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E8 Structure Decoded

Hemos posted more than 7 years ago | from the get-it-down-on-paper dept.

Math 127

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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127 comments

Pronounce it "Lee-eh" (3, Informative)

G3ckoG33k (647276) | more than 7 years ago | (#18400415)

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

Re: Pronounce it "Lee-eh" (4, Funny)

Anonymous Coward | more than 7 years ago | (#18400443)

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

Re:Pronounce it "Lee-eh" (0)

Anonymous Coward | more than 7 years ago | (#18400555)

From TFA :
E8, (pronounced "E eight") is an example of a Lie (pronounced "Lee") group.

Re:Pronounce it "Lee-eh" (4, Informative)

Anonymous Coward | more than 7 years ago | (#18400629)

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

Re:Pronounce it "Lee-eh" (4, Informative)

G3ckoG33k (647276) | more than 7 years ago | (#18400777)

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...

Re:Pronounce it "Lee-eh" (0)

Anonymous Coward | more than 7 years ago | (#18400991)

Actually the summary is correct. Pronounce it Lee as in Bruce. (I just had a lecture in the auditorium named after him)

Re:Pronounce it "Lee-eh" (0)

Anonymous Coward | more than 7 years ago | (#18403139)

...and you probably pronounce the second letter of the Greek alphabet "bay tuh" since that's what they say in lectures. What do those Greeks know, anyway?

Re:Pronounce it "Lee-eh" (0)

Anonymous Coward | more than 7 years ago | (#18402919)

As a German I would pronounce it "Lee" as well. But instead of E8 I would say something
like "A" Acht. I would also say stuff like

"Would someone please pass me the butter?" - "Wuerde mir jemand bitte die Butter reichen?"
          "Here please" - "Hier bitteschoen"
"When will the next train for ... leave?" - "Wann faehrt der naechste Zug nach ... ab?"
          "The next train will leave in ... hours" - "Der naechste Zug faehrt in ... Stunden."
"Would anyone like more wine?" - "Moechte jemand noch jemand Wein?"
          "Yes, please!" - "Ja bitte!"
"Ich habe meinen Ausweis vergessen!" - "I forgot my papers!"
          "I have to arrest you!" - "Ich muss Sie festnehmen!"

These are arbitrary samples of sentences that are spoken throughout Germany, Austria and
Switzerland every day by millions of German speaking people. Now if you only knew the
pronounciation.

Re:Pronounce it "Lee-eh" (0)

ghoti (60903) | more than 7 years ago | (#18404247)

"Moechte jemand noch jemand Wein?"
That's usually the sign that they've had too much ...

Re:Pronounce it "Lee-eh" (0)

Anonymous Coward | more than 7 years ago | (#18401409)

I'd think so myself, but my mathemathics teacher pronounced it lee, and he should have known, that being his name and all. (I don't think he was related, though!)

Re:Pronounce it "Lee-eh" (2, Funny)

Cheapy (809643) | more than 7 years ago | (#18401587)

Lee-eh! L-E-E--E-H! L-E-E--E-H!

Poor mathematician. He must've been killed by Snu-Snu. Or maybe lucky mathematician...

iPod (4, Funny)

slashdottinitup (912090) | more than 7 years ago | (#18400431)

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:iPod (2, Insightful)

Dara Hazeghi (1076823) | more than 7 years ago | (#18400651)

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:iPod (2, Funny)

Short Circuit (52384) | more than 7 years ago | (#18400883)

It's better than LoCs and telephone books. I just wish they'd mentioned the encoding bitrate...

Re:iPod (0)

Anonymous Coward | more than 7 years ago | (#18401135)

60GB/45day = 123.45679 kbit/s

Re:iPod (2, Informative)

Short Circuit (52384) | more than 7 years ago | (#18401321)

Nope. Actually, it's 129.453827 kbps [google.com] . (Is there anything Google can't do?)

Re:iPod (1)

maxwell demon (590494) | more than 7 years ago | (#18402015)

Is there anything Google can't do?

Decode the structure of E8?

Re:iPod (0)

Anonymous Coward | more than 7 years ago | (#18403981)

See why kids love Cinnamon Toast Crunch?

Re:iPod (4, Insightful)

SatanicPuppy (611928) | more than 7 years ago | (#18400937)

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:iPod (2, Funny)

Wooster_UK (963894) | more than 7 years ago | (#18401699)

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?

Re:iPod (0)

Anonymous Coward | more than 7 years ago | (#18401943)

42 and 42, respectively.

It seems lame to us.. (2, Funny)

Peter Trepan (572016) | more than 7 years ago | (#18401803)

Typical geek attitude. If it's not Vorbis, it's LAME [wikipedia.org] .

Re:It seems lame to us.. (1)

alienmole (15522) | more than 7 years ago | (#18403323)

You don't have to shout.

Re:iPod (1)

skeevy (926052) | more than 7 years ago | (#18403269)

...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.

Re:iPod (1)

Plutonite (999141) | more than 7 years ago | (#18403733)

I'm personally glad they didn't say anything about football fields.

Re:iPod (1)

bkr1_2k (237627) | more than 7 years ago | (#18404559)

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 size to them.

It's like the distance from one end of the solar system to the other. Most people simply can't comprehend the difference because they don't need to and they have no association. If you compare that distance to something we understand and can actually grasp, say the distance from London to New York, then it becomes an almost imaginable thing.

Re:iPod (1)

illeism (953119) | more than 7 years ago | (#18405447)

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...

Re:iPod (1)

SomeoneGotMyNick (200685) | more than 7 years ago | (#18402933)

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]

Pronounce... (5, Funny)

spazmolytic666 (549909) | more than 7 years ago | (#18400441)

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

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

No practical applications? (1)

PIPBoy3000 (619296) | more than 7 years ago | (#18400453)

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.

Re:No practical applications? (4, Informative)

necro81 (917438) | more than 7 years ago | (#18400535)

But of course it has practical applications: it applies to string theory! [aimath.org]

mandatory Wikipedia link (4, Informative)

cpct0 (558171) | more than 7 years ago | (#18400481)

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.

Re:mandatory Wikipedia link (5, Insightful)

kestasjk (933987) | more than 7 years ago | (#18400609)

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

Re:mandatory Wikipedia link (3, Insightful)

Tx (96709) | more than 7 years ago | (#18400763)

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.

Re:mandatory Wikipedia link (4, Insightful)

superwiz (655733) | more than 7 years ago | (#18401511)

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:mandatory Wikipedia link (2, Insightful)

mbrod (19122) | more than 7 years ago | (#18402231)

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 the back. And then how a index in the back organized in way A vs. way B is better or worse. There are always analogies to be found that people understand. Requires a good writer though and certainly not all of us are as good as Kaku.

Re:mandatory Wikipedia link (5, Insightful)

jd (1658) | more than 7 years ago | (#18403361)

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.

Re:mandatory Wikipedia link (1)

kabocox (199019) | more than 7 years ago | (#18405879)

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 sitting in the waiting room or the nurse taking your weight ect. until the doctor actually sees you. I explain anything like re-installing OS/major apps as drastic surgery with a chance of causing death if anything goes badly wrong. Giving mom that kinda of expectation, she is always pleased that the computer runs after I touch it and not entirely dead. Of course my boss thinks that I can raise the dead so it all evens out.

Re:mandatory Wikipedia link (1, Insightful)

eh2o (471262) | more than 7 years ago | (#18401867)

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 that information I can determine if its worth the effort to actually learn it. This sort of information can also be found in books like Hyperspace, and IMHO, is also just about the only real information they contain other than some historical details.

Re:mandatory Wikipedia link (0)

Anonymous Coward | more than 7 years ago | (#18403065)

Since this is basically informational content it is readily found on Wikipedia or elsewhere and typically vastly easier to understand than the concept itself

Your argument is that it shouldn't be in Wikipedia because it can be found in Wikipedia.

Re:mandatory Wikipedia link (2, Interesting)

asninn (1071320) | more than 7 years ago | (#18402197)

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-theory]] and [[M-theory simplified]]. 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. :)

Re:mandatory Wikipedia link (0)

Anonymous Coward | more than 7 years ago | (#18402367)

[Can't be bothered for an account, so posting AC]

As a mathematician, I think a lot about explaining what I do to the layperson. I'm somewhat of the opinion that most current mathematics can not be explained in every day language, or at least not in 10 minutes. Given some one with some interest in the subject I could reasonably quickly give them an overview in a "what things do I work on, and why?" sort of way. But reasonably quickly here is painfully slow to what most people want. I'd need at least a week, several hours a day, and probably longer than that considering that people can only absorb so many new points of view at once. It took several years for me to learn this stuff, and there's only so much I can compress it down.

So what I'm reduced to is saying something like "Remember graphing equations like x^2+y^2=1 in high school? It's like that, but better. We look at more complicated equations like x^3 * y^2+z^4=0. What does it look like? Can we classify the possible shapes an equation can give?" And so on. But actually, this is only tangentially related to my area (commutative algebra). Most people just don't have any thing they can relate to even the basics of my area. If they haven't had any physics then I can't say, "A module over a ring is basically like a vector space," because they don't know what a vector space is. And a module is the basic, ground-level idea. Most of what I work with is an abstraction of an abstraction, and they are probably not familiar with the concrete example this all was abstracted from. Add to this the fact that saying math in words to people who are not used to hearing math in words causes instant confusion.

I would dearly love to be able to share some of the excitement of my discipline, but I honestly don't know how it can be done in a single article or a 10 minute pitch.

And let's not forget the near universal reaction when someone hears that I do math: "Oh? I always hated math in school."

Re:mandatory Wikipedia link (0)

Anonymous Coward | more than 7 years ago | (#18401175)

A general encyclopedia, yes. A mathematics encyclopedia, no. If you want a technical definition, there are technical sources.

Re:mandatory Wikipedia link (2, Interesting)

LordSchnitzel (677741) | more than 7 years ago | (#18401609)

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.

Re:mandatory Wikipedia link (1)

foniksonik (573572) | more than 7 years ago | (#18401769)

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.

Re:mandatory Wikipedia link (0)

Anonymous Coward | more than 7 years ago | (#18403635)

My brother wrote his PhD thesis on something about Lie groups, but I bet he can't completely decipher the article either.

Re:mandatory Wikipedia link (1)

pfafrich (647460) | more than 7 years ago | (#18405177)

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_diagra 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 articles which could do with someone taking the time to write in terms more accessable to the layman.

Which Century? (0)

Anonymous Coward | more than 7 years ago | (#18400519)

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.

NCIS reference (0, Redundant)

Stephan Seidt (803125) | more than 7 years ago | (#18400557)

Tony: Gibbs, how could you possibly know that?
Gibbs: Well Tony, my GUT told me.

Not a Lie Group. (4, Informative)

WK2 (1072560) | more than 7 years ago | (#18400567)

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]

obvious joke! (0)

Anonymous Coward | more than 7 years ago | (#18401007)

so does that make them the biggest group of liers in the world then?

Sorry!

Re:Not a Lie Group. (1, Informative)

Anonymous Coward | more than 7 years ago | (#18401149)

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 :-)

Re:Not a Lie Group. (1)

sconeu (64226) | more than 7 years ago | (#18401261)

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..."

Re:Not a Lie Group. (4, Funny)

haakondahl (893488) | more than 7 years ago | (#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:Not a Lie Group. (2, Funny)

pfafrich (647460) | more than 7 years ago | (#18404953)

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 infinite sequence, higher dimensional spaces kind of get simpeler after a while which don't allow for E_11 to exist.

Re:Not a Lie Group. (0)

Anonymous Coward | more than 7 years ago | (#18405199)

which don't allow for E_11 to exist.

*engage ultra-pedant mode*

Actually, there is a Lie group E_{11}; there are even conjectures (according to Wikipedia, YMMV) that it relates to string theory. It's just not a very nice object (it's a nonaffine Kac-Moody group); for most purposes, one rarely sees any E_n for n>9, and E_9 isn't that common.

Re:Not a Lie Group. (5, Funny)

Alsee (515537) | more than 7 years ago | (#18401897)

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

It seems somebody flunked basic set theory. :D

-

Re:Not a Lie Group. (1)

Dachannien (617929) | more than 7 years ago | (#18402291)

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

QED!

Representation Theory (5, Informative)

l2718 (514756) | more than 7 years ago | (#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.

Vogan mathematics... (5, Funny)

Anonymous Coward | more than 7 years ago | (#18400715)

is, of course the third worst in the universe.

Re:Representation Theory (0)

Anonymous Coward | more than 7 years ago | (#18400727)

O_o .. So what does it do? (In English.. PLEASE )

Re:Representation Theory (2, Funny)

LiquidCoooled (634315) | more than 7 years ago | (#18401005)

CAT: [to RIMMER] What IS it?
RIMMER: It's a rent in the space-time continuum.
CAT: [to LISTER] What IS it?
LISTER: The stasis room freezes time, you know, makes time stand still. So whenever you have a leak, it must preserve whatever it's leaked into, and it's leaked into this room.
CAT: [to RIMMER] What IS it?
RIMMER: It's a singularity, a point in the universe where the normal laws of space and time don't apply.
CAT: [to LISTER] What IS it?
LISTER: It's a hole back into the past.
CAT: Oh, a magic door! Well, why didn't you say?

Re:Representation Theory (1)

lpangelrob (714473) | more than 7 years ago | (#18400759)

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!"

Re:Representation Theory (1)

guruevi (827432) | more than 7 years ago | (#18400871)

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:Representation Theory (1, Funny)

Anonymous Coward | more than 7 years ago | (#18401435)

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:Representation Theory (2, Informative)

nanosquid (1074949) | more than 7 years ago | (#18401237)

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:Representation Theory (3, Funny)

pushing-robot (1037830) | more than 7 years ago | (#18401249)

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.

Re:Representation Theory (0)

Anonymous Coward | more than 7 years ago | (#18403313)

Best HHGTG reference yet!

Amusing quote from article (3, Funny)

CrazyJim1 (809850) | more than 7 years ago | (#18400615)

"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.

Re:Amusing quote from article (1)

56ker (566853) | more than 7 years ago | (#18400663)

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!)

Re:Amusing quote from article (1)

Tom Womack (8005) | more than 7 years ago | (#18403435)

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 routinely done commercially for chip simulation or seismic inversion.

On the other hand, even if some of the tricks they used were fairly routine (you have a reasonable idea how large the coefficients are? The coefficients are obtained only by multiplication and addition? Why not calculate modulo lots of coprime one-byte integers and save a factor eight in storage space?) it's remarkably clever work.

http://atlas.math.umd.edu/kle8.narrative.html [umd.edu]

and

http://atlas.math.umd.edu/kle8.html [umd.edu]

are a description of the project aimed at reasonable mathematicians, with a lot more in them than the press release; but I think this item is mostly useful to tell mathematicians how to write a press release which gets picked up about what is fairly abstruse work by the standards of computational group theory.

Re:Amusing quote from article (1)

PlusFiveTroll (754249) | more than 7 years ago | (#18405819)

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 of.

Re:Amusing quote from article (1)

anothy (83176) | more than 7 years ago | (#18401031)

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?

Re:Amusing quote from article (0)

Anonymous Coward | more than 7 years ago | (#18401127)

Library's of Congress are good, but my preferred Metric is how quickly can this devour an entire cow.

Oh Please (-1, Redundant)

imikem (767509) | more than 7 years ago | (#18400617)

They're obviously Lieing.

Yep, thought that one up all by myself. Off to stand in the corner now... facing the wall.

Now they can move on to... (0, Offtopic)

Alzheimers (467217) | more than 7 years ago | (#18400765)

Now they can move on to their next task, understanding why anyone would drink V8 [wikipedia.org] .

Re:Now they can move on to... (0, Offtopic)

hpc4u (978056) | more than 7 years ago | (#18401059)

Well, I laughed. I drink the stuff from time to time.
Flamebait seems a bit harsh. Offtopic, maybe.

I'm no mathemtician but... (4, Funny)

east coast (590680) | more than 7 years ago | (#18400795)

So now we're going to have truth and lie tables?

Stop this crazy planet. I want to get off!

Bad Poetry (0)

Anonymous Coward | more than 7 years ago | (#18401019)

To me it all sounds like bad Vogan poetry...

- Peder

Re:I'm no mathemtician but... (2, Funny)

MarkGriz (520778) | more than 7 years ago | (#18401155)

"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.

Re:I'm no mathemtician but... (-1, Troll)

Anonymous Coward | more than 7 years ago | (#18402897)

when reading about "mapping a Lie group" I first thought they meant that the conspiracy between the USA, Great Britain, and some other European countries about "invasion of Iraq" and "war on terrorism" had been unraveled...

I bet the American mathematicians..... (-1, Flamebait)

Anonymous Coward | more than 7 years ago | (#18400825)

in the team made the tea for the European mathematicians on this one. When has the US ever done any clever thinking?

Re:I bet the American mathematicians..... (0, Offtopic)

Anonymous Coward | more than 7 years ago | (#18400933)

If you've ever tried tea made by an American you'll know that your previous statement is false.

Units? (2, Funny)

Hemogoblin (982564) | more than 7 years ago | (#18400921)

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)?

Re:Units? (1)

dohzer (867770) | more than 7 years ago | (#18401547)

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?

See the symmetries of the standard model (4, Informative)

sweetser (148397) | more than 7 years ago | (#18400927)

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 Character Table for E8, or (0)

Anonymous Coward | more than 7 years ago | (#18400955)

How We Wrote Down a 453,060 x 453,060 Matrix and Found Happiness,"

2nd worst, poetry, ever, professor Vogon.

my GUT instinct tells me.. (2, Funny)

laggist (784355) | more than 7 years ago | (#18401069)

the answer is 42!

Well-known! (1)

bdonalds (989355) | more than 7 years ago | (#18401097)

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!

Re:Well-known! (1)

alienmole (15522) | more than 7 years ago | (#18403445)

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. :)

Gee whiz I remembered (1)

ibm1130 (123012) | more than 7 years ago | (#18401177)

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?

Ouch, my head!! (1)

purpleraison (1042004) | more than 7 years ago | (#18401721)

I'm not sure, but I think my head exploded into E8 pieces...

wrong century (1)

1u3hr (530656) | more than 7 years ago | (#18401903)

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?

Re:wrong century (0)

Anonymous Coward | more than 7 years ago | (#18403833)

Sophus Lie died in 1899. So not "last" century.
I'd chalk it up to an off-by-one error on Lie's part.

genetic algorithm? (1)

Tablizer (95088) | more than 7 years ago | (#18402133)

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.
     

Sage the "super" computer (3, Insightful)

LotsOfPhil (982823) | more than 7 years ago | (#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:Sage the "super" computer (1, Informative)

Anonymous Coward | more than 7 years ago | (#18404275)

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.

Shouldn't it read "century before last" ??? (0)

Anonymous Coward | more than 7 years ago | (#18403117)

The 1800's would now be century before last. (He's probably still writing 1st. millennium on checks)

Summary by a mathematician (3, Interesting)

Ambitwistor (1041236) | more than 7 years ago | (#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."

What are the generators? (1)

GrEp (89884) | more than 7 years ago | (#18405377)

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?

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