El Naschie Discussion

I have been following the work of Mohamed El Naschie for decades. This man has never bad mouthed, ignored or downplayed any one or any contribution. He also acknowlesges every single person who contributed to his work unless he genuinely did not know and then he will immediately apologize for the unintended omission. I accept nothing less from Garrett Lisi and look forward to read his explanation. With genuine good luck wishes for both Garrett and Mohamed

The following question is directed to Dr. Garrett Lisi: Your theory is that of unification and not only grand unification but quantum gravity unification of all fundamental forces. In such a case the unification coupling constant is one of, if not the most important result. It is the illusive point where all the four fundamental forces meet. What is the value of this coupling? El Naschie claims that he found the exact value of this coupling to be 1 divided by 26 assuming super symmetry. So what is the value coming out of your own calculations?

Dear Garrett

I am sure you are inundated by too many irrelevant comments and confused remarks all apart of unfounded and poisonous so-called criticism on a site ironically called "The Reference frame". By contrast I hope I could bring to you some constructive suggestions which may be of help. It seems to me it is important to embed E8 in some kind of spacetime and create a substitute to ordinary classical dynamics. This point has been made by Mohamed Elnaschie in frequent lectures which I have attended and also various publications. Elnaschie started following the usual counting of the degrees of freedom of spinors in order to fix the gauge. In his case this is merely fixing the scaling. Starting by 10 dimensions, we have 32 32 = 64 complex component equal to 128 degrees of freedom for a Dirac spinor. One goes on halving this number to 64 majorana, 32 majorana-Weyl, 16 light cones and 8 on-shells. Adding all together we find exactly your 248 dimensions of E8. Subsequently Elnaschie proceeded to embed E8 in 4D spacetime and found 252. Remembering that his average scaling exponent is 2 we see that doubling this number leads to 504. This is the dimension of the simple linear Lie group SL (2, 8) = 8(64-1) = (8)(63) = 504 and corresponds to a standard model with 126 particles or when spin up and spin down are not counted as two different particles, we have 126 divided by 2 equal 63 particles. This result as I will reason is not accurate. In fact it is wrong as Elnaschie pointed out because you need at least 8 dimensions to embed E8 and not 4. Nevertheless 63 and 126 are consistent with Heterotic string theory. In this theory the number of first level massless states is 8064. Thus dividing by the corresponding spinor degrees of freedom namely 32 32 = 64, one finds 126 which are 63 multiplied by 2. By contrast if we give E8 the minimum embedding one would find 248 8 = 356 which leads to 64 particles. When not embedding E8 at all, one finds 248 divided by 4 to be 62 particles or (62)(2) = 124 particles counting up and down as different particles. The main point which Elnaschie is demonstrating is that embedding E8 in the 26 bosonic spacetime dimensions of string theory leads to 248 26 = 274. This is exactly twice the value of the inverse fine structure constant of electromagnetism (2)(137) = 274. The doubling corresponding to E8E8 which have (2)(248) = 496 must be (2)(274) = 548 which is Elnaschie well-known total dimensions of the exceptional Lie symmetry group hierarchy involving the sum of the dimension of E1 to E8 as shown in various of his published work. The total number of particles in this case is 137 or 68.5 if spin up and spin down are not counted as two different particles. Thus there are still 137 - 120 = 17 elementary particles or equivalently 8.5 elementary particles to be discovered in addition to the already experimentally discovered 60 or (60)(2) = 120.

Much of what I have written here and more is on Elsevier science direct in several papers by Elnaschie. I recommend: "String theory, exceptional Lie group hierarchy and the structural constant of the universe. Chaos, Solitons & Fractals," 35(2008) 7-12 and "Light cone quantization, heterotic strings and E-Infinity derivation of the number of Higgs bosons", Chaos, Solitons and Fractals, 23(2005) pp. 1931-1933.

Summing up, I think embedding E8 in D = 26 would solve a great deal of problems for the Garrett Lisi model. However and in all events, I would like to congratulate Lisi on his achievement.

R. Marek

Garrett

Your theory as I understand it has a sort of fields democracy. You can derive any field from E8 by letting it, as you like to say, "dance" on our 4 D spacetime. Well this sounds pretty similar to Elnaschie. He uses the golden mean transformation, in fact simple scaling to deform E8 into a Penrose-like fractal tiling. This Penrose universe is in fact an example of a non commutative space as explained in detail in the classical books of A. Connes. This space is homomorphic to the compactified Klein modular curve and possesses 336 3 = 339 hierarchical degrees of freedom. Using the 496 of E8E8 and the 20 of Einstein's gravity tensor, Elnaschie found the electromagnetic inverse constant to be 496 - (339 20)= 137.

I think these results and the connections to non-commutative geometry may be quite important to your work. The particular paper in question is "On Penrose's view of transfinite sets and computability and the fractal character of E-infinity spacetime" published in Chaos, Solitons & Fractals, 25(2005) pp. 531 - 533.

With my best wishes,

Dietmar Kohlhass

Garrett - it seems you have set a trend toward maximal simplicity. I read about a new theory in the Telegraph using what is called Adellic function for prime numbers. The P-Adic theory was given for P=2 in one quarter of a line:

2-Adic of 137 = 1

Or in more intelligible terminology, looking at 137 from a P=2 reversed magnifying glass it is exactly equal to 1. The physical interpretation of this mathematical scaling of a number field is the tantalizing bit. We know 137 is the inverse electromagnetic constant which is the weakest coupling. But 1 is the largest coupling possible and is believed to be that of the Planck mass to the Planck spacetime or Planck Aether. Second,137 is the exact number of elementary particles in the standard model while there is only one type of particles in the Planck Aether. This is remarkable confirmation of the Planck Aether theory which was developed by one of Heisenberg's students who is a retired Professor at the University of Nevada in the USA.

The Telegraph is referring to a paper published by El Naschie in Chaos, Solitons & Fractals. It would be great to know your views on the ramification of this remarkable unification which must be deeply related to the theory of P-Adic quantum mechanics.

J. Schiffer

Hi Garrett,

Fashion as much as dogmas reign in science as in any other aspects of human endeavors. It should not come as a surprise that the cheapest shot in the trade is asking where is the Lagrangian? A little bit of history of science may help although it will never cure.

The action principle was introduced in science as a mere alternative albeit more formal way of arriving at Newton's equation of motion. It is connected to the name of Maupertius although he dealt only with the elementary problem of minimizing a work function. The more profound problem of minimizing a function was solved by Euler. It then became fashionable to formulate the laws of mechanics without drawing a single picture or diagram in contrast to Newton. At the end we had two schools of thinking, that of the imaginative H. Poincare and that of the sterile Bourbacki group. An abstract method such as the action and variational principle is without doubt of great help in a field such as particle physics where pictures and diagrams are not as helpful as in classical mechanics. But this and quantum field theory was fiercely resisted in the USA as in the Soviet Union. However a detente took place, then a change of guards in the USA as in Russia brought the opposite situation and without a Lagrangian you are not supposed to make a single move. Habit and mental inertia do the rest. Lisi's work is free of such artificial constraints. He seems to work in three steps just like in the work of Elnaschie. First a clear model, then an enlightened counting, then algebraic manipulation to find what he expects to find. Other physicists like Lisa Randal marvel at the enormously complex mathematic and algebraic computation she is capable of doing as if this is what it is all about. Others like Lisi seek maximum simplicity to find an answer to a physical question and not to demonstrate a supernatural talent for computation as for instance in the case of the proof of the four color problem. Lisi and his followers are theoretical physicists in the mould of Poincare and Einstein. The majority nowadays are mathematical physicists of the Bourbacki type. Lisi has to live with that until the tide of fashion changes.

Robert Fisher

The comment written by anonymous on May 4 2008 is worth considering. He is both right and wrong. First he is somewhat wrong because topological singularity theory is used in string theory. However these are structurally stable singularities called by R. Thom catastrophe theory. You can read about that in the McGraw Book published in 1990 in London and authored by Elnaschie, a Professor of Engineering Mechanics at Sibley School of Aeronautics and Astronautics in Cornell, U.S.A. A brief account maybe found in a book by M. Kaku published by Springer. Also physically whenever you have a mini black hole you have a singularity and string theory uses length scale equal to the radius of a Planck mass which is a mini black hole.

The second point is more involved. Quantum chaos theory is not a classical chaos theory because the quantum suppresses ordinary chaos. But the anonymous comment is quite potent! One could describe the work of Nobel Laureate G. 'tHooft, as well as the same Engineering Professor mentioned above Elnaschie, as searching for the common roots of classical mechanics and quantum mechanics and finding that in classical chaos. However the exact relation of ''tHooft and Elnaschie's work to the work of G. Casati and Boris Cherecov and the quantum chaos community in general is far of being clear at the moment as far as I am aware. But in general you are right. Neither string theory nor loop quantum gravity have place for the fuzziness of chaos, classical or quantum and it would be a great achievement if Garrett theory could incorporate chaotic symmetries in the sense of field and Glotobiski as discussed in many popular writings by the very talented Ian Stewart.

Dr. Robert Fisher

Disillusioned by conventional quantum mechanics, Richard Feynman invented path integral. I think we are facing a similar situation today with Lisi's E8 proposal. In fact it is possible to interpret Elnaschie's method as moving from ordinary path integral to summing over all exceptional Lie symmetry groups. This intriguing point is however this: there are finite numbers of exceptional Lie and Stein manifolds. This way the problem such as Gribor copies is illuminated in a totally unexpected way.

M. Kavorkian

On its own as a single Lie symmetric group E8 cannot do the entire job of unification. On the other hand by summing over all exceptional Lie groups it can be done. This was the program of Prof. Mohamed El Naschie with whom I have had the honour of collaborating on this subject for some time.

To Wong and Kavorkian. You have both spelled the name of the great Russian Theoretical Physicist wrong. He is Professor V. Gribov. He is the first to point out that the usual procedure for fixing the gauge freedom in non-Abelian gauge theories is ambiguous. This puts classical theories of quarks confinement in doubt. This has to do with super conductivity of magnetic monopoles as well as gauge invariance. That is why Elnaschie used summing over exceptional Lie and stein spaces and used a different argument for deriving confinement from phase transition of spacetime to a Planck Aether with a single Planck mass as mini black hole.

L. Cran

At long last Scientific American took notice of E8. On page 16 of the April 2008 issue, Graham P. Collins gives a somewhat mixed up review of the theory and comments on Lisi's work. Of course he does not mention the work of Green, Schwarz, He, Crnjac, Elnaschie or anyone else, only rejoice that Lisi's paper was wiped out from the internet archive. The present Stalinistic regime of theoretical physics ayotallahs do not permit that a wonderful theory such as that of Lisi's becomes respectable. The beautiful small world complexity neural network is not allowed to exist because of the archbishops of superstrings and quantum field theory. People like Lee Smolin and 'tHooft are rare species nowadays and the Telegraph proved to be more scientifically minded than Scientific American.

B. Kerek

Pleased to read Ray Munroe's recent comment dated May 22, 2008. This is the sort of comments acceptable on a respectable site. Yes without digging deeper there is no such thing as E12 because E8 is the largest exceptional Lie symmetry group. Any larger group will have an infinite dimensional Lie algebra. However, Prof. H. Nicolai from Max Planck Einstein Institute in Berlin-Germany worked with E10 and E11. These are special forms of Exceptional Lie group extended beyond the initial idea. It all started by H. Gorgi, M. Elnaschie, J. Schwarz and many others who noticed that by systematically modifying the Dynkin diagram one will find that SO(10) may be called E5 while SU(5) is E4.

Subsequently, M. S. Elnaschie at Frankfurt-Germany proposed to work with a hierarchy of Exceptional Lie Symmetry group leading to a total symmetry group dimension equal to 548. By including all two and three stein spaces, he finds not only 4 alpha bar =548 where alpha bar = 137 but also 5 alpha bar 1 = 686 as dimensions. From all of that we can easily conclude that Ray Munroe may be well justified in inventing E12. He said it is 684 dimensional which means only 2 less than what Enaschie has calculated and only 1 less than (5)(137) = 685. It maybe worthwhile that Munroe looks at Elnaschie's work and vice versa and that both should be thankful to the work of Lisi and this site. Most of Elnaschie's work is published in Nonlinear Dynamics Journals. Here are few samples:

(1) One and two stein space hierarchies in High energy physics, Chaos, Solitons & Fractals. 36(2008) pp. 1189-1190.

(2) The internal dynamics of the exceptional Lie symmetry groups hierarchy and the coupling constants of unification. Chaos, Solitons & Fractals (2008) doi:10.1016/j. Chaos. 2008.04.028.

(3) Montonen-Olive duality and the mass spectrum of elementary particles via E-Infinity. Int. Journal of Nonlinear Science and Numerical Simulation. 9(3), 307-308.

Bob Meyers

Two brand new papers came to my attention and they may be more than relevant to Garrett Lisi's research. The papers are by a Saudi scientist at King Abdullah Institute for Nano and Advanced Technologies, KSU, Riyadh, Saudi Arabia. Both papers are on Elsevier science direct.

(a) E-eight exceptional Lie groups, Fibonacci lattices and the standard model.

(b) Towards a quantum field theory without Gribov copies and similar problems.

The two papers are published by Elsevier and the name of the Journal is Chaos, Solitons & Fractals and author's name is M. S. Elnaschie.

A. Kasim

Dear Bob Meyers,

Thank you for the observation that 5 x 137 = 685 is only one element larger than my 684-plet of "E12". I have been aware of Sir Arthur S. Eddington's old work regarding the Fine Structure Constant for many years, but I have not followed Prof. Mohamed S. Elnaschie's work. Personally, I am a proponent of Five Fundamental Forces, Five Generations of Fundamental Fermions (there's that number FIVE again), and I'm a big fan of Dirac's Large Numbers Hypothesis regarding the number ~10^40. But I've always been suspicious of theories built around the number 137, because the Fine Structure "Constant" of QED varies with the renormalization mass scale (for instance, the Weak-scale alpha bar is ~128), and how does that affect the theory?

Nonetheless, your observations have raised my interest. I need to visit Florida State University's Dirac Science Library, and read Elnaschie's ideas.

Sincerely,

Ray Munroe

p.s. - A correction to my earlier posting: The G2 of color bosons contains basis: g3, g8; roots: 6 gluons & 6 squarks/ anti-squarks; and singlet: selectron/ anti-selectron. The adjunct G2 of color fermions contains basis: electron/ positron; roots: 6 gluinos & 6 quarks; and singlet: gluino-3/ gluino-8. I think it is sloppy to mix bosons and fermions in the same representation group, when we know that there is an adjunct Supersymmetric representation.

Dear Ray,

Thank you for responding to my comments. I can give you more definite things of which I have just become aware. In hyperbolic geometry volume is an invariant. There is a hyperbolic manifold called M4 studied by some Swiss mathematician in Zurich and used by Mohamed El Naschie in high energy physics. Believe it or not, the so-called two volume of M4 is exactly your dimension 684. El Naschie published that in several journals of nonlinear dynamics in various versions of varying sophistication. It is incredible because M4 is based on a Coexter polytope representing a 120 cell gossett for E8. You need two of them to construct E8. Since dimension is invariant just as volume, I am now convinced your E12 is the mother of all exceptional Lie groups. In a sense you have reached summing over all existing stein and exceptional groups by simply calculating the hyperbolic volume. On reflection this is not astonishing at all. Volume is a higher dimensional area and you get an area by integration. Integration is summation. So it is merely tautology. We are just using different languages. But the message is the same.

You don't need to go to Florida. One of the closest students of Prof. El Naschie is Nasr Ahmed working in Newcastle. He works with a prominent student of Steven Hawking, Prof. Ian Moss. Nasr will send you all of El Naschie's work free of charge because I think he has it. And if not, he can put you in contact with Prof. El Naschie. I know El Naschie is as elusive as an electron and I wonder sometime if he is real or a collection of scientists with a pseudo name like Bourbake in France because he works in politics, philosophy, literature, engineering and science.

Regarding Eddington's work and El Naschie's interpretation, this is nothing to be suspicious of at all. It is straightforward mathematics. Let me give you the simplest form of it. You know that E8E8 which is 469 takes care of all interactions. Now particle physics consumes 336 3 of them. Gravity has 20. Subtracting both all what is left is 137 for electromagnetism. But 137 itself is variable in El Naschie's theory. It is 137 at our low energy scale. It is 128 or 127 at various electroweak scales. It is 42 at grand unification and it is 26 at complete quantum gravity unification. Finally it is exactly equal to 1 at the Planck Aether scale. Being the coupling of the Planck masses to the Planck Aether. So it is of course a variable. It is a variable in disguise and it varies from 137 to 1. El Naschie published a remarkable equation based on P-Adic analysis. The equation says the P-Adic norm for P = 2 of 137 is exactly 1. There is much more to say for instance in El Naschie's theory alpha bar is not 137 only. It is 137.082039325. This is exactly equal to 20 multiplied by the inverse of the golden mean to the power of 4. So El Naschie doesn't build his theory from 137 but from the golden mean which is the basic element of the generalization of the Platonic bodies including the E8 gossett. Without the golden mean, there are no E8 gossetts and no octonions and there is no Lisi's theory. In fact most of the Platonic bodies will also disappear.

Thank you very much for giving me the opportunity to have this exchange of thoughts and my sincere wishes for the success of your forthcoming book. I really hope you, Lisi and El Naschie and all the people working with you succeed in bringing us one step further rather than staying in this stalemate from which theoretical physics is suffering because of the internal civil war between the different factions of the so-called mainstream. I recall a word I read in an article by El Naschie about Thomas Mann's book Death in Venice, Prof. Achenbach's friend said: Do you know what lies at the bottom of the mainstream........Mediocrity!

Bob Meyers

To Bob Meyers

I was really flabbergasted to see a paper published four years ago using a manifold with exactly (2)(342) = 684 something. This is exactly the order of Ray Munroe's E12 not one centime less.

To Ray Munroe:

I said 684 something because this was not called dimension but twice the four-dimensional volume invariant of a manifold called M4. This manifold is based on a 120-cell coexter polytope and therefore is related to the E8 Gosset. Elnaschie noted that (26 +k)(26 +k) = 685. This volume invariance may be regarded as a substitute to dimension. The paper titled: Super-symmetry, transfinite neural networks, hyperbolic manifold, quantum gravity and the Higgs, is a clear validation of Munroe's E12 which has F theory spacetime dimension as 12. The paper is published in Chaos, Solitons and Fractals No 22 (2004) pp. 999-1006. The author is M. S. Elnaschie from Cobham, Surrey, UK. It is amazing that the hyperbolic volume of M4 is equal to E12 dimensions. However, it is unbelievable that it is almost equal to the 686 of the sum of all exceptional Lie symmetry groups and stein spaces. These are entirely different theories and formulations leading to exactly same results. It is beautiful and must be true.

A. Kasim

Dear Garrett:

To whom it may be of interest, I would like to say that the E12 proposal of Ray Munroe has taken me by surprise for more than one reason. I am a follower of the work of Professor Ruth Kellerhals who is a student of the famous Swiss mathematician Prof. Hof, University of Basel, Switzerland. Her wonderful review article is published in Mathematical Intelligencer. My then Ph.D. co-advisor, Prof. Mohamed El Naschie made several references to her paper. She established the hyperbolic 4-manifold M4 found by Dr. M. Davies based on 120-cell coxeter polytope that has a hyperbolic volume 104 multiplied by pi square divided by 3 which is 342.146286. Since El Naschie needs two of them to compare to E8E8, one must multiply by two and find 684.232572. He subsequently reasoned that the exact expression is simply alpha bar divided by 2 and multiplied by 10. In other words it is the 137 alpha bar multiplied by 5. Thus Ray Munroe has found an exceptional symmetry group hyperbolic manifold because (137)(5) = 685. El Naschie calls the exact expression, the transfinitely exact expression:

(137.082039325)(5) = 685.410197

If we would have taken only the integer part from the outset we would have found Ray's value which is:

(2)(342) = 684

The implication is breathtaking because El Naschie obtained the same results using path integral and Yang-Mills theory combined in his paper titled "Topics in the mathematical physics of E-Infinity" which unfortunately is published in an Elsevier Journal - Chaos, Solitons & Fractals - rather than freely on the world-wide-web (www). Prof. El Naschie is an enormously kind person who did himself a bad service by boycotting internet publications and relying mainly on periodicals which with the exception of Nature, Science and Physics Review, no one reads any more. However a particular paper on this 685 hyperbolic manifold published in the International Journal of Nonlinear Science and Numerical Simulation, an Israeli Journal, was chosen by Thomson - ESI Essential Science Indicator as a most cited hot paper. This is found on the internet at: www.esi-topics.com/nhp/2006/September-06-MohamedElNaschie.html. The title of the paper is: "On a Fuzzy Kahler-like manifold which is consistent with the two slit experiment" and in the same journal, vol. 6, issue 2 pp. 95-98 (2005). Editor in chief Prof. Ji-Huan He, Shanghai, People's Republic of China.

I must end by congratulating Ray Munroe on his E12 discovery. However this would have not happened or at least would not have been appreciated without G. Lisi, Lee Smolin and the courageous Telegraph science writer.

Sonja Kaliski

Bob - I live in Tallahassee, Florida. The Dirac Science Library is on the other side of town, and they subscribe to many of El Naschie's favorite journals. I agree that modern research has become "big business" and too many capable researchers have sold out to the mainstream. It's "publish or die" and the mainstream controls most of the journals, which is why I published on Lulu after two years of rejections by journals who wouldn't say much more than that my paper "wasn't appropriate" for their journals. Some good friends of mine have had copies of my book since November 2007, but I haven't heard good or bad critiques or comments from any of them. They might have too much to lose from siding with an outsider like me. It's OK - I understand. I'm not a tenured Professor with hundreds of publications, but I do have a Doctorate in Particle Physics and a few publications. That should qualify me to discuss these topics, whether other researchers choose to agree with me or not.

Bob, A. Kasim, and Sonja - El Naschie and I both defy the mainstream, but we might be different flavors of non-conformity. However, the ties between E12, 5 x 137, and M4 plus E8 are amazing. El Naschie is working with a Minimal Supersymmetric Standard Model of Particle Physics, whereas I have introduced new force quanta, new Hyperflavor/ Kaluza-Klein types of fundamental fermions, and new generations of leptoquark fermions. Although my fundamental representation might be E12, I also have singlet states and Supersymmetric partners. Adding up the degrees of freedom, I have at least 1,416 = 12 x 118 different elements in my theory. If we subtract the four 12-plets of singlet states from the 118 sets of 12-plets, and add the 12 dimensions back in, then we have 118 - 4 12 = 126, which looks similar to alpha bar at the electroweak scale. How's that for a little bit of El Naschie-like numerology?

You might all enjoy reading Chapters 3 and 4 of my book "New Approaches Towards A Grand Unified Theory" on Lulu.com. I have extended the free preview to include these Chapters about my efforts to fit the fundamental coupling constants (including the fine structure constant) with Quantum Statistical Grand Unified Theory (a thermodynamic GUT/ TOE of the low-energy coupling constants).

Prof. M.S. El Naschie - Your ideas are interesting, but moderately difficult to find. Have you considered organizing your best ideas into one book? Lulu.com makes self-publishing easy and affordable, and non-conformists are welcome. I would buy your book if it was reasonably priced!

Garrett - Sorry for hijacking your blog site... What are you up to? I haven't heard from you in a while.

Sincerely, Ray Munroe

Dear Ray:

You can contact Prof. El Naschie directly or through his student nasr2000@gawab.com.

As far as I am aware El Naschie abhors internet, doesn't use it and he doesn't read it. He is really truly old-fashioned in this respect and guards his privacy jealously. But I can tell you could become friends.

However friendship must be based on true understanding. The expression El Naschie-like numerology is a complete misrepresentation of what it is. First the Balmer formula was a constructive piece of numerical simulation. You see nature and you try to simulate it. It was of course Bohr who improved things and then came Schrodinger and showed simply they are Eigen value of an Eigen value problem. This is how we at last understood the atom and found a deeper theoretical justification for the numerical simulation of the Balmer formula. Yet we don't know why we have to use complex numbers in quantum mechanics and this caused all the development which took place from Lie to Lisi. Your 126 is not numerology although in your text you obtained it in a numerological way. There is a world of difference between numerology and enlightened counting. Without enlightened counting as Nobel Laureate Steven Weinberg calls it, we could have no quantum field theory. El Naschie combined enlightened counting with deep theoretical and mathematical reasoning. Let me show you how your 126 comes about. Forget spin up and spin down, then we have exactly 48 fermions and 12 bosons - all experimentally well documented forming our standard model. This makes 60 physically present types of elementary particles. Now we haven't added the graviton nor two additional bosons similar to the w, one charged positively and the other charged negatively. We could also say we have 3 bosons, 2 charged and one neutral and forget for the time being gravitons. Either way we end with 63 particles- 60 real and 3 still to be confirmed. This is what El Naschie and Nobel Laureate Weinberg call enlightened counting.

Next comes the theoretical part. Hetoretic string theory predicts that the total number of massless states is the multiplication of left and right movers and this comes to 8064 massless states. In this counting every spin degree of freedom is considered a different particle. This is unrealistic and we can show that there are 128 different directions. If we consider up and down to be different particles, then they are 64 directions which should be eliminated by dividing 8000 by 64, we get our 126 particles. This is what you have got and it is ridiculous to call El Naschie's procedure numerology. Well the correct result is of course 137. The simplest way to demonstrate that is by embedding the 126 in supergravity's 11 dimensions and get 137. The more sophisticated way is to use the Kahler manifold with fuzzy dimensions which is discussed in the paper of El Naschie - referred to in earlier discussions.

There are many misunderstandings due to superficial readings of most theories and if all famous scientists and Nobel Laureates would have been right all the time, there would have been no history of science.

To Garrett, I don't think we hijacked your blog site because really everything said here was stimulated by your work and what we are saying is very relevant to it.

Bob Meyers