## E8 Structure Decoded 127

Posted
by
Hemos

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)."*
## Pronounce it "Lee-eh" (Score:4, Informative)

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

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

## 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...

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

## The story of how it all happened (Score:1)

## iPod (Score:3, Funny)

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

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Decode the structure of E8?

## 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.

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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].

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I still do, no kidding. I use a copy of

War and PeaceI got off of Project Gutenberg to use as a largish text file for performance testing. It runs just over 3MB.Interestingly enough

Les Miserablescomes in at 50k larger.## Re: (Score:1)

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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

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Sorry, I'm still trying to convert it to furlongs per fortnight [slashdot.org]

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I was going to rail about the encoding bit rate, whether the MP3's had tags filled in, etc., but someone

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## Pronounce... (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!

## 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)

## 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)

## Re:mandatory Wikipedia link (Score:4, Insightful)

## Re:mandatory Wikipedia link (Score:5, Insightful)

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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.

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An explanation of mathematics only needs to provide information such as

Similar to explaining 1 astronomical unit, the reader neither needs to memorize the number, nor fully comprehend the distance, just an idea of where it fits in in the general scheme of measurements.

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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

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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

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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

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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-

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They were planning on a Lie groups for Dummies(tm), but it was still over 100 billion pages long, so they canned it.

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They put some things in layman's terms

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## 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]

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It does not get even into top ten as there are infinite number of bigger Lie groups

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Or do you mean "E8 is not

just aLie group..."## Re:Not a Lie Group. (Score:5, Funny)

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.

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

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

somebodyflunked basic set theory.-

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

## 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

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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.

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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

somemathematicians, 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.

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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.

## 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.

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You should see how much memory predicting the weather takes and that's just 4 dimensions (not 248!)

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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

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## I'm no mathemtician but... (Score:5, Funny)

Stop this crazy planet. I want to get off!

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What do you mean "now"?

These have been around since the days of the first engineers and politicians.

## Units? (Score:2, Funny)

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Or does the Manhattans-covered-in-paper SI unit specify a standard font size?

## 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)

## Well-known! (Score:1)

I find it fascinating that some things are so well known that I need instructions on how to pronounce them!

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## Gee whiz I remembered (Score:1)

## Ouch, my head!! (Score:1)

## wrong century (Score:2)

These were developed by the well-known mathematician Sophus Lie (pronounce Lee) in the last centurySophus Lie died in 1899. So not "last" century. TFA said "19th-century Norwegian mathematician ...".

Y2K? PEBCAK?

## genetic algorithm? (Score:1)

Calculation on paper would cover ManhattanIf 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 (Score:4, Insightful)

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

FYI, sage is fully (GPL/GPL-compatible) open source.

## 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."

## What are the generators? (Score:2)

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