I personally think that the split-octonions[1] hold promise for physics. The subset of the split-octonions where the i, j, k, and l components are 0 have a metric that is similar to that of Minkowski space[2].

  (t + xli + ylj + zlk) * (t - xli - ylj - zlk)
  = t^2 - x^2 - y^2 - z^2

[1] https://en.wikipedia.org/wiki/Split-octonion [2] https://en.wikipedia.org/wiki/Minkowski_space

I believe this is somewhat controversial

That was an interesting read! Interestingly, John Baez, author of the originally posted link is also quoted in it.