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Would you agree that an alien civilization completely separate from humans but equally intelligent would also be likely to discover Pythagoras theorem (with a d

Would you agree that an alien civilization completely separate from humans but equally intelligent would also be likely to discover Pythagoras theorem (with a different name and different symbolics)? To me that would imply that its truth is independent of human perception.

disconcision 3y ago
i don't find this argument convincing. it depends, at minimum, on bounding 'aliens' to mean something reasonably close to humans. if we allow aliens to be arbitrarily different, than i don't see a reason to bound their abstract symbolic technical development any more than arbitrarily distant to human development. otoh, if we assume that aliens are significantly similar to humans in some specific respects, then it seems likely to me that their technical development will also have substantial similarities, including but not limited to their abstract symbolic development. the space of abstractions seems large, and our particular path through it is historically contingent in both obvious and likely non-obvious ways; likewise for the formal inferential constructs which we use to parameterize this space
danbruc 3y ago
Math and logic are fundamentally some kind of game, you make up some rules and axioms and then you figure out the consequences. So the interesting question is which rules and axioms you pick and I would guess aliens in our universe would pick similar rules and axioms as we did because they will want to describe the same universe. And they would probably discover the Pythagorean theorem. But in a different universe without space dimensions or multiple time dimensions or discrete space dimensions or something completely incomprehensible to us for which we do not even have concepts and words, there I am not sure that they would certainly come up with the axioms of Euclidean space and discover the Pythagorean theorem, or it might be a very esoteric mathematical structure to them at best. So it seems there is still something universal in there, the idea of inventing rules and axioms and figuring out the consequences, which could maybe essentially boil down to computations or something like that. But even there I am not so sure that it is truly universal, the original idea of a Turing machine is an abstraction of repeatedly modifying some state over time, and can we not imagine a universe where updating state over time makes no sense?

disconcision 3y ago

i don't find this argument convincing. it depends, at minimum, on bounding 'aliens' to mean something reasonably close to humans. if we allow aliens to be arbitrarily different, than i don't see a reason to bound their abstract symbolic technical development any more than arbitrarily distant to human development. otoh, if we assume that aliens are significantly similar to humans in some specific respects, then it seems likely to me that their technical development will also have substantial similarities, including but not limited to their abstract symbolic development. the space of abstractions seems large, and our particular path through it is historically contingent in both obvious and likely non-obvious ways; likewise for the formal inferential constructs which we use to parameterize this space

danbruc 3y ago

Math and logic are fundamentally some kind of game, you make up some rules and axioms and then you figure out the consequences. So the interesting question is which rules and axioms you pick and I would guess aliens in our universe would pick similar rules and axioms as we did because they will want to describe the same universe. And they would probably discover the Pythagorean theorem. But in a different universe without space dimensions or multiple time dimensions or discrete space dimensions or something completely incomprehensible to us for which we do not even have concepts and words, there I am not sure that they would certainly come up with the axioms of Euclidean space and discover the Pythagorean theorem, or it might be a very esoteric mathematical structure to them at best. So it seems there is still something universal in there, the idea of inventing rules and axioms and figuring out the consequences, which could maybe essentially boil down to computations or something like that. But even there I am not so sure that it is truly universal, the original idea of a Turing machine is an abstraction of repeatedly modifying some state over time, and can we not imagine a universe where updating state over time makes no sense?