4 ms·

If a magic oracle tells you p=np, that's useless. How would that change anything?

by HWR_14 1mo ago

czgov 1mo ago
If it’s an oracle and we know it’s an oracle then it’s not useless. Humans make mistake and there are examples of published results that were widely believed to be correct by experts that later proved to be wrong. Why do you think human verified proofs are better than machine verified proofs? Suppose an oracle tells us the Riemann Hypothesis is correct. There are a vast number of results of the form: If RH is correct then A. It would be very useful to have an oracle tells us whether or not RH is correct.
- Jensson 1mo ago
  > It would be very useful to have an oracle tells us whether or not RH is correct. For what? Which product becomes better if it is correct?
  - czgov 1mo ago
    You have an unfortunate view of the value of knowledge. The frontiers of science would be static if everyone believed as you do.
    - deleted 1mo ago
      [deleted]
    - Jensson 1mo ago
      The whole point why anyone cares about these proofs is that the things we learn as we make the proof might add value, proving p = np itself isn't interesting, that knowledge has no application and therefore no value in itself. I have published mathematics so I do value knowledge, but for most of mathematics the value of the knowledge isn't the thing you try to prove it is all the things you learn as you try to prove it. p = np is one such thing. So the whole interesting bit about it is the proof, not the fact.
      - czgov 1mo ago
        You are wrong as far as most mathematicians believe. The fact is important. The proof of the fundamental theorem of algebra is interesting and important but the theorem itself is also important. For what? Which product becomes better if it is correct? This sentiment is anti-thetical to the whole point of pure math and theoretical science. No product became better when Euler proved the fundamental theorem of algebra.
    - customguy 1mo ago
      Someone claimed it would be "useful", without saying what for. Hence the questions "what for?". To try to shame people for that question in the name of science of all things is wild.
      - czgov 1mo ago
        Which product becomes better if it is correct? Tying the worthiness of theoretical knowledge to the whether or not it improves a product is asinine in my opinion.
        customguy 1mo ago
        I generally[0] agree, but IMO that should be taken up with https://news.ycombinator.com/item?id=49369458 https://news.ycombinator.com/item?id=49369458 more than with people who ask for examples for that claim. [0] and am only adding that "generally" because I can think of examples where I'd disagree, e.g. a kid that wants to count all stars in the night sky before it has dinner would just starve and then not be able to count stars, either.
- HWR_14 1mo ago
  I asked how would it change anything. What's the next step if an oracle were to tell you p=np that changes anything about the world? We all believe it. It's a magic oracle. Now what?
  - czgov 1mo ago
    If it is known that A is provably true then one can study the consequences of A being true. It changes things becuase the body of knowledge has expanded.
    - mahdi7d1 1mo ago
      In this case won't this oracle also tell you what is the consequences as soon as it tells you RH is true and also much more? At this point what is the point of you knowing what is true and what is not?
      - czgov 1mo ago
        There is no actual oracle. In this discussion oracle means Lean.
    - saithound 1mo ago
      > If it is known that A is provably true then one can study the consequences of A being true But one can already study the consequences of P=NP right now. You don't need to know that it's provably true in order to do that. Knowing an actual proof would be useful, but an oracle revealing merely that it's true (or even provable) without telling you the proof does not let you do anything you couldn't do before.
      - czgov 1mo ago
        Some people (almost all mathematicians) wouldn’t want to spend time on consequences of a false statement. In the present discussion it’s not about letting me do something I can’t do now but about whether or not the endeavor is worthwhile. A lot of people spent a lot of time and effort to prove or disprove the Jacobian Conjecture. AI solved it easily. It is increasingly becoming the case that humans are not as good at mathematics as computers. You are free to ignore computer generated proofs but I don’t think this position will win out in the long run.
js8 1mo ago
Oh it would change a lot. It would be an enormous psychological boost for everyone to find a practical algorithm. In any case, I think it's better to read PP as somebody would find a practical, albeit incomprehensible, algorithm for solving NP complete problems. Although I probably disagree with PP, because even a candidate algorithm that mysteriously works without proof would have practical value, so this case is not predicated on proving. I think a better example of genuinely practical but rather uninteresting (YMMV) mathematical proofs are proofs of convergence of numerical methods, FEM for example. (I have been through it in school, it was a torture.)
- enriquto 1mo ago
  > a practical, albeit incomprehensible, algorithm for solving NP complete problems. It would not not necessarily be practical, even if it ran in polynomial time. It may have cost O(n^c), with a totally out of order exponent like c=A(5,5) or whatever.
  - js8 1mo ago
    I know, the goal was to strongman the argument.
- aleph_minus_one 1mo ago
  > > If a magic oracle tells you p=np, that's useless. How would that change anything? > Oh it would change a lot. It would be an enormous psychological boost for everyone to find a practical algorithm. OK, I tell you that P=NP, and that I am a magic oracle. So, you have you psychological boost for finding a practical algorithm for free. :-)
  - js8 1mo ago
    Kinda pointless, because a) I am already convinced that P=NP b) You have to convince many other people as well (that you're a magic oracle), because for the effect to work, lot of people would have to work on the problem (or at least spend tokens) Nevertheless, a plausible magic oracle (such as Lean-verified proof, even if non-constructive and incomprehensible for humans) would convince many to take a 2nd look.
wavewrangler 1mo ago
I thought the point of publishing was a matter of dissemination, to make available for people to then try to understand it? This is like saying, I don’t like music, so I’m going to tear down the venue. Then, all music genres suffer as a result, and all of society does, too. This idea is no good. Somebody, eventually, somewhere would understand it, or at least aspire to understand it. And even if he doesn’t, what have they learned in the process? About themselves, about their environment? About failure? I would bet a lot. How useful then, can we say that it is, not because we can understand it, but because we can try? That is useful. This is about the journey. Sometimes the journey is the point. This is like if math was fascist, this is what would happen. When you start controlling the flow of knowledge like this, it will be bad news all around. And who is to say whether or not something can be understood?Aside from the math nazis. If we are going to dictate what gets published like this, why bother publishing anything? This feels like a gatekeeping…that’s exactly what it is. Ya’ll getting nervous?
DiscourseFan 1mo ago
I would hope the magic oracle would continue to tell me ways in which I can use this knowledge practically.

If a magic oracle tells you p=np, that's useless. How would that change anything?

by HWR_14 1mo ago

If a magic oracle tells you p=np, that's useless. How would that change anything?

czgov 1mo ago

If it’s an oracle and we know it’s an oracle then it’s not useless. Humans make mistake and there are examples of published results that were widely believed to be correct by experts that later proved to be wrong. Why do you think human verified proofs are better than machine verified proofs? Suppose an oracle tells us the Riemann Hypothesis is correct. There are a vast number of results of the form: If RH is correct then A. It would be very useful to have an oracle tells us whether or not RH is correct.

Jensson 1mo ago
> It would be very useful to have an oracle tells us whether or not RH is correct. For what? Which product becomes better if it is correct?
- czgov 1mo ago
  You have an unfortunate view of the value of knowledge. The frontiers of science would be static if everyone believed as you do.
  - deleted 1mo ago
    [deleted]
  - Jensson 1mo ago
    The whole point why anyone cares about these proofs is that the things we learn as we make the proof might add value, proving p = np itself isn't interesting, that knowledge has no application and therefore no value in itself. I have published mathematics so I do value knowledge, but for most of mathematics the value of the knowledge isn't the thing you try to prove it is all the things you learn as you try to prove it. p = np is one such thing. So the whole interesting bit about it is the proof, not the fact.
    - czgov 1mo ago
      You are wrong as far as most mathematicians believe. The fact is important. The proof of the fundamental theorem of algebra is interesting and important but the theorem itself is also important. For what? Which product becomes better if it is correct? This sentiment is anti-thetical to the whole point of pure math and theoretical science. No product became better when Euler proved the fundamental theorem of algebra.
  - customguy 1mo ago
    Someone claimed it would be "useful", without saying what for. Hence the questions "what for?". To try to shame people for that question in the name of science of all things is wild.
    - czgov 1mo ago
      Which product becomes better if it is correct? Tying the worthiness of theoretical knowledge to the whether or not it improves a product is asinine in my opinion.
      - customguy 1mo ago
        I generally[0] agree, but IMO that should be taken up with https://news.ycombinator.com/item?id=49369458 https://news.ycombinator.com/item?id=49369458 more than with people who ask for examples for that claim. [0] and am only adding that "generally" because I can think of examples where I'd disagree, e.g. a kid that wants to count all stars in the night sky before it has dinner would just starve and then not be able to count stars, either.
HWR_14 1mo ago
I asked how would it change anything. What's the next step if an oracle were to tell you p=np that changes anything about the world? We all believe it. It's a magic oracle. Now what?
- czgov 1mo ago
  If it is known that A is provably true then one can study the consequences of A being true. It changes things becuase the body of knowledge has expanded.
  - mahdi7d1 1mo ago
    In this case won't this oracle also tell you what is the consequences as soon as it tells you RH is true and also much more? At this point what is the point of you knowing what is true and what is not?
    - czgov 1mo ago
      There is no actual oracle. In this discussion oracle means Lean.
  - saithound 1mo ago
    > If it is known that A is provably true then one can study the consequences of A being true But one can already study the consequences of P=NP right now. You don't need to know that it's provably true in order to do that. Knowing an actual proof would be useful, but an oracle revealing merely that it's true (or even provable) without telling you the proof does not let you do anything you couldn't do before.
    - czgov 1mo ago
      Some people (almost all mathematicians) wouldn’t want to spend time on consequences of a false statement. In the present discussion it’s not about letting me do something I can’t do now but about whether or not the endeavor is worthwhile. A lot of people spent a lot of time and effort to prove or disprove the Jacobian Conjecture. AI solved it easily. It is increasingly becoming the case that humans are not as good at mathematics as computers. You are free to ignore computer generated proofs but I don’t think this position will win out in the long run.

js8 1mo ago

Oh it would change a lot. It would be an enormous psychological boost for everyone to find a practical algorithm. In any case, I think it's better to read PP as somebody would find a practical, albeit incomprehensible, algorithm for solving NP complete problems. Although I probably disagree with PP, because even a candidate algorithm that mysteriously works without proof would have practical value, so this case is not predicated on proving. I think a better example of genuinely practical but rather uninteresting (YMMV) mathematical proofs are proofs of convergence of numerical methods, FEM for example. (I have been through it in school, it was a torture.)

enriquto 1mo ago
> a practical, albeit incomprehensible, algorithm for solving NP complete problems. It would not not necessarily be practical, even if it ran in polynomial time. It may have cost O(n^c), with a totally out of order exponent like c=A(5,5) or whatever.
- js8 1mo ago
  I know, the goal was to strongman the argument.
aleph_minus_one 1mo ago
> > If a magic oracle tells you p=np, that's useless. How would that change anything? > Oh it would change a lot. It would be an enormous psychological boost for everyone to find a practical algorithm. OK, I tell you that P=NP, and that I am a magic oracle. So, you have you psychological boost for finding a practical algorithm for free. :-)
- js8 1mo ago
  Kinda pointless, because a) I am already convinced that P=NP b) You have to convince many other people as well (that you're a magic oracle), because for the effect to work, lot of people would have to work on the problem (or at least spend tokens) Nevertheless, a plausible magic oracle (such as Lean-verified proof, even if non-constructive and incomprehensible for humans) would convince many to take a 2nd look.

wavewrangler 1mo ago

I thought the point of publishing was a matter of dissemination, to make available for people to then try to understand it? This is like saying, I don’t like music, so I’m going to tear down the venue. Then, all music genres suffer as a result, and all of society does, too. This idea is no good. Somebody, eventually, somewhere would understand it, or at least aspire to understand it. And even if he doesn’t, what have they learned in the process? About themselves, about their environment? About failure? I would bet a lot. How useful then, can we say that it is, not because we can understand it, but because we can try? That is useful. This is about the journey. Sometimes the journey is the point. This is like if math was fascist, this is what would happen. When you start controlling the flow of knowledge like this, it will be bad news all around. And who is to say whether or not something can be understood?Aside from the math nazis. If we are going to dictate what gets published like this, why bother publishing anything? This feels like a gatekeeping…that’s exactly what it is. Ya’ll getting nervous?

DiscourseFan 1mo ago

I would hope the magic oracle would continue to tell me ways in which I can use this knowledge practically.