one direction and you get a long tube, and then you roll the whole thing together in the other direction and you get exactly the same thing as just taking one square and hooking up the sides.

OK, now -- strangely enough -- that also works even with triangular lattices in two-dimensional space, even though you can't actually do that without embedding it in the higher-dimensional space of crystals, actually physically do that. But the important thing is that you get higher-dimensional toruses by doing this on the lattices, which would be much more complicated lattices than the ones we're talking about.

Here's the point: the point is that once you get this torus in that way, that torus is, if you have the right one -- you have, that is to say, the right number of dimensions, and the right characteristics for the lattice, involved -- then you have the hidden dimensions of space-time.

And in fact, we have reason to believe now through recent developments in Superstring Theory evolving into Membrane Theory, that there is a kind of a master seven-dimensional lattice, which is one that I've been working on for some time, called the E-7 Lattice, that creates the seven hidden dimensions of eleven-dimensional space-time, because seven plus four (for the four dimensions of ordinary space-time) gives us eleven.

That's what we call a supergravity theory which contains -- as has been shown recently -- it contains two complete ten-dimensional superstring sub-worlds that are in contact with each other only gravitationally, not through any of the other forces -- with light [the electro-magnetic force] for instance. And it's been proposed that this might be a solution to the dark-matter problem.

MISHLOVE: Saul-Paul, what you're describing to me, as a layman, what you're describing to me seems to me some sort of structures within our consciousness, which, if we follow them, will take us mentally into higher and higher dimensions. We'll have a chance to explore the relationship of all of this physics to consciousness with my guest, Saul-Paul Sirag, on Virtual U after these messages from WisdomRadio.

[Break]

MISHLOVE: Saul-Paul, we have a question that was Emailed to me by one of our regular listeners, Reuben Gogo, who asks what I think is a very cogent and pertinent question. He says, "How much of the structures that physics researchers come up with, to a certain degree, are a result of their expectation to find particles or waves or strings, or something that human researchers can relate to, how much of physics is just a metaphor for human consciousness, or do you think that these so-called structures are true to the universe?"

"Excuse the pun", he says, "the universe at large?"

SIRAG: That's a very deep question, of course, that physicists and philosophers have dealt with for a long time. It's sort of: physics is caught between two philosophical tendencies; and it must keep both of these tendencies active. There's the rationalist tendency, which is I think what you're referring to as we, in a sense, invent things like particles, strings, and so on, as entities that we can rationally cope with.

The other philosophical stance that we must uphold, also, is called empiricism, which means that we have to test these wonderful rationalist ideas that we come up with in the so-called real world; that is to say, we do experiments. Physics is ultimately an experimental science, not merely an exercise in logic or philosophy.

There's another aspect to it that's lost sight of sometimes: and that is, where do we get our ideas from? That is to say, for the rational side of things, and even to a certain extent in doing experiments, we have to come up with creative ideas. Where do these ideas come from?

To a certain extent, as Einstein said, they're free inventions of the human mind. But they also come, as Einstein also said, from mathematics. One can argue whether the mathematical ideas are free inventions or not, but the mathematicians don't seem to think so. They seem to think they're exploring some kind of Platonically real realm, not necessarily physically real, but that the forms really are there, before they look, before they come along like Magellan exploring a vast world.

In most recent physics: the more we do physics, the more we see mathematical ideas playing a bigger and bigger role. So I think we have to be concerned about to what extent we simply make things up, which we call our theories. The only thing that keeps the theories honest, ultimately, is the test of experiments.

For instance, Superstring Theory of course accounts for a lot of the physics that we already know -- like Superstring Theory predicts Einstein's Theory of Gravity, for one thing, which is a very big thing to be able to do, among other things. But it also predicts something totally new, which is Supersymmetry partners to all the particles, and that's a very radical prediction.

We haven't found these particles yet, in particle accelerators; and if we do, then that will give us the feeling that the theory is probably right.

MISHLOVE: Now, Saul-Paul, you and I used to both have the same mentor, Arthur Young, and he took an attitude towards all of this particle physics in constantly coming up with new particles, that they would find anything they looked for, because in those high-energy accelerators, you can practically create anything!

SIRAG: The particles are, in a sense, created in the accelerators, but these particles would also exist in Nature in very, very high-energy events, like supernova explosions, and in the early phases of the universe, in the first few seconds of the universe, the energies are so high that we would predict that there would be all kinds of very exotic particles.

To speak to Arthur Young's concerns, I remember Arthur didn't believe in the existence of neutrinos, for instance, you know, having no (or almost no) mass and no electric charge, and only a tiny bit of spin. His belief in particles stopped somewhat short of the neutrino, which was predicted in 1932, but was not experimentally shown to exist until 1955.

So it was a very long period of time that the neutrino was very much up in the air. Theoreticians tended to believe in it, but experimentalists were skeptical about it. It's very much like what goes on now: experimentalists are very skeptical about the existence of the supersymmetry partners, but the theoreticians working on the Superstring Theory have to believe in them in order for the Theory to work.

MISHLOVE: Can you define them in a few seconds?

SIRAG: Yes. Supersymmetry particles are particles that exist by virtue of a symmetry that we call supersymmetry; and as to what supersymmetry does is, it changes all of the matter particles into force-like particles and vice versa.

We call matter particles fermions. They're particles with half-integral spin, and particles with integral spin are force-like particles,

MISHLOVE: Why don't we pause right there, Saul-Paul,

SIRAG: OK.

MISHLOVE: For more messages from WisdomRadio, and we'll be back again after those messages, with my fascinating guest, Saul-Paul Sirag, an expert on physics and consciousness.

[Break]

MISHLOVE: Saul-Paul, I'd like to jump ahead with you now. We've been talking about the crystallographic structure in hyperspace, and your particular interest which you referred to as the "E-7 Lattice", as I recall.

Now when we think of, let us say, the shamanistic traditions, or the various spiritual traditions, they postulate realms of consciousness that are outside of our three-dimensional space. In simple terms, you have the upper and the lower realms, the heavenly realms and the demonic realms, and of course then we have our physical realm of consciousness, and all throughout our culture, poets have spoken about the human soul as existing simultaneously in these realms, that we carry them with us.

Would you say that the crystallographic structures that you're encountering, these Lie groups and other mathematical structures, could begin to provide a mathematical framework within which we could begin to comprehend more precisely what these mythological systems are saying?

SIRAG: Yes, that's a very deep topic, but what one has to realize is that from a purely mathematical point of view, setting aside any physical considerations -- that is to say, particle physics and Unified Field Theory -- just from a mathematical point of view, there are an infinity of crystallographic type structures of the type I've been describing. I mentioned one type, E-7, as having a particular relevance in Unified Field Theory, but actually there are three "E" type lattices, very closely related, E-6, E-7, and E-8. So that, of course, as the numbers suggest, the dimensionalities for the lattices involved, are just a six-dimensional lattice, and an eight-dimensional lattice, on either side of the seven-dimensional lattice. And those lattices are very important for Unified Field Theory as well.

And then there's an infinite number of what we call D-type lattices and an infinite number of A-type lattices. These are all very closely related to each other through the nesting of the higher-dimensional lattices in lower-dimensional lattices; and what it really suggests to me is that there are different realities -- realms, you might say -- one associated with each of these lattice types. And the nesting of the lattice types would correspond to the relationships of different realities to each other.

So if this idea works out, then of course it would provide a way of actually mapping, in a sense, the relationships of different realities -- or just call them realms. There are many other aspects to this: the "A-D-E" classification scheme, which is what mathematicians call it, got started in the thirties with the first thing classified, which was the classification of the hyperdimensional crystallographic structures.

That was done by a mathematician named Coxeter, who is now in his nineties; he's still alive; he's at the University of Toronto, a very great mathematician -- perhaps the greatest living geometer, in some sense.

But then the same structures were used to classify different Lie group structures -- you just mentioned Lie groups -- which are very closely related to these lattice structures that we're talking about in certain ways. But since then, a whole host of different mathematical structures are classified in the same way. That's a very powerful thing because it means we can transform from one type of mathematical object to another, or transform the dimensionality of the mathematical object.

Now, from a physicist's point of view, it's very interesting that all of the mathematical structures that have been classified so far (twenty-some that I know of) they all are of extreme importance in physics, and in particular, Unified Field Theory -- and most particularly, in the Superstring Theory version of Unified Feld Theory, and so on. All these are closely related things.

So it's very suggestive to me that, well, the mathematicians are saying that each type of object that's classified in this way -- this "A-D-E" classification scheme -- is simply a different window into some vast underlying object which we don't know the details of yet. But from a physicist's point of view, I say that it's very likely that the vast underlying object is Nature, because of the fact that all these different classification schemes that have been, so far, brought into the "A-D-E" set-up, relate to physics: they're all important mathematical-physics objects.

And these "A-D-E" objects are very suggestive for consciousness, too. Things such as error-correcting codes, and analog to digital schemes, sphere-packing schemes, which are of course very closely related to error-correcting codes

[ Note: sphere packings are closely related to the crystallographic vertices, and thus to the eigenvalues mentioned earlier]. And other things that are probably too abstract to talk about.

MISHLOVE: Let me interrupt for just a second to say, I think what you're getting at here is kind of a re-affirmation of the Pythagorean and Platonic idea that these mathematical structures are in some very important sense real, and that they underlie both the realms of consciousness and the realms of physical reality.

SIRAG: Yes, well, it's interesting you bring up Plato because this is called "platonics". What I'm talking about is called "platonics" by Russian mathematicians who have done a lot of work along this line.

MISHLOVE: We'll be back, Saul-Paul, after these messages from WisdomRadio. I'm Jeffrey Mishlove, host of Virtual U, and my guest is Saul-Paul Sirag, a physicist working in consciousness and hyperspace.

[Break]

MISHLOVE: My guest, Saul-Paul Sirag, has just pointed out that the modern work that's going on today in unifying Einstein's Theory of Relativity with Quantum Physics, is related to a particular branch of mathematics that is known as "platonics." It's very interesting because the Western esoteric mystical tradition itself is very largely based on the work of the great Greek philosopher Plato and his predecessor Pythagorus and his followers, the neo-platonic philosophers, and it suggests that what's happening today at the very frontiers of theoretical physics is actually carrying on a tradition which has been identified with Western spirituality and mysticism for thousands of years.

SIRAG: Yes. The use of the word "platonics" by mathematicians emphasizes the fact that for one thing, they feel that these mathematical objects really exist independently of the mathematicians discovering them. In other words, the mathematicians make discoveries, they don't invent.

They invent, of course, ways of describing, they invent systems of nomenclature and symbols, but that's a really superficial aspect of mathematics. Mathematicians feel that those are just ways of getting at the Platonic reality.

Now in an even more concrete sense, though, the "E" type lattices correspond directly to the Platonic solids. In fact, E-6 corresponds in a certain beautiful way to the tetrahedron; and the E-7 corresponds to the octahedron, and the cube, which are dual to each other and so have the same symmetry structure; and similarly, the E-8 corresponds to the icosahedron and dodecahedron, which are dual to each other and therefore have the same symmetry structure.

So all five of the Platonic solids are accounted for in this scheme, and that's another reason for calling this Platonics. That's perhaps where the name first arose, in the context of describing that relationship.

There's another very interesting aspect of Superstring Theory which recalls Greek and medieval thinking about "the Music of the Spheres" which, I think Jeffrey, you were referring to earlier. Now I haven't said much about the strings of superstring theory, but the key idea is that the strings are vibrating and vibrating in many vibrational states. In other words, the harmonics of the strings are what we used to call "particles".

And in membrane theory, which is just a generalization of this, you have higher-dimensional objects which are vibrating. And have all the lower-dimensional objects vibrating inside them -- like a membrane itself would be a two-dimensional vibrating object, sort of like a drum-head that has one-dimensional strings that are vibrating inside it, and so on, all the way up to nine-dimensional membranes sitting inside a ten-dimensional space-time -- all vibrating. And that's a kind of Music of the Spheres which goes way, way beyond what the Greeks had in mind, of course. But it's very interesting.

What the clue was, that started this whole thing of Superstring Theory -- in fact, this was the problem with the early versions of the String Theory, which didn't have anything to do with gravity at first, they were attempts to deal with the strong force, back in the early seventies -- and the problem was that the basic vibrational state was actually a very peculiar state which was a spin-2 state, and they didn't know what to make of it until 1974 when a physicist named John Schwarz suggested that: well, we know that the gravitron is supposed to be a spin-2 particle, so probably that's the graviton; and we shouldn't be considering this as fundamentally a theory of the strong force at all, but a theory of gravity.

He was the first one to suggest that String theory be considered a gravity theory; and that didn't catch on for ten years, until 1984 when he and another physicist named Michael Green proved in 1984 that Superstring Theory is a viable, consistent quantum-gravity theory; and then that proof in 1984 created a bandwagon effect; and hundreds of physicists suddenly decided this is something worth paying attention to, and they worked on it. Now, you know, it's one of the main things happening in theoretical physics.

MISHLOVE: Saul-Paul, to a layman like myself, and I'm sure, to many of our listeners as well, a lot of this is hard to follow. For one thing, the very notion of a "graviton" is odd. I've been taught recently that gravity has to do with the curvature of space, and now the term "graviton" suggests a particle. And I guess this is one of the many paradoxes that we find in modern physics.

We're almost out of time tonight and I don't think we're going to get too much further, but I hope to have you back many more times so that we can probe more deeply into these mysteries.

SIRAG: Mm-hmm. Do I have time to say anything?

MISHLOVE: You do have some time and maybe you can comment on the paradoxical nature of it all.

SIRAG: Yeah. Well, you see, the graviton is what we believe must be the quantum mechanical form of the gravitational force. It's the quantum of gravity. What General Relativity says is that the curvature of space-time is the gravitational force, and if we quantize that idea, we wind up having to have every mass-energy exchange particles that are spin-2 in order for the force to be always attractive.

That's why we know it has to be spin-2.

MISHLOVE: And gravity is a great attractor. Saul-Paul, we're out of time for now. We'll be back after these messages.

[Break]

MISHLOVE: We just have about two or three minutes to wrap up what is a conversation that could go on for twenty or thirty years, and has been for twenty or thirty years between Saul-Paul and myself, and I hope it goes on for another twenty or thirty years.

We have about two minutes left, actually, maybe about one.

SIRAG: OK.

MISHLOVE: But we'll have you back again, I trust.

SIRAG: Yes. I probably haven't said enough about consciousness, but that's a very deep subject. But let me re-emphasize the over-all idea that mathematical developments, at least to me, suggest very strongly that there are many realms of consciousness or of being, really, and different states or realms of consciousness would be associated with, and all interconnected, and to a certain extent, bleed into each other. Exactly how that bleeding occurs --there'd be a physics of that, actually, that could be developed and predictions made about that.

MISHLOVE: We'll have you back, Saul-Paul, for more!

[End WisdomRadio program, Virtual U, 3/29/99, with Saul-Paul Sirag]

Transcribed by Joyce Rosenfield.