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E8 Structure Decoded
arobic writes "A group of mathematicians from US and Europe succeeded in mapping the E8 structure, an example of a Lie group. These were developed by the well-known mathematician Sophus Lie (pronounce Lee) in the last century and are used for many applications, mainly in theoretical physics. This is an important breakthrough as it could help physicists working on Grand Unified Theories (aka GUTs)."
Pronounce it "Lee-eh"; At least that is how I would do it as a Scandinavian.
The magnitude and nature of the E8 calculation invite comparison with the Human Genome Project. The human genome, which contains all the genetic information of a cell, is less than a gigabyte in size. The result of the E8 calculation, which contains all the information about E8 and its representations, is 60 gigabytes. This is enough to store 45 days of continuous music in MP3-format.
Hear that? That's the sound of Apple's iPod marketing finally reaching absolute ubiquity.
-The Wolf
Pronounce it "Lee-eh"; At least that is how I would do it as a Scandinavian.
It's PRINCESS "Lee-eh" you insensitive clod!
Help! I've fallen in a karma hole and I can't get up!
Obviously they didn't read this book
It does remind me of string theory a bit, though. Heavy on cool math. Light on any practical application.
http://en.wikipedia.org/wiki/E8_(mathematics)
Seriously, these articles, as most in Math category, are totally undecipherable to most normal users. TG there is a Wikipedia somewhere, sometimes they are closer to layman.
Last Century? If by last century you mean the 1800's, then that's officially 2 centuries ago. The 'last century' was the 20th century.
Tony: Gibbs, how could you possibly know that?
Gibbs: Well Tony, my GUT told me.
E8 is not a Lie Group. E8 is the biggest Lie Group. Here are a few links for more accurate info:
. stm
http://news.bbc.co.uk/2/hi/science/nature/6466129
http://en.wikipedia.org/wiki/E8_(mathematics)
Write your own Choose Your Own Adventure. http://www.freegameengines.org/gamebook-engine/
Apologies -- this post uses a lot of technical jargon. However, the article is so badly written that I decided to post some remarks. And yes, I am a professional mathematician.
First, what they mapped was not the "structure" of the Lie group E_8 -- the structure of the group has been known for a long time. What they mapped is what are called the "representations" of the group E_8, which is part of Vogan's program to understand the "unitary dual" (=list of representations) for all (reductive) Lie groups.
Second, this has no relevance to grand unified theories. Even though a (compact) form of E_8 can be the gauge group of a GUT, the relevant representations are finite-dimensional and have been classified by Weyl decades ago.
Finally, this is an important result. It is relevant to number theory, and to abstract mathematics in general. The fact that a (finite) computer calculation can help determining an infinite list of representation is very nice.
"The result of the E8 calculation, which contains all the information about E8 and its representations, is 60 gigabytes. This is enough to store 45 days of continuous music in MP3-format."
Because we know physicsts and mathematicians that would be interested in this problem would have no idea how a computer works and have to translate it into teenager speak.
God spoke to me.
is, of course the third worst in the universe.
Now they can move on to their next task, understanding why anyone would drink V8.
So now we're going to have truth and lie tables?
Stop this crazy planet. I want to get off!
Dedicated Cthulhu Cultist since 4523 BC.
Hello:
n tum/standard_model/standard_model.html
The standard model has the symmetries U(1)xSU(2)xSU(3). The one in the middle, SU(2), is a unit quaternion, where a quaternion is like a real or complex number, but has four parts. I have developed the software to visualize quaternions at http://quaternions.sf.net/ using one number for time, three for space. SU(2) can be represented by the quaternion function exp(q-q*). Feed a thousand random quaternions into exp(q-q*), and get POVRay to make a nice animation. Do the same for q/|q| exp(q-q*), and you have a visual representation of the electroweak symmetry. Smash two of these together, and you get the symmetry of the standard model.
Visually, there is a clear message: if you want to smoothly represent all possible events in spacetime as quaternions, the group description must be U(1)xSU(2)xSU(3). You won't read that in a journal because it has to be done with animations.
http://www.theworld.com/~sweetser/quaternions/qua
doug
Working on new views of old physics at http://VisualPhysics.org
If you've ever tried tea made by an American you'll know that your previous statement is false.
How We Wrote Down a 453,060 x 453,060 Matrix and Found Happiness,"
2nd worst, poetry, ever, professor Vogon.
so does that make them the biggest group of liers in the world then?
Sorry!
To me it all sounds like bad Vogan poetry...
- Peder
the answer is 42!
I find it fascinating that some things are so well known that I need instructions on how to pronounce them!
The most important thing to do in your life is to not interfere with somebody else's life. -FZ
Some 30 odd years ago when I was studying Modern Algebra I remember the professor mentioning Lie Groups and their use in theoretical physics. Whats really scary is that "Lie Group" popped into my mind the instant I saw the E8. Now where did that come from?
I'm not sure, but I think my head exploded into E8 pieces...
I am open source, and Linux baby!
Typical geek attitude. If it's not Vorbis, it's LAME.
Step into a huge movement. Don't Tread In Me.
Sophus Lie died in 1899. So not "last" century. TFA said "19th-century Norwegian mathematician ...".
Y2K? PEBCAK?
Calculation on paper would cover Manhattan
If the math is that big, then why not use a genetic algorithm to evolve the equation to fit the model, via lots of scenarios to test against? Normally genetic algorithms create difficult-to-read and long equations when used for such, but it is hard to do worse than Manhattan-sized.
Table-ized A.I.
This post climbed Mt. Washington.
The 1800's would now be century before last. (He's probably still writing 1st. millennium on checks)
Category theorist John Baez has a summary of this work from a mathematician's perspective. Unfortunately, you need at least an undergraduate math degree to make full sense of it, but it gives more flavor of what's really going on than a news story, and he at least defines mathematically what E8 and KLV polynomials are.
He begins by noting, "You may hear some hype about this soon, because it's a really big calculation, and the American Institute of Mathematics has coaxed a lot of science reporters to write about it -- in part by comparing it to the human genome project. Computing the Kazhdan-Lusztig-Vogan polynomials for E 8 is certainly nowhere nearly as important as the human genome project, nor as hard! But the final result involves more data, in a sense."
This being slashdot I doubt I would get an answer, but what is the smallest Symmetric group on n elements does this embed in, what is the smallest known number of generators, and what permutations on n elements are they?
bash-2.04$
bash-2.04$yes "Don't you hate dialup connections?"| write USERNAME
Great, something else for second year math students to memorize. There is nothing mathematics curriculum designers take more pleasure in than reducing students to memorizing solutions to problems that can only be solved by machines. There was a time when education involved thought, today it is an exercise in rote memory skills.
Differential calculus anyone? Integral sure, it can be comprehended by the human brain. Basic point group theory, sure it can be grasped by the human mind. Group theory of insanely complicated objects solvable only by machine? No thanks.
Differential equations are why we developed computers. (Ballistics firing solutions) Now the measure of a students intelligence and viability for graduate studies and finally primary research is based purely on memorization skills. This is why primary research in graduate science studies today has suffered so, only memorizers are allowed to participate, not thinkers.
Oh well fuck it, the world sucks, I don't really care anyway, though I feel obliged to comment.
> A group of mathematicians from US and Europe succeeded in mapping E8
Brave men. I wouldn't go in to Hackney, myself.
can be found at http://www.liegroups.org/kle8.narrative.html
"The Atlas team consists of 18 researchers from around the globe." USA: Adams, Vogan, Dan Barbasch (Cornell), John Stembridge (University of Michigan), Peter Trapa (University of Utah), Dan Ciubotaru, (MIT's), Alfred Noel, University of Massachusetts FRANCE: Marc van Leeuwen (University of Poitiers) Fokko du Cloux (University of Lyon). DEAD That one french guy is reprezenting the whole gloge =)