[jvkersch]

Not quite -- the comment refers to the fact that R^d has the structure of a normed division algebra in dimensions 1, 2, 4, and 8. This means that you can multiply things together in a nice way when you're in one of those spaces. For R^1, this is just multiplying real numbers, for R^2 it's multiplying complex numbers, R^4 is quaternions, and R^8 is octonions. As you go up in dimensionality, you lose more and more nice properties: the quaternions are not commutative and the octonions are also not associative (which is why there's no mention of them in the blog post). The point is that in dimension 1, 2, and 4 all sorts of interesting things happen. John Baez has a paper about this: http://math.ucr.edu/home/baez/octonions/node1.html