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Comment by fyp | Hacker News Reader

Can someone help me imagine what a world with different math is like? It’s easy enough to imagine a world with different physics (such as in video games). But math is just a list of rules/axioms and the results of following those rules. They might find different axioms more applicable but our math should still work in their universe even if it’s considered pure math with no applications.

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It's tricky because "world" already makes us imagine a reality whose fundamental operation works like it does here. In fact, "reality" and "operation" already come with that baggage. The very mechanism that we know as "mind" (or at least, intellect) may be incapable of imagining other possibilities. On the other hand, very strong psychedelic experiences (a la DMT) or meditation can certainly give the impression that other possibilities exist. The problem is, you can't bring those possibilities back here via memory.

Mathematics generally may not be a property of the universe or "world", but the world may constrain what mathematics may be understood or computed within it.

The choice of axiomatic system limits what is provable in mathematics, as demonstrated by Godel's theorem in the case of natural number arithmetic. The world may limit that choice of axiomatic system or the computability of theorems. There may be mathematical theories which are true but we can not prove within the physical bounds of our universe.

I believe that due to our environment being based on "our type of math" and thus our thinking processes essentially running on that mathematical substrate in a way any mathematics you could imagine would just be an extension of our math and thus either there is no other math or we just can't imagine it. As for axioms and assumptions, it can work but it would probably be possible to formulate them in terms of existing math.

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