Geoffrey Dixon
Dear Geoffrey,
I rarely feel so lucky and pleased to read something with which I agree almost completely. Your essay gave me this high satisfaction, so thank you. There may be two points where we slightly diverge, but only as a matter of preference. The first one is that I may be a bit biased towards geometry and consider complex, quaternionic, and octonionic structures as living on real vector spaces. The second one follows from the first one, since the compositions of transformations preserving structures is associative. I fully agree with the paramount role of spinors, but consequently I tend to see them as representations of Clifford algebras (a quite mainstream position among mathematicians). So my views about the Standard Model are shaped by this. Not that I would disagree with you, in fact I think you are right from another perspective. Another consequence of my view is that it kept me away from properly investing time in studying your work, although I I knew about the Dixon algebra and that you made a mathematically beautiful and physically insightful model for leptons and quarks. It's time to fix these lacunae I have and read carefully your writings. Your essay convinced me of this, even though you mentioned your work only incidentally, being focused on answering the question "what is 'fundamental'". I also just included in my paper about the Standard Model based on a Clifford algebra a mention of your model (fortunately my manuscript is still under review). I think your work deserves more attention. What I find intriguing is that, unlike Clifford algebras which are infinitely many, the Dixon algebra is one of a kind. Since I still am a bit biased against nonassociativity, I would like to ask you if you know some physical consequences of this feature of octonions. Congratulations for your excellent essay, and success!
Best wishes,