WOW!

Its seems as if a Spark has come up with a Total Theory of Everything based on the E8 simple Lie algebra root system. Gravity, strong nuclear force, weak nuclear force plus electromagnetism (electroweak) now can be mapped onto a diagram of unimaginable complexity.

This diagram or structure is the Everest of the math world: long thought insoluble, new breakthroughs in computer science allowed a dedicated team of 18 mathematicians around the world, working for years, to map out E8. This structure has 248 dimensions. It occupies a matrix of 453060 x 453060 values. If written out on paper, the equation describing it would cover the island of Manhattan. See the news release from MIT here.

I honestly do not understand even the basics of the concept.

A root system is any two lines (actually, vectors) that satisfy a certain set of conditions such that they have a symmetry: for example, the right angle (half pi) in a square and the acute angle in the hexagon (one third pi) are what allows squares and hexagons to fill up a checkerboard with no left over space, a property that octagons (for example) do not share. Those angles can be deduced from what are called Rank 1 and Rank 2 root systems. Irreducible root systems are those that cannot be described as a union of mutually disjointed orthogonal subsystems. The investigations of these ranks produces four classical cases and five exceptional cases. The most interesting (and largest) exceptional case is the E8 case. It is mind-bogglingly symmetrical in a mind-boggling number of dimensions.

What is interesting is that a small part of this diagrams seemed to describe or map onto certain parts of the subatomic particle bestiary investigated by modern physics. Particles were correctly predicted to exist merely because of gaps in the diagram that appeared when the number values for certain particles were mapped onto a small part of this E8 diagram.

Well, now that the whole of the E8 diagram has been defined by this team of mathematicians and their flotilla of computers, a Spark named Garrett Lisi has pointed out more symmetries and relationships that exist between other fundamental particles and forces and other parts of this 248-dimensional object.

Ladies and Gents, this is the stuff science fiction is made of. What if Lisi is correct? What if the reconciliation of quantum mechanics and special relativity just took place? What if this diagram actually holds the key to the fundamental way the physical constants of the universe are put together?

E8 Root System