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Mathematics is uniquely weird in that anywhere in the universe, a species can come up with the same things... So to say Mathematics is not real, and yet it is i

Mathematics is uniquely weird in that anywhere in the universe, a species can come up with the same things... So to say Mathematics is not real, and yet it is independently discoverable by anyone is just really weird to me.

eyelidlessness 6y ago
There are very credible linguists who theorize that there’s a universal human grammar and language foundation. It’s not a stretch to think that if they’re right about humans, the theory may apply to other life with language which we haven’t encountered yet. If that’s the case, the property you’re describing belongs to abstract thought and language generally, of which mathematics is a subset.
- gizmo686 6y ago
  The idea of universal grammar is that it is the portion of human language that is hardcoded into the genetics of humans. We would not expect other species to have the same universal grammar that humans do.
  - eyelidlessness 6y ago
    The notion is that there’s a commonality, the presupposition is that it’s genetic. But without knowing the mechanics of those genetics I don’t think you could say one way or another whether the expectation would be limited to humans.
ukj 6y ago
The line of reasoning is purely speculative. Since we are the only species who have Mathematics, I will continue insisting Maths is invented, till we can compare notes with other life forms.
- eyelidlessness 6y ago
  We’re the only species with which our species communicates maths. But we observe other species expressing mathematical properties we communicate. Does (for example) a snail “know” or “understand” the “golden ratio”? Who knows! But a snail’s shell expresses it. That’s partly something we can observe (so it can be designated “invented”), but partly something that appears so much it’s either a biological commonality, subject to some unknown universal constant, or an expression that many forms of life find a way to express.
  - ukj 6y ago
    Note how you are ascribing Mathematical meaning to a snail shell. You are somehow insisting that the mathematical expression (1 + sqrt(5))/2 is in some ways similar to a snail shell. Don’t you find it even a little strange that just about anyone not schooled in algebra/arithmetic would doubt your claim?
    - eyelidlessness 6y ago
      I’m confused. I’m not saying there’s “meaning” to it of any kind, only that the ratio is present and observable. I’m not “insisting” anything. Maybe you’re accustomed to every thought being a conflict, but if I wasn’t clear already I was expressing wonder around a fairly common phenomenon whose commonality isn’t well known or understood.
      - ukj 6y ago
        It's not at all a conflict. I am simply pointing out that where both of us observe/experience the pattern, your mind ascribes to it significance by relating it to the Mathematical construct called "Golden ratio". My mind doesn't make that relation. I call that pattern (and other patterns like it) a "snail shell pattern". We index the experience differently. From your perspective a Mathematical expression describes the pattern. From my perspective an English expression does.
        eyelidlessness 6y ago
mekkkkkk 6y ago
I think basic math is just a natural part of most languages, since it describes a useful aspect of reality. Similar to distance, space or existence. I'd hazard that most languages has ways of expressing those concepts as well. The fun begins when it comes to the deeper extrapolations of what can be readily observed. It seems possible that an alien civilization could be much more knowledgeable than us, yet never formulated the equivalents of our QM equations.
disconcision 6y ago
afaik there's not even a lot of cross-cultural evidence for this, let alone cross-species, let alone pan-universal. what is or isn't considered math, or more specifically what kinds of reasoning are considered convincing/sound/etc have evolved a lot over history, and is continuing to do so. lakatos' 'proofs and refutations' is a nice short introduction to some of the issues involved here. long story short, what it really means to say 'math is universal' is actually pretty hard to pin down precisely enough to make anything even resembling a testable assertion
- ukj 6y ago
  I don't have strong feelings towards anything you've said (in fact, I read Lakatos' paper just last weekend). You could say that I agree in general. Much of what you point out is also what Quine identified in his paper "The two Dogmas of Empiricism" which is trivially the question "Is logic/mathematics empirical?". In my world-view inductive types (computations) are empirical. But since you seem to be optimising for "pinning things precisely", general consensus/agreement may not be of any empirical value ;)

eyelidlessness 6y ago

There are very credible linguists who theorize that there’s a universal human grammar and language foundation. It’s not a stretch to think that if they’re right about humans, the theory may apply to other life with language which we haven’t encountered yet. If that’s the case, the property you’re describing belongs to abstract thought and language generally, of which mathematics is a subset.

gizmo686 6y ago
The idea of universal grammar is that it is the portion of human language that is hardcoded into the genetics of humans. We would not expect other species to have the same universal grammar that humans do.
- eyelidlessness 6y ago
  The notion is that there’s a commonality, the presupposition is that it’s genetic. But without knowing the mechanics of those genetics I don’t think you could say one way or another whether the expectation would be limited to humans.

ukj 6y ago

The line of reasoning is purely speculative. Since we are the only species who have Mathematics, I will continue insisting Maths is invented, till we can compare notes with other life forms.

eyelidlessness 6y ago
We’re the only species with which our species communicates maths. But we observe other species expressing mathematical properties we communicate. Does (for example) a snail “know” or “understand” the “golden ratio”? Who knows! But a snail’s shell expresses it. That’s partly something we can observe (so it can be designated “invented”), but partly something that appears so much it’s either a biological commonality, subject to some unknown universal constant, or an expression that many forms of life find a way to express.
- ukj 6y ago
  Note how you are ascribing Mathematical meaning to a snail shell. You are somehow insisting that the mathematical expression (1 + sqrt(5))/2 is in some ways similar to a snail shell. Don’t you find it even a little strange that just about anyone not schooled in algebra/arithmetic would doubt your claim?
  - eyelidlessness 6y ago
    I’m confused. I’m not saying there’s “meaning” to it of any kind, only that the ratio is present and observable. I’m not “insisting” anything. Maybe you’re accustomed to every thought being a conflict, but if I wasn’t clear already I was expressing wonder around a fairly common phenomenon whose commonality isn’t well known or understood.
    - ukj 6y ago
      It's not at all a conflict. I am simply pointing out that where both of us observe/experience the pattern, your mind ascribes to it significance by relating it to the Mathematical construct called "Golden ratio". My mind doesn't make that relation. I call that pattern (and other patterns like it) a "snail shell pattern". We index the experience differently. From your perspective a Mathematical expression describes the pattern. From my perspective an English expression does.
      - eyelidlessness 6y ago

mekkkkkk 6y ago

I think basic math is just a natural part of most languages, since it describes a useful aspect of reality. Similar to distance, space or existence. I'd hazard that most languages has ways of expressing those concepts as well. The fun begins when it comes to the deeper extrapolations of what can be readily observed. It seems possible that an alien civilization could be much more knowledgeable than us, yet never formulated the equivalents of our QM equations.

disconcision 6y ago

afaik there's not even a lot of cross-cultural evidence for this, let alone cross-species, let alone pan-universal. what is or isn't considered math, or more specifically what kinds of reasoning are considered convincing/sound/etc have evolved a lot over history, and is continuing to do so. lakatos' 'proofs and refutations' is a nice short introduction to some of the issues involved here. long story short, what it really means to say 'math is universal' is actually pretty hard to pin down precisely enough to make anything even resembling a testable assertion

ukj 6y ago
I don't have strong feelings towards anything you've said (in fact, I read Lakatos' paper just last weekend). You could say that I agree in general. Much of what you point out is also what Quine identified in his paper "The two Dogmas of Empiricism" which is trivially the question "Is logic/mathematics empirical?". In my world-view inductive types (computations) are empirical. But since you seem to be optimising for "pinning things precisely", general consensus/agreement may not be of any empirical value ;)