I think that whether P is NP or not could turn out to be undecidable and in fact one could add either equality or inequality as an independent axiom. The theory of computational complexity is about asymptotic results as the size of the instances goes to infinity and involves `there exists` statements whose meaning when applied to infinite sets is typically ambiguous. For instance, it turned out to be a matter of choice whether or not you want the set of all subsets of real numbers between zero and one to equal or to be strictly larger than the set of so called measurable sets. And whether or not a set is measurable can be characterized in a very concrete way about the possibility of approximating it by unions of intervals. So the question of whether or not there exist non measurable sets turned out to depend on `what you mean by set`in a way which people hadn´t thought about before. I suspect the question whether or not P is NP will depend on what we mean by P and NP in ways which so far no one thought about.
P ≠ NP
221–230 of 233 posts
Re: P ≠ NP
#222Earlier quoted context omitted.
Scott Aaronson does not explicitly say the proof is wrong, but says > If P≠NP has indeed been proved, my life will change so dramatically that having to pay $200,000 will be the least of it. […] If P≠NP is proved, then to whatever extent theoretical computer science continues to exist at all, it will have a very different character. and > I can afford $200k, but not in the same way Bill Gates can afford $200k.
Discussed here: http://news.ycombinator.com/item?id=1587405 As randomwalker says, it's not entirely obvious that Aaronson is betting against the proof.
It is.
Re: P ≠ NP
#223Re: P ≠ NP
#224We created a prediction market for the next winner of the Clay Prize here http://smarkets.com/current-affairs/clay-prize/next-winner
Re: P ≠ NP
#225Earlier quoted context omitted.
Discussed here: http://news.ycombinator.com/item?id=1587405 As randomwalker says, it's not entirely obvious that Aaronson is betting against the proof.
It is.
It wasn't, when the comment you just downmodded was written. There's a reason Aaronson's posted multiple clarifications, after all...
Re: P ≠ NP
#226Re: P ≠ NP
#227Earlier quoted context omitted.
Money is the last thing to care about if you solve P ?= NP. Humanity will remember you in same league as Turing Pythagoras Gauss and others.
You can't eat prestige. Nor find joy in a life of isolation. Look at Rembrandt's philosopher if you want the true picture of the life of the mind. How history remembers you only matters after you're dead. Can you really tell someone to live a life of solitary confinement? The isolating parts of academia honestly suck. But everyone convinces themselves that academia is so great, in part because so many have gone befor…
First, Well the guy in question works in R&D lab of HP, and must be getting paid at least 120k$ per year. He also seems to have a good family and thus a social life :D
I fail to understand why you draw such a poor picture of a Maths / Physics PhD's life. Professors have a lot of interaction with students thus it is not exactly solitary confinement. Your picture of Academia is too dark.
I agree that there are people who get stuck in doing one Post-Doc after other and never get any tenure in life, surely it sucks for them but there are several Physicists and Mathematics PhD students who end up as a Quants on Wall Street and earn huge money.
If you read any posts / articles written by professors advising aspiring PhD students, you would rarely find them portraying a PhD life as fantasy filled life. So in my opinion Caution signs are already there.
Re: P ≠ NP
#228Earlier quoted context omitted.
Money is the last thing to care about if you solve P ?= NP. Humanity will remember you in same league as Turing Pythagoras Gauss and others.
You can't eat prestige. Nor find joy in a life of isolation. Look at Rembrandt's philosopher if you want the true picture of the life of the mind. How history remembers you only matters after you're dead. Can you really tell someone to live a life of solitary confinement? The isolating parts of academia honestly suck. But everyone convinces themselves that academia is so great, in part because so many have gone befor…
I don't think academia is really like that. One of my former roommates was a Physics PhD student at MIT, so I know him and his colleagues. They all drank beer and played chess and cards in this one basement bar in Cambridge, did stuff like hang gliding, rock climbing, ultimate frisbee and played in various awful experimental-folk bands. They were nerds but they were all bros and even attracted the weird kind of cyber-hippy chicks who are into dudes like that. They all eventually got married. They seemed pretty happy to me. In contrast I once got stuck in a corporate programming job, which was the most uninteresting and socially isolating experience of my entire life.
Whenever I read these HN screeds against academia, I wonder what they are comparing it against. In my experience academia was way more interesting and fun than working as a professional programmer. The only thing good about the later is that it pays a lot.
Re: P ≠ NP
#2294 possible problems with the proof:
http://rjlipton.wordpress.com/2010/08/09/issues-in-the-proof...
Re: P ≠ NP
#230Earlier quoted context omitted.
You can't eat prestige. Nor find joy in a life of isolation. Look at Rembrandt's philosopher if you want the true picture of the life of the mind. How history remembers you only matters after you're dead. Can you really tell someone to live a life of solitary confinement? The isolating parts of academia honestly suck. But everyone convinces themselves that academia is so great, in part because so many have gone befor…
I don't think academia is really like that. One of my former roommates was a Physics PhD student at MIT, so I know him and his colleagues. They all drank beer and played chess and cards in this one basement bar in Cambridge, did stuff like hang gliding, rock climbing, ultimate frisbee and played in various awful experimental-folk bands. They were nerds but they were all bros and even attracted the weird kind of cyber…
Well maybe those physics PhDs are a lot better at socializing than me. I remember spending years of my PhD trying to make friends, going to bars/rock climbing/dances/running clubs etc to try and meet friends, but never got any where, and just feel this crushing depression every day I have to go to work and sit down at a computer for 8 hours. I feel roughly the same in a corporate or academic environment, it's the result of so much being by oneself. Perhaps I shouldn't have gone into computers?
However, Academia for the most part I think is just that sort of environment, I have commiserated with numerous PhD students who say the same thing. If one is into computers, both academia and computer engineering as career tracks are rather isolating, but some seem to like it, vs some get lonely, perhaps it's something psychological, and I'm not really intended to be such an introvert. Who knows.
I don't think academia is a bad career as long as one can get tenure at a good school, or in a good industry lab, so as to work with good people. I guess whether one can take it psychologically just depends on the individual.
Although I do agree that maybe if one had kids+wife or worked hard to be social, the 8 hours of isolation a day wouldn't be that bad. It might even be relaxing! So maybe professor is a good job for one in old age. But still I would worry about causing my students to suffer through isolation.