Comment by Aardwolf | Hacker News Reader

Comment by Aardwolf | Hacker News Reader

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Would in a completely different universe with completely different physics where some life and civilization (for whatever that means in those different physics) manage to emerge, this civilization have similar mathematics, or completely different?

Is it possible for a universe to exist where those who can think and would follow all possible logic rules, find that e.g. the natural base of logarithms turns out to be something else than 2.71828, or get different prime numbers in the integers despite using similar addition and multiplication rules, or other such changes..., or would they find exactly the same?

I think they would find exactly the same (when it comes to the real actual logic, they may use different conventions and focus on different things if they got e.g. a different amount of dimensions in their universe etc...), I simply can't think how following logic rules could conclude something else no matter in what universe...

This depends a lot on how different you imagine this universe could be.

For example, in this different universe, if I have an apple and you give me another apple, how many apples do I have? If I have 2, just like in our own universe, then you're probably right. But what if I have 3 apples? What if I still have 1 apple?

We can certainly create number systems that don't behave like the integers, or addition operations where 1 + 1 = something other than 2. We haven't explored many of those too much because they're not very interesting, but they still have structure and may have similar concepts to what we call prime numbers etc. The integers and regular addition happen to be much more useful for understanding our world than all of these other systems.

In a vastly different universe, the opposite may happen: if they studied this weird operation where 1+1=2, they would reach the same conclusions as we do. But they never study it, because it doesn't match their universe at all.

> the natural base of logarithms turns out to be something else than 2.71828

The Euler number has a very concrete definition (or, actually, quite a few equivalent ones). The answer is clear if definitions are the same (all - including the operations we perform and structures we use).

Yet, math we know revolves around the abstraction of (discrete) language AND that we operate with things that we count. Even if we were slime molds (well within the same universe), we may have never developed the concept of integers. At the same time, there could have been 3D geometry without words.

Maths in other planets or universes can be different only if they have different sets of axioms and/or different logical inference rules.

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