Dear Dr Dray,
Thank you so much for leaving your comments, they're well-taken.
We were happy to reference your and Dr Manogue's "Quaternionic spin" paper in the essay [9], in which you discuss dimensional reduction from 10 to 4 in detail, using octonionic spinors. Important works on octonions, e.g. by M. Günaydin, F. Gürsey, S. K. Adler, S. Okubo, F. Toppan, and many more could not be referenced, due to the constraints of the essay contest (5000 words, enjoyable, less technical than a review article, original content). We had to leave out octonion treatment of the strong force, supersymmetry, Yang-Mills instantons, and octonion uses in GUTs and String Theory, and instead focus on space and time operators, what a non-associative background infers for the time evolution of a general operator, and how extraction of information over time is somewhat "unnatural" to a quantum system.
Whether the proposal in this essay is any more "natural" than what is put in question, remains speculative, and I hope that we have left appropriate wording at the right places. "Guilty until proven innocent", I would respond to your second comment, and agree that further investigation is needed. However, I do find Dr Gogberashvili's treatment of the light cone convincing, as e.g. in "Octonionic Electrodynamics" arXiv:hep-th/0512258, and "Octonionic Geometry" arXiv:hep-th/0409173. Together with Dr Dzhunushaliev's treatment of unobservables ("Hidden structures in quantum mechanics" arXiv:0805.3221, and "Non-associativity, supersymmetry and hidden variables" arXiv:0712.1647), it creates the appearance as if quantum theory on octonions would not care to distinguish parameters from properties.
Thanks again for writing, and also my congratulations to you and Dr Manogue for winning the 2008 FQXi grant, for work on octonions! I am eager to see your "Octonions, E6, and Particle Physics" conference proceeding from September this year, to show in print (is a preprint version available?).
Best wishes,
Jens