248-Dimensional Math Problem Solved

[Doctordick]

This concerns a spot in the January 2008 publication of Discover Magazine. I have quoted the entire statement there published.

One hundred dtwenty years after it was first discovered, mathematicians have successfully mapped out a 248-dimensional object called [imath]E_8[/imath]. The complete description of [imath]E_8[/imath] - one of the most complicated structures in all of mathematics - is a table with more than 200 billion entries. Printed out on paper it would cover all of Manhattan.

 

Scientists hope to use the map to simplify calculations and help them understand the universe. David Vogan, the MIT mathematician who announced the project's completion in March, calls it a map of possibilities, “a little bit like the periodic table is for chemistry.”

 

Objects similar to [imath]E_8[/imath] keep showing up in the real world. One of them describes the motions of the solar system and the positions of electrons surrounding atoms; another defines how a single wave travels down a canal or traffic flows on a highway.

 

What [imath]E_8[/imath] will do for us is not yet clear. It was correctly predicted in 1887 to be the most complex of Lie (pronounced LEE) groups, which are collections of symmetries. One of the simplest sets of symmetries is the group that comprises the symmetries of a sphere: Rotate a sphere as much as you like around any axis or flip in inside out, and it looks exactly the same. [imath]E_8[/imath] is the group that comprises the symmetries of a 57- dimensional object. Superstring theorists have already employed this group in potential theories of everything. Whether or not those string theories turn out to be true, Vogan says, [imath]E_8[/imath] probably reflects the real world somehow: “Everything interesting does>”

Jessica Ruvinsky

Now keep that in mind and go reread my post on “A simple geometric proof with profound consequences”. Symmetries are what it is all about. Anyone interested in understanding reality should take the trouble to understand the nature of the issue referred to by the term “symmetry”. Take a careful look at three posts on “physicsforums.com”: my post on the what symmetries are, selfAdjoint's response to that post and my response to selfAdjoint.

 

And you might also make a careful read of my post to Bombadil. And, Buffy, you should look at all of this very carefully.

 

Have fun -- Dick

[InfiniteNow]

Dick - I cannot locate your source. Since you referenced a January 2008 publication of Discover, it is not on the web. Can you please source your quote above (with a direct link) so I may view the quoted text in its full context? If you would oblige, I would be greatly appreciative. I hope all is well with you and the quilt making wife. ;)

[Doctordick]

Dick - I cannot locate your source. Since you referenced a January 2008 publication of Discover, it is not on the web. Can you please source your quote above (with a direct link) so I may view the quoted text in its full context? If you would oblige, I would be greatly appreciative. I hope all is well with you and the quilt making wife. :)

Apparently I am the first to post this on the web. I have, in my hands, the January 2008 issue of Discover magazine (I recieved it in the mail today) and I copied the quote directly out of the magazine itself. I quoted the entire text so there is no additional context.

 

Not only am I on the cutting edge of modern science but I am a hundred miles ahead of these people. ;) :lol: :lol:

 

Have fun -- Dick

 

PS She's already got the new quilt a quarter done. The girl is fast!

[Rade]

Here is the E8 publication abstract:

[0711.0770] An Exceptionally Simple Theory of Everything

 

And the paper:

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

[Turtle]

We have a News story on the E8 problem, with some discussion, here at Hypography from this past March. >> http://hypography.com/forums/general-science-news/10841-mathematical-solution-another-dimension.html?highlight=E8%2A

[Rade]

We have a News story on the E8 problem, with some discussion, here at Hypography from this past March. >> http://hypography.com/forums/general-science-news/10841-mathematical-solution-another-dimension.html?highlight=E8%2A

I read that Lisi is working on the mass of the 20 new particles that his E8 equations predict to be present when LHC begins at CERN in 2008. He better send the information to CERN because they cannot capture all the data they will generate when the LHC experiments begin. Most of the data is lost forever (yes, that is correct, much data is not captured and stored--it is lost) they only keep information from the collisions that are predicted by current models and theory--and I have no idea if the E8 theory of Lisi is one of them. Does anyone know Lisi ? Has he contacted CERN ? What a shame if CERN discards the very data needed to experimentally verify his E8 theory of everything only because it is "outside" what is expected based on current theory.

[Turtle]

I read that Lisi is working on the mass of the 20 new particles that his E8 equations predict to be present when LHC begins at CERN in 2008. He better send the information to CERN because they cannot capture all the data they will generate when the LHC experiments begin. Most of the data is lost forever (yes, that is correct, much data is not captured and stored--it is lost) they only keep information from the collisions that are predicted by current models and theory--and I have no idea if the E8 theory of Lisi is one of them. Does anyone know Lisi ? Has he contacted CERN ? What a shame if CERN discards the very data needed to experimentally verify his E8 theory of everything only because it is "outside" what is expected based on current theory.

 

This bit implies he is in contact with those folks, but doesn't say so explicitly.

 

...The crucial test of Lisi's work will come only when he has made testable predictions. Lisi is now calculating the masses that the 20 new particles should have' date=' in the hope that they may be spotted when the Large Hadron Collider starts up.

 

"The theory is very young, and still in development," he told the Telegraph. "Right now, I'd assign a low (but not tiny) likelyhood to this prediction.

 

"For comparison, I think the chances are higher that LHC will see some of these particles than it is that the LHC will see superparticles, extra dimensions, or micro black holes as predicted by string theory. I hope to get more (and different) predictions, with more confidence, out of this E8 Theory over the next year, before the LHC comes online."...

[/quote']

Surfer dude stuns physicists with theory of everything - Telegraph

[Rade]

Here is link to a recent publication by Lee Smolin that extends the E8 theory of Lisi:

[0712.0977] The Plebanski action extended to a unification of gravity and Yang-Mills theory

[Turtle]

Here is link to a recent publication by Lee Smolin that extends the E8 theory of Lisi:

[0712.0977] The Plebanski action extended to a unification of gravity and Yang-Mills theory

 

Thanks Rade. I couldn't follow the math notation, but I did like the turn of phrase from the article which I boldened in the quote below. :) :eek:

 

... Another way in which Lisi’s proposal breaks the gauge invariance is by a strategy of incorporate fermions by means a BRST extension of the connection. In section 4.1 below I propose an alternative way to incorporate the fermions, which would not break the gauge symmetry. It is based on proposals that matter degrees of freedom arise in loop quantum gravity as a result of the phenomena of disordered locality discovered by Markopoulou[13, 14]. This is in fact a version of a proposal of Misner and Wheeler from 1957 that matter might be nothing but the mouths of Planck scale wormholes[15] and, in the context of loop quantum gravity, this was argued previously to give fermions. ...