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Math Science

E8 Structure Decoded 127

Posted by Hemos
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)."
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E8 Structure Decoded

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  • by G3ckoG33k (647276) on Monday March 19, 2007 @09:02AM (#18400415)
    Pronounce it "Lee-eh"; At least that is how I would do it as a Scandinavian.
  • iPod (Score:3, Funny)

    by slashdottinitup (912090) on Monday March 19, 2007 @09:04AM (#18400431) Journal
    FTFA:

    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
    • Re: (Score:2, Insightful)

      by Dara Hazeghi (1076823)
      You find it funny. I find it a little sad... It's sad that storage size in "layman's terms" is now related to hours of MP3 playback. A whole generation of people are not going to understand storage outside of the iPod universe.
      • Re: (Score:2, Funny)

        by Short Circuit (52384) *
        It's better than LoCs and telephone books. I just wish they'd mentioned the encoding bitrate...
      • Re:iPod (Score:5, Insightful)

        by SatanicPuppy (611928) * <Satanicpuppy@[ ]il.com ['gma' in gap]> on Monday March 19, 2007 @10:02AM (#18400937) Journal
        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.
        • Re: (Score:2, Funny)

          by Wooster_UK (963894)
          So how many War and Peaces are in an hour of continuous mp3?

          And more to the point, how many War and Peaces are there in a New Jersey?
        • Typical geek attitude. If it's not Vorbis, it's LAME [wikipedia.org].

        • by skeevy (926052)

          ...they were still measuring things in "War and Peace"'s a few years ago!

          I still do, no kidding. I use a copy of War and Peace I got off of Project Gutenberg to use as a largish text file for performance testing. It runs just over 3MB.

          Interestingly enough Les Miserables comes in at 50k larger.

        • by Plutonite (999141)
          I'm personally glad they didn't say anything about football fields.
        • 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.
          They [aimath.org] also give a more "war & peace"-type of the analogy:

          The magnitude of the calculation is staggering: the answer, if written out in tiny print, would cover an area the size of Manhattan.
      • by bkr1_2k (237627)
        And why should they? Times change, people's understanding of technology changes. Find one kid born after 1990 or so that can tell you how much space 200 records takes up. Or how much you can store (in data) on a cassette tape.

        People use currently applicable "measurements" because people simply have no idea what a gigabyte is. For most of the population a gigabyte is meaningless because it simply doesn't matter in their lives. So knowing that a gigabyte can hold X number of songs brings relavence of siz
        • by illeism (953119) *

          Find one kid born after 1990 or so that can tell you how much space 200 records takes up. Or how much you can store (in data) on a cassette tape.
          Dang - I was born in the 70's and I can't tell you that...
          • by bkr1_2k (237627)
            Yeah, most folks even from the 80s can't but I hedged my bets. There's always some smartass who will pipe up with an answer and miss the point entirely, just to prove you wrong.
    • 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.

      Sorry, I'm still trying to convert it to furlongs per fortnight [slashdot.org]
    • by peektwice (726616)
      <humor>I have been on a personal crusade, or jihad as it were, about these bad "layman's terms" analogies for a little while now. Thankfully, I now have brethren with me to take up the banner. I feel my rants have fallen on deaf ears, or perhaps I have been written off as crazy by the illuminati (illiterati ?), but you have lifted my soul, and given me sustenance to rant another day.</humor>
      I was going to rail about the encoding bit rate, whether the MP3's had tags filled in, etc., but someone
    • by operon (688118)
      People should not continue to tell that all the genetic information of a cell is in the DNA. There are lots of epigenetic information in other cell molecules. Also, if we consider all the biological information in a cell, it could easily go far than 60 gigabytes.
  • by spazmolytic666 (549909) on Monday March 19, 2007 @09:05AM (#18400441) Journal
    Pronounce it "Lee-eh"; At least that is how I would do it as a Scandinavian.

    It's PRINCESS "Lee-eh" you insensitive clod!
  • Obviously they didn't read this book [amazon.com]

    It does remind me of string theory a bit, though. Heavy on cool math. Light on any practical application.
  • by cpct0 (558171) <.moc.sianodlehcim. .ta. .todhsals.> on Monday March 19, 2007 @09:10AM (#18400481) Homepage Journal
    http://en.wikipedia.org/wiki/E8_(mathematics) [wikipedia.org]

    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.
    • by kestasjk (933987) * on Monday March 19, 2007 @09:27AM (#18400609) Homepage
      Should an encyclopedia try to give a layman's definition of something that probably really is beyond the reach of the average person?
      • by Tx (96709) on Monday March 19, 2007 @09:43AM (#18400763) Journal
        IMHO, yes. There are few subjects where the layman (that's me) can't at least be given an idea of what the subject is about, if the material is written well. I hold up books such as Hyperspace by Michio Kaku as examples of how to convey complex subject matter to the layman, in a very readable and comprehensible way.
        • by superwiz (655733) on Monday March 19, 2007 @10:59AM (#18401511) Journal
          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.
          • Re: (Score:3, Insightful)

            by mbrod (19122)
            Kaku devoted a whole book to his explanation and the previous poster actually wanted to understand what Kaku was talking about.

            If the reader actually wants to know, most people really don't, well I should say they just don't care, then given a moderate sized layman's explanation of it in a paper or book will usually suffice.

            You stated:

            optimization of some process involved in database storage

            Something like this is simple to explain to people unaware of the inner workings of databases. You just explain it referencing something similar like a book with an index at

          • by jd (1658) <[moc.oohay] [ta] [kapimi]> on Monday March 19, 2007 @01:31PM (#18403361) Homepage Journal
            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.

          • by kabocox (199019)
            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.

            I just use the doctor analogy. I make sick computers well. I delete temp files, defrag, and run a virus scanner. It's the same as take two of these and call me if you still feel bad tomorrow. I explain that running defrag and the virus scanner is like si
          • by Pikoro (844299)

            Could you explain what that means to your mother (assuming your mother does not have a technical background)?

            What in the world are our kids going to say when they are our age (mid 30's) since by then, nearly everyone will have a technical background.

            "Could you explain how a database works to your ...."
        • Re: (Score:2, Insightful)

          by eh2o (471262)
          Most technical jargon has very precise semantics and can't be transcoded into "laymans' terms" without an absurd explosion of verbosity that ultimately takes more time to wade through than just learning the technical vocabulary in the first place.

          However, speaking as an applied mathematician, I look for a list of applications of a concept. Since this is basically informational content it is readily found on Wikipedia or elsewhere and typically vastly easier to understand than the concept itself. Given tha
        • Re: (Score:2, Interesting)

          by asninn (1071320)
          To paraphrase what my history teacher used to say, Wikipedia articles like this (in fact, any article in any encyclopedia!) should be as simple as possible, but at the same time as complex as necessary. In other words, simplifying the presentation of a concept or an object is good, but it shouldn't reach a point where the actual nature of the concept or object in question is warped.

          That being said, there's always the option of having both a "thorough" and a "simple" version of an article, too; see e.g. [[M-
          • There's no reason why in addition to [[Lie group]], there shouldn't also be a [[Lie groups simplified]] or [[Lie groups for dummies]] or so. :)


            They were planning on a Lie groups for Dummies(tm), but it was still over 100 billion pages long, so they canned it.
            • by asninn (1071320)
              I once did see a "Vertex operator algebras for dummies" - just a spoof picture, of course, not a real book, but I thought it was cute.
      • Re: (Score:2, Interesting)

        by LordSchnitzel (677741)
        I've found that the mathematics pages on Wikipedia really are attempting to explain to the layman. Granted - to understand the issue you may have to spider around to various other articles - like the (very good) main pages on Groups and Topology. For comparison look at the equivalent pages on mathworld.wolfram.org where the material is presented with far less explanation. Wikipedia here is probably a non-mathematicians best shot at getting the point of the issue.
    • All you need to know is that the analysis of e8 took 60 GB to store:

      This is enough to store 45 days of continuous music in MP3-format.


      They put some things in layman's terms ;-p as apparently math people reading up on this obscure topic can't figure out what 60 GB of storage can really hold.
    • by pfafrich (647460)
      As a wikipedia maths editor yes we have been caught short by this. E8 is a pretty obscure topic, out of about 10,000 maths articles kind of low down the priority list. You may find http://en.wikipedia.org/wiki/Coxeter-Dynkin_diagr a m [wikipedia.org], http://en.wikipedia.org/wiki/Circle_group [wikipedia.org], http://en.wikipedia.org/wiki/Lie_group [wikipedia.org], and http://en.wikipedia.org/wiki/Root_system [wikipedia.org] to be related articles which may be a little easier to understand. As with any open source project, if you don't like it fix it. Theres plent of art
  • Not a Lie Group. (Score:3, Informative)

    by WK2 (1072560) on Monday March 19, 2007 @09:21AM (#18400567) Homepage
    E8 is not a Lie Group. E8 is the biggest Lie Group. Here are a few links for more accurate info:

    http://news.bbc.co.uk/2/hi/science/nature/6466129. stm [bbc.co.uk]
    http://en.wikipedia.org/wiki/E8_(mathematics) [wikipedia.org]
    • Re: (Score:1, Informative)

      by Anonymous Coward
      Actually, it is not the biggest, it is "just" the most complex.

      It does not get even into top ten as there are infinite number of bigger Lie groups :-)
    • by sconeu (64226)
      If it's not a Lie Group, how can it be the biggest Lie group?

      Or do you mean "E8 is not just a Lie group..."

    • by haakondahl (893488) on Monday March 19, 2007 @10:47AM (#18401379)
      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.

      • Re: (Score:3, Funny)

        by pfafrich (647460)
        As other had said it is not the biggest Lie group, there are two families Ak and Dk of lie groups which are infinite sequences. You can think of Ak as the symmetry of the trianagle, tetrahedron, 4-simplex, ..... there one of these for each dimension. Likewise Dk is related to the symetry of the square, cube, hyper-cube and n-dimensional cube. To these are added the so called exceptional groups, sort of like the icoshedron and its four dimensional analogue. It just so happens that these do not for an infinit
    • by Alsee (515537) on Monday March 19, 2007 @11:35AM (#18401897) Homepage
      E8 is not a Lie Group. E8 is the biggest Lie Group.

      It seems somebody flunked basic set theory. :D

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

      QED!

  • by l2718 (514756) on Monday March 19, 2007 @09:24AM (#18400593)
    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 [wikipedia.org].

    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.
    • by Anonymous Coward on Monday March 19, 2007 @09:38AM (#18400715)
      is, of course the third worst in the universe.
    • The fact that a (finite) computer calculation can help determining an infinite list of representation is very nice.
      That could be a good line for a processor advertising campaign. "Here at Acme, our teraflops turn infinity into finity!"
    • by guruevi (827432)
      which is part of Vogan's program to understand the "unitary dual" (=list of representations) for all (reductive) Lie groups.

      You know, only the Vogon's would be attracted to something that produces that much paperwork.
      • Re: (Score:1, Funny)

        by Anonymous Coward

        You know, only the Vogon's would be attracted to something that produces that much paperwork.
        Boy am I glad that you put that apostrophe in to let me know an s was coming. There is nothing worse than being startled by a surprise plural!
    • Re: (Score:2, Informative)

      by nanosquid (1074949)
      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.

      Well, maybe that's surprising to some mathematicians, but this sort of thing is nearly half a century old.
    • Re: (Score:3, Funny)

      The fact that a (finite) computer calculation can help determining an infinite list of representation is very nice.

      Sadly, Mr. Vogan was later lynched by a rampaging mob of respectable physicists who had finally realized that the one thing they really couldn't stand was a smartass.

    • by siwelwerd (869956)

      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.

      I'd hardly call what they did "mapping" by any means. They wrote down the character table of the group.

      I would agree the article is terrible. They've somehow managed to make it unreadable by both layman and mathematician alike.

  • by CrazyJim1 (809850) on Monday March 19, 2007 @09:28AM (#18400615) Journal
    "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.
    • by 56ker (566853)
      It's more "snappy quote for journalists" speak the press release author/article writer has converted it to. 60 gigabytes is less than the size of most people's hard drives.

      You should see how much memory predicting the weather takes and that's just 4 dimensions (not 248!)
      • by Tom Womack (8005)
        The interesting feature of this announcement is how little computation and how much intelligence in software development was involved by the standards of other large computational projects. The calculation took three days on SAGE, which is an eight-socket dual-core Opteron system with 64GB of memory; it's perhaps three orders of magnitude less calculation than the factorisation of RSA200, or than IBM's work modelling hafnium silicates for developing 45nm processes. It is very much less work than is routin
      • You should see how much memory predicting the weather takes and that's just 4 dimensions (not 248!)

        I'm not a meteorologist but I would think weather computations involve many move then 4 dimensions when computing a forecast. With only four, your predicting a location and a time :).

        Longitude, latitude, altitude, and time would only the first four. Wind speed, wind direction, barometric pressure, humidity, and temperature, would bring the count up to at least 9. There are probably more I'm not thinking o

    • by anothy (83176)
      poor journalism with stupid, useless metrics. why can't they just stick to established industry norms? how am i supposed to know how many Libraries of Congress this is?
  • by east coast (590680) on Monday March 19, 2007 @09:45AM (#18400795)
    So now we're going to have truth and lie tables?

    Stop this crazy planet. I want to get off!
    • Re: (Score:3, Funny)

      by MarkGriz (520778)
      "So now we're going to have truth and lie tables?"

      What do you mean "now"?
      These have been around since the days of the first engineers and politicians.
  • Units? (Score:2, Funny)

    by Hemogoblin (982564)

    If written out on paper, the calculation describing this structure, known as E8, would cover an area the size of Manhattan.
    I'm having trouble understanding this. Could someone please restate in LOCs (Library of Congresses)?
    • by dohzer (867770)
      Screw congress. I want to know how many Manhattans it would cover if printed in size 1000 font.
      Or does the Manhattans-covered-in-paper SI unit specify a standard font size?
  • by sweetser (148397) <sweetser@alum.mit.edu> on Monday March 19, 2007 @10:01AM (#18400927) Homepage
    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/ [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 [theworld.com]

    doug
  • the answer is 42!
  • by the well-known mathematician Sophus Lie (pronounce Lee)


    I find it fascinating that some things are so well known that I need instructions on how to pronounce them!
    • by alienmole (15522)
      Lie is well-known amongst people who know mathematicians, but given that the Slashdot audience is more general than that, the pronunciation help is needed. This is actually an example of why natural language is challenging for computers to understand -- which means, I'm afraid, that you fail the Turing Test. Ask your programmer to work on your contextualization module. :)
  • 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...
  • These were developed by the well-known mathematician Sophus Lie (pronounce Lee) in the last century

    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.
         
  • by LotsOfPhil (982823) on Monday March 19, 2007 @12:45PM (#18402819)

    In the end the calculation took about 77 hours on the supercomputer Sage. [washington.edu]
    Supercomputer my foot!

    The connection has timed out
    The server at sage.math.washington.edu is taking too long to respond.
    • Re: (Score:1, Informative)

      by Anonymous Coward
      It is just our luck that the the server room is undergoing major renovations this week...

      See a mirror, e.g. http://sage.scipy.org/sage/ [scipy.org]

      FYI, sage is fully (GPL/GPL-compatible) open source.
  • by Ambitwistor (1041236) on Monday March 19, 2007 @02:44PM (#18404315)
    Category theorist John Baez has a summary [utexas.edu] 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?

    • by GrEp (89884)
      http://modular.math.washington.edu/sage.html [washington.edu] This was the "supercomputer"? A 16 node AMD box? Your local library's computer lab would like to have a word with them.
    • Re: (Score:2, Informative)

      by leuffi (830572)
      E8 is not a finite group so it cannot be embedded in a finite symmetric group.
      • by GrEp (89884)
        How about if you took it "modulo" powers of 2 or something. Are there any useful finite analogs?
        • by leuffi (830572)
          The closest would be its compact model, which is pretty well understood. It is possible to describe E8's Lie algebra in terms of generators and relations.

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