>>7779229 >implying there's only one way to represent these laws, and that aliens couldn't possibly come up with another system different from ours, maybe reflecting these alien's way of thinking, which may be different from our way of thinking.
Depends. We really can't say, and the more you know about why our own brain made mathematics the way it did, the less you're able to try to say how you believe it would go.
Otherwise, people who believe the universe is math, mathematics being discovered, etc, will give a resounding "yes" because in their view it can be no other way. People who don't will be apt to say no.
As far as I'm concerned, the universe might well "be" math, and language, but it's certainly something more beautiful and grand than our hacked together versions. Our math is not -the- math.
Probably, although it may be quite different from what we know, retaining its core principles. Look, throughout history we had several ''ways of doing math'', we kinda figured some stuff out, but when we could not go any further, due to the impossibility of the way we did the math, we changed stuff a little.
Romans and Babylonians, for example, had quite different way of doing math, yet, for the simple stuff, it was rather useful. But then we came out with the way we do now.
Think of it like if it were math, but in another language... and since we have improved the way we do math over the years, it is possible that it may also be a bit more complicated as well; if they are smarter than us, that is.
PS: complicated= perfected, better, or more accurate.
>>7779344 You're acting like you could determine what the laws of nature are All you know is how they work here, in the observable universe Why couldn't a different part of the universe be expanding more rapidly than this part, and therefore have different relative "laws" given by apparent "constants"?
I see now way around them finding the function concept useful and then the'll not the range of constructive operations
In particular, as the Church Turing thesis seems to hold, if they are clever, then the'll know z, Sz, SSz, SSSz, ... S being "next"
i.e. some incarnation of N
N -> A are lists of a's, which are of type A x A x A x ··· x A
And then the'll inevitable classify the possible functions
A -> A always has the identity
A x B -> B x A always has the permutation
Functions can be indexed, so there are function spaces B^A
etc. etc., and they'll recognize those constructions as a formalization of intuitionistic logic, i.e. if 'proposition A is true' then 'proposition A is true', if 'proposition A is true' and 'proposition B is true', then 'proposition B is true' and 'proposition A is true' (commutativity of [math]\land[/math]) i.e Curry-Howard isomorphism
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