Octonion:
In mathematics, the octonions are a normed division algebra over the real numbers, a kind of hypercomplex number system. The octonions are usually represented by the capital letter O, using boldface O or blackboard bold {\displaystyle \mathbb {O} }. Octonions have eight dimensions; twice the number of dimensions of the quaternions, of which they are an extension. They are noncommutative and nonassociative, but satisfy a weaker form of associativity; namely, they are alternative. They are also power associative. [Wikipedia]
That’s opaque, if I may be polite. Noted in “Octonions: The strange maths that could unite the laws of nature,” Michael Brooks, NewScientist (20 August 2022, paywall):
Mathematicians are excited because they reckon that by translating our theories of reality into the language of the octonions, it could tidy up some of the deepest problems in physics and clear a path to a “grand unified theory” that can describe the universe in one statement. “This feels like a very promising direction,” says Latham Boyle at the Perimeter Institute in Waterloo, Canada. “I find it irresistible to think about.”
Sounds exciting. I wish I had a brain that worked that way.
I’d dust it every day and never let the cat play with it.
