CQT's John Baez introduces the "octonions' to a popular audience

Scientific American article "The strangest numbers in string theory" co-authored with John Huerta.
18 May 2011

The Centre for Quantum Technologies harbours people of many talents, and in May's issue of the popular science magazine Scientific American, CQT Visiting Professor John Baez displays his mathematical pedigree with a tour of alternative number systems.

In "The strangest numbers in string theory", John and his graduate student John Huerta of the University of California, Riverside (John Baez's permanent home as a Professor of Mathematics), recount the history of an eight-dimensional number system known as the octonions.

Invented in the 19th century then largely neglected, octonions gained new fans with the development in physics of string theory and M-theory. These theories seem to imply that our Universe has 10 or 11 dimensions, respectively. Might a reliance on the mathematics of octonions be the underlying reason? Take their eight dimensions and add one of time, plus another one for strings or two for membranes, and the totals tally.

The article mixes explanation of the number systems, graduating from the real numbers (1,2,3...) to octonions through complex numbers and quaternions, with historical whimsy. There's even mention of a case of mathematical graffiti.

You can read more of John Baez's writing at his blog, Azimuth. As well as pursuing his mathematical interests at CQT with work on network theory, he is nurturing an online community of mathematicians applying their acumen to environmental issues.