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Comment by dbsmith83 | Hacker News Reader

> Mathematics is most definitely a human endeavor, and so we can’t really make claims about its existence in the universe independent of humans.

Can you give an example of a mathematical concept which could be different?

I believe that math is universal. We may use models to understand it (infinity, perfect circles, etc.), but the underlying mathematical truth is independent of humans. The same is true for science. There are physical laws which we look to discover. We use models in science to understand them, but the models are not the same as the underlying truth

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> I believe that math is universal

The only thing that is "universal" is Nature itself. Mathematics, on the other hand, is a reflection of Nature in the human mind; or, put differently, it's Nature's language we humans are capable of understanding. It is therefore conceivable that other creatures, far removed from us, could "hear" a language that is just as far removed from ours.

> I believe that math is universal. We may use models to understand it (infinity, perfect circles, etc.), but the underlying mathematical truth is independent of humans.

Humans (probably) perceive and understand a slim subset of reality. We have an illusion of universalism of our perceptions because we perceive nothing outside of them. Also, we are the dominant species of the planet, which gives us a reason to believe that our perceptions are "more accurate" than, say, a bat's.

Personally, I don't think an alien's perceptions and understanding would contradict our own, but if it's given that our perceptions are a subset of reality, then an alien's understanding might include elements of reality that we literally cannot perceive or even understand.

> Can you give an example of a mathematical concept which could be different?

By definition, no. But, hmm. What would number and a mathematical system look like from creatures who thought in logarithms? Or in primes? Or that had no concept of "number"? What if even "greater than" and "less than" had no relevance to an alien civilization?

All of this is arguments for why our understanding of science and the nature of the universe might differ. It can also explain how our mathematics might evolve very differently and we will have made different mathematical discoveries and do math in very different ways (all of which I agree are very likely). However it doesn't explain how an alien race will look at one of our mathematical proofs that we have proven True and be able to prove that it is False.

> However it doesn't explain how an alien race will look at one of our mathematical proofs that we have proven True and be able to prove that it is False.

Where is this coming from? Is this relevant to what I wrote?

If both their math and our math agree on what statements are true and false then both our maths are functionally the same.

Well, sure, because the term "math" already presupposes a lot. There are two possibilities, here:

1) Math describes reality, so human math and alien math are the same thing, just different perspectives of reality and so, ultimately compatible.

2) Math is a language that humans use to describe their perceptions of reality to other humans. Perception is not reality, but a kind of isomorphism or pared-down heuristic, driven as it is by the evolutionary imperative to streamline for survival. Therefore a language that appears to be universal will only make sense to entities that employ the same perceptual framework for understanding, which is to say, human beings.

I agree that something that is "true" in human math will not be directly "false" in an alien math. 2+2 really does equal 4. The question is whether 2+2=4 is relevant or even understandable to an alien.

But see I don't think think what your saying contradicts the above post. If our subset intersects with the alien subset of perception, then we both will have a perception of an underlying truth, and we could conceivably understand the alien models and vice versa because they address the same subject.

UP said that mathematics is universal. I believe it models only our perception and understanding, which are informed by our biological, evolutionary imperatives.

Reality itself is beyond us. All that we have at our disposal are our perceptions, which is what we are modeling when we "do math". Mathematics is not universal, it's a language that we use to communicate what we perceive to other humans.

It's speculative, whether an alien species, with a perceptual and cognitive system evolved entirely elsewhere under other pressures, would have an understanding that intersects with our subset of reality. I personally think it's unlikely. What that would mean is that we wouldn't be able to communicate, never mind trade technology and mathematical ideas.

> It's speculative, whether an alien species, with a perceptual and cognitive system evolved entirely elsewhere under other pressures, would have an understanding that intersects with our subset of reality. I personally think it's unlikely. What that would mean is that we wouldn't be able to communicate, never mind trade technology and mathematical ideas.

I mean, maybe, but this is conveniently unprovable, much like the flying spaghetti monster, since you are saying we could not communicate because our slices of reality don't intersect. I disagree and think that most likely we would live in a reality that was largely the same, but I guess we'll never know!

> this is conveniently unprovable

Perhaps. I was responding to the assertion that Mathematics exist independently of biology or perception of reality which is at least as unprovable

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