Sparling’s paper, which was published in the Proceedings of the Royal Society A, lays the groundwork for his theory.

Although the theory is not definitive, Sparling explains that several major ideas in current physics would likely play a role (such as condensed matter physics, category theory, non-commutative geometry, string theory, and the structure of superfluids). Such connections might also point the direction to a unified theory, though this is currently very speculative.

A very good treatment of this topic can be found at: Mathematician suggests extra dimensions are time-like

Orignal paper (PDF): Spacetime is spinorial; new dimensions are. timelike WARNING: Dense math