... octonions are the crazy old uncle nobody lets out of the attic: they are nonassociative.
Comes from a a quote by John Baez. Clearly, the sucessor to quaterions from the Cayley-Dickson process is a numerical beast, but has anybody found any real-world uses for them? For example, quaterions have a nice connection to computer graphics through the connection to SO(4), and that alone makes them worth studying. What can be done with a nonassociative algebra like the octonions?
Note: simply mentioning that they
have applications in fields such as string theory, special relativity, and quantum logic.
is not what I'm looking for (I can read wikipedia too). A specific example, especially one that is geared to someone who is not a mathematician by trade would be nice!