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Feynman on Fermat's Last Theorem

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Re: Feynman on Fermat's Last Theorem

#101

Post by Chinjut »

jsprogrammer wrote: post #98
Chinjut wrote: post #96

Earlier quoted context omitted.

It's true I did not understand you were joking, but I didn't personally malign you either. If you are referring to the word "moron", I didn't call you a moron; I was shocked that you thought P vs. NP was so trivial, and asked whether you therefore thought everyone puzzling over it was a moron.

I didn't say you maligned me. You implied others were morons (or, at least that I would think that). You should be directing your disbelief at Feynman's remains. He is the one that made the claim. I just explained the joke. Anyway, it is still true that the physical model of P != NP is definitionally trivial.

I didn't malign others, either, as I didn't call anyone a moron... Yes, it's true I implied that you might think that others who puzzled over P vs. NP were morons. I was, after all, laboring under the belief that you thought P vs. NP was trivial. Is that a malignment?

Anyway. Nevermind that. Feynman joked that P was trivially not equal to NP? Where can I find that joke given by Feynman?

Re: Feynman on Fermat's Last Theorem

#102

Post by Chinjut »

jsprogrammer wrote: post #98
Chinjut wrote: post #96

Earlier quoted context omitted.

It's true I did not understand you were joking, but I didn't personally malign you either. If you are referring to the word "moron", I didn't call you a moron; I was shocked that you thought P vs. NP was so trivial, and asked whether you therefore thought everyone puzzling over it was a moron.

I didn't say you maligned me. You implied others were morons (or, at least that I would think that). You should be directing your disbelief at Feynman's remains. He is the one that made the claim. I just explained the joke. Anyway, it is still true that the physical model of P != NP is definitionally trivial.

As for whether "the physical model of P != NP is definitionally trivial", I suppose it depends on what "the physical model" is, but I don't see any physical reason why it should trivially be impossible to decide the Boolean satisfiability problem in polynomial time... Why shouldn't there be some algorithm to do so?

Re: Feynman on Fermat's Last Theorem

#103

Post by jsprogrammer »

Chinjut wrote: post #101
jsprogrammer wrote: post #98

Earlier quoted context omitted.

I didn't say you maligned me. You implied others were morons (or, at least that I would think that). You should be directing your disbelief at Feynman's remains. He is the one that made the claim. I just explained the joke. Anyway, it is still true that the physical model of P != NP is definitionally trivial.

I didn't malign others, either, as I didn't call anyone a moron... Yes, it's true I implied that you might think that others who puzzled over P vs. NP were morons. I was, after all, laboring under the belief that you thought P vs. NP was trivial. Is that a malignment? Anyway. Nevermind that. Feynman joked that P was trivially not equal to NP? Where can I find that joke given by Feynman?

>Where can I find that joke given by Feynman?

Approximately 6 parents up this comment tree.

I'll address your other comment here (HN has an inexplicably bad rate limit):

The physical model is the literal characters:

P != NP

:)

Re: Feynman on Fermat's Last Theorem

#104

Post by Chinjut »

jsprogrammer wrote: post #103
Chinjut wrote: post #101

Earlier quoted context omitted.

I didn't malign others, either, as I didn't call anyone a moron... Yes, it's true I implied that you might think that others who puzzled over P vs. NP were morons. I was, after all, laboring under the belief that you thought P vs. NP was trivial. Is that a malignment? Anyway. Nevermind that. Feynman joked that P was trivially not equal to NP? Where can I find that joke given by Feynman?

>Where can I find that joke given by Feynman? Approximately 6 parents up this comment tree. I'll address your other comment here (HN has an inexplicably bad rate limit): The physical model is the literal characters: P != NP :)

I mean a cite that Feynman made that joke; where can I find that?

Re: Feynman on Fermat's Last Theorem

#105

Post by DanBC »

jsprogrammer wrote: post #91
Chinjut wrote: post #70

Earlier quoted context omitted.

NP is most certainly not "trivially definitionally not equivalent (equal) to P". (Do you think everyone puzzling over the question of whether P = NP is a moron? You are aware there is a million dollar prize for a proof one way or the other, yes?). What definition are you using for NP?

P=deterministic algorithms in polynomial time NP=non-deterministic algorithms in polynomial time See, it is a definitionally trivial logical negation. That's the joke! Edit: Also, why cannot I report/flag your post? Your personal malignment is uncalled for.

> Edit: Also, why cannot I report/flag your post?

You can't downvote or flag comments that are replies to you.

Re: Feynman on Fermat's Last Theorem

#106

Post by jsprogrammer »

Chinjut wrote: post #104
jsprogrammer wrote: post #103

Earlier quoted context omitted.

>Where can I find that joke given by Feynman? Approximately 6 parents up this comment tree. I'll address your other comment here (HN has an inexplicably bad rate limit): The physical model is the literal characters: P != NP :)

I mean a cite that Feynman made that joke; where can I find that?

https://news.ycombinator.com/item?id=12019310

I wouldn't consider it authoritative though.

Re: Feynman on Fermat's Last Theorem

#107

Post by tgb »

jordigh wrote: post #99
tgb wrote: post #86

Earlier quoted context omitted.

No, I'm not talking about integrating the probability that n >= 42. What's the chance that a random number in [n] is 42? It's 1/n, if n is at least 42. Sum that over all x in [n] and you get 1, i.e. the probability that there is a number in [n] that is 42.

You're still talking about different events. The event that there is 42 in [n] is different from the even that x = 42.

Then I guess I just don't understand what you're trying to conclude from this argument.

Re: Feynman on Fermat's Last Theorem

#108

Post by jordigh »

tgb wrote: post #107
jordigh wrote: post #99

Earlier quoted context omitted.

You're still talking about different events. The event that there is 42 in [n] is different from the even that x = 42.

Then I guess I just don't understand what you're trying to conclude from this argument.

Richard Feynmann was trying to argue probabilistically about the possible existence of a counterexample to FLT. To do this, he more or less tries to put a probability value on the event "a counterexample exists". The problem is that his kind of reasoning is similar to the probability of an event such as "x = 42". Counterexamples to FLT may, a priori, be as rare as the number 42 is within the integers, i.e. with probability tending to zero as you consider larger and larger sets of integers. But a very small probability of a counterexample, even a probability that tends to zero, does not mean a counterexample doesn't exist anymore than it says that 42 doesn't exist.

Re: Feynman on Fermat's Last Theorem

#109

Post by tgb »

jordigh wrote: post #108
tgb wrote: post #107

Earlier quoted context omitted.

Then I guess I just don't understand what you're trying to conclude from this argument.

Richard Feynmann was trying to argue probabilistically about the possible existence of a counterexample to FLT. To do this, he more or less tries to put a probability value on the event "a counterexample exists". The problem is that his kind of reasoning is similar to the probability of an event such as "x = 42". Counterexamples to FLT may, a priori, be as rare as the number 42 is within the integers, i.e. with proba…

See I can't see the analogy from your argument to Feynman's for the following reason: you are computing the probability that x=42 for an individual x and saying that it is going to 0 as x->infinity. Feynman first computes the probability that N is x^n + y^n but then integrates that over all N and n in order to get the probability that there is a solution anywhere. His argument takes into account the fact that there could be just one single lone solution in a infinite sea of non-solutions, since his probability estimate is for "there is a solution anywhere" not "this particular number is a solution". And I think that when you add that part to your estimate, you do get a probability of 1 that 42 exists somewhere, even if individually you get a low probability of it being at any given large x.

Re: Feynman on Fermat's Last Theorem

#110

Post by jordigh »

tgb wrote: post #109
jordigh wrote: post #108

Earlier quoted context omitted.

Richard Feynmann was trying to argue probabilistically about the possible existence of a counterexample to FLT. To do this, he more or less tries to put a probability value on the event "a counterexample exists". The problem is that his kind of reasoning is similar to the probability of an event such as "x = 42". Counterexamples to FLT may, a priori, be as rare as the number 42 is within the integers, i.e. with proba…

See I can't see the analogy from your argument to Feynman's for the following reason: you are computing the probability that x=42 for an individual x and saying that it is going to 0 as x->infinity. Feynman first computes the probability that N is x^n + y^n but then integrates that over all N and n in order to get the probability that there is a solution anywhere . His argument takes into account the fact that there…

This detail doesn't matter. He's still computing a tiny nonzero probability that is only zero in the limit. We came up with other examples of tiny nonzero probabilities that are zero in the limit that can lead to the wrong conclusion, such as saying that 42 doesn't exist.

Feynmann's argument is clumsy and wrong. This kind of approximation is ok for a physicist but it doesn't work for mathematics.

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