Regarding octonions, sedenions and physics Tony Smith has a huge amount of pertinent ideas on his website, e.g.
http://www.innerx.net/personal/tsmith/QOphys.html http://www.innerx.net/personal/tsmith/d4d5e6hist.html His ideas are colorful and speculative, but also deep and interesting. One could spend a very long time soaking up all the ideas on the site. By the way, Tony is a very nice guy, who did a postdoc under Finkelstein (of quantum set theory fame) and earns his living as a criminal-law attorney. I spent some time a few years back trying to create a novel physics theory based on discrete Clifford algebras, which relate closely to quaternions and octonions. My effort was unfinished, and I turned my attention to other types of science, but some of my notes are at: http://www.goertzel.org/papers/main.htm (scroll to the bottom to see a list of documents under the heading "Some Incomplete Speculations on the Foundations of Physics" -- Ben Goertzel