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Checking the Math on a Huge Theoretical Problem
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Checking the Math on a Huge Theoretical Problem

Research News

Checking the Math on a Huge Theoretical Problem
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SCOTT SIMON, host:

This week mathematicians at MIT presented the results of four years' labor on a huge series of equations, more than 200 billion equations they say. Can't all those mathematicians be more precise than that? Now, the mathematicians says the resulting computations could help them understand the theory of everything, also known as string theory.

That's the theory that the universe is made up of tiny vibrating strings. Will it help us understand why a small is a tall and a medium is a grande? Our math guy, Keith Devlin, joins us now from New York. Keith, thanks very much for being with us.

KEITH DEVLIN: Hi, Scott. Thanks for having me on.

SIMON: Now, this story has gotten a lot of attention this week. And in fact our colleagues over at weekday edition - I'm sorry, ALL THINGS CONSIDERED - spoke to the director of the American Institute of Mathematics. But you heard that. What's the whole story? What were researchers trying to calculate?

DEVLIN: Okay. So this is all about a concept known as symmetry. The mathematical concepts of symmetry. Now, we like many other creatures are hardwired to respond to symmetry. The movie stars we find the most attractive are the ones with the most symmetrical faces. We respond to symmetry in bridges and buildings, other kinds of architecture and so forth.

And it turns out that the universe also likes symmetry. The essence of symmetry is simply looking the same from different perspectives. Now science is about finding as many perspectives as you can on things in the universe that are not visible to the visual eye, fundamental particles, fields, the kind of thing that matter is made of.

And to understand those, we write down mathematical equations. And when we write down those equations, they in a sense provide us a way of seeing those things. And sometimes when we see these things through equations, we recognize that they also have symmetries. They have the same mathematical appearance however we look at them.

SIMON: How searched-for has this answer been?

DEVLIN: In the early part of the 20th century, a Norwegian mathematician called Sophus Lie develops a kind of - a variance of group theory, this kind of fancy multiplication tables, to enable to understand the patterns of physics. He was able to recognize four different families of these so-called - we now call them Lie groups in his honor - which captured most of the symmetries that arise in physics.

However, subsequent mathematicians discovered that there were five unusual multiplication tables that didn't fit these patterns. One of them, E8, was like the Mount Everest of Lie groups. Because E8 describes the symmetries of the object in the mathematical universe, which is the most symmetrical that we can ever have. It's the most interesting symmetry, the most complicated symmetry there can ever be.

A square, for example, has just one way it's symmetrical. If you would turn it to 90 degrees, it looks the same. E8 describes the symmetries of an object with 57 dimensions. And this particular object has 248 different ways in which it's symmetrical.

SIMON: What's been established this week that makes our understanding of symmetry deeper?

DEVLIN: To understand the universe, you have to understand its symmetries. That means you have to use the language of group theory. So practically all of 20th century physics is written in the language of group theory. Chemists use it to study crystallography. Internet security, security of digital files often depends upon group theory. That's a fundamental language of the universe.

SIMON: Keith, my mind is reeling, but in a good way. Keith, thanks very much.

DEVLIN: Okay. My pleasure, Scott.

SIMON: Our math guy, Keith Devlin, speaking with us from New York.

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