21 Mar 2007

And Then There Was Much More Maths....

It's scary some times how I can be doing stuff and then just a short time later something relating to it pops up on the Internet. This has just happened with my earlier post regarding my stunning discovery, while building a new garden fence, that mathematics doesn't work.

I start to spread the word, then, lo and behold, I find this lot!! It's obvious to me that I have hit a nerve in the academic world and they have ganged together in an attempt to fight back. Personally, I believe they are just digging themselves further and deeper into a hole. I mean really, Lie groups and the ever popular E8?

They have even added a picture of the type I ridiculed in my post. You believe that? And just what IS he doing on that blackboard? Remember what I said? Look closely - no numbery things, no dividy stuff, so where's the maths?

This, by the way, is not a set up; this is as I found it on the web. Oh, alright, I added the garden fence bitties. But that's all. Honest. So read on, but remember the basic findings I made earlier; MATHEMATICS DOES NOT WORK.

Familiar structures such as balls, cones and garden fences have symmetry in three dimensions, and there are Lie groups to describe them. E8 is much bigger. {Guess they are moving on from dividy and multpli... multypl... times by stuff.}

"What's attractive about studying E8 is that it's as complicated as symmetry can get", observed David Vogan from MIT.

"Mathematics can almost always offer another example that's harder than the one you're looking at now, but for Lie groups, E8 is the hardest one. Especially for garden fence builders".

Professor Vogan is presenting the results at MIT in a lecture entitled The Character Table for E8 and Garden Fences, or How We Wrote Down a 453,060 x 453,060 Matrix and Found Happiness. {Each to his own I guess.}

A garden fence is one of the most symmetrical mathematical structures in the universe. It may underlie the Theory of Everything that physicists seek to describe in the universe and the garden.

Eighteen mathematicians spent four years and 77 hours of supercomputer computation to describe this structure, with the results unveiled Monday at a talk at MIT. {Only took me two days. Could this be why it didn't fit?}

But it's still not easy to describe the description, at least not in words. {loosing me now.....}

"It's pretty abstract," conceded Jeffrey D. Adams, the professor who led the project. {You could say that.}

A 19th-century Norwegian mathematician, Sophus Lie wrote down what are now known as Lie groups, sets of continuous transformations — meaning the changes could be a little or a lot — that leave an object unchanged in appearance.

For example, rotate a sphere or garden fence any distance around any axis, and the sphere of fence looks exactly the same. {Makes sense to me.}

Later mathematicians found five exceptions to the four classes of Lie groups that Lie knew about. The most complicated of the "exceptional simple Lie groups" is E8. It describes the symmetries of a 57-dimensional garden fence that can, in essence, be rotated in 248 ways without changing its appearance. {Or how it fits, apparently.}

Why are there five exceptional Lie groups? "It's just one of the beautiful magical things that happen in mathematics and fence building," Dr. Adams said.

"You can't really picture it," Brian Conrey said. {That's obvious from the blackboard stuff don't you think?}

Remarking on a suburban garden fence, Dr. Conrey said, "It's some sort of curvy, torus, fency type of thing. Now you start to move it around in different ways. It's an amazingly symmetric fence."

To understand using E8 in all its possibilities requires the calculation of 200 billion numbers. That is what Dr. Adams's team did. {OK. And then?}

Robert L. Bryant, a mathematician at Duke who was not involved in the project, gave a biological analogy. Scientists can learn a lot about a garden fence from its DNA, but to understand it fully "you have to build one and then study it," Dr. Bryant said. "In a certain sense, that is what the E8 team did. They used massive computation to fully develop the group E8 and its representations so that they could list its important features relating to garden fences."

One eventual use, other than garden fence building, could be understanding the universe, another example of physics taking advantage of abstract math.

"All of the physics of the 20th century is tied up with this language", Dr. Conrey said.

E8 is the Lie group underlying some superstring theories that physicists are pursuing in an effort to tie gravity and the other fundamental forces of the universe into one theory.

"It could be E8 that determines the deep inner structure of all garden fences." Dr. Adams said. {So there you go then.}

Quote - Bertrand Russell;

Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.

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