I agree, I just wonder how much that might be because it’s the system we’re exposed to the most and how much it’s innately compatible to how we’ve evolved (that is to ask: how much is the wiring nature or nurture?).
Obviously it seemed “natural” to the ancient Sumerians, Babylonians, Greeks and Indians who laid the foundations of our system, but they were already working within a cultural framework. Just as learning a primary language shapes how one thinks about language generally, I wonder if the the same could be true of mathematical systems.
Also, even if something doesn’t or cannot feel natural to humans, it doesn’t necessarily mean it’s the most effective way for understanding something “outside” of us. There are things that would take many more lines of code in Java that you could do much more efficiently in C++. And while in principle any programming language can be used to achieve the same ends as any other, we shouldn’t assume math is the same. Programming languages work that way because they all follow the same underlying mathematical rules (on classical computers anyway).
Which returns me to the question I raised before of whether there’s a shared logical base for axiomatically different mathematical systems.
Also, I mention classical computers because quantum computers require different mathematics. That’s actually what I do for my bread and butter. I’m basically a glorified translator of algorithms for nonlinear problems. But there are some things a classical computer’s mathematics can’t solve in finite time. I wonder: what is the relationship between different mathematical systems, if any?
