The calculation involved 18 mathematicians for four years? That’s almost as bad as a UK Self Assessment. But the result was worth it – the E8 Lie Group is beautiful, especially when mapped out graphically.
E8 is the greatest Lie of all: a 248-dimensional representation of the symmetries of a 57-dimensional object. The result is a matrix of over 200bn entries, each cell describing a representation of a symmetry group and in relation to its surroundings. (With all those dimensions, I’m a bit surprised that the matrix itself could be written on an Excel spreadsheet, even if the spreadsheet would be bigger than Manhattan. However, most of the values in that spreadsheet are themselves complicated polynomials, so that’s all right then.
What’s exciting for theories of everything like strings is that E8 connects geometry to an important feature of the cosmos – symmetries. Strings are all about symmetries in high dimensions. What if reality is symmetrical, and a Lie Group describes it?
What if E8 is the universe?
It’s a beautiful thought: that the cosmos could one day be described in a great-looking poster.