## Saturday, January 1, 2011

### Theory Update 31

Now we can't have the neutrinos all crammed into a point, so let us expand the path diagram to the $81$ dimensional $4$ qutrit space. Now the outer hexagon has nine edges, or six of varying length ($1$ or $2$). The vertices of this hexagon still form a $24$ dimensional space.

1. And note the interior inverted $54$ dimensional triangular hexagon! This has six times the $9$ paths for two qutrits. This is the dimension of one of kneemo's bioctonion Jordan algebras. Many other nice spaces also appear.
2. Hmmm, the number $6/26$ is very close to the CKM parameter $0.231$ (which comes from the Cabibbo angle). Can you find the $26$?