Pieces of E8

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

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,

pagsure mo oie!!!!

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!Attachment #1: Excerpt_on_GUTTOE_from_B.S.Day.docAttachment #2: 1_Excerpt_on_GUTTOE_from_B.S.Day.doc

Garrett ... I emailed you a couple of months ago regarding a strange coincidence I noticed

Most everything

in your paper here -

http://arxiv.org/PS_cache/arxiv/pdf/0711/0711.0770v1.pdf

goes 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."

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

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?

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 www.Lulu.com - 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

Ray,

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 existence are perceived as sacred because in contemplating them one is contemplating the origin of all things. By studying the nature of these forms and their relationship to each other, one may seek to gain insight into the scientific, philosophical, psychological, aesthetic and mystical laws of the universe." It would indeed make sense that this e-8 lattice be described as "beautiful." The "contemplating the origin of all things" bit really makes me wonder, because this geometric display truly would describe the nature of all things, which are really the confluence of forces described in the lattice.

Much of this reminds me a of a quote I once heard from an interview with Clifford Pickover

Pickover: Mathematics and mysticism have fascinated humanity since the dawn of civilization. Has humanity's long-term fascination with mathematics arisen because the universe is constructed from a mathematical fabric? Is God a mathematician? Certainly, the world, the universe, and nature can be reliably understood using mathematics. Nature is mathematics. In THE LOOM OF GOD, I take the position that nature is almost always describable by simple formulas not because we have invented mathematics to do so but because of some hidden mathematical aspect of nature itself. I do not know if God is a mathematician, but mathematics is the loom upon which God weaves the fabric of the universe.

I'm more of an agnostic, but can definitely understand where he is coming from here.

I would also check out the following perhaps for some more inspiration...

The "Fruit of Life" symbol is composed of 13 circles taken from the design of the Flower of Life. The Fruit of Life is said to be the blueprint of the universe, containing the basis for the design of every atom, molecular structure, life form, and everything in existence. It contains the geometric basis for the delineation of Metatron's Cube, which brings forth the platonic solids.

The Fruit of Life pattern contains the basis for the layout of Metatron's Cube. The Fruit of Life has thirteen circles. If each circle's centre is considered a "node", and each node is connected to each other node with a single line, a total of seventy-eight lines are created, forming a type of cube. Within this cube, many other shapes can be found, including two-dimensionally flattened versions of the five platonic solids. However, as can been seen by the illustrations below, the points of intersection in a flattened Dodecahedron don't conform to the nodes of the circles, and thus the shape doesn't conform to Metatron's cube as the other shapes do. This is because the Dodecahedron is formed by rotating the overall cube, which is a 3-dimensional object. By dividing the sides using the Golden Ratio, one can draw in the lines needed to form the Dodecahedron on the 2-dimensional cube.

http://en.wikipedia.org/wiki/Flower_of_Life#Tree_of_Life

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

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.

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.

Why?

Lois J. Wetzel

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?

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

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.

I am searching for Garret Lisi to discuss his theory.

stevenkayser@simplysurf.ca

Garrett

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

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 ?

Garrett,

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...

Garrett,

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.

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.