The octonions are not the founation of physics

I recently read a very interesting piece on the octonions and some argument for that they should be used to form the foundation of physics.

My (current and not very informed) take on this is that they should not. The algebra of the octonions is non-associative. But our world is associative. This really says that our world is not based on he octonions. Instead one should focus on finding a generalized quantum theory based on the quaternions. They capture our world most closely by being non-commutative. As rotations in 4d space is.