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This is a discussion on t-shirt within the General Discussions forums, part of the Community Boards category; Originally Posted by laserlight I do not see how that is the case. You are essentially finding an easy solution ...

  1. #31
    (?<!re)tired Mario F.'s Avatar
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    Quote Originally Posted by laserlight View Post
    I do not see how that is the case.
    You are essentially finding an easy solution to a complex problem. That's the basic formulation of a Belief.

    Anyway, an easy fix is to ask instead: P = NP ?
    (P == NP) ? dont_work() : work();

    Or, more t-shirt friendly, I guess:

    (P != NP) ? work() : slack();
    Last edited by Mario F.; 04-02-2010 at 09:53 AM.
    The programmer’s wife tells him: “Run to the store and pick up a loaf of bread. If they have eggs, get a dozen.”
    The programmer comes home with 12 loaves of bread.


    Originally Posted by brewbuck:
    Reimplementing a large system in another language to get a 25% performance boost is nonsense. It would be cheaper to just get a computer which is 25% faster.

  2. #32
    C++ Witch laserlight's Avatar
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    Quote Originally Posted by Mario F.
    You are essentially finding an easy solution to a complex problem.
    So... how that does support your claim that "by believing in P != NP without the ability to prove it, one is in fact making a strong case for P = NP"?
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  3. #33
    (?<!re)tired Mario F.'s Avatar
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    Err... maybe I didn't explain myself well.

    Because, under a belief, it becomes as easy to provide as is to verify the solution. A belief proves itself by simply existing. There's no need for scientific formulation or testing, other than rudimentary logic.

    So by believing in P != NP, one is making a case for P = NP.
    The programmer’s wife tells him: “Run to the store and pick up a loaf of bread. If they have eggs, get a dozen.”
    The programmer comes home with 12 loaves of bread.


    Originally Posted by brewbuck:
    Reimplementing a large system in another language to get a 25% performance boost is nonsense. It would be cheaper to just get a computer which is 25% faster.

  4. #34
    C++ Witch laserlight's Avatar
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    Quote Originally Posted by Mario F.
    Because, under a belief, it becomes as easy to provide as is to verify the solution. A belief proves itself by simply existing. There's no need for scientific formulation or testing, other than rudimentary logic.

    So by believing in P != NP, one is making a case for P = NP.
    Sorry, but I do not follow your argument. It seems to me that you are jumping to a conclusion. As far as I can tell, believing in a proposition does not make a case for the negation of that proposition; it makes no case at all, since as you say, it does not provide a proof (or a counterexample).
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  5. #35
    (?<!re)tired Mario F.'s Avatar
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    Quote Originally Posted by laserlight View Post
    Sorry, but I do not follow your argument. It seems to me that you are jumping to a conclusion. As far as I can tell, believing in a proposition does not make a case for the negation of that proposition; it makes no case at all, since as you say, it does not provide a proof (or a counterexample).
    It does not need to provide a proof. It's a Belief. And it's solely in that context I'm speaking. In more detail:

    By supporting a position such as P != NP without proper proof, you proposed your solution to the problem. You solved the equation. It's P != NP.

    The solution has no scientific support and you don't feel you need to prove it beyond the formulation of your belief. Your faith in it. When you then look back, you will eventually realize that you are in fact supporting P = NP when you defend P != NP based on faith.

    I guess, the implications of this reasoning may look like I'm making an indirect criticism of religion and faith. But that's not my point at this moment. I'm strictly speaking about the curious paradox you get from supporting P != NP without any proof.

    EDIT:
    Even more paradoxal because, from a purely philosophical view, yet P != NP is a strong support for the existence of God (and by extension, faith). But please, I'm not taking a stab at religion here. Just approaching the problem of belief in the context of the P vs NP problem.

    When I support P != NP, because we have no proof yet, I'm actually approaching P = NP
    Last edited by Mario F.; 04-02-2010 at 10:42 AM.
    The programmer’s wife tells him: “Run to the store and pick up a loaf of bread. If they have eggs, get a dozen.”
    The programmer comes home with 12 loaves of bread.


    Originally Posted by brewbuck:
    Reimplementing a large system in another language to get a 25% performance boost is nonsense. It would be cheaper to just get a computer which is 25% faster.

  6. #36
    C++ Witch laserlight's Avatar
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    Quote Originally Posted by Mario F.
    The solution has no scientific support
    I think that this assertion is not accurate. The current evidence is in favour of P != NP. The evidence does not amount to anything close to a proof, but if I were posed the question of which I think is more likely, I would choose P != NP. If I were posed the question of whether I believed that P != NP, I would say no.

    Quote Originally Posted by Mario F.
    When you then look back, you will eventually realize that you are in fact supporting P = NP when you defend P != NP based on faith.
    Effectively, you are asking me to believe you

    Quote Originally Posted by Mario F.
    I guess, the implications of this reasoning may look like I'm making an indirect criticism of religion and faith. But that's not my point at this moment. I'm strictly speaking about the curious paradox you get from supporting P != NP without any proof.
    Sorry, but I am not opposing you because of religious issues. I am opposing you because this "curious paradox" that you contend is stated without proof.
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  7. #37
    (?<!re)tired Mario F.'s Avatar
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    Quote Originally Posted by laserlight View Post
    I am opposing you because this "curious paradox" that you contend is stated without proof.
    I have no other way of explaining this to you. You seem to insist in bringing the word "proof" to a context that exactly refuses any proof.

    Faith: I believe P != NP. My "proof" is my belief. Thus I equal the solution to the verification of that solution. That means P = NP.

    Science: I do not believe in P != NP, nor in P = NP. I believe in P = NP?.
    The programmer’s wife tells him: “Run to the store and pick up a loaf of bread. If they have eggs, get a dozen.”
    The programmer comes home with 12 loaves of bread.


    Originally Posted by brewbuck:
    Reimplementing a large system in another language to get a 25% performance boost is nonsense. It would be cheaper to just get a computer which is 25% faster.

  8. #38
    C++ Witch laserlight's Avatar
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    Quote Originally Posted by Mario F.
    I have no other way of explaining this to you. You seem to insist in bringing the word "proof" to a context that exactly refuses any proof.
    I do not think so. The way I see it, what you are proposing is tantamount to saying that a flawed proof of conjecture X constitutes support for !X. But the flaw found might just show that X remains a conjecture rather than provide evidence (or even a proof) that !X is a theorem.

    EDIT:
    Quote Originally Posted by Mario F.
    Thus I equal the solution to the verification of that solution.
    I would appreciate it if you elaborated on this sentence as I do not understand what you mean by it.
    Last edited by laserlight; 04-02-2010 at 11:25 AM.
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  9. #39
    Unregistered User Yarin's Avatar
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    Quote Originally Posted by Mario F. View Post
    I have no other way of explaining this to you. You seem to insist in bringing the word "proof" to a context that exactly refuses any proof.

    Faith: I believe P != NP. My "proof" is my belief. Thus I equal the solution to the verification of that solution. That means P = NP.

    Science: I do not believe in P != NP, nor in P = NP. I believe in P = NP?.
    Faith is belief, it seems that when ever you mention 'faith', you're actually referring to axiomatic faith.
    Likewise, science is observation, not proof, which actually says that P != NP.
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  10. #40
    (?<!re)tired Mario F.'s Avatar
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    Quote Originally Posted by laserlight View Post
    I do not think so. The way I see it, what you are proposing is tantamount to saying that a flawed proof of conjecture X constitutes support for !X.
    No. But that on this case, yes.

    I would appreciate it if you elaborated on this sentence as I do not understand what you mean by it.
    The sentence is: "Thus I equal the solution to the verification of that solution." And under the concept of faith, I'm confused what there is to explain that I haven't already. What is that you don't understand?

    How do you verify your faith, if not by the very formulation of the faith itself?

    Quote Originally Posted by Yarin
    Likewise, science is observation, not proof, which actually says that P != NP.
    No. We just don't know yet. It hasn't be proven yet. We can feel more inclined that way, we may accept that as the most probable answer. But we don't know yet. And trying to pretend we know is not science.
    The programmer’s wife tells him: “Run to the store and pick up a loaf of bread. If they have eggs, get a dozen.”
    The programmer comes home with 12 loaves of bread.


    Originally Posted by brewbuck:
    Reimplementing a large system in another language to get a 25% performance boost is nonsense. It would be cheaper to just get a computer which is 25% faster.

  11. #41
    C++ Witch laserlight's Avatar
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    Quote Originally Posted by Mario F.
    The sentence is: "Thus I equal the solution to the verification of that solution." And under the concept of faith, I'm confused what there is to explain that I haven't already. What is that you don't understand?

    How do you verify your faith, if not by the very formulation of the faith itself?
    I can understand that part, but then from what I understand, your conclusion does not follow. How do you manage to conclude P = NP from a flawed proof of P != NP? (EDIT: Or are you saying that from a contradiction, we can derive anything... but there is no clear contradiction since this is an open problem, and even if there was, "anything" includes supporting P != NP.)

    Quote Originally Posted by Mario F.
    No. We just don't know yet. It hasn't be proven yet. We can feel more inclined that way, we may accept that as the most probable answer. But we don't know yet. And trying to pretend we know is not science.
    I think Yarin was trying to be pedantic about the difference in rigour in mathematical proofs and scientific theories.
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  12. #42
    (?<!re)tired Mario F.'s Avatar
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    Quote Originally Posted by laserlight View Post
    I can understand that part, but then from what I understand, your conclusion does not follow. How do you manage to conclude P = NP from a flawed proof of P != NP?
    Ah, I think I can understand the source of our confusion, now.

    I'm not concluding that proves P = NP. I'm merely saying that by their own admission of faith they are in fact making their case for P = NP. Because both the solution and the verification of that solution become equal in complexity.
    The programmer’s wife tells him: “Run to the store and pick up a loaf of bread. If they have eggs, get a dozen.”
    The programmer comes home with 12 loaves of bread.


    Originally Posted by brewbuck:
    Reimplementing a large system in another language to get a 25% performance boost is nonsense. It would be cheaper to just get a computer which is 25% faster.

  13. #43
    C++ Witch laserlight's Avatar
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    Quote Originally Posted by Mario F.
    Because both the solution and the verification of that solution become equal in complexity.
    I do not understand what you mean by this, but...

    Quote Originally Posted by Mario F.
    I'm not concluding that proves P = NP. I'm merely saying that by their own admission of faith they are in fact making their case for P = NP.
    I can more or less accept this, if you mean that this "admission of faith" constitutes admission that this "proof" of P != NP is flawed (i.e., effectively stating that X is a theorem while acknowledging that the proposed proof is not a proof; the fact that it is not a proof means that !X might be the case, so in a sense this makes a case for !X). I will still object to the phrase "strong case" though, since that comes closer to indicating that this admission is a purported proof of P = NP.
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  14. #44
    (?<!re)tired Mario F.'s Avatar
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    Quote Originally Posted by laserlight View Post
    I can more or less accept this, if you mean that this "admission of faith" constitutes admission that this "proof" of P != NP is flawed (i.e., effectively stating that X is a theorem while acknowledging that the proposed proof is not a proof; the fact that it is not a proof means that !X might be the case, so in a sense this makes a case for !X).
    Not exactly. But that the method employed by them to prove P != NP results in P = NP. They will be in fact, unwillingly, making a case for P = NP.

    Both the solution (P != NP) and the validation of that solution end up becoming the same thing. Their belief. Thus the Solution and the Validation of that solution have equal complexity.

    It's thus paradoxical because trying to prove P != NP through a profession of faith, not only invalidates P != NP a priori, but also ends up having them validating P = NP by their own admission.

    I will still object to the phrase "strong case" though, since that comes closer to indicating that this admission is a purported proof of P = NP.
    Agree entirely. It's not. I wouldn't dare dream of it. I'm actually doing my best to show it doesn't. Instead, I'm exactly trying to expose the weaknesses of trying to come up with a "proof" based on belief.
    The programmer’s wife tells him: “Run to the store and pick up a loaf of bread. If they have eggs, get a dozen.”
    The programmer comes home with 12 loaves of bread.


    Originally Posted by brewbuck:
    Reimplementing a large system in another language to get a 25% performance boost is nonsense. It would be cheaper to just get a computer which is 25% faster.

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    By supporting a position such as P != NP without proper proof, you proposed your solution to the problem. You solved the equation. It's P != NP.

    The solution has no scientific support and you don't feel you need to prove it beyond the formulation of your belief.
    Has anyone here said or even suggested that "you don't feel you need to prove it beyond the formulation of your belief"? Certainly not I.

    I of course also considered the more cautious formulation as a question but preferred to state an hypothesis in the form of a claim (to be proved or disproved). Such hypotheses are pretty much always the starting point for proofs because until it's proved one way or another, you don't really know for sure. They give you some direction for exploring proof strategies. And if you keep trying and failing to prove some proposition p, you may then want to try proving not p for a while.

    Obviously the issue isn't settled in mathematics until the proof one way or the other has been provided. But before getting there, one works with hypotheses about the problem at hand in order to develop strategies for what a proof might look like.

    Mario, while I still don't entirely understand why even the dogmatic belief that P != NP would suggest that P == NP, I think you're not drawing a sufficiently strict line between "working hypotheses" and "evidence for" on the one hand and rigorous mathematical proof on the other.

    Just one example of your formulations:
    ... the method employed by them to prove P != NP results in P = NP. They will be in fact, unwillingly, making a case for P = NP.
    You seem to be confused about the difference between "results in" (suggestive of proof and in this case obviously refuting a method which would then result in the logical contradiction P != NP and P == NP) and "making a case for," which is done in mathematics before a proposition is proven. Once proven, you don't have to worry about the much weaker "making a case." The issue is then truly decided.

    In any case, the front of the t-shirt is on my view (obviously) only intended to say that I share the mainstream hypothesis that P != NP. 15+ years ago it was also possible to hypothesize (as many did without being in possession of a proof) something like x**n + y**n = z**n => (n > 2 || x = y = z = 0)

    It's also well-known (and provable) that there are true statements that aren't provable...

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