I think the interesting part is what axioms and operations you back into, based on the environment that you observe. We have ten fingers and needed accountants

I think the interesting part is what axioms and operations you back into, based on the environment that you observe. We have ten fingers and needed accountants, but I don't know that that's a given, and what you find first could very well determine what's interesting later. See Isaac Asimov's "Nightfall" for a society that industrialized before it discovered astronomy.