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E8 Structure Decoded
Posted by
Hemos
on Mon Mar 19, 2007 07:57 AM
from the get-it-down-on-paper dept.
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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A New Theory of Everything? 511 comments
goatherder writes "The Telegraph is running a story about a new Unified Theory of Physics. Garrett Lisi has presented a paper called "An Exceptionally Simple Theory of Everything" which unifies the Standard Model with gravity — without using string theory. The trick was to use E8 geometry which you may remember from an earlier Slashdot article. Lisi's theory predicts 20 new particles which he hopes might turn up in the Large Hadron Collider."
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Pronounce it "Lee-eh" (Score:4, Informative)
Re: Pronounce it "Lee-eh" (Score:4, Funny)
Parent
Re:Pronounce it "Lee-eh" (Score:4, Informative)
Parent
Re:Pronounce it "Lee-eh" (Score:5, Informative)
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...
Parent
Re: (Score:3, Funny)
Poor mathematician. He must've been killed by Snu-Snu. Or maybe lucky mathematician...
iPod (Score:3, Funny)
Hear that? That's the sound of Apple's iPod marketing finally reaching absolute ubiquity.
-The Wolf
Re: (Score:2, Insightful)
Re: (Score:2, Funny)
Re: (Score:2, Informative)
Re:iPod (Score:5, Insightful)
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.
Parent
Re: (Score:2, Funny)
And more to the point, how many War and Peaces are there in a New Jersey?
It seems lame to us.. (Score:3, Funny)
Typical geek attitude. If it's not Vorbis, it's LAME [wikipedia.org].
Re: (Score:2)
Sorry, I'm still trying to convert it to furlongs per fortnight [slashdot.org]
Pronounce... (Score:4, Funny)
It's PRINCESS "Lee-eh" you insensitive clod!
No practical applications? (Score:2)
It does remind me of string theory a bit, though. Heavy on cool math. Light on any practical application.
Re:No practical applications? (Score:5, Informative)
Parent
mandatory Wikipedia link (Score:5, Informative)
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 (Score:5, Insightful)
Parent
Re:mandatory Wikipedia link (Score:4, Insightful)
Parent
Re:mandatory Wikipedia link (Score:5, Insightful)
Parent
Re: (Score:3, Insightful)
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
Re:mandatory Wikipedia link (Score:5, Insightful)
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.
Parent
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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)
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-
Re: (Score:2, Interesting)
Re: (Score:2)
They put some things in layman's terms
Not a Lie Group. (Score:3, Informative)
http://news.bbc.co.uk/2/hi/science/nature/6466129
http://en.wikipedia.org/wiki/E8_(mathematics) [wikipedia.org]
Re: (Score:2)
Or do you mean "E8 is not just a Lie group..."
Re:Not a Lie Group. (Score:5, Funny)
Mine goes to E_11.
Parent
Re: (Score:3, Funny)
Re:Not a Lie Group. (Score:5, Funny)
It seems somebody flunked basic set theory.
-
Parent
Re: (Score:2)
QED!
Representation Theory (Score:5, Informative)
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... (Score:5, Funny)
Parent
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You know, only the Vogon's would be attracted to something that produces that much paperwork.
Re: (Score:2, Informative)
Well, maybe that's surprising to some mathematicians, but this sort of thing is nearly half a century old.
Re: (Score:3, Funny)
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: (Score:2, Funny)
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
Amusing quote from article (Score:4, Funny)
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: (Score:2)
You should see how much memory predicting the weather takes and that's just 4 dimensions (not 248!)
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I'm no mathemtician but... (Score:5, Funny)
Stop this crazy planet. I want to get off!
Re: (Score:3, Funny)
What do you mean "now"?
These have been around since the days of the first engineers and politicians.
Units? (Score:2, Funny)
See the symmetries of the standard model (Score:4, Informative)
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/qua
doug
my GUT instinct tells me.. (Score:2, Funny)
wrong century (Score:2)
Sophus Lie died in 1899. So not "last" century. TFA said "19th-century Norwegian mathematician ...".
Y2K? PEBCAK?
Sage the "super" computer (Score:4, Insightful)
Summary by a mathematician (Score:4, Interesting)
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."