Comments on: E8 http://asymptotia.com/2007/03/19/e8/ Fri, 21 Nov 2008 05:56:44 +0000 http://wordpress.org/?v=2.5.1 By: Mary Cole http://asymptotia.com/2007/03/19/e8/#comment-92340 Mary Cole Thu, 22 Nov 2007 10:03:08 +0000 http://asymptotia.com/2007/03/19/e8/#comment-92340 I apologise on Jason's behalf for not reading the above comments with sufficient care. He just enjoys the opportunity to use the word 'bunkum'! I apologise on Jason’s behalf for not reading the above comments with sufficient care. He just enjoys the opportunity to use the word ‘bunkum’!

]]> By: Clifford http://asymptotia.com/2007/03/19/e8/#comment-92217 Clifford Wed, 21 Nov 2007 23:55:45 +0000 http://asymptotia.com/2007/03/19/e8/#comment-92217 Please read the comments directly above. -cvj Please read the comments directly above.

-cvj

]]> By: Mary Cole http://asymptotia.com/2007/03/19/e8/#comment-92190 Mary Cole Wed, 21 Nov 2007 22:27:40 +0000 http://asymptotia.com/2007/03/19/e8/#comment-92190 So - on the subject of E8: is this all bunkum? http://www.telegraph.co.uk/earth/main.jhtml?xml=/earth/2007/11/21/scisurf121.xml Jason Cole (From Mary's account!) So - on the subject of E8: is this all bunkum?

http://www.telegraph.co.uk/earth/main.jhtml?xml=/earth/2007/11/21/scisurf121.xml

Jason Cole (From Mary’s account!)

]]> By: Elliot http://asymptotia.com/2007/03/19/e8/#comment-90571 Elliot Fri, 16 Nov 2007 19:59:50 +0000 http://asymptotia.com/2007/03/19/e8/#comment-90571 Clifford, Thanks for your thoughts. et. Clifford,

Thanks for your thoughts.

et.

]]> By: Clifford http://asymptotia.com/2007/03/19/e8/#comment-90563 Clifford Fri, 16 Nov 2007 19:41:59 +0000 http://asymptotia.com/2007/03/19/e8/#comment-90563 Hi Elliot, I've nothing intelligent to say that has not already been said in (a small subset of) the comment stream of Bee's post over on Backreaction. See Moshe and Aaron's comments, for example. They seem to get at the heart of the matter, and quite clearly present the things that also puzzle me. It looks like a pretty pattern, - not dissimilar to other work in the literature on using E8 to play with the particle spectrum - but that's it so far. You need more than pretty patterns to do physics, as I'm sure Garrett Lisi knows. Perhaps further work might uncover something concrete. I wish Garret Lisi all the best, and encourage him to keep trying (perhaps guided partly by addressing the questions people are asking) and see if he can beat things into shape, just as we're all doing at various stages in our respective research programs. Best, -cvj Hi Elliot,

I’ve nothing intelligent to say that has not already been said in (a small subset of) the comment stream of Bee’s post over on Backreaction. See Moshe and Aaron’s comments, for example. They seem to get at the heart of the matter, and quite clearly present the things that also puzzle me.

It looks like a pretty pattern, - not dissimilar to other work in the literature on using E8 to play with the particle spectrum - but that’s it so far. You need more than pretty patterns to do physics, as I’m sure Garrett Lisi knows. Perhaps further work might uncover something concrete. I wish Garret Lisi all the best, and encourage him to keep trying (perhaps guided partly by addressing the questions people are asking) and see if he can beat things into shape, just as we’re all doing at various stages in our respective research programs.

Best,

-cvj

]]> By: Blake Stacey http://asymptotia.com/2007/03/19/e8/#comment-90529 Blake Stacey Fri, 16 Nov 2007 17:46:53 +0000 http://asymptotia.com/2007/03/19/e8/#comment-90529 And "Vedic physics" literature says that when the Vedas speak about wild and domesticated animals, they're really talking about fermions and bosons. Oh, and annihilating the native peoples of India — the civilization which built cities like Mohenjo-Daro — really refers to the annihilation of antimatter. No joke. You can look it up in Meera Nanda's <i>Prophets Facing Backward,</i> if you're so inclined. And “Vedic physics” literature says that when the Vedas speak about wild and domesticated animals, they’re really talking about fermions and bosons. Oh, and annihilating the native peoples of India — the civilization which built cities like Mohenjo-Daro — really refers to the annihilation of antimatter.

No joke. You can look it up in Meera Nanda’s Prophets Facing Backward, if you’re so inclined.

]]> By: Elliot http://asymptotia.com/2007/03/19/e8/#comment-90492 Elliot Fri, 16 Nov 2007 15:32:56 +0000 http://asymptotia.com/2007/03/19/e8/#comment-90492 Anyone have an opinion (positive or negative) on this recent paper by Garrett Lisi using E8 as a unification framework? http://arxiv.org/abs/0711.0770 e. Anyone have an opinion (positive or negative) on this recent paper by Garrett Lisi using E8 as a unification framework?

http://arxiv.org/abs/0711.0770

e.

]]> By: stefan http://asymptotia.com/2007/03/19/e8/#comment-90235 stefan Thu, 15 Nov 2007 23:19:36 +0000 http://asymptotia.com/2007/03/19/e8/#comment-90235 the Maharishi mahesh yogi and quantum physicist John Hagelin ( now professor at mum.edu ) relates the 8 dimensions to the prakritis in vedic literature .... 8 fold divided nature of Prakriti the ninth is Paraprakriti, undivided or unified prakriti unmanifest prakriti the tenth is Purusha john hagelin claims when he spoke of the gossett polytrope 421 as a picture of the unified field that Transcendental meditation ( TM ) as taught by maharishi allows the mind to experience sequentially the unified field which the maharishi calls ATMA the Maharishi mahesh yogi and quantum physicist John Hagelin ( now professor at mum.edu ) relates the 8 dimensions to the prakritis in vedic literature …. 8 fold divided nature of Prakriti
the ninth is Paraprakriti, undivided or unified prakriti
unmanifest prakriti the tenth is Purusha

john hagelin claims when he spoke of the gossett polytrope 421 as a picture of the unified field that Transcendental meditation ( TM ) as taught by maharishi allows the mind to experience sequentially the unified field
which the maharishi calls ATMA

]]> By: khanna salil http://asymptotia.com/2007/03/19/e8/#comment-35363 khanna salil Tue, 27 Mar 2007 18:16:28 +0000 http://asymptotia.com/2007/03/19/e8/#comment-35363 greetings !!!! the ancient scriptures mention an 8 sided flat with a 0 face and a 9 face. each of these has 8 opposites out of which one is a polar & another is a reciprocal opposite. sometimes the polar & reciprocal opposites are the same. the final balance is achieved in its rotation of individuality. once that stops it collapses into anhillation or completeness depending on its velocity. its velocity may be much higher than the c-square of light. then suddenly all the illusionary dimensions created by the rotation disappear instantaneously back into its root. i believe modern maths will be able to reach that level of understanding in our lifetime. thanks. greetings !!!!
the ancient scriptures mention an 8 sided flat with a 0 face and a 9 face. each of these has 8 opposites out of which one is a polar & another is a reciprocal opposite. sometimes the polar & reciprocal opposites are the same. the final balance is achieved in its rotation of individuality. once that stops it collapses into anhillation or completeness depending on its velocity. its velocity may be much higher than the c-square of light. then suddenly all the illusionary dimensions created by the rotation disappear instantaneously back into its root. i believe modern maths will be able to reach that level of understanding in our lifetime.
thanks.

]]> By: Plato http://asymptotia.com/2007/03/19/e8/#comment-34670 Plato Sat, 24 Mar 2007 07:39:10 +0000 http://asymptotia.com/2007/03/19/e8/#comment-34670 <blockquote>G -> H -> ... -> SU(3) x SU(2) x U(1) -> SU(3) x U(1) Here, each arrow represents a symmetry breaking phase transition where matter changes form and the groups - G, H, SU(3), etc. - represent the different types of matter, specifically the symmetries that the matter exhibits and they are associated with the different fundamental forces of nature </blockquote> Layman thinking. Okay I am now thinking in terms of the phase changes? While someone may of said they had trouble with ten dimensions, let alone 248, that number "248" is supposed to be held to the context of the "eight dimension?" Any of those points of the 248, "within" the context of the 8th dimension as well? While it is "complex in it's arrangement" given the image above, it is held to an aspect of how we view the symmetry in that case? It is a quantum "directional view of the complexity of information" at that level?

G -> H -> … -> SU(3) x SU(2) x U(1) -> SU(3) x U(1)

Here, each arrow represents a symmetry breaking phase transition where matter changes form and the groups - G, H, SU(3), etc. - represent the different types of matter, specifically the symmetries that the matter exhibits and they are associated with the different fundamental forces of nature

Layman thinking.

Okay I am now thinking in terms of the phase changes?

While someone may of said they had trouble with ten dimensions, let alone 248, that number “248″ is supposed to be held to the context of the “eight dimension?” Any of those points of the 248, “within” the context of the 8th dimension as well?

While it is “complex in it’s arrangement” given the image above, it is held to an aspect of how we view the symmetry in that case?

It is a quantum “directional view of the complexity of information” at that level?

]]> By: Arun M Thalapillil http://asymptotia.com/2007/03/19/e8/#comment-34644 Arun M Thalapillil Sat, 24 Mar 2007 04:58:10 +0000 http://asymptotia.com/2007/03/19/e8/#comment-34644 Interesting post. Thanks for pointing this out. Is it to be understood that a similar feat has already been achieved for E6 ? Interesting post. Thanks for pointing this out. Is it to be understood that a similar feat has already been achieved for E6 ?

]]> By: Antonio http://asymptotia.com/2007/03/19/e8/#comment-34505 Antonio Fri, 23 Mar 2007 05:26:48 +0000 http://asymptotia.com/2007/03/19/e8/#comment-34505 The pattern is strikingly similar to those religous circles that is very familiar here in Asia. I must hav last seen them in Hindu, with elephants around its border or a variation thereof in Buddhism with the great Boddhisatva seated in enlightened bliss in the center. I congratulate the West, in finally establishing their rational foundation which this side of humanity has timelessly accepted by faith. The pattern is strikingly similar to those religous circles that is very familiar here in Asia. I must hav last seen them in Hindu, with elephants around its border or a variation thereof in Buddhism with the great Boddhisatva seated in enlightened bliss in the center. I congratulate the West, in finally establishing their rational foundation which this side of humanity has timelessly accepted by faith.

]]> By: Clifford http://asymptotia.com/2007/03/19/e8/#comment-34299 Clifford Wed, 21 Mar 2007 14:52:03 +0000 http://asymptotia.com/2007/03/19/e8/#comment-34299 He's talking about the fact that if you were to use E<sub>8</sub>xE<sub>8</sub> as a four dimensional gauge group you would have 496 gauge bosons, whereas the Standard Model of particle physics has gauge group SU(3)xSU(2)xU(1), which gives the 8 gluons of the strong interactions and the four gauge bosons associated the weak interactions and electromagnetism. 8+4=12. This brilliant observation has nothing whatsoever to do with the discussion of the structure and beauty of E<sub>8</sub>, of course. -cvj He’s talking about the fact that if you were to use E8xE8 as a four dimensional gauge group you would have 496 gauge bosons, whereas the Standard Model of particle physics has gauge group SU(3)xSU(2)xU(1), which gives the 8 gluons of the strong interactions and the four gauge bosons associated the weak interactions and electromagnetism. 8+4=12.

This brilliant observation has nothing whatsoever to do with the discussion of the structure and beauty of E8, of course.

-cvj

]]> By: Plato http://asymptotia.com/2007/03/19/e8/#comment-34284 Plato Wed, 21 Mar 2007 11:28:15 +0000 http://asymptotia.com/2007/03/19/e8/#comment-34284 <i>More relevant here is that some people complain about 496 = 2*248 gauge bosons, since experiments only see 12.</i> Maybe you could elaborate some more and give the experiment you are referring? If one was to see this diagram and it's complexity as structure above, does this experiment not appeal to further possibilities ? More relevant here is that some people complain about 496 = 2*248 gauge bosons, since experiments only see 12.

Maybe you could elaborate some more and give the experiment you are referring? If one was to see this diagram and it’s complexity as structure above, does this experiment not appeal to further possibilities ?

]]> By: Thomas Larsson http://asymptotia.com/2007/03/19/e8/#comment-34266 Thomas Larsson Wed, 21 Mar 2007 07:07:35 +0000 http://asymptotia.com/2007/03/19/e8/#comment-34266 <blockquote> ... <b>I would need a 248 dimensional space </b> ... . . . and some people complain about ten dimensions. :-/ </blockquote> More relevant here is that some people complain about 496 = 2*248 gauge bosons, since experiments only see 12.

… I would need a 248 dimensional space …

. . . and some people complain about ten dimensions. :-/

More relevant here is that some people complain about 496 = 2*248 gauge bosons, since experiments only see 12.

]]> By: IrrationalPoint http://asymptotia.com/2007/03/19/e8/#comment-34206 IrrationalPoint Tue, 20 Mar 2007 20:36:57 +0000 http://asymptotia.com/2007/03/19/e8/#comment-34206 Wicked. Wicked.

]]> By: donna http://asymptotia.com/2007/03/19/e8/#comment-34180 donna Tue, 20 Mar 2007 16:13:18 +0000 http://asymptotia.com/2007/03/19/e8/#comment-34180 Weird. I see that pattern all the time when I'm going to sleep at night.... Weird. I see that pattern all the time when I’m going to sleep at night….

]]> By: Blake Stacey http://asymptotia.com/2007/03/19/e8/#comment-34165 Blake Stacey Tue, 20 Mar 2007 13:47:31 +0000 http://asymptotia.com/2007/03/19/e8/#comment-34165 Clifford Johnson wrote, emphasis added: <blockquote>E8 is a 248 dimensional group, which means that if I were to try, using its most natural representation, to describe all its elements and the relations between them using points in a space, <b>I would need a 248 dimensional space</b> (recall that we live in just the three spatial dimensions), and the fact that it is a Lie group means that the resulting set of points forms a smooth mathematical shape known as a “manifold”.</blockquote> . . . and some people complain about <i>ten</i> dimensions. :-/ Clifford Johnson wrote, emphasis added:

E8 is a 248 dimensional group, which means that if I were to try, using its most natural representation, to describe all its elements and the relations between them using points in a space, I would need a 248 dimensional space (recall that we live in just the three spatial dimensions), and the fact that it is a Lie group means that the resulting set of points forms a smooth mathematical shape known as a “manifold”.

. . . and some people complain about ten dimensions. :-/

]]> By: Mary Cole http://asymptotia.com/2007/03/19/e8/#comment-34144 Mary Cole Tue, 20 Mar 2007 11:09:16 +0000 http://asymptotia.com/2007/03/19/e8/#comment-34144 What a hugely satisfying image. Why is symmetry so pleasing? I was in a rather old fashioned toy shop yesterday and discovered a 'spirograph' set. I was really pleased to see these are still being made, as I loved them as a child! What a hugely satisfying image. Why is symmetry so pleasing? I was in a rather old fashioned toy shop yesterday and discovered a ’spirograph’ set. I was really pleased to see these are still being made, as I loved them as a child!

]]> By: Plato http://asymptotia.com/2007/03/19/e8/#comment-34094 Plato Tue, 20 Mar 2007 05:21:28 +0000 http://asymptotia.com/2007/03/19/e8/#comment-34094 Is Coxeter related to these issues? <blockquote>Geometry is a branch of mathematics that deals with points, lines, angles, surfaces and solids. One of Coxeter’s major contributions to geometry was in the area of dimensional analogy, the process of stretching geometrical shapes into higher dimensions. He is also famous for “Coxeter groups,” the inversive distance between two disjoint circles (or spheres).</blockquote> See <a href="http://www.science.ca/scientists/scientistprofile.php?pID=5" rel="nofollow">here</a>. I find the image above very pleasing. I know you said they weren't flowers from your garden but I wonder sometimes at the <a href="http://flowermandalas.blogspot.com/" rel="nofollow">complexity of such flowers</a> if given to handling in a computer sequence. I have my other reasons of course, but that is beside your point. Polytopes in regards to Coxeter as well were worth looking in too? <b>The Man Who Saved Geometry</b> <blockquote>Coxeter lectured about ``the beauteous properties of triangles," about circles and spheres, and about the Platonic solids: the tetrahedron, cube, octahedron, icosahedron, and dodecahedron. According to a recent cosmological hypothesis (and a similar theory put forth by Plato) the dodecahedron is a potential model for the shape of the universe-bound by 12 walls, each the shape of a pentagon.</blockquote> See <a href="http://www.boston.com/news/globe/ideas/articles/2006/09/10/the_man_who_saved_geometry/" rel="nofollow">here</a> for a media report When you mentioned Dynkin diagrams I was trying to understand the way in which mapping is done in dimensional spaces. I first learn of the Dynkin diagrams from PP cook <a href="http://ppcook.blogspot.com/2005/05/e11-in-reference-frame.html" rel="nofollow">here</a> Unfortunately I had not gone much further with Dynkin Diagrams until you mention your post today. Although, I was still looking at Sylvester surfaces and Cayley. Of course the genus figures. It just a different way of thinking in the non-euclidean geometries? Is Coxeter related to these issues?

Geometry is a branch of mathematics that deals with points, lines, angles, surfaces and solids. One of Coxeter’s major contributions to geometry was in the area of dimensional analogy, the process of stretching geometrical shapes into higher dimensions. He is also famous for “Coxeter groups,” the inversive distance between two disjoint circles (or spheres).

See here.

I find the image above very pleasing. I know you said they weren’t flowers from your garden but I wonder sometimes at the complexity of such flowers if given to handling in a computer sequence. I have my other reasons of course, but that is beside your point.

Polytopes in regards to Coxeter as well were worth looking in too?

The Man Who Saved Geometry

Coxeter lectured about “the beauteous properties of triangles,” about circles and spheres, and about the Platonic solids: the tetrahedron, cube, octahedron, icosahedron, and dodecahedron. According to a recent cosmological hypothesis (and a similar theory put forth by Plato) the dodecahedron is a potential model for the shape of the universe-bound by 12 walls, each the shape of a pentagon.

See here for a media report

When you mentioned Dynkin diagrams I was trying to understand the way in which mapping is done in dimensional spaces. I first learn of the Dynkin diagrams from PP cook here

Unfortunately I had not gone much further with Dynkin Diagrams until you mention your post today. Although, I was still looking at Sylvester surfaces and Cayley. Of course the genus figures.

It just a different way of thinking in the non-euclidean geometries?

]]>