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E8 Structure Decoded

Posted by Hemos on from the get-it-down-on-paper dept.

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)."

16 of 127 comments (clear)

  1. Pronounce... by spazmolytic666 · · Score: 4, Funny

    Pronounce it "Lee-eh"; At least that is how I would do it as a Scandinavian.

    It's PRINCESS "Lee-eh" you insensitive clod!

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  2. Re: Pronounce it "Lee-eh" by Anonymous Coward · · Score: 4, Funny

    Pronounce it "Lee-eh"; At least that is how I would do it as a Canadian.
  3. mandatory Wikipedia link by cpct0 · · Score: 4, Informative

    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.

    1. Re:mandatory Wikipedia link by kestasjk · · Score: 5, Insightful

      Should an encyclopedia try to give a layman's definition of something that probably really is beyond the reach of the average person?

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      // MD_Update(&m,buf,j);
    2. Re:mandatory Wikipedia link by superwiz · · Score: 4, Insightful

      Actually, that's not the case. To give an analogy, say you are working on optimization of some process involved in database storage. Could you explain what that means to your mother (assuming your mother does not have a technical background)? You couldn't say anything beyond vagueries like "making faster" or "making more efficient". Well, on that level, Lie groups describe continuous symmetries (like rotations of a sphere). To get to a level even a little bit deeper would take a 1 semester undergraduate course just to learn what is going on. Sometimes specilization creates escoteric fields. That's just how it is. Math is "universal" because all the math that you are used to seeing was developed 200+ years ago, so it is the root of all knowledge that we now call mathematics. So as every laymen who knows some abc's, you want to think that the specilized knowledge in the subject is not outside of your grasp. Well, again, try explaining to your mother the finer points of what you do. And again (again) realize that specilized knowledge in a discipline does not make the knowledge useless -- it markes the discipline as a professional (rather than hobbyist) endeavor.

      --
      Any guest worker system is indistinguishable from indentured servitude.
    3. Re:mandatory Wikipedia link by jd · · Score: 5, Insightful
      Well, yes. There are usually analogies to any computational process that mere terrans (as opposed to us elves from the planet Tharkquark) can understand.

      Let's take the database optimization. Databases are merely methods of storing and organizing data. Let's say that you are denormalizing a relational database, splitting it into locally-connected "islands" and running each island on its own load-balancing system. This is no trivial setup - you have changed the structure of the data and are running it on a cluster where each "node" on that cluster is itself a cluster. This is no trivial thing that - computationally - is outside the realms of more than a few database engineers. How many companies do you know that run database hypercubes as a matter of course?

      Can this be explained to the layperson? Sure. Denormalizing is duplicating information. If your mother didn't build a deck of cards holding favorite recipes from a bunch of recipe books, she's probably the only one who didn't. Duplicating data to make it easy and quick to look up is something almost everyone does at some time or other. If you're having trouble explaining this, point to the examples around you.

      Load-balancing? Virtually everyone is familiar with sharing the workload.

      Dividing up into self-contained sets of records and clustering them? That doesn't sound very real-worldish. Well, yes it is. Departments, compartments, apartments - all different ways to describe isolated groups of self-relating entities that nonetheless can interact in defined ways.

      There is absolutely no problem in computing that you can describe that does not have a real-world counterpart. This is a direct consequence of Turing's definition of Computable. If the layman doesn't understand, it is not because they can't, it's because nobody took the time.

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  4. Re:No practical applications? by necro81 · · Score: 4, Informative

    But of course it has practical applications: it applies to string theory!

  5. Representation Theory by l2718 · · Score: 5, Informative

    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.

  6. Re:Pronounce it "Lee-eh" by Anonymous Coward · · Score: 4, Informative

    As a Norwegian, I would pronounce it "Lee". It's a bit strange I agree, but that's how that name is usually pronounced.

  7. Vogan mathematics... by Anonymous Coward · · Score: 5, Funny

    is, of course the third worst in the universe.

  8. Re:Pronounce it "Lee-eh" by G3ckoG33k · · Score: 4, Informative

    Thanks!

    I had to check it with a Norwegian colleague, who confirmed you pronunciation.

    (I had thought it meant 'scythe' (Sw. 'lie', No. 'ljå' [pronouced 'yaw'!]), but actually it was 'slope' (Sw. lid; with a pronouned 'd' in the high form, but silent in dialectal forms).

    So, all those years calling the Tryggve Lie a scythe was in in vain...

  9. I'm no mathemtician but... by east+coast · · Score: 4, Funny

    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.
  10. See the symmetries of the standard model by sweetser · · Score: 4, Informative

    Hello:

    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/quan tum/standard_model/standard_model.html

    doug

    --
    Working on new views of old physics at http://VisualPhysics.org
  11. Re:iPod by SatanicPuppy · · Score: 4, Insightful

    It's not sad. Jesus, they were still measuring things in "War and Peace"'s a few years ago! At least now they're measuring it in an actual digital object, and moreover, it makes sense to a lot of people because a lot of people have gotten to the point where they actually appreciate that those files on their computer have an actual "size" at all!

    It seems lame to us...Hell I remember when hard drives measured in tens of megabytes, and space was a real issue, all the time. Geeks deal in so many different types of digital files, so many different formats...Tell a geek its "45 hours of mp3 music" and they'll say, "At what bitrate?"

    But for a layman to actually be able to measure space in terms of things that you can't physically touch? That's a pretty big accomplishment.

    --
    ad logicam Claiming a proposition is false because it was presented as the conclusion of a fallacious argument.
  12. Re:Not a Lie Group. by haakondahl · · Score: 4, Funny
    From TFA: Mathematicians study symmetries in higher dimensions. E_8 has 248 dimensions. "What's attractive about studying E_8 is that it's as complicated as symmetry can get. Mathematics can almost always offer another example that's harder than the one you're looking at now, but for Lie groups E_8 is the hardest one," Vogan said.

    Mine goes to E_11.

    --
    Don't trust anyone under thirty.
  13. Re:Not a Lie Group. by Alsee · · Score: 5, Funny

    E8 is not a Lie Group. E8 is the biggest Lie Group.

    It seems somebody flunked basic set theory. :D

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