An Exceptionally Simple FAQ

--Can you sum up your current work in a way that a layman could understand? I understand that you're applying differential geometry to the problem of uniting general relativity and quantum field theory, but at the risk of sounding too simplistic, how does that work? And exactly what is differential geometry, anyway?

Differential geometry is the study of smooth manifolds, usually in many dimensions -- it's calculus on steroids. There are ways of classifying symmetric manifolds, and this links up with all other branches of mathematics; so differential geometry is sort of a hub where a lot of mathematics comes together. Now, there is one manifold in particular -- the largest simple exceptional Lie group manifold, E8 -- that is the most beautiful. The system of roots in the picture I sent you describes the 248 symmetries of E8. What I'm working on is identifying each of the elementary particle fields of the standard model and gravity as one of these symmetries. It turns out that this match is... perfect, as far as I've been able to tell. This model is very new, and there are still things I don't understand about it, but it looks perfect so far. You have to be very careful with these things though, as they can encounter a fatal difficulty at any turn -- and when theory contradicts experiment, or requires unreasonable revision, you have to toss it and move on. But this theory of fitting all the standard model and gravitational fields into E8 is working very well so far.

When we have a nice symmetric manifold, like E8, we can mathematically describe how this shape twists and turns over the four dimensional spacetime we live in. This description is called a principal bundle, and the field describing the twists and turns is called a connection, which determines the curvature. What I'm doing is identifying all the standard model and gravitational fields (everything) as parts of an E8 principal bundle connection, and it's working amazingly well -- it appears to have all the correct fields and their interactions. Each symmetry of E8 is a different part of this connection, and each symmetry manifests itself as a different type of elementary particle that we have in our universe. When someone unifies gravity with the other fields like this, it's called a Theory of Everything -- that's what I'm after.

--In the notes for your Perimeter talk, you call this an Exceptionally Simple Theory of Everything, but it looks pretty complicated to me. Is this the kind of theory that you're going to have to know a lot of advanced math and physics theory to understand, or is it something that can eventually be explained in a way that the average person might be able to comprehend?

Heh, I said it was exceptionally simple, I never said it wasn't complicated. Someone is going to need quite a bit of advanced math and physics in order to fully appreciate it, but I think even the average person has a shot at understanding the basics. The symmetric structure of E8 is described by how these points are arranged around the center of the picture I gave you. We can find the interaction between any pair of elementary particles by adding their two corresponding points (as vectors) to get a third. The rest of the theory consists of equations describing the dynamics of these particles. Even if someone can't fully understand the physics and math, there are many beautiful patterns in this E8 root system, and I find it very satisfying that something this mathematically and aesthetically beautiful could be at the foundation of our universe.

--Can you talk a little bit about the background of relating symmetries in mathematical structures to physical theories? Can you give our readers an example of when this has been done in the past, and how successful it has been?

Well, there are two different kinds of mathematical symmetry that have been extremely useful for physics.

The first is structural symmetry of the physical laws themselves. The shining example of this was in Maxwell's work on electromagnetism. Basically, Maxwell was playing with the equations as they were known at the time and noticed they were not structurally symmetric -- there seemed to be a term missing. When he added this term, the equations came together in a much more elegant whole. With this new, unified theory, he was able to describe the propagation of light as an electromagnetic wave -- when previously light had been considered an independent phenomenon. It was a very dramatic theoretical achievement. The biggest advances in physics have often come from unifications: Euler, Lagrange, and Hamilton's reformulation of mechanics; Einstein's special relativity; Feynman's path integrals; etc. The guiding principal is that the equations themselves -- the mathematics describing the universe -- should be symmetric and beautiful.

The second type of mathematical symmetry is more specific and familiar: the symmetry of patterns and shapes. In mathematics this goes by the name of group theory -- and the success of twentieth century high energy physics can largely be attributed to this kind of symmetry. A notable application was the construction of the quark model in the sixties, by Murray Gell-Mann and others. At the time, there was a large zoo of independent particles and no one knew why they had the properties they did. He managed to explain these properties in terms of symmetric patterns -- later understood as the group theory of SU(3). Currently, our best model of how the universe works at small scales, the standard model of particle physics, is based on group symmetries.

--Question 1: What exactly is a gauge group?

A gauge group is a high dimensional surface with many symmetries. Basically, it's a pretty shape. The complete set of these shapes was discovered and organized by mathematicians at the beginning of the twentieth century, and they're the centerpiece of modern mathematics and theoretical physics. Among the groups there are five "exceptional" groups that have special structures distinguishing them from the others -- of these, E8 is the largest, and the most beautiful, with 248 fundamental symmetries. The symmetries of a gauge group can be described by a pattern of points in eight dimensions, one for each symmetry.

Essentially, what I've done is associate each E8 symmetry with an elementary particle field of physics, including the entire zoo of standard model particles and gravity. Other physicists have previously matched the standard model particles to gauge groups, including E8 -- these are called Grand Unified Theories -- but I'm including gravity as well, which is something new, and technically this makes it a Theory of Everything.

--Question 2: What is a "principal bundle"? If the explanation is very technical, perhaps you could explain in which field principal bundles appear? What are they usually used to describe? How do they help you understand the symmetries that you are looking at?

A principal bundle is a playground for group symmetries.

If you have a group, it just sits there, looking pretty -- but when you let a group dance over another space, like the one we live in, you get all sorts of fields with interactions and dynamics. Mathematicians call this a principal bundle. These are the main object of study of differential geometry -- which is where calculus ends up if you stay in college for ten years. The basic idea is to allow a gauge group, such as E8, to twist around the spacetime we live in -- the twists are described by the "connection field." This way, each group symmetry looks to us like an elementary particle field -- parts of the connection. The dynamics of the fields, and their interactions, corresponds to the curvature of the twists.

--Question 3: You talked (in a separate message) about the symmetries of the particles in the standard model. How do you relate particle symmetries with symmetries in general relativity? That is, what features of general relativity have symmetry and then how do you compare those features with the particles of the standard model, in order to unify them? It seems like trying to compare apples and oranges.

You're right, it's strange. I didn't think it was possible to describe gravity purely as gauge symmetries until I saw Lee Smolin, Laurent Friedel, and Artem Starodubtsev do it in a 2004 paper. They referred to a somewhat obscure discovery made by MacDowell and Mansouri in 1977. They revealed that gravity can in fact be described using a particular Lie group. This was the seed idea that led me to combine gravity with the other fields, and led to the unification of... well, everything, using the E8 gauge group.

I'm not sure why someone didn't come up with this idea long before I did -- my guess is the physics community was distracted by string theory. Also, there's a theorem by Coleman and Madula that discourages this sort of unification. But the MacDowell-Mansouri trick gets around the Coleman-Madula theorem by using a different Lie group for spacetime.

--Question 4: What do you mean by a "really weird pattern"? How do you analyse the pattern? If it something purely mathematical, how do you interpret it and what features stand out as weird?

I had described the fields as elements of a big matrix, and this matrix was... lopsided. I had never seen a matrix that looked like that related to a group -- it looked weird.

--Question 5: Once you began to see this connection, how did you test it? What convinced you that it was correct? Did the theory predict features that we see in general relativity and the standard model (e.g. masses of the standard model particles, strength of forces)?

It didn't dawn on me slowly -- the realization struck all at once, and my brain buzzed with the implications. So it wasn't a "hmm, maybe this will work" kind of thing, more of a "holy crap, that's it!"

The interactions between the two hundred or so fundamental particle fields we know of are all known. This exact structure is there in the E8 root system. As far as I've been able to tell it's a perfect match of tens of thousands of interactions, all corresponding to the most beautiful mathematical structure there is. How cool is that!

There are still features of this correspondence that I don't completely understand. I'm learning more about it every day. And, you know, as good as these things start out looking, they can always turn out to just not be true about nature. So, this theory I've cooked up may be wrong. But it's looking very good so far. I haven't gotten to the point with the theory yet where I can confidently predict new relationships between the physical constants such as mass, but that's where it's heading. This theory is only a few months old. What I'm going to do is write up what I've found so far and publish a paper, so others can see the details and play with it.

--Question 6: Is there a way that we can test your theory? Are there predictions that it makes that will help it stand out from rival theories? Does your theory do away with the need for supersymmetric particles, or predict other particles that we could perhaps look for at the LHC?

That's correct, there are no superparticles in this theory. I made a bet with a pair of string theorists that superpartners won't be seen at the LHC -- we'll get to see how that goes. I think I'll be able to use this theory to predict a handful of new particles that might be seen at the LHC, but I'm not yet far enough along to say more. It's very exciting. I have a fun year of work ahead of me.

--Question 7: You mentioned that you weren't interested in working on string theory? What advantages does your approach have over rival theories, such as string theory, both in terms of what it can explain, and also aesthetic appeal?

There are lots of good things about string theory. It appears to be quantizeable, and can accommodate gravity in a fairly natural way. It also has restrictions that come out, due to anomaly cancelation, that say what can and cannot be a "good" quantum string theory. Originally people thought this would be enough, when coupled with the right background manifolds, to get all the standard model particle fields to correspond to oscillations of a string. But it's never worked quite right. In order to get it to work at all, string theorists have to bend over backwards and put in all sorts of things by hand. This is the main warning sign that a theory doesn't correspond to nature. What happens is, a theory looks promising, so people invest time in developing it. If it looks like it's matching nature, that's great. But if it doesn't quite fit nature, people have already invested a lot of time in the theory, so instead of abandoning it, they try to revise it -- they add stuff and try to patch it up. But the more you have to add by hand, without any experimental guidance, the worse the theory looks and the less likely it is to be true about how nature works.

I suspected at the end of the 90's that string theory had left nature behind, and was going off in its own direction without any connection with reality. And it wasn't spreading out in a proper search either, it was barreling along in one direction like a freight train, guided by a handful of theorists with many followers who were devoting their lives to the theory. I've never been much of a follower, so I walked off to search on my own.

For the record, I do think it's good that very talented people, like Brian Greene, are working on string theory. Everyone should be able to work on what they want, and strings may yet turn out to be the true theory of nature. I just have other ideas.

(If you write about my dislike of string theory, please include that I do think it's worthwhile for some people to work on it.)

This theory I'm working on has the main advantage of being testable -- it will very clearly be right or spectacularly wrong about nature. If it's wrong, I'll try to figure out if it's fixable, or I'll abandon it and move on. Another advantage with this theory is its relative simplicity -- there is just one geometric field, the connection over spacetime, and the interactions and dynamics come from its curvature. And, at the heart of this theory is the most beautiful geometric structure in mathematics -- it's very pretty.

--Question 8: What next? If you have unified general relativity and the standard model, does that mean that all the four fundamental forces are now accounted for? What is left for you to do? What do you think you will need to do or demonstrate to gain support for your theory?

Yes, all fields are present and accounted for. Nevertheless, there is a ton of work to do. First, I need to confirm that the particle assignments and interactions are all in agreement with known physics. Any deviations could be fatal. Second, I need to see what new predictions come out: existing particle masses, coupling strengths, new particles, etc. Third, the proper quantum description needs to be worked out. Right now the theory matches up well with methods of loop quantum gravity, which is why I've been hanging out so much with the LQG community. To tell you the truth, it's much too much for one person to work on -- but if it keeps going as well as it has been, it won't be just me working on it.

The talks I've been giving have generated a lot of interest -- one week ago I delivered a one hour talk to a packed seminar room at the Perimeter Institute. That went VERY well. I'm going to have a paper out on the arXiv soon, with full details, so people will be able to consider it and play with it for themselves.

I feel funny calling it "my" theory, since I've learned so much from the work of others. And if it works as well as it looks, other physicists will play with these ideas and develop the theory far more than I could. It's a little early to say, but what I think, at this point, is that this is nature's theory.

--Question 1: Have theoretical physicists been able to associate the other four exceptional groups with physically observed phenomena? If so, what?

No, as far as I know this hasn't been done before. In the paper, I describe how each of these exceptional groups are related to a known subset of particles and interactions, and how they all combine into E8.

I should have a first draft of the paper ready tomorrow. If you'd like to look at it and you can keep it under your hat until Nov 7 or so, I'd be happy to send you a copy.

--Question 2: Are these 248 symmetries just symmetries in rotation, and mirror symmetries? Are there other symmetries?

There are other symmetries. They are not easy to describe, but together they make up E8. The pretty picture of the E8 root system describes how the 248 symmetries are related.

It is possible though to describe the symmetries of E8 in terms of the rotational symmetries of the root system polytope in eight dimensions. If you do this... there are 696,729,600 rotational symmetries! It's a very beautiful and complicated shape.

--Question 3: Are there 248 of these particles forces? Or do you run out of particles and forces to associate with the symmetries and have to postulate the existence of extra particles or forces?

That's right, after the standard model and gravitational fields are fit to the 248 there are a handful of extra particles and forces -- new particles. I currently only have some clues as to what these are, so I can't make definite predictions about them yet. It's still a year or so until the LHC turns on...

Question 4: For the cases where they matched the standard model but not gravity to E8, were there "spare" symmetries left over, that hadn't been associated with anything? And if so, why didn't anyone think to stick gravity in?

Two reasons. First, most people were distracted by working on string theory, which handles gravity differently. Second, the Coleman-Mandula theorem says you can't combine the Poincare group with other groups in a larger group that includes gravity. So people weren't looking for it, and if they were they didn't think it was possible. But there's an obscure way of describing gravity, compatible with Einstein's general relativity, called MacDowell-Mansouri gravity, invented in 1977. When I learned about this from people in the loop quantum gravity community, I saw how it could all fit together. Using this formulation, gravity can be fit together with the other symmetries, and it dodges the Coleman-Mandula theorem by not using the Poincare group. The Poincare group is the symmetry of a flat spacetime background -- the MacDowell-Mansouri formulation implies we should use a curved spacetime background instead, called deSitter spacetime. Conveniently enough, this also means there should be a positive cosmological constant, which is what we see.

--Question 5: At first, I thought that you were saying that you *begin* by identifying the particles and the forces with symmetries. But here it sounds more like the elementary particles and fields fall out only after you have set up E8 and started manipulating it? Which is correct?

Both.

We know there are a bunch of particles with charges, and we know how they move and interact. And the two are related. I've used these known charges to identify the particles as symmetries of E8, and using the curvature we can write down the action that describes how they move in a way thats compatible with what we know.

In order to know what charges particles have, you have to work backwards from how they move and interact.

-- Question 6: How do we see or recognise these fields in the maths? Don't they just manifest themselves as other symmetries? What I mean is, intuitively I could imagine associating particles with symmetries and then letting that group "dance over a space" and seeing gravity and other forces appear as interactions. But you have associated the forces _with_ symmetries too, so what sort of interactions and fields are now being created? What do they correspond with physically?

The interactions only happen through the exchange of particles. As you probably know, the electric force corresponds to the exchange of photons -- the field quanta of electromagnetism. A particle, physically, is what you have when you quantize the symmetry fields, mathematically. This can get very tricky, especially when you bring gravity into the picture. No one knows yet how to properly quantize gravity this way.

Each of these fields, corresponding to a group symmetry, dances over spacetime and interacts with the others -- producing all the known particles and forces between them.

--Question 9: What do you mean by the "root system"?

A "root" is what the points are called in the pretty pattern that describes the Lie algebra. They're also called eigenvalues. Or, if you're talking about this pattern in eight dimensions, these roots are the vertices of the E8 polytope.

A polytope is a fancy word for a polyhedron in a higher dimensional space.

Question 10: What sorts of things do these interactions correspond to? Specific strengths of forces between any two particles?

They correspond to which particles interact with which, to make other particles. For example, an electron can interact with an electroweak boson and become a neutrino, a quark can interact with a gluon and become another quark, etc. These interactions correspond to Feynman diagrams, which is what quantum field theorists use to predict things amazingly well.

--Don't worry, Garrett, I'm not interested in printing a story about an imaginary fight between you and the string theorists. It's just that most of our readers have heard of string theory, so they would be interested to know why this is better.

Heh. The fight isn't imaginary.

I'm just one guy, and I'm the first to admit this E8 theory is a longshot, but it looks pretty good. If it works it will be a beautiful unified theory that agrees with the standard model and gravity, as well as predicting a few new particles. And it's better because it works without strings, branes, extra spacetime dimensions, superparticles, Calabi-Yau manifolds, or other weird string theory inventions that there's no evidence for.

If I thought string theory was better, I'd work on that instead.

--Question 12: How do you model the curvature of spacetime using E8?

The Riemann curvature of spacetime is part of the curvature of the E8 connection.

Question 13: So this is an important point for me to clarify. I had thought that if your theory is correct it would do away with the need for people to work on either string theory or loop quantum gravity. But it sounds like maybe your work is showing that LQG is productive. So would the best way to think about it be to say that E8 provides the foundation for LQG?

Close. This E8 theory is a competitor to string theory, but string theorists could easily work on it since it's much simpler. It will be interesting to see how that develops -- see if anyone defects. I don't expect string theorists to work on it though, because I'm not in their club.

LQG... A better way to think about it is that LQG provides a foundation for E8 theory. The whole thing came together when I was trying to figure out how to combine the standard model with recent work in LQG. In LQG the field describing gravity is a connection. I was able to use a larger connection to include... everything. I was amazed that it worked! So what E8 theory will be, when it's quantized using the methods of LQG, is Loop Quantum Everything. Heh, that's going to be a good title for someone's paper in the future.

For a magazine image, you may want to use the image of G2 and use some arrows and text box overlays to describe how the interactions between particles correspond to visually adding together the points in these diagrams. This will be the best part of this theory for most people -- you can actually determine how all the particles interact by how these points add together in these pretty pictures.

For example, if you look at the picture of the G2 root system in the paper: Take the green up triangle (that's a green quark) and add the blue circle on the far right (a red-anti-green gluon) and you get the red up triangle (a red quark). This is how the quarks interact with the gluons. It's vector addition -- maybe you can overlay some arrows over the G2 picture to describe how this works for your readers.

When we do the same thing with the points in any of the E8 pictures, we get all the allowed interactions between the particles. :)

--If there was no universe -- to my naïve thinking -- we wouldn't have (or need) string theory or LQG. But the logic of E8, as a pure mathematical object would still exist and the mathematical properties it has would still be true without there having to be an actual universe in which E8 is realized. So, intuitively, it seems to me that E8 should be more fundamental than LQG (and string theory). Does that make sense? And if not, what is wrong in my reasoning?

That's not so naïve -- that's the Platonist world view, and is shared by many physicists and mathematicians. The E8 Lie group is a more central structure in mathematics than spin networks or strings. But spin nets and and strings are mathematical structures in this same way you're describing -- so you can't necessarily exclude them just for being more messy.

What I think is that the universe is pure geometry -- basically, a beautiful shape twisting around -- and this shape is described by mathematics. This is a slightly different view than believing the universe IS mathematics, but it's close. Since E8 is perhaps the most beautiful structure in mathematics, is very satisfying that nature appears to have chosen this geometry. And quantum mechanics seems necessary for everything to happen.

--2) Also, I was reading something Lee Smolin is quoted as saying about LQG. He mentioned that LQG may need to invoke a multiverse, just like string theory. Does E8 do away with the need for a multiverse? (At last, we can explain why everything is the way that it is -- and it's down to the shape of E8.)

I'm afraid E8 doesn't say anything directly about quantum mechanics, so it doesn't help that way. Although there are hints of how it might connect to quantum mechanics, algebraically.

The multiverse is what you get when you think about quantum mechanics operating on the scale of cosmology. Personally, I think "many worlds" and "multiverse" are just fanciful ways of saying there are many possibilities for what can happen.

--3) Does your analysis of E8 explain the relative strengths and ranges of the forces, and the relative masses of particles? (Sorry, if you have answered this one already.)

This is the goal. Right now it looks promising, but it's not there yet. All the pieces are in place to calculate these things, but some parts aren't perfectly clear, and it's going to take more work to find out one way or the other whether the correct coupling constants (force strengths) and masses come out. This is an "all or nothing" kind of theory -- it's either going to be exactly right, or spectacularly wrong. I think it has a good chance of making successful new predictions, which is why I work on it, but it could still turn out to be wrong. It aint over 'til the LHC sings.

-You probably answered this in another email that I buried, but I'm not sure whether to refer to E8 as an 8-dimensional object or a 248-dimenisonal object (or something else.)

The E8 Lie group is a 248 dimensional object. It is a very complicated, and very beautiful, smooth, curved manifold with many different symmetries. ("Manifold" is a fancy name for "surface.") This Lie group is the pretty shape at the heart of E8 theory.

The E8 root system, which is what's shown in the pictures, is a pattern of 240 points in 8 dimensions. This pattern of points describes the shape of the E8 Lie group, through its Lie algebra. The pattern in 8 dimensions is projected onto the 2 dimensional page from different angles to make the different pictures. By understanding this pattern, we get a better understanding of the E8 Lie group.

The elementary particles correspond to points in the E8 root system, which correspond to elements of the E8 Lie algebra, and thus to symmetries of the E8 Lie group.

I'm sorry this is so complicated, but I hope that's clear.

--Thinking in terms of a hypercube when we say, think of a cube in 3D and then you can think of another axis, orthogonal to the first three and that would give you 4D, etc...and in that way you can keep going and describe an n-dimensional cube. In THAT sense is E8 eight-dimensional (existing in the same space an 8D cube)? Or is it 248-dimensional, existing in the same space as a 248-dimensional cube.

The E8 root system is eight-dimensional in this sense. And it is a polytope, like the cube and 8D cube are polytopes.

The E8 Lie group is not a polytope, it is a smooth, 248 dimensional surface.

--I also wondered if the NS version is correct, see below.

It has some slight errors (physics has never been just a hobby for me -- it's my life), but for the most part it is accurate. I don't see any significant embarrassing errors or misstatements in the article.

--Does this mean we do not need any more than four dimensions, for example?

That's correct -- this E8 Theory only works in four dimensions.

--And how likely is it that the LHC could find one of those 20 new particles?

The theory is very young, and still in development. Right now, I'd assign a low (but not tiny) likelyhood 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.

--If you could let me know today, that would be great.

Certainly. Things are developing very quickly with this new theory.

I posted the paper to the physics arxiv on Wednesday, Nov 7:

http://arxiv.org/abs/0711.0770

It received an unusual (perhaps unprecedented) amount of attention from physics bloggers (in chronological order):

http://backreaction.blogspot.com/2007/11/theoretically-simple-exception-of.html

(This is the best and most informative review of the paper.)

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

(This is string theorist who, not surprisingly, hates it. Fortunately, his only real arguments against it are vacuous.)

http://www.math.columbia.edu/~woit/wordpress/?p=617

(Another level headed review)

Those are the main reviews and discussions of the paper so far, though there are several others (Physics Forums, etc).

Two hours ago, I presented a one hour talk on the theory to the International Loop Quantum Gravity Seminar:

http://relativity.phys.lsu.edu/ilqgs/

That is a weekly teleconference with a consortium of researchers at fourteen universities around the world. I'm happy to say it went very well.

I'm a little overwhelmed by all the attention, as I'm a bit of a hermit. But I'm quite pleased the physics community is as excited as I am about this new E8 Theory.

--1. First of all, in laymans terms: What the heck are you talking about?! Seriously, is there any way to impart to the average Joe what a unifying theory is, and why it's important?

Most people may be familiar with some of the various kinds of elementary particles, like electrons, quarks (that make up protons and neutrons) and photons (particles of light). These particles have charges. The electron, for example, has an electric charge of negative one. But there are also several other forces we know of, besides the electromagnetic force corresponding to the exchange of photons. The four forces are electromagnetic, weak, strong, and gravity -- and each force has a set of particles attached to it, and a different kind of charge. Each elementary particle can be uniquely identified by the charges it has. And there are a lot of elementary particles! About 200 or so. What I found was that the charges of all of these particles are not just random numbers, but that they match a pattern. The pattern represents the most beautiful geometric object in mathematics, E8. This is the "largest exceptional Lie group" -- essentially, it's a very large, very beautiful shape. And this is why it's so exciting. If this E8 theory is correct, it means everything in the universe corresponds to how this beautiful shape twists and dances over our four dimensions of spacetime. It would be very satisfying if our universe corresponded to the most beautiful geometry known to mathematics.

--2. Your work is showing up among the most popular discussions on the web; what do you think about all the attention?

I enjoy a quiet, contemplative life, interspersed with playing outside. The media attention has been amusing, but stressful for me. I think it's wonderful if I've motivated people to think a bit more about how the universe works. And it's great that people are so interested in this theory I've put forward. It is a beautiful theory about nature, but it might be wrong -- that's how science works. It's not enough that it's beautiful, it needs to agree with experiments. Also, this theory is young, and still in development -- it may change significantly, or it might turn out to not work. If it doesn't work, I go back to the drawing board. But in any case, it's a good adventure, and there's nothing I'd rather spend my time doing.

--3. The criticism I've read seems to span the spectrum, from you're brilliant, the next Eistein, to... Well, you know. What do you think about the critiques?

Einstein's construction of the equations of general relativity was the most amazing and beautiful accomplishment in theoretical physics. And it provided true insight into nature, with testable predictions that have held up for a century. Even if this E8 Theory is successful, it won't equal what he did to revolutionize physics. Also, this E8 Theory did not come from my effort alone. The program to unify the laws of physics has a long history, and many people have built it up over decades. I just hope I've advanced physics a little further with my ideas. And I expect that others will use this paper I've written, and continue developing E8 Theory in ways I haven't imagined. Or, the theory may fail. One needs to maintain a healthy skepticism, especially for ideas without experimental support, however beautiful they are. Criticism of a new theory is healthy. The scientific process will work it out.

--4. From a physics stand point, which is better, surfing or snow boarding?

Ha! There's more going on while surfing, with water and wind rushing all around you -- it's about chaos and taking chances. Snowboarding lets you draw a cleaner line -- it's more geometric and deterministic. The difference between these two is a lot like the difference between particle physics, with it's many quantum particles careening off one another, and Einstein's theory of gravity, the smooth geometry of curved spacetime. I think, for completeness, you need both.

--You added the charges of each quantum particle and came up with the E8 group. Or did you plug the particles into the E8 and found that they corresponded correctly? (What I mean is, would it be closer to likening your process as plotting out different particles as a different symmetry, and overlaying them accurately coincides with E8; or did you calculate the charges of each particle and, on a graph, what emerges is E8?)

The two different descriptions you're giving are related (thus the confusion). The E8 Lie group is a large (248 dimensional) symmetric manifold. It has 248 symmetries, each corresponding to a Lie algebra element. The relationship between these symmetries can be described by a pattern of points in an abstract eight dimensional space, with each point corresponding to a symmetry of E8. This is where the pretty patterns come from. Each elementary particle corresponds to a symmetry of E8, and hence to one of these points in the pattern. And each of these has eight coordinates, corresponding to the eight quantum numbers (charges) for the particle.

The main thing I've done is to figure out all the quantum numbers of the particles in the standard model, and found that these match the points corresponding to E8.