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E8 Structure Decoded
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)."
Apologies -- this post uses a lot of technical jargon. However, the article is so badly written that I decided to post some remarks. And yes, I am a professional mathematician.
First, what they mapped was not the "structure" of the Lie group E_8 -- the structure of the group has been known for a long time. What they mapped is what are called the "representations" of the group E_8, which is part of Vogan's program to understand the "unitary dual" (=list of representations) for all (reductive) Lie groups.
Second, this has no relevance to grand unified theories. Even though a (compact) form of E_8 can be the gauge group of a GUT, the relevant representations are finite-dimensional and have been classified by Weyl decades ago.
Finally, this is an important result. It is relevant to number theory, and to abstract mathematics in general. The fact that a (finite) computer calculation can help determining an infinite list of representation is very nice.
Should an encyclopedia try to give a layman's definition of something that probably really is beyond the reach of the average person?
// MD_Update(&m,buf,j);
is, of course the third worst in the universe.
E8 is not a Lie Group. E8 is the biggest Lie Group.
:D
It seems somebody flunked basic set theory.
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- - You can't take something off the Internet! That's like trying to take pee out of a swimming pool.
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.
It's a small world and it smells funny; I'd buy another if it wasn't for the money; Take back what I paid (SoM)