^{A close-up of the E₈ group’s extensive use of socks and sandals.}

Earlier this year, we gave the Chinscratcher Award For The Sexiest Mathematic Theory Of 2007 to “The E₈ Root System”. In that article, I examined the use of “Socks and Sandals” by the theoretical mathematicians involved. To be honest, I was not aware that others had noticed the “Sock and Sandals” phenomenon previously. However, I think I am first to note the unique predilection of mathematicians for this style of footwear. To demonstrate what I am talking about, I ask the reader to examine the E₈ group photo in detail (click below to see larger version). Here you see the footwear in its raw, uninhibited state:

^{Theoretical Mathematicians Computed The E₈}

The use of socks and sandals here is both extensive and divergent. It cannot be explained by happenstance alone. To understand it, we must look further at the personalities involved here. I am compelled to postulate that the kinesics of this photo can be analyzed using E₈ principles. There is a definite balance between the two sides of mathematicians — the professor on the right withe the blue shirt and very high pants, is probably a unspoken rival to the professor in shorts on the left. Moreover, I posit that the woman in the center group with the blue track suit longs to be head of the group. But she is misguided — because, I believe the true genius of the E₈ here lies inside this fellow:

I believe that this fellow masterminded the intricate complexity of the E₈. In fact, he seems to embody his higher dimensional mathematics in every fiber of his being. Now examine how he is positioned relative to the others in the photograph. Are his kinesics not transcendent of mundane geometries? There is no doubt in my mind that multitudinous E₈ levels that can be explored within this photograph. I hope that others will assist me in the endeavor in the months ahead.

A close-up of part of the E₈.

^{A close-up of the E_8.The E₈visualisation was generated by John Stembridge, who based his computer generation code on a hand-drawn E₈ system by Peter McMullen in the 1960s.}

The Chinscratcher Award for “The Sexiest Mathematic Theory Of 2007″ goes to…“The E₈ Root System”

The E₈ is a 248 dimensional Lie algebra, and you can find out what that means here, or you can watch this colorful video:

Why did the E₈ get the award? First of all, the E₈ Root System is related to the “Exceptionally Simple Theory of Everything” by A. Garrett Lisi. The name of this theory alone brought a glint of envy to my eye. But when it was linked to the exceptionally complex vector drawing above, the sexiest of this theory increased by a power of eight. You can enjoy the E₈ diagram in all its glory by downloading as a PDF file.The E₈ calculation is actually 60 gigabytes in size. Here’s a synopsis of the theory:

All fields of the standard model and gravity are unified as an E8 principal bundle connection. A non-compact real form of the E8 Lie algebra has G2 and F4 subalgebras which break down to strong su(3), electroweak su(2) x u(1), gravitational so(3,1), the frame-Higgs, and three generations of fermions related by triality. The interactions and dynamics of these 1-form and Grassmann valued parts of an E8 superconnection are described by the curvature and action over a four dimensional base manifold.

But perhaps even more interesting than the theory itself, are the people who brought this calculation to life. Their work required a mix of theoretical mathematics and intricate computer programming. They worked on the calculation for four years.

Click on the image above to see the full-size photo. When I look at this photo, one thing I note right away is their feet. If I”m ever trying to hire a mathematician, I’ll just stoop and look under the desk at her feet. If she’s wearing sandals and socks, I’ll hire her on the spot.

^{A close-up of the E₈ group’s extensive use of socks and sandals.}

The other thing I’m pretty sure about is this fellow masterminded most of the E₈ complexity:

I am also compelled to postulate that this photo can be analyzed using E₈ principles. There is a define balance between the two sides of mathematicians, for example the professor on the right withe the blue shirt and very high pants, is probably a direct rival to the fellow in shorts on the left. Truly, there are multitudinous E₈ levels that can be explored within this photograph.