Very cute argument, and very much in his style--he was famous, as the author notes, for heuristic arguments that weren't very formalizable but had a lot of beauty.
One story I heard is that a computer scientist tried to explain the P=NP? problem to him; Feymnan couldn't understand why this was a problem. It was obviously true that P != NP, what even needed proving?
Per "Surely You're Joking" and the article, one of the cognitive techniques Feynman used was to keep a physical example, a demo, in his mind that conformed to the math being explained. I wonder if he used that for this, and what his model was.
If you imagine it as a logical statement, represented physically in writing: P <=> ~P
Then, I think it is clear the statement is not true. NP is trivially definitionally not equivalent (equal) to P.
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?
I think this was a joke
Yes, we are talking about an anecdote from the book, "Surely You're Joking, Mr. Feynman!": Adventures of a Curious Character
?
Why would Feynman not have published a full(er) proof?
I presume you mean the idea of physical examples in general comes up in "Surely You're Joking"; I can't find any discussion of P vs. NP (or Fermat's Last Theorem, for that matter) within it.
As for why Feynman didn't publish a full(er) proof: a full(er) proof of what? He didn't have anything near a proof of P != NP or of Fermat's Last Theorem... There was nothing of the sort to publish.
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.
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?
>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.
This whole talk is about it
https://www.youtube.com/watch?v=v3pYRn5j7oI
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?
> Edit: Also, why cannot I report/flag your post?
You can't downvote or flag comments that are replies to you.
Do you know what P and NP mean? What's your ~ supposed to mean?
(You seem to be implying logical negation. But P is not meant to be a logical statement, thus can't be negated.)
Plus what Chinjut said.
~ is a standard character for logical negation.
See my replies elsewhere.
Oh, my question was more in the vein of "Obviously the standard notation doesn't make sense here. I assume you are not an idiot, so you must have meant something else."
Alas, jokes and sarcasm don't travel well over text. One of the reasons they are frowned upon in the HN guidelines.