**Float to the top or sink to the bottom. Everything in the middle is the Churn.**

I wrote a paper, and, when requested, I published it (https://link.springer.com/article/10.1007/s00006-018-0820-8). It’s a very pretty paper, extending the notion of 8-d Bott periodicity in Clifford algebras to a 24-d periodicity. This mirrors the exceptionality of the dimensions 2, 8, and 24 in lattice theory. Hyper-cool.

**“There was a button,” Holden said. “I pushed it.” “Jesus Christ. That really is how you go through life, isn’t it?”**

As is true of almost everything I’ve written and often published in theoretical and mathematical physics, the paper linked to above (call it *Bobbie*) utilizes the 3 division algebras, **C**, **H**, **O**, which are linked to even more fundamental topological objects, the parallelizable spheres of dimensions, 1, 3, and 7.

I frequently encounter papers exploiting the split octonions in their theory building. This requires replacing 4 of the 8 basis elements of **O** with i times those elements, where customarily i is taken to be the imaginary unit of **C**. One can also make split versions of **H** by similarly modifying 2 of its basis elements. But this method does not extend to **C**, as i is an element of **C** already. This is rather annoying.

In *Bobbie* this problem was remedied by replacing i by a new imaginary unit ι, and supplementing **C**,**H**,**O** with a distinct complex number field, *C.* Via the imaginary unit ι, all 3 of the division algebras have split versions. It’s very cool.

**I am that guy.**

Then it occurred to me …

**C** is generally assumed to be the number system from which arises all of complex analysis. **C** is recognized to be part of a unique and exceptional finite series of division algebras, and inspired by this fact over the past several decades many have tried to turn **H** and **O** into analytical doohickeys in the manner of **C**. These efforts have met with varying degrees of failure. And why?

Because **C** *is not* the foundation of complex analysis, *C* is. **C**,**H**, and **O**, are a set of mathematical objects relating to topology, geometry, and algebra. They are architectural. They can be viewed as real algebras, but they are really *C* algebras, where *C* is the mathematical field from which all our nice analysis – Green’s functions, Cauchy-Riemann equations, QFT, … – arise. So, because something is true of *C* does not mean it can be generalized to **H** and **O**. The field *C* is separate; it is not part of a series of mathematical objects.

Got it? All the division algebras have split versions. **H** and **O** are not the foundations of higher dimensional analytical theories. And **C** isn’t either.

Mother Nature suspects you will doubt this obvious Truth. Punishment is being prepared to meet your obstreperous petulance.