Digital picture of the Universe by Yuri Benjamin Danoyan

The ratio 3:1 is not surprising me, and no simple ratio would surprise me.

Note that from 3:1 you have also 1:3 and thus why not 1-1:3=2:3, then 3:2, or 1:(1+3)=1:4, etc.

I am quite sure that most physical phenomena exhibits simple ratios.

Since the physicists have modeled many physical phenomena, then most simple ratios should be many times encountered. Cenverting them so that the 3:1 appears is just an exercise which should be frequently successful.

Would a ratio of two big integers (without common divisors) surprise you ?

Probably they would be more surprising than simple ratios, and in this case, all ratios would be surprising, discarding their value.

To summarize, I cannot deduce anything informative from the ratio 3:1

Regarding the difference between static and dynamic symmetry and the diffrence between discrete and continuous symmetry, I would say that they are rather artificial.

An unifying definition of symmetry, such as the one I publihed in 2007 (pdf downloadable from http://petitjeanmichel.free.f/itoweb.petitjean.symmetry.html) should cover all these situations, so that the concept of metasymmetry does not appear to me as being necessary.

Of course, I would be delighted if you can exhibit a symmetry situation for which you prove that it cannot be covered from the general definition. But in this case, you must also state why it is anyway a symmetry situation, thus refering to an other definition of symmetry (please cite it rigorously, not intuitively).

All my best,

Michel Petitjean.

Oh dear, a miscommunication effect, I should have put a link to Mr Levin's essay, click here.

Alan

Hi ,

What is interesting is the first division, 1 2 3 or 1 3?

If we consider the ultim fractal....

Regards

Steve

Yes, for me doesn't matter 3:1 or 1:3,because you can read from left to right or right to left.

I am agree that most physical phenomena exhibits simple ratios.

You cannot deduce anything informative from the ratio 3:1.

I never see before such rich collection (as my) ratio 3:1 , concerning fundamental questions, before.

I try to understand where are roots this phenomenon.

It seems to me, It is in nature bosons & fermions and their interactions.

It seems to me, we havn't full understanding nature of "spin"

Here I see big difference between my metasymmetry idea and supersymmetry idea.

I think not such important baryon asymmetry problem,as a fermion asymmetry problem.

1,3,12 interesting for me, because the rotational symmetry groups of the tetrahedron - 12.

I don't think that simple ratios exhausted own potentialities.

and +2 x4...the polyhedrization spherization seems under a specific serie of fractalization of the main spherical volume.Now a kind of metosis meiosis is important for a specific distribution of volumes.After it's the gravity and its codes which form by spheres and its properties with polyhedrons.4/3piR³...if the numbers of a and s are harmonized with the 4 forces we see the different forms in evolution of mass.That's why the only possiblity is the sphere which gives all others forms by deformation of spherical volumes.If now the canonicl equations are inserted x²/a²+y²/b²+z²/c²=1.....all that is fascinating even for the hyperboloids correlated with the evolution...the spherization appears naturally.The center is so so so important and its volumes also, this system is quantically and universally linked.

Best Regards

Steve

The computing or our realism,of course when we create a picture, it is diferent than our objectivity.But the laws are the laws after all.It's the most important.

spin.....rotating spheres! proportional with mass.

Now...ratio.....bose einstein expression and Fermidirac expression with a stirling aproximation and lagrange of course.....and the rotations appear as a beautiful oscillations.....as a partition function.....if the real number is inserted and the volumes from the main central particle(sphere of course)...and the serie is HOW....IF THE VOLUMES IN AN EUCLIDIAN SYSTEM ARE INSERTED WITH THEIR PURE FRACTAL and their rotations spinals and orbitals.the sortings are easier.

Steve

In the russian magazine "Химия И жизнь", 1982г, №9, стр40 have been printed my note " Geometry of Microcosmos". It has been shown formal analogy between properties non-Euclidian geometries on the one hand, and properties of fermions and bosons on the other hand.

I have sent copies of notes to Professors Lev Okun, Yakov Zeldovich, and subsequently to Professor Vitaly Ginzburg with the request to express the opinion.

Here their short answers:

Lev Okun "Your analogy "Fermi-Riemann, Bose-Lobachevsky is original, but whether there is in this comparison any sense, i don't know."

Yakov Zeldovich "I think that according to the theory of a relativity curvature depends from... (Roughly-density of energy) and character of particles doesn't feel."

Vitaly Ginzburg "I join opinions of Zeldovich and Okun.

Yuri,

I am not sure why but I find the question you are posing tantilizing. It has been keeping me pondering while painting. Upon reading your essay as opposed to glancing through the document you refered to me I have come to realize that the 3 you are talking about isn't the 3 degree gap in the vectors of time I was referring you to. However, understanding the geometric structure of the tetrhedrons that define the space that the quantum phenomena you are observing is critical if you are going to apply them consistently to come up with an answer to the question in your essay.

In a nutshell,the tetrahedrons and triangles that are formed are not necessarily equilateral. Point connections between the three time vectors is perpindicular, while point connection angles on the plane are not. When you look at your different ratios you need to be consistent in how you are characterizing the layout of the four points of the tetrhedron. My recommendation to you is if you are looking at half of something, relate it to pi. If you are looking at something in balance, relate it to 2 pi. If you are looking at something relative to the observer, relate it to 3 pi. When you do that all angles will become some multiple of either 45 degrees or 30 degrees.

If you do this your question becomes is pi/3 a comprehensive principle of the universe, or is 2pi/3, or is 3pi/3 which leads you to is pi a comprehensive principle. The answer to that is yes. You do not need any verification scientifically for that.

Hi Yuri,

I have also played with broken tetrahedra. In Section 7.2 of my book, I used a tetrahedron of Hyperflavor-Electro-Weak, then I broke the Tetrahedral symmetry with different mass-energy scales.

Have you read Vladimir Tamari's essay? He uses tetrahedra with spinning vertices to try to build a TOE. Coincidentally, Gingras also used tetrahedra with spinning vertices to explain his Magnetic Spin Ice quasi-particle analogy of the Dirac Magnetic Monopole.

These tetrahedral symmetries are important, but I am also working with pentachoral (4-D extension of the tetrahedron) symmetries. This introduces a five-fold "pentality" symmetry (the Petrie diagram of a Pentachoron is a Pentagon/ Pentagram with Golden Ratio component properties) that I think is related to the origin of mass based on Coldea et al's experimental results involving the mass ratios of magnetic quasiparticles near their critical point.

Have Fun!

Dr. Cosmic Ray

Yes, i read Vladimir Tamari essay and Vladimir read my essay

He wrote me: "You need to explain this Logic and how the tetrahedron relates to to 3:1".

My answer to him:

"Best model of Metasymmetry is Tetrahedron, which has 4 faces and each face is a triangle. This means there is 1 closed side and 3 open sides when a tetrahedron comes to rest on a flat surface. 3 vertexes lie in one plane, while the one is not. Аny Tetrahedron can also be proof of the ratio of 3:1.

I call this effect "Logic of Tetrahedron ".

No reaction...

Hi Yuri,

I've played with these symmetries a lot. I think it may have something to do with an SU(4) (15 degrees-of-freedom, dgf's) decomposing into an SU(3)xU(1) (8+1 dgf's) plus 6 hidden (perhaps too massive to condense out of the "vacuum" of our low-energy Universe) degrees-of-freedom. Please check out Section 7.2 of my book. Compare and contrast the SU(4) Hyperflavor tetrahedron from my book with the SU(3) Hypercolour equilateral triangle lattice in my last CS&F article.

Have Fun!

Dr. Cosmic Ray

I think your theory close to Bodo Lampe

http://arxiv.org/find/all/1/all:+AND+bodo+lampe/0/1/0/all/0/1

Have you read his article?

http://arxiv.org/abs/gr-qc/9707010

If you are acknowledging that every point in real or imaginary space has to mathematically take the form of a complex number, then I can state to you that that is absolutely true. You need to keep that in mind when you work with ratios. If you say 1 for example you have to specify... one what?

Hi Yuri,

I just skimmed some of these papers. As usual, I need to review them more closely when I have enough time. On the last page, Barbieri has 6 vectors e_1 through e_6. In my models, each of these 6 vectors represents a boson (and the anti-directional vector represents that boson's anti-particle - here we must treat the photon as a superposition of B_0 and W_0, because anti-photons do not exist). These 12 states may be represented by an SO(4)xSO(4)~Spin(4). If we also include the three basis vectors (the x,y,z in which the tetrahedron exists), then we have the 15 degrees-of-freedom of an SU(4)~SO(6).

Thank you for introducing me to Lampe's papers. I assumed that Lisi's trialty (also see Raymond Aschheim's essay) was good enough to explain the origin of three generations. Lampe is worried about the "spin problem" in his Tetron model. I don't think it should be a "Tetron" - lets call it a "Penton" where the fifth component is a tachyon that introduces the origin of mass (similar to the mass ratios of Coldea et al's magnetic quasi-particles), and requires a new type of spin-statistics (as Lampe suggests, but these tachyons probably behave like anyons on an M2 Black-brane as Lawrence Crowell and I have discussed). In my opinion, Lisi's misunderstanding about this 5-fold "pentality" or "Penton" symmetry was one of the most significant errors in his E8 TOE.

Have Fun!

Just in case

http://motls.blogspot.com/2010/08/why-complex-numbers-are-fundamental-in.html

Dear Yuri,

Yes - Lubos Motl gave me a difficult time about the fact that E8 (and Garrett Lisi's proposed TOE) does not have complex representations.

In graduate school (in the early 1990's - prior to Super Kamiokande's discovery of Neutrino Oscillations), I learned that the TOE must include complex representations. For that reason, I concentrated heavily on the Special Unitary Groups - I especially like SU(5), SU(7), SU(11) and SU(27). Perhaps I am ignorant and never disected that part of TOE theory, but I thought that Super-Kamiokande's implicated discovery of right-handed neutrinos, and a proper representation for right-handed neutrinos within a theory (Lisi's was nearly correct), negated the necessity for complex representations.

I argued with Lubos until it was obvious that he thought I was crazy, but E8xE8*~SO(32). E8 has 240 real roots plus 8 basis vectors. SO(32) has an order of 496 and has complex representations. SU(11) has an order of 120 and has complex representations.

I reason that either:

1) Lisi's E8 TOE (240 roots) is wrong, and should have been based on SU(11)xSU(11) (120 order times two) with complex representations, or

2) Lisi's E8 TOE (248 order) is wrong, and should have been a Supersymmetric E8xE8*~SO(32) (496 order), where our E8 has exclusively real roots, our E8* has exclusively imaginary roots, and the two are "twisted together" (like a "twistor" algebra) into an SO(32) TOE with complex representations.

Lisi's E8 Gosset lattice implies Octonion Algebra. If we twist a real Octonion together with an imaginary Octonion, then we can generate a real Sedenion (where the progression of Clifford division algebra is: Real, Imaginary, Quaternion, Octonion, Sedenion...).

Peter - Imaginary analysis is part of our mathematical game. Certainly, we must eventually observe real numbers when we perform an experiment, but that does not negate the importance of imaginary numbers.

Besides, e^iPi +1=0 really is cool. Where else can you relate three different kinds of oddball concepts (such as e, pi, and i) into a simple equation?

Have Fun!

Dr. Cosmic Ray

Dear Peter,

You said "If you are acknowledging that every point in real or imaginary space has to mathematically take the form of a complex number, then I can state to you that that is absolutely true. You need to keep that in mind when you work with ratios. If you say 1 for example you have to specify... one what?"

I agree that "units" are as important as the mathematics (real and/or imaginary "bits") that we use to measure the "it". I think that Julian Barbour's "Bit from It" essay addressed this idea very well. Barbour's example is: I cannot eat the number "1", unless that number has units of something like "apple".

I realize that I misread your comment, and gave an inappropriate answer earlier (although that answer may have been mostly appropraite for Yuri).

Have Fun!

Dr. Cosmic Ray