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FLY interviews Saul Paul Sirag:

FLY: Robert Anton Wilson?

SAUL: Yeah, i first introduced him to Jack,

SAUL: Yeah, well he learned about this Bell's theorem stuff from Jack and me, i introduced Jack to Wilson, that was when he was living in Berkeley.

FLY: Oh, the trick top hat

SAUL: what?

SAUL: The trick top hat', oh, yeah, the trick top hat, yeah that’s the next one i think, and the third one is called 'homing pigeons', trick top hat is the one that has references to both Jack and Me as coming up with futuristic kind of physics that changes things drastically and so on.

FLY: That’s interesting as John Lilly just recently spoke about the...erm...form of law

SAUL: Laws of form?

FLY: yeah, and the trick top hat relates to that somehow?

SAUL: I'm very interested in the Laws of form also, yeah he talks about it in both his fiction and he has written a lot of non-fiction too of course, and maybe more none-fiction than fiction actually, although, you know he's one of these people that mixes the two together a lot, kind of like Borges' the Argentinean writer, well, B draws a fine line between lit. criticism that is not fiction and the fiction that he's criticizing, B's criticism is so speculative and interesting that it reads almost as fiction, you know.

FLY: I like the idea of exploring our unreality's. At the back of the book "Secret Chamber by Robert Bauval" there's an appendix in which the author mentions Wilhelm Reich and something he calls Cosmic ambience. Terence Mckenna is quoted at length, talk of probing into unreality's, but now were realizing that's our reality too.

SAUL: One of the most important pieces of criticism that's really fascinating, and it's about that famous British poet - William Taylor Coleridge - and you see what's interesting about that poem is that Coleridge calls it a - fragment of a poem - the reason he calls it a fragment is that he actually dreamt' the whole poem, he woke up and just started writing it down, but he got the first part of it written down, and a visiter came and visited, and he forgot the rest of it, so he calls it a fragment of a poem anyway, its a beautiful poem all by itself, but here's the weird thing that Borges points out - there really was a Khan who was a builder - and he was the grandson of Genghis Khan; who was just a conquerer, but Kubilai Kahn was a builder. What Coleridge never knew is that Kubilai Kahn really did order a pleasure dome to be built, and that was enough, but what wasn't known in Cooleridge's time is that it itself was an incomplete building, and that was discovered by archeologists after Cooleridge's time, eh, so what Borges says is there's a kind of archetype, a vast archetype thats trying to get in through our reality, the first time its comes in the form of a building Kubilai Kahn wants to build, and for some reason its not completed, and the second time it takes the form of a poem about Kubilai Kahn's building, and that's incomplete too, because of this guy who walks in and disturbs his memory of the dream. So then Borges speculates that it will try to come in a third time, and he thinks that the form will be different, in some way. My feeling about that is that the form, having my own prejudices about forms, is that the form is what Mathematicians have discovered, a beautiful set of structures, they call it the Coxeter graphs, named after the canadian H. S. M. Coxeter, who's still alive in his 90's still doing math very accurately, and he invented these graphs in the 1930's to classify hyper-dimensional crystal structures, well that already sounds like Kubilai Kahn and Coleridge - and then in the 40's totally independent of Coxeter'mathematicians work because it was in a totally different part of mathematics, a Russian mathematician named Dinken, invented the same set of graphs to classify very different kind mathematical objects, something called; lie algebras and lie groups. Then in the 60's a french mathematician called Rene' Thom invented a whole new field of mathematics called Catastrophe theory, which deals with dynamic systems that can undergo drastic changes due to a very small change in the parameters that they are dependent on, thus the word catastrophe, but catastrophe is to be taken in a neutral sense, that is to say a lot of catastrophes are good.

In fact what RT was trying to model was the changes that living systems go through, he wanted a mathematics to deal with living systems, especially development and growth and so on; which is very difficult to deal with mathematically.

Well then a Russian mathematician named V.I Arnold looked at Rene Thom's work and said Thom just delt' with a lower, small set, 7 of them in turned out, of catastrophe structures, but actually there is an infinite series and they are classified by these same graphs, so then of course the obvious idea that Arnold had was that the must be a whole bunch of other mathematical objects that can be brought into this classification scheme and so he set that up basically as a program for his students and himself to work on over the years and a lot of other mathematicians have been involved in this. And it has the feel of an archeological dig like their digging up this vast.... see because, Here's why, its because all these mathematical objects are related to each other by way of these graphs, the graphs form a kind of bridge between different types of mathematical objects, that’s a very powerful thing to be able to do in mathematics because what's very difficult to see with one type of math object and if you have a bridge between the two and you can switch back and forth and get a much broader and much more accurate feel for what's going on.

And so the idea now is that the mathematicians are wondering what the vast underlying object is that the whole set of graphs ultimately refers to and that object is this archeological structure in some sense, and its being dug up, its not a ruin its not something that’s incomplete because its mathematical, its - gotta’ be whole - so to speak. And a very interesting thing from the point of view of science is that all the math objects that have been brought into the classification scheme with these Coxeter graphs are of great use and interest in physics. In fact especially in unified field theory type physics, that’s cutting edge now, like string theory, uses all these kinds of objects usually without the physicist realizing that they're grabbing objects that are related to each other by way of these graphs, because for the most part they don't know about the history of these discoveries and that it’s kind of ongoing, sort of at the cutting edge of mathematics, a kind of unification in mathematics concurrently with a unification of the forces of physics, and these two programs are intimately interrelated, and so what i think is that this vast underlying object that underlies all these graphs, is simply reality - reality in all its forms - you know.

A physicist is going to want to call it physics, because they want to bring everything into the physics program, someone else might want to call it something else, like life or something , it has the feeling of a living breathing creature, its a bit like Phil Dick's idea of VALIS: Vast Active Living Intelligence System, and yeah, ironically he claimed that the definition is in some Soviet encyclopedia of some distant year, and of course the soviet Union is long gone, but still the idea of VALIS is still valid i feel.

FLY: valid VALIS!

SAUL: Laughs.

FLY: I’m also interested in the parable between the yang-mills field theory and the work of the mathematician Ramanujan.

SAUL: Yeah, oh yeah, see that’s related to this ADE stuff too. It all is. Yang-mills fields was first a generalization of the electromagnetic field, the em field is mathematisized in a sense, by a simple group which is a circle called U1, a unitary one group, and its a communicative group, in other words the way in which you rotate a circle does not matter, 30 degrees plus 60 degrees equals 60 plus 30 degrees, so it doesn't matter, and that;s a communicative group, and in the language we use today we say thats the gauge group of electromagnetism.

But what Yang and Mills did back in the 1950's, 54 i think was the year, generalized the group into a bigger group that deals with rotations ultimately rot' in a 3d space, and thats the gauge group; they were trying to model the strong force, but it turned out to be the right group for the weak force, then in the 60' there was the unification of the st and weak force by simply putting U1 and SU2 together as a bigger gauge group, work by Weinberg, Salem and Glashow, and this had certain experimental implications, like the existence of certain particles that were then found which verify the theory, but in fact there are still parts of the theory we are still trying to verify, like the Higgs particle, which hasn't been found yet, and thats part of the theory, and we think that eventually it will be found, but generally these gauge groups are groups that are classified by the ADE groups, now SU actually is an ADE classification, simply the very first rung on the ladder so to speak, in order to bring in the other forces like the strong for force they have to go to a larger gauge group, put all 3 forces together, weak the strong and the electromagnetic force, they had to go to SU5, which is a 3 dim group, that work was done in 74 i guess, by Glashow and Geogee, the same Glashow that did the work on electro-weak theory.

But then in order to bring in gravity which is a lot harder to do because gravity entails Einstein's theory of general relativity which is so different from Quantum mechanics, these other forces are modelled by way of the rules of general relativity, which are very different, almost opposite from the rules of Quantum Mechanics, so it’s very hard to put these theories together; to assume sub theories, or some bigger theories. But thats been done now with superstring theory. Yeah, since 1984 superstring theory has been proven to be a viable consistent quantum gravity theory, and thats what started a sort of bandwagon effect in physics and when lots of young physicists got interested in studying strings.

But the gauge groups involves in string theory are huge groups, like E8 x E8. There are 3 groups, which is interesting, an infinite A's, An Infinite D's and then only 3 E's, E6 E7 and E8, the dimensionality is huge. E6, is a 78 dimensional group, E7 is a 133 dimensional group and E8 is a 240 dimensional group, and they use 2 copies of it. They have an E8 x E8 version of superstring theory, they have 496 dimensional group actually, and the E8 x E8 gives you 16 very special dimensions which they use to interpolate between the 26 dimensional superstring theory and the 10 dimensional theory in a very clever way. And all this is an out-growth of what you mentioned - the yang-mills theory of 1954 - it’s an out-growth of other developments too, but that was a key development in 1954 and i just wanted to plug that in and see how that fits into the ADE scheme itself, you see?

FLY: I see a parallel between the superstrings and the strings on an instrument

SAUL: Yeah, well it is like strings on an instrument in this sense, that the harmonics, what we call vibrational states, quantized vibrational States are exactly harmonics, auk, and string harmonics are what we used to call particle states, OK, that’s how string theory corresponds to particles, and the way the correspondence works is by way of the gauge groups that are classified by these ADE graphs so the ultimate tool is simply these graphs, which go way back into the 30's to Coxeter's work, not knowing the way these things were be used in the future but he really started something there and Dinken in Russia you know, the same graphs, classifying "Lie algebras which are the algebras of the gauge groups as we use them in physics now and he had no idea that development was going to happen, he was a pure mathematician not a physicist, even physicists in the 40's should not foresee that development.

And you mentioned RAM earlier, and some of the more esoteric discoveries of RAM are actually very fundamental parts of super string theory and special membrane theory, and so people thought of RAM's work as not only been rather fantastic of course, its amazing he came up with those identities, allot of his work involved saying "this is equal to that, and the two things are so deferent that, you know, you might never in a thousand years think that was true, they're still working on proving RAM's ideas, and a lot of people are working on that now in mathematics. But a lot of his ideas are being brought into physics by Super-string theory funnily enough.

FLY: One of the things i found really interesting in the work of Buckminster Fuller was the isotropic vector, (Vector equilibrium you mean?) yeah... i'm looking for relationships between the superstrings and Bucky's work...

SAUL: The vector equalibrium is an object that has 12 vertices, ok, and actually that object, is one of these crystallographic objects, in fact that crystallographic object exists exactly in what i call the reflection space, or you could call it a crystallographic space of the SU(4) group. OK, and in fact of course; those 12 vertices actually correspond to what we call; eigen values of the S4 group which correspond to what we call the gauge particles, or the force particles. You see; there's two types groups of particles in quantum theory these force particles and matter particles.

One of the fundamental ideas in particle theory is that matter particles interact by exchanging force particles, and mathematically the way that works is that in these gauge group structures you have two different types of crystallographic structure, you have the matter c.s and the force c.s, and in the case of SU(4) the matter crystallographic structures are like tetrathedra, you have two tetrahedra making a cube and those exactly correspond to the eigen values of the quarks and anti-quarks, and the electrons and the neutrinos. OK. So those are all matter particles, but then there are actually 15 force particles involved because SU4 is a 15 dimensional group but 3 of the force particles have zero eigen values, and 12 of them have none zero eigen values and those eigen values exactly correspond to the vertices of what Bucky fuller calls the 'vector equilibrium'. So that object is being used but in a totally different way to what he thought of it.

Fly Agaric: yeah.

Interview with Saul Paul Sirag, in North Beach, San Francisco: 27/05/2000. Recorded and transcribed by Steven "Fly Agaric 23" Pratt.

NOTES AND QUOTES:

"In 1936 Coxeter moved to the University of Toronto, becoming a professor in 1948. He was elected a Fellow of the Royal Society of Canada in 1948 and a Fellow of the Royal Society in 1950. He met Maurits Escher and his work on geometric figures helped inspire some of Escher's works, particularly the Circle Limit series based on hyperbolic tessellations. He also inspired some of the innovations of Buckminster Fuller. --http://en.wikipedia.org/wiki/Coxeter

A Fuller explanation: the synergetic geometry of R. Buckminster Fuller

By Amy C. Edmondson

Toward a science of consciousness: the first Tucson discussions and debates

By Stuart R. Hameroff, Alfred W. Kaszniak, Alwyn Scott

Ramanujan: essays and surveys

By Bruce C. Berndt, Robert Alexander Rankin

The Trouble with Physics: The Rise of String Theory, the Fall of a Science ...

By Lee Smolin

Strings, conformal fields, and M-theory

By Michio Kaku

http://www.ted.com/talks/murray_gell_mann_on_beauty_and_truth_in_physics.html

The search for a unifying theory was interrupted by the discovery of the strong and weak nuclear forces, which could not be subsumed into either gravity or electromagnetism. A further hurdle was the acceptance that quantum mechanics had to be incorporated from the start, rather than emerging as a consequence of a deterministic unified theory, as Einstein had hoped. Gravity and electromagnetism could always peacefully coexist as entries in a list of Newtonian forces, but for many years it seemed that gravity could not even be incorporated into the quantum framework, let alone unified with the other fundamental forces. For this reason, work on unification for much of the twentieth century, focused on understanding the three "quantum" forces: electromagnetism and the weak and strong forces. The first two were unified in 1967–68 by Sheldon Glashow, Steven Weinberg, and Abdus Salam as the "electroweak" force.

^{[7]}However, while the strong and electroweak forces peacefully coexist in the Standard Model of particle physics, they remain distinct. Several Grand Unified Theories (GUTs) have been proposed to unify them. Although the simplest GUTs have been experimentally ruled out, the general idea, especially when linked with supersymmetry, remains strongly favored by the theoretical physics community

In current mainstream physics, a Theory of Everything would unify all the fundamental interactions of nature, which are usually considered to be four in number: gravity, the strong nuclear force, the weak nuclear force, and the electromagnetic force. Because the weak force can transform elementary particles from one kind into another, the TOE should yield a deep understanding of the various different kinds of particles as well as the different forces. The expected pattern of theories is:

| | | | Theory of Everything | | ||||||||||||||||||||||||||||||||||||||

| | | | | | | | | |||||||||||||||||||||||||||||||||||

| Gravity | | | | | Electronuclear force (GUT) | | ||||||||||||||||||||||||||||||||||||

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| | | | Strong force SU(3) | | | | | | Electroweak force SU(2) x U(1) | | ||||||||||||||||||||||||||||||||

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| | | | | | | | | | | | | | | | ||||||||||||||||||||||||||||

| | | | | | | | Weak force SU(2) | | | | | Electromagnetism U(1) | ||||||||||||||||||||||||||||||

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| | | | | | | | | | | | | | | | | | | | | | | |||||||||||||||||||||

| | | | | | | | | | | Electric force | | | | | Magnetic force | | ||||||||||||||||||||||||||

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In addition to the forces listed here, modern cosmology might require an inflationary force, dark energy, and also dark matter composed of fundamental particles outside the scheme of the standard model. The existence of these has not been proven and there are alternative theories such as modified Newtonian dynamics.

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