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Luke Leighton: on 3/6/17 at 12:19pm UTC, wrote

Luke Leighton: on 3/6/17 at 12:18pm UTC, wrote antony, hi, veery interesting to see your insights. did you notice the...

Brooke Davis: on 1/17/17 at 12:40pm UTC, wrote wiki

Jonathan Dickau: on 7/2/14 at 13:58pm UTC, wrote That is, It needs to be recognized that the measurement system extends...

Jonathan Dickau: on 7/2/14 at 13:38pm UTC, wrote I'll offer this, Darius... The Flower of Life figure depicts a measurement...

Alice lewis: on 3/21/14 at 8:17am UTC, wrote I think about the extent of the vitality circle that need to exist, and the...

Geoffrey Dixon: on 10/21/11 at 14:27pm UTC, wrote Hi Garrett I will ultimately (by year's end) put a link to a downloadable...

Garrett: on 10/16/11 at 21:29pm UTC, wrote Hey Geoffrey, Looks good -- I'd be interested to have a look at it. Would...

November 25, 2017

CATEGORY: High Energy Physics [back]
TOPIC: Pieces of E8 [refresh]
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Member Antony Garrett Lisi wrote on Jun. 9, 2007 @ 16:51 GMT
There are very few moments in theoretical physics that qualify as... thrilling -- moments that send shivers of excitement down the spine and make the brain tingle. It's such an abstract pursuit, you wouldn't think the effects would be so visceral. The thoughts take years to accumulate, and are often disjoint and haphazardly organized. On a very rare occasion, a new insight brings a cascade of...

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FrankM replied on Feb. 4, 2011 @ 17:53 GMT
One of the Issues I have had with the many theoretical forms of the atom is the lack of "structures" that would support the various energy types we know that are produced within it. The complexity of the E8 structure appears to provide ample structural forms to provide the "energy loops" that have to exist to produce the various energy types. For those energy types that are known to emanate from the atom, electromagnetic and gravity, the structure has to provide for isotropic emission.

At the moment, it cannot be assumed that there are dedicated "energy structures" for each energy type, that is, some part of the energy loop for generating an electromagnetic emission is not shared by the energy loop that generates gravity. Based upon current accepted theories on these two energy types, electromagnetic and gravity, one might think that there would be separate energy loops; there seem to be no similarities.

Consider the size of the energy loop that has to exist, and the time it has to exist, to produce an electromagnetic output with a wavelength of 21.1 cm; that is a huge wavelength in comparison to the size of the atom. Perhaps a mathematician could determine just how many elements of the E8 matrix would be needed to produce an energy loop that will support the generation of the 21.1 cm wavelength. Keep in mind that a half or quarter wavelength "energy structure" can generate a full wavelength if the energy loop has the proper properties.

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Mark Stowe wrote on Nov. 20, 2007 @ 19:56 GMT
Is anything recursive/self referential in the mathematics of your theory?

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Stéphane Beauregard wrote on Nov. 21, 2007 @ 22:15 GMT
Are there any experiments that could be done in the near future that might test predictions of your theory? Or will the energies be out of reach for a long, long time, like they are for other grand theories of everything?

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Andrew Dayton, wrote on Nov. 23, 2007 @ 01:07 GMT
Being only a humble carpenter, would this mean that since we know how weak, strong, e/m, and now gravitional forces are linked, can we now begin to learn to artifically manipulate a gravitational field?

Because we specialize in difficult and unusual builds, I thought it might be nice to offer my clientel anti-gravity sleeping quarters on earth or maybe a house that floats.

I apologize if this insults anyone, but I can't hang mentally with the bunch of you for long. Seriously though, can gravity now be manipulated?

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Matthew Fisher wrote on Nov. 23, 2007 @ 02:40 GMT
Are there any implications or unknown properties of Gravity or Magnetism that are implied by this theory? For that matter are there any other implications of this theory on other known laws or theories?

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Emile Lunardon wrote on Nov. 23, 2007 @ 22:16 GMT
Dear M Lisi,

Can your interpretation of the E8 group shed some light on the "Cosmic Galois Group" conjonctured by M P.Cartier(*) which acts as an universal group of symmetries on the coupling constants of renormalizable physical theories and which is expected to solve the problem of divergences in quantum field theory.

(*) A Mad Day's Work : From Grothendieck to Connes and Kontsevich. The evolution of concepts of space and symmetry.

Bull.Amer.Math.Soc. (N.S.) 38 (2001) ,no. 4 389-408

attachments: 001_from_grothendieck.pdf, Connes_Marcolli.pdf

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Member Antony Garrett Lisi wrote on Nov. 25, 2007 @ 06:54 GMT

Is anything recursive/self referential in your question?


It's still to early to say what they are, but the theory appears to be sufficiently restrictive that as it develops there will certainly be testable predictions, right or wrong.


We're still stuck with gravity -- just do the best you can with wood. Be creative.


The theory is built from the ground up to match what we know. If all goes well, it will continue to agree with what we know and predict some new things that we don't.


I'm afraid I'm not familiar with that.

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Lois J. Wetzel wrote on Nov. 25, 2007 @ 17:38 GMT
As a long-time artist/meditator I applaud your method of study. It allowed you to spend a lot of time in altered states of consciousness (like surfing, snowboarding) so that you COULD come up with this kind of theory. Very clever of you, indeed.

If you (or anyone reading) are not a student of sacred geometry, you might want to check into the work of Ibrahim Karim, an Egyptian architect who is studying/teaching sacred geometry from the inner chambers of the Egyptian pyramidal tombs, and further developing the studies of the French Radiethesiests. There is some VERY interesting information there. Sacred geometry is apparently how spirit creates matter.

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Tommaso Bolognesi wrote on Nov. 25, 2007 @ 18:44 GMT
Your E8 theory shows that the smallest known bricks of matter and force fit a very beautiful (and complex) symmetry.

Up in the biosphere, symmetry in shape (or a flower, a runner, etc.) is not a free gift; it is achieved by an evolutionary process.

Is it at all conceivable that the E8-particles and their symmetry be the result, by emergence, of the evolutions of

an exceptionally simple (maybe deterministic, discrete, computational) system, in the spirit of, say, cellular automata?

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Bryan wrote on Nov. 26, 2007 @ 17:33 GMT
I may ask this question clumsily, but bear with me a moment. The symmetries of the particles extend to the forces themselves which govern them. Fusion (strong nuclear) is balanced by fission (weak nuclear) and they are, in some way, inverses of one another. Aristotle coined the word for "gravity" to describe the force which causes things to sink or fall and Newton picked it up. But Aristotle coined two words for opposing balanced forces: gravity and levity. There was some talk in the past decade about an antigravity fifth force in the universe, indetectable at micro scales, but readily apparent in the macrocosm -- Einstein's Fudge Factor, the force propelling the acceleration of expansion in the universe, etc. And the famous "inflationary universe" soon after the Big Bang signals its separation from the symmetry. Does E8 allow for a missing force? Are the 20 missing elements related in some way as a family? Or are they scattered through the matrix? What is your opinion on levity?

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Bryan wrote on Nov. 27, 2007 @ 06:29 GMT
PS: The fellow who asked about recursive or self-referential (Mark) was asking, I think, whether E8 has the nature of a fractal or if it is fractal geometry.

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Member Antony Garrett Lisi wrote on Nov. 30, 2007 @ 02:26 GMT

Wow, "altered states of consciousness"... here I thought I was just having fun. ;) Also, I do like geometry a great deal, but "sacred" seems too strong a word. It would be impossible (and arrogant) for me to say with certainty that ancient philosophers couldn't have obtained deep insights into the geometry of the universe through omphaloskepsis, but I prefer using math. If people are struck by the beauty of geometry, I would encourage them to use this as motivation to learn a bit of the related mathematics. Physics and math are the best magic I know -- most of the other kinds are fake.


Yes, this is possible. I try to follow Occam's razor in these matters, but it's conceivable that there's a simple system for which E8 is an emergent symmetry. Though I'm going to spend more time working on the E8 Theory itself first, before I consider how it might emerge from something else.


Yes, I feel levity is very important in physics. (I think that's apparent from my paper title.) And if this E8 Theory turns out to be true about nature, it will include a few new particles, corresponding to new forces. But these are going to have to be sufficiently weak that they don't contradict the standard model, which very accurately describes the world on our human scale.

Bryan II:

If so, then the answer is no, E8 is a complicated (simple) Lie group, but not a fractal.

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Wizard Gynoid replied on Jun. 2, 2010 @ 11:05 GMT
Does the E8 have the nature of a fractal? Consider the quadrahedral symmetry axis. It looks like this:

A spiral fractal in the quadrahedral symmetry axis of the E8 Polytope

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mike wrote on Nov. 30, 2007 @ 03:22 GMT
To the extent human tropical water monkeys see randomness in events ... time is a ride exactly between quantum and astronomical. That would make self conscious life actually THE unifed field and quite a beautiful answer as well.

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Tommaso Bolognesi wrote on Nov. 30, 2007 @ 11:23 GMT
Occam's razor is one of my favorite tools too (maybe not for posts, though...). After your november 2007 paper, precisely two distinguished concepts are filed in my mind under 'particles' + 'beauty': one is the system of roots for the 248 symmetries of the E8 manifold; the other is Wolfram's elementary cellular automaton 110, with its amazing interacting particles emerging from basically any initial condition, including the simplest.

While it is clear that the universe can't be a cellular automaton, one can expect a lot of beautiful things to emerge when trying to transpose the simple ideas behind them -- and the computational-universe view -- to the discrete, graph-like structures considered in LQG (spin networks, foams, knots, braids...), or just to plain, finite trivalent graphs, as suggested by Wolfram himself.

That's what I am after, and although I well understand that your priority is still on the internals of the E8-Theory, I wonder whether you'd have at hand a 'natural' candidate for a sequence of increasingly complex symmetries X1, X2, ..., Xn, with Xn = E8, so that research and experimentation on emergence in graphs could be more realistically directed towards cracking X1 first.

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TG wrote on Nov. 30, 2007 @ 21:30 GMT
A piece of the answer hides in the Coral Castle. See you in the water sone day.TG.

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Tom Greenhaw wrote on Dec. 2, 2007 @ 21:01 GMT
Looks like I'm going to have to go back to math school for a few years to anwer my own questions about how your idea affects cosmology. In the meantime...

Have you considered that some of the unnasigned points on E8 could apply to "dark matter"? Does your idea rule out dark matter or make it easier to know how and what to look for?

As an alternative to dark matter, does your idea show that the effect of gravity is not perfectly linear in its relation to space?

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anna wrote on Dec. 3, 2007 @ 14:18 GMT
it's imazing now to look at the 12th century cathedral's roses (copies of Solomon temple probably)?

attachments: valencia_cathedrals_rose.jpg, rose_nord__de_Notre_Dame_de_Paris.JPG

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Daniel P. Fitzpatrick wrote on Dec. 3, 2007 @ 20:39 GMT
Is it possible that quark spinors, emulating electron spinors in magnetism and sigma and pi chemical bonding, could be responsible for gravity and inertia?

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Phil wrote on Dec. 10, 2007 @ 18:34 GMT
Is this related to Star Trek Voyager's episode regarding the Omega Project, where there find the ultimate element? Seven says the element is symbolic of Perfection.

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Michael Cecil wrote on Dec. 11, 2007 @ 11:56 GMT
Just a few questions:

Would not a theory of *everything* have to say something about the consciousness that created it, or through which it emerged?

(I suggest that a theory of *everything* would have to be able to explain its own origin. This is not my idea. It was told to me by another searcher for Truth back in 1972.)

Inasmuch as science originates in self-reflection and the thought of the 'thinker', a true theory of *everything* would have to determine whether this is the only dimension of consciousness. (It isn't. There is also the chaotic Lorentz attractor form descriptive of "psychosis", as well as the "observing consciousness" which is capable of observing the 'movement' of self-reflection in the first place.) (The 'classical' consciousness originating in self-reflection and thought cannot observe this because it does not yet exist.)

Would not a rigid adherence to Occam's Razor result in the conclusion that there is neither a 'mind', nor a 'thinker', nor a 'self' but merely thoughts?

If this E-8 is, in fact, a theory of everything in the physical world, how could it be related (through metaphor, archetype, synchronicity etc.) to a complete description (based upon observation, not thought or self-reflection) of the full dimensions of human consciousness?

In other words, maybe E-8 is not a TOE but a crucial *half* of a theory of everything: a TOEBH or a theory of everything by half.

Michael Cecil

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Eric Bremner wrote on Dec. 12, 2007 @ 17:47 GMT
"consciousness that created it, or through which it emerged?"

-Michael Cecil wrote on Dec. 11, 2007 @ 11:56 GMT

Not so much. If I were write down 2+2=4. that doesnt tell you anything about my consciousness. Nor does it tell you anything about its "inventors" consciousness. Of course 2, +, =, and 4, are all different theories, the most basic part of these theories were developed in multiple places without any intereference from outside forces. (Unless there was aliens! woooOOOoo!, but I'll put that theory on the dusty shelf where it belongs for now) Because the same theory was developed by multiple, and entirely different consciousness' it is impossible to say that the theory has anything to do with its inventor, the theory is of itself.

I think you are trying to say that there may be "bias" in the equation, which is a perfectly valid question. But some things simply "can't" have bias. But of course I can not tell you for sure about this quation, because I havn't read All of the original creators work. And to have an equasion work out, while biasing the numbers to your own "whim" is an accomplishment of its own accord.

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Michael Cecil wrote on Dec. 12, 2007 @ 20:23 GMT
Not so much. If I were write down 2+2=4. that doesnt tell you anything about my consciousness.

Eric Bremer wrote.

Of course it does. It tells me that the origin is the 'classical' consciousness originating in self-reflection and thought.

And, if I tell you that thought originates in fear and desire, that also tells you something about the consciousness that makes this observation: it is not the 'classical' consciousness, which is incapable of observing thought.

The bias I am referring to is the bias which requires the preservation of the 'classical' consciousness itself. Descartes, for example, postulated the thought of the 'thinker' in order to escape the psychosis described in the opening passages of Meditation II. Of course, it is necessary, in some sense, to preserve sanity; but, at the same time, the resultant view of reality is distorted by that motivation. It is not an objective view of reality.

The observations of the "observing consciousness", on the other hand, have nothing to do with fear or desire; and, for that reason, can provide an objective view of reality beyond the view of the 'classical' consciousness.

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Member Antony Garrett Lisi wrote on Dec. 29, 2007 @ 19:25 GMT

We always see randomness in events, but I think self conscious life is a question, not an answer.


Yes, this is a great way to proceed. And I think LQG is the best place to start if one is going to work up to a fully quantum description of the whole enchilada.


Amusing, but within the realm of coincidence.


The theory isn't developed well enough yet to say anything definitive about dark matter.


Yes, the appeal of symmetry has spanned many centuries. It's interesting to consider to what degree this aesthetic appeal is grounded in the fundamental nature of the universe.


Sounds kinda weird.


Shh! Don't give away my sources!


For the paper's title, I used "Theory of Everything" in the technical sense of combining a description of general relativity and gauge symmetries as parts of a single, larger symmetry group. The theory has nothing to say about consciousness. If you want to build up from fundamental physics to an understanding of consciousness, that's a long hard path -- but a potentially worthwhile and successful one.




You're correct that we're all biased. However, science works, so this is promising.

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Tom Greenhaw wrote on Jan. 16, 2008 @ 01:22 GMT
I've been looking at E8 and a couple other TOE mathematical models that imply unobserved dimensions. The thought occurred to me that what we percieve as a 2 dimensional timeline could potentially be a vector through multidimensional time.

While this concept can very neatly address the issue of missing dimensions, proving it experimentally is an interesting exercize.

Perhaps this idea may prove of some use to your work...

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bidou wrote on Jan. 16, 2008 @ 21:25 GMT
Yahou !!

Me, I found the exeptionnaly simple theory of nothing :



Garett, What do you think about my theory ?

report post as inappropriate wrote on Jan. 19, 2008 @ 08:21 GMT
Great Job Mr Lisi, this is a really logical theory. I hope you will soon be able to test this with the new CERN scientist toy. ;)

But... I started reading your AESTE and it seems you postulate the Higgs' boson exists. As the Higgs as been created to fill the holes in the standard theory and as far as I heard of, it's never been seen (maybe it will with the LHD but who knows...)don't you think it's going to bias (blow) the geometry if the actual gravity explanation is false.

I read another Theory by Lafreniere that explains all the forces maybe it will help... or not. but both your theories seems valid, well Lafreniere is not a physician and is axplainations are far less mathematical but it sounds coherent too...even if is...hum writing style is... weird. just take a look if you have some time and let us know what you think of it.

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N. Tantilov wrote on Jan. 24, 2008 @ 14:59 GMT
Dear Dr. Lisi,

I'm sorry - I posted in the the wrong thread, which won't be replied to, so once more my question regarding TOEs:

Kurt Gödels Incompleteness Theorem ...

means *any* TOE will end up being a "TO almost E".

Guess this doesn't touch your present work at all, but in the long run you must have some sort of opinion about it ... ? Hope it's not too indiscreet to ask.

One more thing - I like your statements about a beautiful theory. The search for truth and the search for beauty are in a way related - the ancient Indian seers called the Ultimate Reality they found:

Satyam, Shivam, Sunderam - the True, the Good and the Beautiful.

- And pardon me for mentioning still one more thing - you have a nice way of using words. The titling of your paper, "Pieces of E8" ...

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Sava wrote on Jan. 31, 2008 @ 13:22 GMT
Can anybody translate this theory in Ukrainian,or russian?

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Matt J. wrote on Feb. 1, 2008 @ 03:26 GMT
Dr. Lisi-

I know you are a "surfer dude", but somehow, I think it is best to start off with a salutation more appropriate for someone who really has earned his PhD.

Anyway, on to the real topic: I see you say you have a lot of calculation to do. Have you found a Computer Algebra package suitable for it? Is Octave, Axiom or Sage suitable? As I read the descriptions of these packages, they sound somewhat promising, but they all seem to be missing something. GAP, for example, my old favorite, only handles Lie Algebras over fields of prime characteristic and small dimension or over GF(2). But if you want to know the Normalizer etc. of the Weyl group, that GAP can do -- if you tell it the Weyl group;)

Then again Atlas sounds promising too, though the only description of it I found on the Net is rather dated

(, and sparse in describing what else other than "Kazhdan-Lusztig-Vogan polynomials" it will compute. Somehow, "structure theory and admissible representations of real groups" still sounds too vague. And their "Spherical Unitary Explorer" works only for the Classical Groups.

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JKD wrote on Feb. 1, 2008 @ 11:21 GMT
Hi Lisi,

(Condensed matter physicist speaking :-)

The action in Eq. 3.8 involves an integral over a 4-manifold. I assume this is a Cartesian 3+1 space, is this correct?

So, how would you quantize the theory? Would you find the field modes and their conjugate momenta on this manifold and proceed in the usual way?

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Ford Prefect wrote on Feb. 28, 2008 @ 05:10 GMT
Dear Lisi,

How does this have anything to do with 42?

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Guglielmo P wrote on Mar. 3, 2008 @ 22:51 GMT

As your theory is a gauge theory with all its apparatus, for it to make sense it should be renormalizable or even finite(what string theory are). I just run across your papers, but didn't took the time to read it, so I ask you:

Is your theory renormalizable ? (which is, as far as I can remember the main plague of quantum gravity and the reason to look at supersymmetry and string theory. Is it not so ?)

Thanks for you answer.

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Albert Soler wrote on Mar. 6, 2008 @ 06:07 GMT
What fun it's been reading about this new idea!

Just like I may never be able to play linebacker in a pro football game, I can still love the game as a spectator.

Being new to this game, there are so many *really* basic questions. I'll just ask one or two here:

- The dimension thing. Very confusing. (Except, strangely enough, for the vertices corresponding to elementary particles. Perhaps because it's such a neat idea (as in tidy): So, E8 is an 8-dimensional polytope. But has a 248-dimensional surface. To help me encapsulate this concept, how many dimensions would the surface of a 3-dimensional *dodecahedron* have? (Would that be 20 dimensions? Same as vertices?)

*A little homage to the late Gary Gygax.*

- So, we have an 8-dimensional polytope. A 248-dimensional surface. Where/how does 4-dimensional space-time fit into E8?

- Okay, three questions: So, it looks like this might describe all the fundamental particles in nature and all their possible interactions. But, does General Relativity naturally arise from the model? Can it explain why there are three spatial dimensions and only one time dimension? Or, why time is so different?

Really more than three questions. But hey, it's such a fascinating idea!

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alhdi konadeh replied on Apr. 12, 2011 @ 00:43 GMT
a 3D dodecahedron has a 2D surface.

But here, do we have we have an 8D polytope with a 248D surface? I don't understand.

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Kris Michael Krieger wrote on Mar. 8, 2008 @ 01:32 GMT
I'm a complete layman, not at all a amthematician, so I hope it's OK for me to post here with a very basic question, because I don't know where else to ask.

Is the rlationship between the E8 shape, and particles, in any way similar/parallel to the relationship between position on the Periodic Table, and characteristics of elements...? Similarly, would the "colored lines" connectivng the vertices relate to some sort of commonality and/or transition from the qualities of one particle, to those of adjoining particles? IOW, if one "line" is blue, and anotehr "red", do the colors represent different correspondences of qualities between the particles, where A could have X in common with B, but Y in common with other adjoining particle C...?

TIA, and thanks for your patience with my simple question...

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Ray wrote on Mar. 10, 2008 @ 18:42 GMT
Neat stuff, Dr. Lisi.

I am excited about progress with this theory so I won't hinder it by posing you self-indulgent questions. I trust understanding will filter down to me in time. You keep at it, and good luck!

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Nelson Ferreira Alves wrote on Mar. 21, 2008 @ 02:18 GMT
And if 'All' happened in the Bulk?

Big Bangs, big explosion's big 'everything', Branes colliding and so on...

In the out there Dark is just what we can yet see, if we ever seen...

We are happy to be in a small universal blt of stars...

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Member Antony Garrett Lisi wrote on Mar. 25, 2008 @ 19:08 GMT

A lot of people have considered multiple timelike dimensions -- it is a neat idea, but tends to run into problems by predicting tachyons.


It lacks something.


I'm more curious about his fanatical followers...


There are some theories that work without a Higgs, but they tend to be more complicated. It's a good bet that the...

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Member Antony Garrett Lisi wrote on Apr. 7, 2008 @ 18:03 GMT

Nah, I'm sticking with 42.

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Dr. Ray Munroe wrote on Apr. 17, 2008 @ 15:31 GMT
Dear Dr. Garrett Lisi,

I recently published a book on “New Approaches Towards A Grand Unified Theory” and noticed some interesting similarities between your research paper “An Exceptionally Simple Theory of Everything” and my book – despite the fact that we approached the problem from very different perspectives, and I just read your paper (so it didn’t influence the ideas in my book).

Similarities – 1) Both approaches expect at least a minimal left-right symmetric weak force, 2) both approaches need 16 Higgs scalars (my book uses two complex Higgs scalar doublet fields, one of the complex doublets couples to the Standard Higgs vev of 246 Gev, and the other appears to couple to an energy scale of 20,000 TeV), 3) both approaches may explain the CKM and PMNS matrices (my book unifies and complicates these matrices), 4) both approaches contain SO(8) algebras that may not have been expected, 5) both approaches may explain the three generations of matter – your “triality” – although my book predicts a total of five generations that condense into three low-mass generations, and 6) both approaches derive their gravity representations from Clifford algebra (although they yield different conclusions).

Ultimately, I came to the conclusion that a 14-dimensional Supersymmetric SU(15) Lie Algebra may be the best effective theory (short of the over-kill “True” 26-dimensional theory), and that this theory can condense into a 10-dimensional SU(11) “Boson GUT”, an effective 8-dimensional SO(16) “Fermion GUT”, and a 4-dimensional SU(5) Supersymmetry. Within the framework of my book, your E8 representation may be a good effective theory in 8 dimensions, and with an order of 8 x 31 it is large enough to contain two SO(16)’s of order 8 x 15. It isn’t clear to me whether the 10-dimensional SU(11) “Boson GUT” is collapsing into an effective 8-dimensional SU(9) or whether it is being misrepresented by an 8-dimensional SO(16).

Most of my ideas on GUT Lie Algebras are in Chapter 7. The earlier parts of my book address grand unification from a thermodynamic perspective. And I have a few pages on the Creation –Design – Chance – Necessity Debate as it relates to the Anthropic Principle that might appeal to your “blog followers”.

I received my Ph.D. in Particle Physics from Florida State University in 1996 under Prof. Howie Baer, taught full-time until 1999, taught part-time until 2003, and I’ve been in the business world full-time since 1999.


Dr. Ray Munroe

Tallahassee, FL

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Dr. Ray Munroe wrote on Apr. 27, 2008 @ 05:07 GMT
Hi Garrett,

Have you had an opportunity to read my book “New Approaches Towards A Grand Unified Theory” yet? I’m trying to resolve my ideas with your ideas with String Theory and with Supersymmetry.

My wife, daughter and I came to the beach this weekend. The Florida Gulf coast doesn’t have the waves that you’re used to, but it is relaxing. And suddenly, the answer hit me in the middle of the night.

The E8 group is based on the 5-simplex, the Hexateron (which has 30 nearest neighbors). I think that the natural extension to E8 would be based on the 6-simplex, the Heptapeton (which has 42 nearest neighbors), and this group would have an order of 430 (10 x 43), and a rank of 10. For lack of a proper name, can we call this E(10)? In my book, I related rank and dimension – thus, I expect this group to exist in 10 dimensions, which should delight the String Theorists. (Yippee!) With an order of (10 x 43), it is large enough to include my 10-dimensional SU(11) “Bosonic GUT” of order (10 x 12), and a 10-dimensional SO(21) “Fermionic GUT” of order (10 x 21), and 100 (10 x 10) of my Supersymmetry operators.

Although my book gives the background for these ideas, these are new extensions of my theory. I didn’t push fermions to the natural limit, and I was happy with two SO(16)’s of fermions, but the 21 charges of SO(21) arise from: SO(21) → SO(10) basic “Fermion GUT” + 7 subtypes of Hyperflavor + 2 New Generations (for a total of five fermion generations) + 2 new types of Leptoquarks (a, ψ). Now 21=10+7+2+2, and SO(21) has an order of 210 that reflects both the seven-fold symmetry of hyperflavor and the five-fold symmetry that we expect from five generations.

Regarding the 100 Supersymmetry operators, I had a supersymmetric SU(15) that decomposed into an SU(11) “Bosonic GUT” and an SU(5) of supersymmetric operators that related the spin quintet: (0,½,1,1½,2). SU(15) has an order of 224 and SU(11) has an order of 120. 224-120=104. Of these 104 supersymmetric operators, four are diagonal components that do not affect spin, whereas the other 100 components do affect spin. You thought you had GHOSTS in the machine, but you may have relic operators from Supersymmetry (and what I called Hyper-SUSY).

There it is! I’m only good for models – you are the Differential Geometry Master! Now go include Hyperflavor, WIMP-Gravity and Supersymmetry into an “Exceptionally Complicated” E(10) Theory of Everything, and RIDE THAT WAVE!

Ray Munroe

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Ann wrote on Jun. 11, 2008 @ 17:47 GMT
Dr. Lisi,

i'm really sorry to see that your blog has turned into a trash bin. why is someone approving all the garbage comments here?

i am a programmer with just a masters degree in math from UofMD,

but i have been reading all your dialogues in this blog with real scientists since you started to post, and have enjoyed these open science forum discussions. but i guess i'll have to stop since you don't seem to post anything of interest anymore. hope to see you resurface in some legit form again. i look forward to your future publications.

thanks for all the great ideas,

good luck with your research,

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Anonymous wrote on Jul. 26, 2008 @ 08:44 GMT
pagsure mo oie!!!!

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David Woods wrote on Aug. 23, 2008 @ 04:09 GMT
Amazing. Poet/Songwriter Leonard Cohen must have been thinking of all you guys when he wrote that wonderful refrain "Give Up Your Tiny Vision of Pain."

In all these erudite postings I find not a single bit of imaginative, broadly interdisciplinary speculation about the possibility that the GUT/TOE quest could have implications beyond the physical sciences. An explanation of how things began and will or will not end could, for example, be the Rosetta Stone ending centuries of conflict and bringing science and religion together.

Maybe that new accelerator tunnel in Berne should have a few resident researchers who are not scientists; say a poet, a priest and maybe even a peasant.

Most non-scientists at least once in a while read something scientific. I hope you all do the same with poetry or fiction. Google, for example, "Buffalo Snow Day" to get a comic but perhaps plausible look at how a broad approach to GUT/TOE fictionally transforms Buffalo, yes Buffalo, into an Athens for the 21st century. Or, read the attachment to this message, a six page excerpt of spirited GUT/TOE interaction between a fictional though reality based Nobel Laureate in Physics and his friend, a leading theologian.

God Speed!

attachments: Excerpt_on_GUTTOE_from_B.S.Day.doc, 1_Excerpt_on_GUTTOE_from_B.S.Day.doc

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Mike wrote on Sep. 8, 2008 @ 21:28 GMT
Garrett ... I emailed you a couple of months ago regarding a strange coincidence I noticed

Most everything

in your paper here -

s way over my head, however, I couldn't help noticing an

interesting geometric coincidence (maybe I am just attempting to

create a connection where one does not exist). The two geometric

representations on pages 19 and 20 are strikingly similar to that of

"Metatron's Cube" which is a figure containing all five platonic

solids and has some religious connotation. From wiki "The simplest

means of constructing Metatron's Cube is to begin with a cube

flattened along a space diagonal, such that it becomes a 2D figure,

equivalent to a regular hexagon divided via its own diagonals into six

equilateral triangles. The vertices of this 2D figure are then

connected with additional lines. Several steps later, the full

Metatron's Cube figure is formed. This method requires dividing

vertices according to the golden ratio. There is also a method of

construction from the Flower of Life. The cube resembles the fourth

dimensional analog of the cube, or the Tesseract."

About half-way down there is a figure on the left hand side of the

page (comparing this image to that on pg 19 and 20 of your ToE looks

eerily similar, at least from my perpsective).

Any insigh from anyone, or am I just crazy?

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Dr. Ray Munroe wrote on Sep. 10, 2008 @ 12:57 GMT
Dear Mike,

I don’t think you’re crazy, unless you mean “crazy like a fox”. The exceptional groups and the set of quasi-exceptional groups that I recently proposed are all VERY geometrical. The geometries implied by these exceptional groups seem to be as important as the group algebras themselves. These geometries may imply fundamental particle multiplets and the structure of hyperspace itself. The G2 group has the symmetries of the triangular group (and the tetrahedral rotational subgroup). The F4 group has the symmetries of the octahedral group. And the quasi-exceptional E6’ has the symmetries of the icosahedral group (and the tesseract). If you read my book “New Approaches Towards A Grand Unified Theory” (a free partial preview is available at – read pages 47-55 and 77-84), you will see that I partially addressed all three of these symmetries.

Metatron’s cube contains the triangular lattice (Star of David), the octahedron, and the icosahedron. Likewise, E8 contains the component symmetries of E6’, F4 and G2. Therefore, Metatron’s cube does seem relevant to these symmetries. Would you mind if I use Metatron’s cube in a future paper? My favorite quasi-exceptional group, E12 has even more complicated symmetries.

Personally, I think that Lisi’s Figure 4 on page 20 looks more like the triangular lattice of G2 (see Lisi’s Table 1 on page 5 – Lisi ignored the color-neutral leptons and gluinos g3~ and g8~ at the origin that complete the triangular lattice. My next paper in the Journal of Chaos, Solitons and Fractals “Symplectic Tiling, Hypercolour and Hyperflavor E12” will clarify this omission), and Lisi’s Figure 3 on page 19 looks similar to the octahedral symmetries of an F4 projected onto two dimensions. As such, neither of these figures looks exactly like Metatron’s cube, but both look like symmetries that are implied by that cube.

The fact that the golden ratio is involved in Metatron’s cube is also very interesting. For years, El Naschie has related the occurrence of the golden ratio in these sorts of problems to the fractal nature of Cantorian Spacetime, and an implication for the necessity of E-Infinity.

Thanks for the inspiration!

Sincerely, Ray Munroe

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Mike wrote on Sep. 10, 2008 @ 21:57 GMT

Thank you for your reply, I was anxious for somebody, anybody, to tell me that I was not crazy - but was willing to accept crazy as well ha. Go ahead and use the cube in your paper, it's not like that's not public information. I'll have to check out your book.

By the very definition of 'sacred geometry' as seen here ... "According to this belief system, the basic patterns of...

view entire post

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Dr. Ray Munroe wrote on Sep. 12, 2008 @ 13:19 GMT
Dear Mike,

I’m glad to help. You clearly put a lot of thought into your geometry and philosophy. Yes, I also read about the Fruit of Life and the Flower of Life.

Dear Garrett,

Your fans need you. You can teach them and learn from them. Come back or I will hijack your blog site.

The recent propaganda and slander against the Large Hadron Collider proves that we have failed to teach science in America. That disturbs me greatly as a former teacher (I love teaching, but gave it up for a higher-paying job – I still consider myself an ambassador of science). Too many American scientists seem to be “Elitists” – and I mean that in a bad way, not a good way. We (purposely?) talk over the heads of non-scientists – it sets us apart and empowers us.

Yes, America is a democracy, and we all have a right to our respective opinions; but to call the Large Hadron Collider (LHC) a “Big Bang” machine or a “Doomsday” machine is slanderously bad science and irresponsible news. People already fear that which they don’t fully understand. The LHC has a center-of-mass energy (up to 14 TeV) that is only several times greater than Fermilab’s Tevatron (nearly 2 TeV). We have observed cosmic ray impacts on the Earth’s atmosphere as powerful as 300,000,000 TeV. And, if a Theory of Everything (TOE) exists, it is on a scale of 10,000,000,000,000 to 10,000,000,000,000,000 TeV. We will never figure out if you (or me, or String Theorists, or many other scientists with grand theories) are right or wrong if we don’t push our experimental science to the highest safe and affordable threshold.

My only fear of the LHC is that it might not discover anything new. And though a null result might eliminate some theories in favor of others, it would also lead to the cancellation of the proposed International Linear Collider (a proposed electron-anti-electron supercollider that would be the “scalpel” with a clean signal-to-background ratio to complement the LHC “hammer” that is more powerful but full of background noise) and lead to the realization of Richard Thomas’ prediction that the LHC is a new “Tower (Tunnel?) of Babel”.

Your fans need you. You can teach them and learn from them. Come back or I will hijack your blog site.

Sincerely, Ray Munroe

report post as inappropriate wrote on Feb. 22, 2009 @ 19:45 GMT
Lisi, I have a theory alot like yours, only it explains everything! I think it would be very nice if I were able to share my idea with you. Please email.

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Lois Wetzel wrote on Mar. 12, 2009 @ 14:19 GMT
Well, after my initial post in November of 2007 mentioning Sacred Geometry and altered states of consciousness I decided not to post again. Why? Dr. Lisi's dismissal of my words as irrelevant, referring to "magic" and saying geometry was probably not sacred (too strong a word) and referring to omphasoskepsis I just thought, hmmm... He is not getting what I am saying.

I see now that eventually a lot more people, about a year later, began discussing Sacred Geometry (Flower of Life, Metatron's Cube, etc.) and then Dr. Lisi dropped out of the equation.


Lois J. Wetzel

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K wrote on Mar. 13, 2009 @ 18:23 GMT
Why does he think that matter is made up of strings? If anything wouldn't matter be made up of some sort of spiral centripical force.

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Jason Wolfe/ wrote on Mar. 14, 2009 @ 20:23 GMT
Help! I'm looking for a string theorist who can shed light on superstrings.

I made the assumption that superstrings can be described as solutions to the Schrodinger equation. Schrodinger equations basically says that for some potential energy topography (like an infinite square well), if there is a particle in their, it's wave function will be a solution to the Schrodinger equation.

I thought that solution would provide the available states that a "superstring" can be in.

The problem is that, for the hydrogen atom, the electron particle wave amplitude takes the form of spheres and dumbells. But spheres and dumbells are not strings.

Where am I going wrong?

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Ray Munroe wrote on Mar. 18, 2009 @ 17:21 GMT
Dear Lois,

Metaron's cube is interesting, but these lattices, Lisi's E8 and my E12, are much more complicated.

Regarding "Sacred Geometry", I think it is a human characteristic to find significance in coincidences, regardless of that person's Spirituality or Religion.

In the Sciences, too much talk about Design relegates your ideas to the category of "Pseudoscience". This is part of why scientists are avoiding String Theory - because 10^500 parameters can be interpreted as Design, and therefore pseudoscience. On the contrary, I think that the number 10^500 is related to Dirac's Large Number of 10^40, and we need a large number of hidden variables to properly define the gravitational coupling constant.

Is that "pseudoscientific design", or the greatest of coincidences?

Sincerely, Ray Munroe

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Jason Wolfe/ wrote on Mar. 21, 2009 @ 18:26 GMT
If it we'ren't for sacred geometry, meditation, and the creativity of the crackpots/mystics/psychics (seers), humanity would still be swinging from the trees, dodging tigers and peeling bananas. I think that mystical experience inspires people to think outside of the box. It is the UFO enthusiasts and the psychic hotline people who disturb our rigid belief systems enough until someone decides to look more closely at it and discovers a new facet of Truth. We need these people; unless you like just hanging around eating bananas and dodging tigers.

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Steven Kayser wrote on May. 15, 2009 @ 19:58 GMT
I am searching for Garret Lisi to discuss his theory.

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jr wrote on Jun. 2, 2009 @ 19:37 GMT

does E8 shed any light on why space is three dimensional ?

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jr wrote on Jun. 4, 2009 @ 17:06 GMT
Garrett -

Baez says that E8 comes from OxO

but since O has 480 distinct multiplication tables

is there a separate one for each - or does it relate

different octonions ?

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re castel wrote on Oct. 10, 2009 @ 12:12 GMT

I am not adept at these very advanced maths - blame my aberrant schooling. I envy your skill in the advanced maths.

Now, I understand the idea of a "principal bundle" in terms of kinematic constructs, with each particle field represented by a resolved tensor vector, and thus the bundle would be a group of particle fields (with each field represented by a resolved tensor vector). And my understanding is that a "group dance" corresponds to the interactions of all the particle field tensors in the group. My understanding is that our knowledge of the particle field tensors that have already been 'measured' allows the prediction of the existence of unknown particles on account of the force/vector discrepancies in a given group.

My question is:

Do you see a hierarchy of the particle field tensors in terms of what pf tensors initiate the twists and what pf tensors dominate a given group? Or, do you arbitrarily assign what pf tensor initiates a twist?

To give you a little background of where I come from - I have been working on my version of the theory of kinematic relativity. And I believe I am thus far still just scratching at the surface of the theory of kinematic relativity. My theory of kinematic relativity describes motion transformations within a 3-d space 'dimension' and absolute duration transformation along a 1-d time 'dimension'. I use the idea of a kinematic continuum as the matrix of the physical transformations (i.e., the obervable phenomena), which is why I have the idea of kinematic (i.e., kinetic or motion) constructs examined using a pure 'vectorial analysis' approach instead of the prevalent (mixed-up) 'dimensional analysis' approach.

Both my logical language and my mathematical language can be considered unconventional. But I hope you won't mind so much.

Kind regards...

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re castel wrote on Oct. 10, 2009 @ 12:45 GMT

When I hear a reference to multiple 'dimensions' I understand it as a reference to multiple vectors of motion. Thus, to me a multi-dimensional object would be an object described using multiple motion vectors. I do not consider the time 'vector' a vector of motion; rather, I consider it as an independent vector of duration.

Again, kind regards.

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Geoffrey Dixon wrote on Oct. 31, 2009 @ 09:29 GMT
To jr

There are 480 renumberings of the octonion multiplication table. It's the same algebra for each renumbering. They're just symbols, an interface between the human mind and mathematics. I could use any collection of 8 symbols, or even let the symbols vary over time. Still the same algebra.

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Anonymous wrote on Jan. 5, 2010 @ 23:50 GMT
As I watched Einstein's Big Idea, a PBS film based on the Book E=mc2 by David Bodanis, I was stuck by the beauty of the universe and thankful for the sole constant in the world's most famous equation - God. The following are my reflections on Albert Einstein's greatest discovery.

Physicists and a host of other scientists understand and believe E=mc2 represents a blue print of creation and...

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gs wrote on Mar. 20, 2010 @ 08:03 GMT
can I have the multiplication table in computer readable form ?

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Rodney Bartlett wrote on Jan. 12, 2011 @ 13:23 GMT
Science Out Of The Straitjacket: Rethinking General Relativity, E=mc2 … and String Theory

I saw a video today (“Hidden Dimensions: Exploring Hyperspace” - in which it was stated that mathematicians are free to imagine anything while physicists work in a very different environment constrained by experiment, and that the American...

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forex brokers reviews wrote on May. 28, 2011 @ 16:25 GMT
This web site is really a walk-through for all of the info you wanted about this and didn’t know who to ask. Glimpse here, and you’ll definitely discover it.

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Wilhelmus de Wilde wrote on Jul. 18, 2011 @ 15:29 GMT
I don't know what is happening here, but all these kind of the last posts are in my opinion inappropriate, we are discussing an intelligent theory and all of a sudden all kind of nono's interfere, I feel ashamed for Garrett Lisi.



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refrigerator repair wrote on Sep. 25, 2011 @ 15:05 GMT
Just killing some in between class time on Digg and I discovered your article . Not usually what I choose to read about, but it was absolutely price my time. Thanks.

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appliance repair Aliso Viejo wrote on Oct. 3, 2011 @ 11:16 GMT
You got a very great website, Glad I noticed it through yahoo.

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Geoffrey Dixon wrote on Oct. 8, 2011 @ 18:23 GMT
Blatant self-promotion for any interested in my previous work on division algebras and physics - I've put together a new volume (Division Algebras, Lattices, Physics, Windmill Tilting) that can be ordered from Amazon at

Much of the material is relevant to much of what has been discussed here. I do not know if this can be order from overseas. If anyone tries and fails, please let me know. Cheers, Geoffrey Dixon

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Garrett replied on Oct. 16, 2011 @ 21:29 GMT
Hey Geoffrey,

Looks good -- I'd be interested to have a look at it. Would be especially good if you could email me a copy, as I try to avoid paper.

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Geoffrey Dixon replied on Oct. 21, 2011 @ 14:27 GMT
Hi Garrett

I will ultimately (by year's end) put a link to a downloadable pdf version at, but for the nonce I'm going to leave it as is. It's worth the cost for the cover alone (smiley face). Waste high here today - must suit up.

Cheers, Geoffrey

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Alice lewis wrote on Mar. 21, 2014 @ 08:17 GMT
I think about the extent of the vitality circle that need to exist, and the time it need to exist, to handle an electromagnetic yield with a wavelength of 21.1 cm; that is a tremendous wavelength in examination to the span of the particle. Maybe a mathematician could focus exactly what number components of the E8 lattice might be required to process a vitality circle that will help the era of the 21.1 cm wavelength. Remember that a half or quarter wavelength "vitality structure" can produce a full wavelength if the vitality circle has the best possible properties.

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Brooke Davis wrote on Jan. 17, 2017 @ 12:40 GMT

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Luke Kenneth Casson Leighton wrote on Mar. 6, 2017 @ 12:18 GMT
antony, hi,

veery interesting to see your insights. did you notice the similarity in layout of the main quarks to the phase map diagram on wikipedia which puts charge against mixing angle? there's a direct one-to-one mapping.

i would be interested to discuss this with you further in the context of the model that i'm developing, where i also come up with the exact same map.


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Luke Kenneth Casson Leighton replied on Mar. 6, 2017 @ 12:19 GMT

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