248 Dimensions

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Here’s a beautifully esoteric piece of math news: a team of mathematicians has meticulously explored and completely mapped a hitherto-unknown 248-dimensional structure, called E8. The E8 is an example of a Lie Group, which represent the best developed theory of continuous symmetry of mathematical objects and structures. Lie Groups underlie any symmetrical object.

From the Atlas Team’s website:

“Lie groups come in families. The classical groups rise like gentle rolling hills towards the horizon. Jutting out of this mathematical landscape are the jagged peaks of the exceptional groups and, towering above them all, E8. E8 is an extraordinarily complicated group: it is the symmetries of a particular 57-dimensional object, and E8 itself is 248-dimensional!”

It took them four years and 77 hours of supercomputer time to unpack the mathematical properties of the entire E8 structure, and the results comprise 60 gigabytes of data. In a surprising attempt to quantify this amount, the Atlas researchers assure us, if we printed this out, it would cover all of Manhattan!

More importantly, however, this mathematical unpacking will aid us in our hunt for a super-unified theory of gravity: if it exists, its underlying symmetries will have to be about as complicated and unique as a Lie Group structure. Maybe E8 fits the bill. Maybe the Theory of Everything looks like this.

The image below is supposed to give us an idea of the root structure of a 248-dimensional object, although it’s actually a Gosset polytope 421, only a 2-dimensional projection of an 8-dimensional object. Hare Krishna!

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It doesn’t matter what you look like, or what you’re made of, or where you come from. As long as you live in this universe, and have a modest talent for mathematics, sooner or later you’ll find it. It’s already here. It’s inside everything. You don’t have to leave your planet to find it.

Carl Sagan, Contact