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Math isn't "cooperative". Math is about truths. The length of circumference. The area of a triangle. The formulas for these are true in an objective sense irres

by glimshe 2mo ago

Math isn't "cooperative". Math is about truths. The length of circumference. The area of a triangle. The formulas for these are true in an objective sense irrespective of whether you understand them. That said, without understanding, Math can't evolve. Comprehension of a proof is very important, but not what Math is fundamentally about. Computer programs are Math. You can use them without understanding how they work.

gsinclair 2mo ago
First of all, mathematics is about so much more than the area of a triangle etc. that any analogy based on such simple things is overwhelmingly likely to be too simple to be of value. Secondly, there is no truly objective truth to the area of a triangle. At bottom, this “truth” is simply “everyone is convinced, and for good reason”. Without persuading other people of the “truths” that you discover, there is no real mathematics.
- d4v3 2mo ago
  > Without persuading other people of the “truths” that you discover, there is no real mathematics. Why? If I sat around and studied math by myself and discovered something true yet not yet known but didn't share it, it's still true. Are you saying I didn't "do math" because I didn't share the result? Math exists on another plane and it has 'truths' that we haven't discovered, yet are still 'true', no?
  - chongli 2mo ago
    No, they're saying that what is true in mathematics is contingent, not absolute. It all depends on which set of axioms use, what assumptions you make. The area of a triangle doesn't have 1 unique formula, it has many, depending on the system you use. A triangle in plane geometry has a different area than a triangle in spherical geometry, and different again in hyperbolic geometry. When you get to studying the geometry of manifolds, you realize the area of a triangle can be any damn thing you want, depending on how you construct the manifold you embed it in.
    - cman1444 2mo ago
      This is a needless qualifier for the argument at hand. A proof can just be "assuming these axioms.....the area of a triangle is X"
  - Scarblac 2mo ago
    Sure, but just that some random statement is true isn't interesting. It's interesting if it helps understand some abstract structure better.
    - sothatsit 2mo ago
      It could also be interesting by having a practical use.
raincole 2mo ago
Math is not about truths, at least not by the meaning of "truth" as a word in daily use. Math has been almost purely arbitrary since ~ late 19th/early 20th century. There are uncountably many correct mathematical theorems. Almost all of them can't even be written in symbols. Even if you have a tape with infinite length (which is already longer than the whole physical universe!) filled with theorems, they are still only 0% of all correct theorems. That's how arbitrary math is. > The area of a triangle Yes, even this is arbitrary. The rigorous definition of triangle is arbitrary. People just subconsciously choose something that vaguely approximates their physical intuition.
- GPerson 2mo ago
  The tastes and interests, and cultural pretext, of human beings are not arbitrary just because they’re not easily described.
  - ziiinq 2mo ago
    Yes and therefore? You seem to be vaguely waving in the general direction of a point, without making any concrete claims or bothering to engage with the GP’s argument. The tastes and interests of humans are absolutely not arbitrary. They are dictated by fate, the sun and the moon gods. Or maybe by the unitary evolution of the universe’s quantum state. Or by the probability distribution of finding ourselves in a particular branch of the universe. What bearing does this have on whether math is a collaborative endeavor? And what is unique to math, that your argument wouldn’t apply equally to physics, sociology or financial markets? All, “truth seeking” disciplines.
    - GPerson 2mo ago
      You seem rather aggressive so replying to you feels pointless and uncomfortable. Nonetheless, the person writes, “ Math has been almost purely arbitrary”. This is simply a misusage of the word arbitrary, which is a word with a specific meaning you can look up if you are unaware, since mathematics is (obviously) not arbitrary in the sense this person wants to convey, in part for the reasons I state. Humans are not choosing arbitrary logical statements to prove true or false.
rain_iwakura 2mo ago
this is primitive understanding of math. what does "truth" mean here? usually arguing over definitions is something i hate, but that's the whole point of mathematics. it starts as a tool for humans, then evolves into a set of interesting properties of those tools, then grows into an art form, a set of "games" where cooperation is half of the point. the other half is discovering beauty in this weird parallel world of our reasoning and imagination. once tools become autonomous and start making up their own games we can't even play then mathematics loses it's meaning as a discipline. the only retort you can come up with is that "it's going to be useful". how would you know? because your autonomous tool that's too smart for you told you so? they could be as useful as morning orange juice to Claude Shannon was in terms of inventing information theory. I.e. you drinking it won't make you any closer to inventing anything of the sort anytime in your lifetime. do triangles exist IRL? is the world discrete or continuous? can you prove it? If you have an answer to all of those I know you're wrong. also in your computer program example just shows you don't understand it at all. those programs ARE NOT understood by you, but someone else who built them did. someone who bothered to read and architect it did. The whole Google codebase might be incomprehensible in its totality if you go bottom up but it is comprehensible by construction by us. Same with math. You don't understand all the bits of it, but someone built every brick and so you know it is "true". once the bricks become black boxes you're screwed.
ves 2mo ago
This hasn't been a remotely reasonable characterization of math since at least Hilbert's time.
- glimshe 2mo ago
  I think Hardy would be very much on the same page with me, as well as Godel and many others. Mathematical truths exist independently from our feelings and processes to discover them. People do and should argue about which truths are interesting to pursue and refine, but all of them are out there to be discovered... or not. Whatever philosophy you prefer, math is about establishing objectively valid logical results, completely independent of the human process used to arrive at them.
  - Jensson 2mo ago
    Axioms don't exist independently from our feelings and processes, we pick axioms we feel are good, and axioms defines mathematics. Mathematicians even argue which axioms we should have, it isn't objective in the slightest, mathematics is therefore very closely linked to our feelings and intuition. Remove that and you just have formal logic, a very different field.
    - glimshe 2mo ago
      Is formal (aka "mathematical") logic part of mathematics? Now that's a philosophical question. From my perspective, I feel you restated what I said with the opposite conclusion. You say that axioms "defines" mathematics. If I were Claude, I'd say that the word "define" is doing a lot of work, is load bearing or something like that. "Define" is where we turn these axioms into consequences - what I call "truth". As opposed to all the other stuff people could say that don't follow from these axioms. These are nonsense and, most certainly, un-mathematical.
ziiinq 2mo ago
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by glimshe 2mo ago

gsinclair 2mo ago

First of all, mathematics is about so much more than the area of a triangle etc. that any analogy based on such simple things is overwhelmingly likely to be too simple to be of value. Secondly, there is no truly objective truth to the area of a triangle. At bottom, this “truth” is simply “everyone is convinced, and for good reason”. Without persuading other people of the “truths” that you discover, there is no real mathematics.

d4v3 2mo ago
> Without persuading other people of the “truths” that you discover, there is no real mathematics. Why? If I sat around and studied math by myself and discovered something true yet not yet known but didn't share it, it's still true. Are you saying I didn't "do math" because I didn't share the result? Math exists on another plane and it has 'truths' that we haven't discovered, yet are still 'true', no?
- chongli 2mo ago
  No, they're saying that what is true in mathematics is contingent, not absolute. It all depends on which set of axioms use, what assumptions you make. The area of a triangle doesn't have 1 unique formula, it has many, depending on the system you use. A triangle in plane geometry has a different area than a triangle in spherical geometry, and different again in hyperbolic geometry. When you get to studying the geometry of manifolds, you realize the area of a triangle can be any damn thing you want, depending on how you construct the manifold you embed it in.
  - cman1444 2mo ago
    This is a needless qualifier for the argument at hand. A proof can just be "assuming these axioms.....the area of a triangle is X"
- Scarblac 2mo ago
  Sure, but just that some random statement is true isn't interesting. It's interesting if it helps understand some abstract structure better.
  - sothatsit 2mo ago
    It could also be interesting by having a practical use.

raincole 2mo ago

Math is not about truths, at least not by the meaning of "truth" as a word in daily use. Math has been almost purely arbitrary since ~ late 19th/early 20th century. There are uncountably many correct mathematical theorems. Almost all of them can't even be written in symbols. Even if you have a tape with infinite length (which is already longer than the whole physical universe!) filled with theorems, they are still only 0% of all correct theorems. That's how arbitrary math is. > The area of a triangle Yes, even this is arbitrary. The rigorous definition of triangle is arbitrary. People just subconsciously choose something that vaguely approximates their physical intuition.

GPerson 2mo ago
The tastes and interests, and cultural pretext, of human beings are not arbitrary just because they’re not easily described.
- ziiinq 2mo ago
  Yes and therefore? You seem to be vaguely waving in the general direction of a point, without making any concrete claims or bothering to engage with the GP’s argument. The tastes and interests of humans are absolutely not arbitrary. They are dictated by fate, the sun and the moon gods. Or maybe by the unitary evolution of the universe’s quantum state. Or by the probability distribution of finding ourselves in a particular branch of the universe. What bearing does this have on whether math is a collaborative endeavor? And what is unique to math, that your argument wouldn’t apply equally to physics, sociology or financial markets? All, “truth seeking” disciplines.
  - GPerson 2mo ago
    You seem rather aggressive so replying to you feels pointless and uncomfortable. Nonetheless, the person writes, “ Math has been almost purely arbitrary”. This is simply a misusage of the word arbitrary, which is a word with a specific meaning you can look up if you are unaware, since mathematics is (obviously) not arbitrary in the sense this person wants to convey, in part for the reasons I state. Humans are not choosing arbitrary logical statements to prove true or false.

rain_iwakura 2mo ago

this is primitive understanding of math. what does "truth" mean here? usually arguing over definitions is something i hate, but that's the whole point of mathematics. it starts as a tool for humans, then evolves into a set of interesting properties of those tools, then grows into an art form, a set of "games" where cooperation is half of the point. the other half is discovering beauty in this weird parallel world of our reasoning and imagination. once tools become autonomous and start making up their own games we can't even play then mathematics loses it's meaning as a discipline. the only retort you can come up with is that "it's going to be useful". how would you know? because your autonomous tool that's too smart for you told you so? they could be as useful as morning orange juice to Claude Shannon was in terms of inventing information theory. I.e. you drinking it won't make you any closer to inventing anything of the sort anytime in your lifetime. do triangles exist IRL? is the world discrete or continuous? can you prove it? If you have an answer to all of those I know you're wrong. also in your computer program example just shows you don't understand it at all. those programs ARE NOT understood by you, but someone else who built them did. someone who bothered to read and architect it did. The whole Google codebase might be incomprehensible in its totality if you go bottom up but it is comprehensible by construction by us. Same with math. You don't understand all the bits of it, but someone built every brick and so you know it is "true". once the bricks become black boxes you're screwed.

ves 2mo ago

This hasn't been a remotely reasonable characterization of math since at least Hilbert's time.

glimshe 2mo ago
I think Hardy would be very much on the same page with me, as well as Godel and many others. Mathematical truths exist independently from our feelings and processes to discover them. People do and should argue about which truths are interesting to pursue and refine, but all of them are out there to be discovered... or not. Whatever philosophy you prefer, math is about establishing objectively valid logical results, completely independent of the human process used to arrive at them.
- Jensson 2mo ago
  Axioms don't exist independently from our feelings and processes, we pick axioms we feel are good, and axioms defines mathematics. Mathematicians even argue which axioms we should have, it isn't objective in the slightest, mathematics is therefore very closely linked to our feelings and intuition. Remove that and you just have formal logic, a very different field.
  - glimshe 2mo ago
    Is formal (aka "mathematical") logic part of mathematics? Now that's a philosophical question. From my perspective, I feel you restated what I said with the opposite conclusion. You say that axioms "defines" mathematics. If I were Claude, I'd say that the word "define" is doing a lot of work, is load bearing or something like that. "Define" is where we turn these axioms into consequences - what I call "truth". As opposed to all the other stuff people could say that don't follow from these axioms. These are nonsense and, most certainly, un-mathematical.

ziiinq 2mo ago

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