## Saturday, April 30, 2011

### War of the Octonions

Forgot the String Wars, sometimes called the Loop vs String Wars, or better known in the modern era as the Woit-Motl War? Well, fret not, it's back! At the center of the action is a piece written by John Baez and John Huerta in the current issue of Scientific American.

Of course, Peter Woit and Lubos Motl weigh in. Why not?

Peter Woit's take, and some very interesting responses by John Baez, can be found at Woit's weblog Not Even Wrong, here .

Lubos Motl's strong disagreements at his weblog The Reference Frame can be found, here.

For a brief review (or an elementary education, even) for those who don't know what an Octonion is, it's one of 4 division algebras, the first one being the ordinary elementary algebra taught in high school (REAL), the second (COMPLEX) known to Calculus students and Engineers and Scientists worldwide, the other two (Quaternions and Octonions) being a bit more involved. For comparison purposes, they take the forms:

R = a

C = a + bi

H = a + bi + cj + dk

O = a + e1i  + e2j +e3k + e4l + e5m + e6n + e7o  , or something.

In any event, it's just notation folks, don't let it scare you.

The following probably has nothing to do with the above, but I ran into it looking for a cool picture for this post, rather than say just copying Lubos'. It's from Marni Dee Sheppeard's Arcadian Pseudofunctor: Feb. 7, 2011:

### Theory Update 61

In this supercool paper, the authors define a tripled Fano plane(yes, that's right, three copies of Furey's particle zoo). It describes a set of $21=3×7$ (left cyclic) modules over a noncommutative ring on eight elements. The ring is given by the upper triangular $2×2$ matrices over the field with two elements. Similarly for right cyclic modules.
The authors are familiar with the connection between octonion physics and so called stringy black holes. They find it odd that this structure is not studied in physics.