To Ray and others who like geometry,

I just wanted to point out that the idea presented in my essay has a geometrical basis in tetrahedral geometry too. If matter, energy, space, and time are the vertices of a tetrahedron, then space-time and matter-energy are edges that are separated by other edges, and rotated by 90 degrees from each other. They never touch, and their relationship to each other is established by the remaining links.

Pretty cool, huh?

All the Best,

Jonathan

Dear Jonathan,

I see your point. Rather than calling the tetrahedral vertices (red, green, blue, white), we could call them (matter, energy, space, time). The vectors that connect these vertices define an SO(3,1)xSO(3,1) 12-plet of operators including: matter-anti-energy, matter-anti-space, matter-anti-time, energy-anti-matter, energy-anti-space, energy-anti-time, space-anti-matter, space-anti-energy, space-anti-time, time-anti-matter, time-anti-energy, and time-anti-space. The edges would be exactly your six fundamental combinations: matter-energy, matter-space, matter-time, energy-space, energy-time, space-time.

Have Fun!

Ray Munroe

Dear Jonathan,

"the map is not the territory."

Maybe, I am wrong when I try to illustrate this as follows and go on claiming that some very basics of physics possibly deserve correction?

models of past processes ----- predicted or planned future processes (abstract)

real processes ---------- Now

I would like to point out that physics so far ignores that models must never be equated with reality. Future processes cannot be observed.

Do you agree?

Regards,

Eckard, 527

Hello Eckard,

Yes; you are absolutely right. It goes to the very core or basis, when one examines the hidden assumptions. It is basic or foundational in Physics to consider the issue of when it is reasonable to work from a model, and when one has crossed the line and mistaken the model for reality. To an extent; the program or method of Science is ruled by meta-programs, which are a basic reality of how we think. But if we can recognize when we are using abstraction as a tool, and how many levels of abstraction we have in play, it is a useful way to gain understanding.

Thanks for taking the time to read and comment. I shall attempt to do the same for you, in the brief time left.

All the Best,

Jonathan

I am not sure about Ray's interpretation of this with anti-energy and so forth. The polytopes hold spinors or quaternions (or quivers thereof) and these root space just defines the eigen-spinors.

Cheers LC

Thanks Lawrence,

I think I agree. Ray's exuberance and your cautionary remarks are noted. Best not to assert more than is appropriate, but it is nice to expand on the possibilities offered by the framework.

I'm glad my comment got a response from both of you, as your remarks are helpful to my understanding. And the contrast between them is useful too.

All the Best,

Jonathan

Dear Jonathan and Lawrence,

Please refer to Tables 7 and 10 of the (as yet unpublished) paper posted below. If it is proper to define the tetrahedral vertices as (matter, energy, space, time) rather than (red, green, blue, white), then the vectors I defined above fall out of the mathematics quite naturally. The wierd part here is that some of these quantities look like vectors (space and matter?), and some look like scalars (time and energy). Do they really belong to the same tetrahedron or not? Perhaps they belong to a tetrahedron that has collapsed (into the C3 and C'8 of Figure 3 and Table 5). After all, most of my K12' lattice has collapsed due to broken symmetries.

Have Fun!

Ray MunroeAttachment #1: 1_A_Case_Study_3.3.pdf

Dear Jonathan,

(1) Congratulations on achieving a high score from the community. Hope you win big money.

(2) If it's a broader framework that you seek, then I wish to point out that B. Kostant in an homage to E. Cartan in 1984 pointed out how the 3 binary polyhedral groups have an amazing connection to group theory in all orders and to all the rest of mathematics. This initial discrete group framework is therefore all inclusive to a great extent!

(3) Therefore, if one wants to discover the rules of the Universe and the limits to physics, I would think that these groups are a good starting place in the quest for that knowledge.

(4) By the way, these are the 3 groups I use for the lepton families, with their 4-D extensions for the quarks. Only the appearance of the b' quark will reveal how good or bad this starting point has been!

Frank Potter

Thank You Frank Potter,

It is good to place high in a field of such able contenders, but for me the best part of it has to be that it greatly increases the chances I will make some lasting contribution, which advances Physics or Science in general. I am decidedly more a philosopher than some of the able scientists who wrote essays for this contest, and my essay is considerably less technical than many, but it does offer some insights which might otherwise be overlooked. Being a generalist or synthesist rather than a specialist, I can focus on how similar patterns arise in a variety of contexts, and sometimes I get to see the 'big picture' which would be missed by others. I guess that's valued here.

Point #2 is way cool, and will have to be examined in great detail. Probably again and again, until all the detail is assimilated. I will examine Kostant's work as soon as I can.

I think using group theory of the 3 binary polyhedral groups as a window into the universal order is likely to be an interesting journey of discovery for me. But the b' quark may not appear. However, if it does - you will have predicted it as arising from the beauty of the Math. And that's pretty cool.

All the Best,

Jonathan

Thanks again Ray,

I skimmed through your longer paper, and it looks very interesting. I'm sure it will take a little while to digest. It looks like Lawrence was technically correct in his comment above, as you were speaking in your comment about the reference (to matter, energy, space, and time) as extended to the dual tetrahedron (3-simplex) you spoke of in that paper. Way cool analogy though.

I am enjoying this discussion greatly. And I'll look forward to seeing how the different TOEs compare after processing the info in your paper.

All the Best,

Jonathan

Dear Jonathan,

I think you misunderstood me. Consider a tetrahedron with four different colored "quarks" at the vertices: (red, green, blue, white). We may change the colors of these quarks with translation vectors (or rotation matrices). Suppose we wanted to change a red quark into a green quark. We would need to operate on that red quark with a green-anti-red gluon (translation vector). The anti-red part of the gluon color eliminates the red quark color, and then the green part of the gluon color gives the quark a net green color. This combination of color-anti-color distinguishes this gluon from the reverse translation of red-anti-green, which would convert a green quark into a red quark.

The tetrahedral symmetry group has 24 component symmetries that may correspond to an SU(5) Georgi-Glashow GUT. Weird stuff like green-anti-red happens at this tetrahedron level, not at the nested dual tetrahedron level. If you add in the nested dual tetrahedron of anti-quarks with anti-colors: (cyan=anti-red, magenta=anti-green, yellow=anti-blue, anti-white) then you assemble a cube, which has an octahedral symmetry. The octahedral symmetry group has 48 component symmetries that may correspond to an SU(7) GUT - twice as complicated as the tetrahedral group.

Realistically, this is more complicated than your model needs. You only need the six edges of the tetrahedron to make your point.

Have Fun!

Ray Munroe

Hello once more,

OK Ray! It looks like you were right all along. I guess skimming your paper after reading your comment and Lawrence's cautionary remark was not quite enough to discern the subtleties involved. Yes; one tetrahedron should be enough and contains all the symmetries you spoke of. My problem is distraction with other things, at this point.

There's a lot of weirdness here now, as my Dad is in the hospital since Thursday with pneumonia, and I'm trying to take care of extra stuff (making sure his important matters don't fall through the cracks). At this juncture I'm still preparing for FFP10 (for which I depart on the 21st), but I may have to stay home if things get worse. Obviously; I'm hoping everything will be OK by then.

All the Best,

Jonathan

Dear Jonathan,

I understand. We all have busy lives. My wife was in the hospital for three nights last month with Lupus-related pleurisy (also lungs, but not contagious),and our daughter had the flu last week. It really hasn't even gotten cold here in Florida yet. Take care of your dad and yourself. I hope all goes better for you.

Sincerely,

Ray Munroe

Hello ,

dear friends ,here is a very good solution for the health in this global system and its parametrs of mutation .

The plants have many properties to fight naturaly ,you buy in a good shop ,a little of salvia officinalis ,a little of Rosmarinus officinalis ,a little of thymus officinalis .The aim is simple ,1 blade of each ,in infusion(2 min in boiling water) ,3/day after eating during 3 weeks .(it is antiseptic ,antibiotic,antispasmodic,diuretic,bactericid ,fongicid,hormonal balance...)

It is a very good natural solution.You add that with an add of oligo elements and mineral salts to dynamize your intrinsic system .With propolis,and honney ,more pollen ,it is very good for the health .For the propolis it is better to buy the natural state ,thus like a masticating matter .Of course more fruits and vegetables ,better without cooking ,they are more essentials .

Take care

Steve

Thank you Ray,

I appreciate the understanding about my Dad's health concerns, and info on your recent life challenges. I hope that the complications of your mundane existence will still allow you to continue your pursuit of answers in Science.

My Dad came home yesterday, and I have just enough time to finish preparing for my trip to Australia for FFP10. Things are often crazy around here, but it's good to have friends on this forum who share my concerns and hope we can all make some good progress in Physics. At least the folks visiting this page all appear to know some changes and progress are needed, for us to address the questions that remain to be answered.

All the Best,

Jonathan

Dear Jonathan,

I'm glad for you and your dad. Good luck in Australia!

Life can be mundane at times. That isn't always a bad thing. Physics is my hobby, not my job. I find inspiration at the strangest times and places. But one good weekend of ideas - some scribbles on a napkin or scrap of paper - can often best an entire month of dedicated work.

Have Fun!

Ray Munroe

Thanks so much Ray,

I appreciate the thoughtfulness and look forward to an interesting journey.

Having mundane affairs to balance out the extraordinary can be liberating sometimes, as it gives you something familiar and/or stable to help keep an even keel. But I've been putting off the extraordinary for too long. However, the wild and crazy world of theoretical Physics is a very demanding pursuit. Not for the weak of heart, nor the feeble wit. Even knowing the answers is not enough, when the real trick is to be able to represent your best ideas in a good light. Perhaps the practice I've had here on the forum pages, talking about my own and others' essays, will serve me well in Perth.

All the Best,

Jonathan