Mathematicians map structure in 248 dimensions!

A very complex structure was invented more than 100 years ago by a Norwegian mathematician, Sophus Lie (pronounced “Lee”). He invented Lie groups, a way of describing symmetrical objects. (A Lie group is a [set theory] group whose objects form a manifold, and whose group operation is a continuous function.) The last one, E₈, has 248 complex dimensions.

Of course you’re asking, “How could he invent it if he didn’t know where all the pieces were?” Well, he defined the rules for deciding if something was in or out of the group; and he knew that the group would have certain characteristics because he based it on a smooth topological surface.

It took 4 years of work by a team of 19 mathematicians. They capped their work by using 3 days of calculating time on a supercomputer to define all of the members of the group. And the process produced 60 times as much information as the human genome project.

Daniel Vogan of MIT says,

“What’s attractive about studying E₈ 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, E₈ is the hardest one.”

Professor Vogan is presenting the results at MIT in a lecture entitled “The Character Table for E₈, or How We Wrote Down a 453,060 x 453,060 Matrix and Found Happiness.”

The complete characterization of this structure might lead to new discoveries in symmetry and in higher-dimensional physics.

Mark Chu-Carroll at Good Math, Bad Math has a much more informative article. He even explains what a manifold is–a locally smooth curve–and that this structure is defined on a topological space that’s an 8-dimensional manifold. And each of the dimensions is defined by a complex number (one that combines a real number and an imaginary number). After that it gets a bit confusing.

Origins of heterosexuality

Box Turtle Bulletin reviews the latest thought on what turns people into heterosexuals.

If you ask a heterosexual, he or she will generally deny that they had any kind of choice in the matter. They say that they were just born that way or at least knew at the first stirrings of sexual awareness that they were heterosexual. “It just feels natural,” they say and seem genuinely puzzled that anyone would wonder about it.

Variant genes in waiting

Follow the link for a nice article about genes that allow or resist deelopmental changes in response to environmental clues, by P. Z. Myers, in Seed magazine.

I want to borrow the picture. When I was about 8, my grandfather brought me a tomato hornworm, like the green one in this picture, from his garden. He built me a sturdy cage for it, mostly wood with a screened window and a pressure-sensitive latch. My mother said that he was not the kind of man to coddle caterpillars, but he did it for me.

(Illustration by Alison Schroeer)