Sadly, I am not going to answer your question, because I am still focussing in my current education on vanilla complex number geometries anyway. Instead, I am going to comment on "are there higher order numbers beyond complex needed for algebraic operations" by emphasizing 'needed' - I always considered math as methods that could be applied to various hypothetical structures/ideas to provide an interesting train of thought. If this is a useful perception of mathematics(and if it is not, please feel free to say so), then would there be a necessary but as-yet undiscovered need for any particular concept? Would it not be better to say, "are there number(data?)-structures that provide for interesting algebras not yet considered?" -Arlo James Barnes
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