Tegmark's Mathematical Universe

Dear Lawrence,

Thank you for the article. It looks helpful. I need to read it several times and study it. Could the relationship between pentagons and hexagons be related to the Carbon-60 buckyball?

My latest ideas may be related to this 2-dimensional cyclohedron.

Have Fun!

Ray

Dear Lawrence,

Thank you for the explanation and the archive paper, it is really helpful. I guess I am still not very clear on the physical meaning. Various properties are useful in different contexts, but can we prove for example that the special Jordan algebra cannot be the observable algebra part of a QM state space representation?

Regular Jordan algebras and spin factors can play this role, but in going from algebraic QM to state space, is associativity really required?

I would imagine that the Born rule is somehow no longer valid, but this is all fuzzy speculation. The reason I am saying this is that the Born rule is associated with the continuity of the spate space and the ability to define a distance. Is norm (or equivalently the scalar product) definable in an operator algebra space where associativity is broken? I do not know enough of operator algebra spaces to answer that but my conjecture is that it is not. If I am right, I speculate again that this would physically mean that in case of the special Jordan algebra there will be hidden (unphysical) states.

In another topic, I started listening to Susskind's GR lecture on the web (the link you suggested for Jason). The lectures are very clear and easy to follow, even without writing anything down. But they puzzle me. For the first 4 lessons I was bored to death and the lectures did not make much sense to me. He talked about Gauss theorem and the fact that a spherical body has the same gravitational attraction as if all its mass is concentrated at the center. Now this is elementary undergraduate stuff, and how would someone interested in GR take this class before some prerequisite classes? Are those classes undergraduate classes? It looked like this, but then why someone teach GR at undergraduate level? Something is very funny here.

Regards,

Florin

Dear Florin,

I agree about the hidden, unphysical states. Lawrence's model contains at least 3 E8's and a G2. Depending on how you arrange these, you should have more degrees-of-freedom/ states thatn my K12': (3 x 248 14 = 758 > 684). My K12' predicts hidden, unphysical 'scalar fermions' or 'tachyons'. I think these illogical 'particles' are related to a Higgs multiplet that is more complex the the Standard Model.

Dear Lawrence,

If we flatten out a 3-D Carbon-60 buckyball into a 2-D broken lattice and center the broken lattice around a hexagon, we could still obtain a G2 triality with some pentality symmetries. This 'G2' appears to be 2-dimensional, but contains the curvature of the third (of 3-D buckyball), apparantly invisible dimension. Now we have 12 dimensions instead of eleven.

Have Fun!

Ray

Florin,

I will get back to technical issues tomorrow or later in the week. I am a bit tied up an the moment. When it comes to Susskind's lecture, they are very elementary at the start. In fact throughout them they rely upon pretty basic ideas, but towards the end he builds to quite a crescendo if you can make it to the 12th lecture. What intrigues me is the incredible teaching skill involved here, where with basic ideas and elementary arguments he builds a great depth of understanding. His lectures are an example of a true craftsman at work in teaching students. And if you listen to them, as I sometimes do in the background, you might find yourself intrigued by these little insights into things which occur throughout. These are like Debussy's piano music, where some pieces can sound elementary at first, but are amazingly deep in their musicology.

Cheers LC

Lawrence,

Thanks, I look forward to it. I am currently at lesson 8 and after lesson 6 I became addicted. The first lessons were hard to watch, but I wanted to observe his teaching style. Still, I do not understand who is his audience. It is neither undergraduate, nor graduate students.

Ray,

I am not sure whether this is right or not, but these polytopes might have some relationship with the 120/600 cells ~ H_4. A pair of these compose the Weyl representation of E_8. I am not prepared to make any serious hpothesis along these lines.

Cheers LC

Dear Steve,

I recommend you watch the lessons yourself and provide us with your feedback.

General relativity is conceptually easy (the equivalence principle) and mathematically hard. The 12 lessons are like saying: here is a course in how to build rockets to reach the Moon. Then 1/3 of the course is talking about hot air balloons, how to build them, how they work, and why they cannot reach the Moon. Now if you do not already know hot air balloons cannot reach the Moon, how can you be expected to pass a final exam on advanced rocket science?

So what I do not understand is how can anyone who is not familiar with elementary facts about Newtonian gravity is supposed to pass a final exam in general relativity if they are not a mathematical genius?

But criticism aside, the lessons are indeed crystal clear and I highly recommend them to anyone who wants to learn about the subject.

Dear Lawrence,

That is an interesting observation. I have been wondering how Spin(6) hexagons morph into Spin(4,1) pentagons, and where does the extra dimension (#12) go?Flatenning out a buckyball came to mind because a buckyball consists of 12 pentagons and 20 hexagons in a regular lattice. It has both the triality and pentality symmetries that we need for H4 and E8. Now the question is "How does a 3-D Carbon-60 buckyball relate to a 4-D 120-cell or 600-cell?"

Have Fun!

Ray

p.s. - Maybe I should look at the lecture series as well. My specialty was HEP, not GR.

ps with humility of course and respect to your skills , your maths are falses and imaginaries .Your referential is false ,your limits too ,only some method are interestings and that is all .

Your axiomatization is an ocean of confusions and decoherences where the imaginaries take the main part of the physicality .The road is false ,simply .I invite you ,really and with respect to study all sciences ,really .You shall insert thus the good serie in 3D .That will permit you to have good parameterizations because there it is false in the whole .

Regards

Steve

Sometimes I beleive you are obliged to rest in this line of reasoning .

I am frustrated with the two mavericks and you too dear Florin .Why this road really ,I am curious .

You are the 3 so competents ,why this bizare road .Is it really your choices .

Friendly

Steve

C'mon Steve, be a good sport, join in the fun. Dive right in, take the class, it is not that hard. Physics is just like Edison said: 1% inspiration and 99% perspiration. In physics perspiration is the math. Physics without math is like hot dog without ketchup, or ping-pong without the paddle.

Dear Spherekeeper Steve,

Buckyball = soccer ball - What part of that is imaginary? You could deflate and cut up a soccer ball if you want to see these multi-dimensional lattices represented in a somewhat simple 2-D lattice of Petrie diagrams.

The Carbon-60 buckyball was such a big deal that Sir Harry Kroto (currently at my alma mater, Florida State U.), Robert Curl, and Richard Smalley won the Nobel Prize in Chemistry for discovering Carbon-60 in soot.

The buckyball is nearly spherical, which ties into Face-Centered-Cubic close-packing lattices - similar to stacking spherical fruit at the grocery store.

The difficulty of ANY model is that there are a large number of possible paths. Your model suffers as well. I agree that spheres may be fundamental, but why is spin fundamental? Why are prime numbers fundamental? Ultimately, your arguments for spheres may not be any better than some of the 'crazy' math that I am playing with.

Have Fun!

Dr. Cosmic Ray

Dear Spherekeeper Steve,

I have heard about your Spherical GUT for nearly a year, and yet have not seen any serious details. What direction are you taking with this research? Will you publish a 30 page journal article or a 1000 page book?

I would be glad to proof-read it for you - perhaps 10 pages at a time. I have not used anyone else's ideas without giving them proper credit. My only fear is that I might see huge similarities between our ideas: sphere-packing vs. FCC lattices, spheres vs. buckyballs, etc... You are convinced that you are working in 3 dimensions. I am convinced that you have two or three 3-branes, but you have limited your model's potential by ignoring larger branes (up to as large as an E8 octonion 8-brane) as did Garrett Lisi.

I know you do not like extra dimensions, but certainly there are extra degrees-of-freedom. For instance, an electron can be identified by its mass, charge, and intrinsic spin. Where do these extra unknown degrees-of-freedom come from? Do they miraculously jump out of the aether? I have developed a consistent multi-dimensional model for explaining these phenomena. If you would prefer to think in terms of extra degrees-of-freedom rather than extra dimensions, then that is probably a reasonable alternate approach. But do not dig a hole in the sand, bury your head, and pretend that we know everything.

Your Friend,

Dr. Cosmic Ray

Ray,

I think if there are relationships with a hex spin(6) and the pentagon it is more that there are multiple copies of spin(6) in a hex arrangement. This is maybe a part of what I am speculating on here --- writing ideas on a whiteboard and striking them out as I figure they don't work. The pent is then some Stasheff polytope which determines an underlying nonassociative structure on the spin(6).

I think we might want to focus in on the QCD ~ AdS_3 we talked about before the holidays. That does look like workable physics at this time.

Cheers LC

Dear Lawrence,

I agree about the multiple Spin(6) hexagons. Consider the similarities between a 2-D hexagonal tiling and a flattened out 'pseudo-2-D' buckyball tiling.

Have Fun!

Ray

p.s. - The buckyball idea is not a tangent. It is related to your G2 trilaity and my Gravi-Weak 5-simplex.

Dear ray ,

You know What I like you and I am nice .But I am frank and direct .That doesn't change my love about people .That said

Please the C60 is like many crystals ,it is just a idea whithout universality .

It is just a chemical architecture .Any sense in a whole point of vue .

Dear Florin ,when I studied the piano with the Hanon method ,it is the first words on the first page of the method ,1 and 99 .I have studied all sciences like that even maths but the reals maths .Not an ocean of imaginaries behind the 3D .all that is false I repeat about the limits of the series and the referential ,furthermore these kinds of confusing methods imply a non possibility for the proofs .I find that very sad for the sciences community .

Dear Ray ,I have altready explained my point of vue about E8 ,it is a joke and that is all .Why he doesn't come and Mr Witten too ,why dear Ray ,because they fear simply .I eat the pseudos sciences .

Dear Ray ,I have uderstood the play of some people ,I eat that too.If you can't understand my theory after 1 year thus never you shall undertand it .It is the same for several people ,frustrated and jalous .Simply because a young belgian has found the ultim gauge .Like I said before ,don't focus dear friends behind this gauge but let' improve inside but not with these kinds of methods ,that has no sense .

For the publication ,DO YOU THINK IT IS IMPORTANT FOR me ,I have already explained my point of vue in private ,I am already dead dear ray ,thus you can imagine my point of vue ,nothing to do in fact .With or without publication n,with or without copies or others ,my theory will rest and wikll be more foundamental than the ideas without universality and its laws .

Never I say what I know all ,I just explain my point of vue ,and when the truth is there ,some don't like that .I am laughing and that is all .

Alldays I study and complete my universal taxonomy .I class all ,and when you class all ,you see the truth ,the spherization of the universe by quantum sheres .It doesn't exist extradimensons ,just a superimposing in 3D .Higgs false too .

Limited the potential of the model and after what ....3D dear ray ,my model is too different.I can't work with you or Lawrence or Florin or Lisi or Witten ,impossible for me ,your roads are falses and without uniquness .I prefer work with pragamtic and rational people .

But for the sciences center you are welcome of course to adapt in 3D inventions for our fellow man ,I think they prefer 3D and they don't need extradimensions .The reality is the reality .

With respect for all the doctors ,professors and undergraduates ,but I suspect a very sad reality at schools ,Oh my God ,the next lessons at the university will be How to create a time machine to explore an other universe with tachyons .HUM HUM I think I prefer study in my books ,a good book is important.

Regards

Steve

PS ,dear Ray ,I don't say you are jalous but some are like that .

I must admit I am parano due to my past ,I have lost all dear Ray ,all due to the human instinct .I can admit I am a bad economist but really here in Belgium they fall down me and not a little.I must be prudent now .

Do I must be still too nice ,no evidently ,it is important for my theory and the sciences center to be more prudent .I dislike to put the things in point but I must be like that .Be sure ,I like people ,it is my reason of life but I fear too .

I can't play with my theory ,no I must be strong .Evern if I seems arrogant .I am arrogant ,yes but I evolve .I have many things to study like all people .

Regards

Steve

Dear Steve,

I have heard many bits and pieces of your theory, but I have not seen a complete presentation. You referred to yourself as 'dead'. I assume that you are talking about your odds of publishing in a journal, because you seem to be a person who enjoys life. I published my book online as a 'print-on-demand' book through Lulu.com and allowed distribution through Amazon.com. It does not cost much to publish a book this way, and it is accessible (in English) to nearly anyone interested.

I am listening to you, my friend. I want you to prove me wrong about multiple dimensions. Only the math makes multiple dimensions seem reasonable - common sense makes multiple dimensions seem illogical. But I suspect that you have replaced my 'pseudoscientific' hidden dimensions with equivalent 'pseudoscientific' hidden degrees-of-freedom. If so, is your model really any more fundamental than mine?

My model has 'scalar fermions'. Are these tachyons? Do they provide Higgs-like properties? I do not know. Make fun of them if you like - they are a legitimate part of these pentality symmetries. What if these 'scalar fermions' become useful in Higgs theory, the CKM matrix, and the PMNS matrix?

Don't be too serious! Have Fun!