On Nov 15, 2007, at 8:34 AM, Gary S. Bekkum wrote:

Didn't Tony Smith have something like this?

Yes, you are right now that I recall. I still have not read the Lisa paper. I see Lubos Motl is compulsively attacking people personally with vague smears again rather than correcting what he thinks may be wrong or not even wrong with their ideas. His list of targets also includes Sir Roger Penrose, Leonard Susskind, Lee Smolin and George Chapline, Jr. George nevertheless, a true Christian turning his other cheek, supports Lubos AKA "Lumos" AKA Abbe Hyupsing Qong http://www.physics.rutgers.edu/~motl/

Tony Smith is among the crackpots thanked to in the acknowledgements. Next time, he may also submit his own paper supported by similar endorsers. And maybe A. Garrett Lisi will become an endorser himself. Really entertaining times will start afterwards: the hep-th era of Jack Sarfatti, Tony Smith, Peter Woit, and their friends.

That's really why he had to leave Harvard Physics department a few months ago and he basically scuttled his academic career. Lubos (Lumo) uses "crackpot" the way the KKK uses the "N" word and the way Senator Joe McCarthy used "Red", "Fellow Traveler". Lubos and others of the so-called "Skeptic Community" use these smear labels as form of totalitarian Orwellian mind-control that we also see in "PC" thinking. Apparently, or so it seems by plausible inductive inference, this connection was not lost on the senior Harvard physics faculty who decided that Lubos was not conducting himself as a potential Ivy League Harvard professor should? By the way you will notice that what Lubos says below is not comprehensible to the intelligent layman who knows some physics. This is in contrast to say Lee Smolin who is able to describe the same ideas in a way that is comprehensible as in "The Trouble With Physics". Lubos is basically a mathematician in physicist's clothing. So like a mathematician! ;-)

Jack Sarfatti wrote:

On Nov 15, 2007, at 7:20 AM, Brian Josephson wrote:
See my comment at the end (timed at 11.38 am) of



linked to the archive freedom site for good measure!

"He's quite lucky that the physics preprint archive (the first link above) didn't bar his paper. There is officially no refereeing of papers, and yet the string theorists who run the archive have a nasty habit of blocking submissions advocating alternative approaches, even when the papers concerned have already been accepted by journals."
Posted by Prof. Brian Josephson on November 15, 2007 11:38 AM

Brian

--On Thursday, November 15, 2007 5:43 -0800 Jack Sarfatti wrote:

E8 is basically an internal symmetry group beyond the standard model
U(1)SU(2)SU(3)



* * * * * * * Prof. Brian D. Josephson :::::::: bdj10@cam.ac.uk
* Mind-Matter * Cavendish Lab., J J Thomson Ave, Cambridge CB3 0HE, U.K.
* Unification * voice: +44(0)1223 337260 fax: +44(0)1223 337356
* Project * WWW: http://www.tcm.phy.cam.ac.uk/~bdj10
* * * * * * *


On Nov 15, 2007, at 5:43 AM, Jack Sarfatti wrote:

Draft 2
I have not read it yet. Be interested what Saul-Paul Sirag thinks since he knows E8. E8 is basically an internal symmetry group inducing compensating gauge boson force fields beyond the standard model U(1)SU(2)SU(3) within the principle of local gauge invariance that my own theory of emergent gravity is consistent with. Note that you need spacetime symmetry groups locally gauged to get the background-independent geometrodynamic tetrad e^a and spin connection fields S^a^b. My theory is background-independent in Lee Smolin's sense and I get e^a and S^a^b from 8 Goldstone coherent phases of the post-inflation vacuum condensate ODLRO very much like
superflow velocity = (h/m)Grad(Phase of superfluid helium)

This is John A. Wheeler's IT FROM BIT.

Lubos Motl seems to think this is a "crackpot" idea. I have no opinion yet on the Lisa paper below not having read it and maybe Lubos is correct about that. I simply do not know at this moment.

Begin forwarded message:

From: ANTIGRAY@cs.com
Date: November 15, 2007 5:26:45 AM PST
To: sarfatti@pacbell.net

Subject: Surfer dude stuns physicists with theory of everything

Surfer dude stuns physicists with theory of everything

By Roger Highfield, Science Editor
14/11/2007

An impoverished surfer has drawn up a new theory of the universe, seen by some as the Holy Grail of physics, which as received rave reviews from scientists.


The E8 pattern (left), Garrett Lisi surfing (middle) and out of the water (right)

Garrett Lisi, 39, has a doctorate but no university affiliation and spends most of the year surfing in Hawaii, where he has also been a hiking guide and bridge builder (when he slept in a jungle yurt). In winter, he heads to the mountains near Lake Tahoe, Nevada, where he snowboards. "Being poor sucks," Lisi says. "It's hard to figure out the secrets of the universe when you're trying to figure out where you and your girlfriend are going to sleep next month." Despite this unusual career path, his proposal is remarkable because, by the arcane standards of particle physics, it does not require highly complex mathematics. Even better, it does not require more than one dimension of time and three of space, when some rival theories need ten or even more spatial dimensions and other bizarre concepts. And it may even be possible to test his theory, which predicts a host of new particles, perhaps even using the new Large Hadron Collider atom smasher that will go into action near Geneva next year.
Although the work of 39 year old Garrett Lisi still has a way to go to convince the establishment, let alone match the achievements of Albert Einstein, the two do have one thing in common: Einstein also began his great adventure in theoretical physics while outside the mainstream scientific establishment, working as a patent officer, though failed to achieve the Holy Grail, an overarching explanation to unite all the particles and forces of the cosmos. Now Lisi, currently in Nevada, has come up with a proposal to do this. Lee Smolin at the Perimeter Institute for Theoretical Physics in Waterloo, Ontario, Canada, describes Lisi's work as "fabulous." "It is one of the most compelling unification models I've seen in many, many years," he says. "Although he cultivates a bit of a surfer-guy image its clear he has put enormous effort and time into working the complexities of this structure out over several years," Prof Smolin tells The Telegraph. "Some incredibly beautiful stuff falls out of Lisi's theory," adds David Ritz Finkelstein at the Georgia Institute of Technology, Atlanta. "This must be more than coincidence and he really is touching on something profound." The new theory reported today in New Scientist has been laid out in an online paper entitled "An Exceptionally Simple Theory of Everything" by Lisi, who completed his doctorate in theoretical physics in 1999 at the University of California, San Diego. He has high hopes that his new theory could provide what he says is a "radical new explanation" for the three decade old Standard Model, which weaves together three of the four fundamental forces of nature: the electromagnetic force; the strong force, which binds quarks together in atomic nuclei; and the weak force, which controls radioactive decay. The reason for the excitement is that Lisi's model also takes account of gravity, a force that has only successfully been included by a rival and highly fashionable idea called string theory, one that proposes particles are made up of minute strings, which is highly complex and elegant but has lacked predictions by which to do experiments to see if it works. But some are taking a cooler view. Prof Marcus du Sautoy, of Oxford University and author of Finding Moonshine, told the Telegraph: "The proposal in this paper looks a long shot and there seem to be a lot things still to fill in." And a colleague Eric Weinstein in America added: "Lisi seems like a hell of a guy. I'd love to meet him. But my friend Lee Smolin is betting on a very very long shot." Lisi's inspiration lies in the most elegant and intricate shape known to mathematics, called E8 - a complex, eight-dimensional mathematical pattern with 248 points first found in 1887, but only fully understood by mathematicians this year after workings, that, if written out in tiny print, would cover an area the size of Manhattan. E8 encapsulates the symmetries of a geometric object that is 57-dimensional and is itself is 248-dimensional. Lisi says "I think our universe is this beautiful shape." What makes E8 so exciting is that Nature also seems to have embedded it at the heart of many bits of physics. One interpretation of why we have such a quirky list of fundamental particles is because they all result from different facets of the strange symmetries of E8. Lisi's breakthrough came when he noticed that some of the equations describing E8's structure matched his own. "My brain exploded with the implications and the beauty of the thing," he tells New Scientist. "I thought: 'Holy crap, that's it!'" What Lisi had realized was that he could find a way to place the various elementary particles and forces on E8's 248 points. What remained was 20 gaps which he filled with notional particles, for example those that some physicists predict to be associated with gravity. Physicists have long puzzled over why elementary particles appear to belong to families, but this arises naturally from the geometry of E8, he says. So far, all the interactions predicted by the complex geometrical relationships inside E8 match with observations in the real world. "How cool is that?" he says. The crucial test of Lisi's work will come only when he has made testable predictions. Lisi is now calculating the masses that the 20 new particles should have, in the hope that they may be spotted when the Large Hadron Collider starts up. "The theory is very young, and still in development," he told the Telegraph. "Right now, I'd assign a low (but not tiny) likelihood to this prediction." For comparison, I think the chances are higher that LHC will see some of these particles than it is that the LHC will see superparticles, extra dimensions, or micro black holes as predicted by string theory. I hope to get more (and different) predictions, with more confidence, out of this E8 Theory over the next year, before the LHC comes online."

http://www.telegraph.co.uk/earth/main.jhtml?view=DETAILS&grid=&xml=/earth/2007/11/14/scisurf114.xml

Jack, this was on Lubos Motl's blog:
Garrett Lisi: An exceptionally simple theory of everything

Wednesday, November 07, 2007 ...

The most entertaining paper that managed to creep into hep-th today is called
An exceptionally simple theory of everything.

Update I : the paper was re-classified from the professional hep-th archive to gen-ph, general physics, an archive mostly dedicated to cranks. Thanks God.Update II: Roger Highfield whom we know from his outrageous article claiming that Einstein may have started the rot has returned. In a new, equally breathtakingly idiotic article, he suggests that crackpot A. Garrett Lisi is a new Einstein.Its author, A. Garrett Lisi , claims to have found nothing less than a theory of everything. An exceptionally simple one. It may sound as a bold statement but from a genius of A. Garrett Lisi's caliber, it shouldn't be surprising. :-) Because the work is based on the E8 group that I love, you bet that I have opened the paper.

Needless to say, the visually intriguing and colorful paper is a huge joke. The first place where I exploded in laughter was the equation (1.1). It says, using words, the following:
My connection of everything = connection for gravity + weak force + strong force + electromagnetism + electron + neutrino + up-quark + down-quark + other-generations

That's pretty cute! :-) The author is not constrained by any old "conventions" and simply adds Grassmann fields together with ordinary numbers i.e. bosons with fermions, one-forms with spinors and scalars. He is just so skillful that he can add up not only apples and oranges but also fields of all kinds you could ever think of. Every high school senior excited about physics should be able to see that the paper is just pure junk. I understood these things when I was 14.
Concerning the title, I present it as a joke but I agree with Freedom of Science that if the title is viewed seriously by some important readers and if the author allows it, it is a case of scientific fraud.

There is not a glimpse of physics in that paper. You won't find anything like a "Lagrangian", "amplitudes", "masses", "cross section", "energy", "force", "Hamiltonian", "entropy", "path integral", "temperature", or other words that you expect in physics paper. When he talks about actions, they're always wrong actions from some previous obscure papers that have clearly nothing to do with observable physics either.

Lubos may be correct on this. I don't know - yet. However, perhaps he should take the mote out of his own eye and show us how any paper he has ever published has any connection with observable physics?

On the other hand, you find a lot of random assignments of particles to vertices of polytopes - something that you know from papers about the octopi.

The main mathematical content in these 30+ pages is the decomposition of the fundamental representation of E8 under its F4 x G2 subgroup. It is an elementary fact that e.g. freshmen in Prague who follow my textbook written with Miloš Zahradník know as equation (12.95) . For A. Garrett Lisi, this single line reflecting a simple calculation that has been done a century ago and that a fraction of freshmen learns is a topic for a 30-page paper and an impressive albeit two-dimensional movie.

If you care how the forces and particles are supposed to be embedded into his group, it's like this. You start with a non-compact real form of E8. You embed a G2 into it. Its centralizer is a non-compact version of F4. Now, you embed the strong SU(3) into the G2 while the non-compact F4 acts as the source of a "graviweak" SO(7,1) group that contains SO(3,1), a "gauge group" that is now fashionable in the crackpot circles to "describe" gravity, and SO(4), their source of cargo cult electroweak symmetry.
So now Lubos smears Utiyama and Kibble as crackpots since their papers of 1956 and 1961 respectively show that Einstein's 1916 GR come from the local gauging of SO(3,1) with T4 (i.e. Poincare P10). This is hardly controversial. What is interesting however is if E8 contains both compact internal symmetry groups like U(1)xSU(2)xSU(3) as well as the non-compact universal spacetime symmetry Poincare group P10 defining 1905 Special Relativity. Two references showing that Lubos is misrepresenting the truth here are:

The Dawning of Gauge Theory ed. Lochlainn O'Raifeartaigh Princeton, 1997 - a "crackpot" press? ;-)

Gauge Theories in the Twentieth Century ed. John C. Taylor Imperial College London Press 2001 - another "crackpot" publisher. Will Lubos have a book burning of crackpot books - at the Octoberfest in Prague perhaps? ;-)

Of course, this group plays a different role (in the vielbein formulation of general relativity) than the Yang-Mills groups and the fact that these two kinds of a group cannot be merged is the content of the Coleman-Mandula theorem to be discussed at the end of my text.
Note that my "crackpot" emergent gravity paper http://arxiv.org/abs/gr-qc/0602022 on the archive does not merge them at all. Indeed, I am very doubtful that such a merger is possible. It is certainly not needed for anything I do which does connect with observable physics mind you. So on this particular I tentatively tend to agree with Lubos. If the Coleman theorem proves it that's fine with me.

Moreover, the fermions clearly can't arise from the connection because they have a different spin and statistics and they don't transform in the adjoint representation. For people like A. Garrett Lisi, it is not hard to unify everything with everything else because they don't know any difference between different concepts in physics.
I agree with Lubos on this point.

You might think that the E8 starting point is analogous to heterotic GUTs. Except that it is completely crucial for physics that E8 in heterotic string theory is compact.

If E8 is compact, I do not think you can get gravity from it. Background-independent gravity is simply a local gauging of non-compact spacetime universal symmetry groups of the invariant actions of all quantum fields treated equally - democratically. It's really is pretty simple.
Non-compact gauge groups would lead to ghosts and negative probabilities.
What about the ghosts in quantum fields with compact Yang-Mills internal symmetry groups , i.e. Faddeev-Popov? http://en.wikipedia.org/wiki/Faddeev-Popov_ghost
Moreover, the whole Standard Model is embedded into the same subgroup of the heterotic E8 once it's broken, e.g. to SO(10). Also, everyone knows that the fermions arise as chiral multiplets and not vector multiplets: they are simply not and cannot be a part of the gauge bundle. Most importantly, no sane person has ever claimed that the E8 portion of the heterotic theory already contains gravity. That would be really silly.

Lubos is correct above, but I don't know if it applies to Lisa's paper not having yet read it.

Endorsement system

A few years ago, such a paper would almost surely be filtered out from hep-th. Paul Ginsparg has introduced the endorsement system which was circumvented in this case and is likely to become a complete joke in the future. Why? Well, we have seen that a completely continuous spectrum of people between serious physicists and manifest crackpots has been created and the recent fashionable trend is to accept an ever broader set of crackpots into the physics circles.

This paper by A. Garrett Lisi had to be endorsed by someone. If you read the acknowledgements, it is not hard to see possible answers. Some of those people may endorse any crackpot because they are both endorsers and crackpots at the same moment. Moreover, they have a vested interest to increase the proportion of similar papers on the arXiv because this is where they belong.

If Ginsparg wants to prevent this possible collapse of his arXiv, he probably has to fine-tune the mechanisms a little bit and make sure that people who are ready to endorse papers like this one are simply not endorsers. Otherwise you can be pretty sure that similar papers will eventually overrun the arXiv.

Tony Smith is among the crackpots thanked to in the acknowledgements. Next time, he may also submit his own paper supported by similar endorsers. And maybe A. Garrett Lisi will become an endorser himself. Really entertaining times will start afterwards: the hep-th era of Jack Sarfatti, Tony Smith, Peter Woit, and their friends.

Coleman-Mandula theorem

Recently I was stunned that a person who has been a string theorist couldn't understand, despite months or years of working on similar questions and months or years of hearing the right answer, what the Coleman-Mandula theorem actually implies. There seems to be a whole industry of people who are just not getting it.

So let me say a few words about the theorem. They asked what symmetries "G" the scattering matrix of a physical theory can have. They assume that it is a group that contains the Poincaré group as a subgroup. If the Poincaré group is not a symmetry, the theory is dead. If the Poincaré symmetry is broken by small effects, a theory may be partially alive or hoping. But if it is broken by effects of order 100 percent, it is the end of the story.

Depends what is meant by "breaking" the Poincare symmetry.

1) Impose a different group like the Galilean group - this disagrees with experiment.

2) "spontaneously break" or "hide" (Coleman) the symmetry in the vacuum state i.e. ODLRO.

3) "locally gauge" the rigid 1905 SR 10-parameter Poincare group to get compensating gravity (geometrodynamic GMD) vector gauge fields, i.e. the 4 e^a and the 6 spin connections S^a^b = -S^b^a where a,b are SO(1,3) indices raised and lowered with Minkowski metric nab. The Einstein tensor fields are bilinear in these compensating GMD fields. The larger action of all fields in nature is invariant under this larger locally gauged P10(x) group, i.e. x's domain is the space of Einstein's "local coincidences" = nonoverlapping Diff(4) "gauge orbits" as explained in Ch 2 of Rovelli's "Quantum Gravity."

Warning: Lubos says the above is "crackpot". In other words, be an empty suit, be a sheep, do not try to think for yourself. Stay in the herd.

The authors show that such a theory must contain a spinless excitation and study the scattering of several copies of such an excitation. The scattering amplitude is constrained by the Poincaré symmetry and perhaps other symmetries. If you require that there exist Noether conserved charges arising from symmetries that are neither internal (scalar charges) nor the momentum (a vector from the Poincaré symmetry), you can see that it is such a strong constraint that the scattering amplitude is forced to vanish. You can do it with various quantities and prove that a theory with these new kinds of symmetries must be non-interacting, which also means physically unacceptable and uninteresting.

This is essentially a bogus argument by Lubos who is assuming the fixed Minkowski background, which is precisely what you cannot do. This is the Achilles Heel of all the string theorists. Lee Smolin explains this very clearly which is precisely why Lubos tars and feathers him as a "crackpot" along with Peter Woit a professor at Columbia - both wrote popular books specifically attacking Lubos's brand of theoretical physics. This explains why Lubos Motl, with a fanatical zeal not seen since the Spanish Inquisition and the burning of Giordano Bruno in Italy, sets himself up as Lord High Executioner in his own Kangaroo Court.

The only exception - found a few years later, in the early 1970s - are spin 1/2 conserved charges associated with supersymmetry. They also constrain the S-matrix dramatically but the interactions can nevertheless remain nonzero.

The local Lorentz group in general relativity is sometimes used analogously to other gauge groups - when we write down e.g. anomalies in supergravity-super-Yang-Mills coupled system - but it is essential that physics of gravity is technically different from physics of Yang-Mills forces.
There are both significant similarities and significant differences.
Gravitons have spin 2 while gauge bosons have spin 1. It is a technical difference that doesn't spoil certain philosophical analogies between gravity and other forces.
What Lubos does not know is that the tetrad quanta are spin 1 and that the gravitons of spin 2 are entangled pairs of spin 1 tetrads. In quantum theory

1 + 1 = 2,1,0

therefore quantum gravity will also have spin 1 and spin 0.

According to Lubos Motl this is "crackpot" but he does not say why. Take it on Pontifical Authority.

Nevertheless, it is a huge technical difference that certainly prevents you from combining the graviton and gauge bosons into the same multiplet.
That may be true and I make no such claim as allegedly Lisa does? So I seem to agree with Lubos on this particular.

It might be a tempting idea to combine fields of a different spin but in field theory, it simply can't work. That's why all of the hundreds (?) of papers that tried to do such a thing have failed and hundreds (?) of similar papers will fail in the future.
Lubos may be correct on this and that's GOOD for my hobby horse theory of emergent gravity as a macro-quantum vacuum ODLRO phenomenon, i.e. a 4D generally covariant "supersolid". Tetrad fields are translationa distortions of the solid leading to torsion dislocation defects. Spin connections are twisting distortions leading to disclination curvature defects. The world lattice spacing is

&L ~ (Lp^2L)^1/3 ~ N^1/6Lp world hologram of Wheeler's "volume without volume".

L ~ 10^28 cm
Lp ~ 10^-33cm
&L ~ 10^-13cm


Some people - see e.g. the recent paper by Nesti and Percacci - think that if they present the vielbein as a Higgs boson that breaks the local Lorentz symmetry (which is of course possible), they achieve a unification of gravity with gauge forces. That's of course a complete nonsense.
I make no such claim and Lubos may be correct here.
If we use the vielbein approach to general relativity, the local Lorentz symmetry is an additional symmetry that is needed to make the new degrees of freedom in the vielbein unphysical.
This is gibberish. The only thing "unphysical" is string theory as Lubos practices it. The vielbeins (tetrads) are the fundamental geometrodynamical GMD fields in a background independent MACRO-quantum gravity. The spin connections are the physical torsion GMD fields needed to explain both dark energy and dark matter. Lubos has thrown the baby out with the bathwater. I doubt that Lubos really understands much condensed matter physics. He may not like to mud wrestle there? ;-)
Besides this symmetry, there is still the old diffeomorphism symmetry of general relativity that hasn't been moved closer to unification, not even by a millimeter.
Yes, that's simply localizing the 4-parameter translation group T4 to T4(x) and forcing zero torsion as an ad-hoc constraint as in Rovelli's eq. 2.89.
Diffeomorphisms and Yang-Mills symmetries (and, correspondingly, graviton and gauge bosons) can only be unified if the fundamental "coordinates" in the theory carry a nonzero spin.

Unclear. Is Lubos pointing to Alain Connes "noncommuting" geometrodynamics

[Xu,Xv] = Luv^wXw =/= 0

In string theory, it is true that the string field or the first-quantized wave function combines fields of different spins. But the spin is only generated because the fundamental object, namely the string, is extended: extended objects such as strings simply can spin.

Clear as a thick coal-fired London fog in Victorian times.

The expansion in the stringy oscillators - the Fourier modes of the coordinates and fermions over the string - generates internal angular momentum. Alternatively, Kaluza-Klein scenarios also unify these things because the higher-dimensional metric tensor is decomposed into fields of different spins in four dimensions, including a gauge field.
If you read Lee Smolin's "The Trouble With Physics" and Sir Roger Penrose's "The Road to Reality." you will see this is all garbage. It's the real joker in the phony deck Lubos is playing you. These are the mad opium pipe dreams of burnt out theorists without any real physical intuition - that's what Feynman thought to his dying day. He was not alone. Lubos has built his House of Cards on a swamp, it's all quicksand. Of course no intelligent layman has a clue of what Lubos says above. Why should a "higher dimensional metric tensor" even apply to the real world? Start there.

But if you do local, four-dimensional field theory which is equivalent to point-like particles, they can't spin. The only way how to add spin to components of a field is to have spacetime coordinates that carry spin themselves.
That's news to Dirac RIP. The Dirac spinor does not require spinning spacetime coordinates. What does that even mean mathematically?

Lagrangians in quantum field theory


[edit]
Dirac Lagrangian
The Lagrangian density for a Dirac field is:



where is a spinor, is its Dirac adjoint, is the gauge covariant derivative, and is Feynman notation for .

[edit]
Quantum electrodynamic Lagrangian
The Lagrangian density for QED is:



where is the electromagnetic tensor

[edit]
Quantum chromodynamic Lagrangian
The Lagrangian density for quantum chromodynamics is [1] [2] [3]:



where is the QCD gauge covariant derivative, and is the gluon field strength tensor.

http://en.wikipedia.org/wiki/Lagrangian

We don't need no stink'n "spinning coordinates" above. Has Lubos really gone mad? ;-)
Again, spacetime and superspaces of various kinds (and the space of internal string excitations may be included) are the only known spaces of this kind. Under various assumptions, we can prove that other solutions can't exist.

Hogwash.

Of course that one has to work a little bit to see that one can't create many new things analogous to the superspace that would be compatible with observations - or at least with basic consistency and qualitative features of physical theories - but different from the well-known superspaces in an essential way. But Jesus Christ, once you have a pretty well-defined candidate, it is a straightforward homework exercise.
Sure Lubos, sure.

Stephon Alexander and Fabrizio Nesti, just sit down and try to derive the free particles and their leading interactions from whatever bizarre theories with mixed internally external symmeties and with frame-Higgses that you consider conceivable. I guarantee that you will fail and mature physicists know why you will fail.
This part is OK and my theory does not do anything of the kind.
Or analyze what global symmetries remain unbroken and try to follow the Coleman-Mandula procedure. What you're doing is just a completely childish and trivial sequence of mistakes and meaningless mathematical masturbation that puts you into the same category as Tony Smith.
And that's the memo.
Posted by Lumo at 8:51 AM

http://motls.blogspot.com/2007/11/exceptionally-simple-theory-of.html



Gary S. Bekkum / Starstream Research