E8 is 248-dimensional? How is that possible?

Question

I just read this article about how mathematicians have solved and mapped E8 and that it is 248-dimensional. Can someone explain how it's possible for something to have 248 dimensions?

http://news.yahoo.com/s/afp/20070319/ts_alt_afp/ussciencemathematicsfrancegermany_070319121747

Answer 1

Sure ... it's mathematical dimensions. not physical dimensions. You've probably taken algebra and are used to x and y as variables. That defines a two dimensional system. Add z and you go up to three dimensions; add more variables like u and w and you're up to five variables or 5 mathematical dimensions. They have no physical meaning. E8 just has 248 variables associated with it.

Answer 2

Dimensions are weird, but they're countable. We live in what we commonly know as 3 dimensions. But there's also 3 1/2 dimensions, 1.343 dimensions, and there's even a pi dimension! It's based on the study of dimensional geometry, which treats dimensions as the creation of shapes. There's no real way to define "dimension" with a concise definition.

Answer 3

Thanks for the heads up about the E_8 article. What's been said about higher dimensions sounds good. Reminds me of one of those philosophical college dorm discussions. The friend who asked me this came to the conclusion that mathematicians pare down what we mean by dimension (just so many variables) in order to work with lots of dimensions. There's lots of neat stuff that happens in higher dimensions, but when we talk about, say, the kissing number in 24-space, those dimensions don't have the same homey feel as the spatial 3 dimensions we inhabit.

Answer 4

A line is one dimentional.
A square is two dimentional.
A cube is three dimentional.

If you imagine a 3D cube, you have the x direction, the y direction, and the z direction. This is like width, length, and height.

All of the directions are perpendicular to eachother. This is the opposite of being parallel, like think of a cross.

Mathematically, if I want to add another dimention, I just add it.
Now I have x, y, z, and w. Obviously since I am working with four dimentions, and I can only see three of them, I have no way to draw in the w direction but I can work with it mathematically just like any other direction as long as I assume it's perpendicular, or at a 90 degree angle so to speak, to all the other directions.

I can actually add as many dimentions as I want but mathematically I don't work with one direction any differentally than another. It just makes the problem more difficult to work with because there's more computing to do.

While mathematically, a dimentions represents a direction, physically it can represent something else, like a moment of inertia, for example.

Answer 5

It is part of string theory...everything in string theory is based on a minimum of 11 dimensions...