7 ms·
Kurt Gödel is Laughing His Ass Off Right Now
- swombat 17y agoAmusing, though I didn't quite get why this would make Kurt Gödel laugh his ass off...? Anyone care to enlighten me?
- alexandros 17y agoJust a guess here, but maybe the author thinks that Kurt Gödel actually "...is widely regarded as the most important innovator in scientific and technical computing today."? Then again, I don't even understand what the term 'technical computing' means.
- bitdiddle 17y agoI also completely miss the connection and I clearly wouldn't put those two in the same league. Godel was a very thoughtful if troubled soul who totally shook the foundations of mathematics.
- ulf 17y agoProbably most people would not put those two in the same league, but I suspect the author thinks that Stephen Wolfram himself would certainly do so.
- HSO 17y agoNo, that would require a modicum of modesty. I think Mr Wolfram compared himself somewhere in writing to Newton himself, but I cannot recall where I read that.
- pierrefar 17y agoA few interesting search results here: http://www.google.com/search?q=Wolfram+newton http://www.google.com/search?q=Wolfram+newton
- mhb 17y agoMy guess is that he is the guy in the left photo next to Wolfram.
- mhb 17y agoOh. I thought those photos were part of the results of the preceding Wolfram Alpha query.
- Herring 17y agoI'm guessing something to do with unprovable statements...
- travisjeffery 17y agoSome of Kurt Godel's most famous works are his 2 incompleteness theorems, which state the inherent limitations of all but the most trivial formal systems for arithmetic of mathematical interest. Which basically means that there are things that just can't be computed but are quite obvious for us humans.
- psygnisfive 17y agoNo, that's not what it "basically means". Firstly, the incompleteness theorem (there's only one) is not about computation but about proofs; specifically that there are some things within an axiomatic system which are true which cannot be proven such within the system itself. Secondly, this does not mean that these things are unprovable, period. For instance, Gödel showed that you can prove these things perfectly fine, you just have to use different system. But this system will have its own unprovable statements. Thirdly, computability was Turing's domain, not Gödels, and has to do with the kinds of algorithms you can use to perform proofs, not the system the proof is for. For example: second-order logic (SOL) can prove things about first-order logic (FOL) that FOL cannot prove about itself, but both systems can by utilized by a universal turing machine. Fourthly, there is no known thing that cannot be proven, period, which is obvious for us humans.
- travisjeffery 17y agoThere are two man, it's the incompleteness theorems, not theorem. And yes it does mean there are things that are unprovable. Because the Axioms of Mathematics can't cover consistently cover everything. Computability and his incompleteness theorems are very closely related.
- psygnisfive 17y agoThere are two things called his incompleteness theorems, but only one actually deals with completeness. The other deals with consistency, which is not coming up with contradictory answers. Basically, it says that any system that asserts it is consistent is necessarily inconsistent. This is I suppose related to things which are true about the system which cannot be proven true in the system, but only in a roundabout way. Computability and completeness are also definitely related, but, not quite so tightly as you implied. Computability is a property of algorithms, while completeness is a property of axiomatic systems. Algorithms operate on axiomatic systems, but are not the systems they implement, and there's no inherent connection between being able to prove statements about a system, and the algorithms used to compute proofs for that system. As I said, SOL can prove FOL to be complete and consistent, and you can do this on a universal turing machine, but FOL cannot prove itself to be complete and consistent even doing this on a universal turing machine. Of course, if your computer _is_ an axiomatic system (and all are), then the incompleteness theorem(s) do say things about what that computer can do, and we know that all turing complete computers have precisely the same sorts of constraints in that regard. The real thing that was irksome, tho, was the assertion that there are some things that are obvious to humans but which are uncomputable. This is just unfounded. Unless you're supposing human brains are somehow not computing things (collections of neurons are computers, after all, just not von Neumann architecture), there is no way for this statement to be true.
- pohl 17y agoI'm pretty certain that the author was making the subtle suggestion that Gödel would delight in concocting questions that would confound Wolframs' Alpha. Fans of Stanislaw Lem might look at it this way... Gödel : Wolfram Alpha :: Klapaucius : Trurl's Electronic Bard ("Have it compose a poem about a haircut. But lofty, noble, tragic, timeless, full of love, treachery, retribution, quiet heroism in the face of certain doom! Six lines, cleverly rhymed, and every word beginning with the letter S!")
- deleted 17y ago[deleted]
- biohacker42 17y agoBecause Alpha's praise of Mathematica and Wolfie is like a rear world example of the incompleteness theorem? The limits of errr... I'm stretching this as far as I can, but it's not enough. It seems like math nerd gossip.
- jganetsk 17y agoIt's because of the self-referential, contradictory nature of Wolfram Alpha's answer. Kind of like trying to assign a truth value to the statement "this statement is false". By putting in "how to program", and having it misinterpret it as "What is the world's most powerful computational software?", having the answer come out as "Wolfram Mathematica", and having the whole thing be powered by Wolfram Mathematica, you get a contradiction (maybe even 2)... in Gödelian style.
- yters 17y agoNot only that. Wolfram's attempt to take Godel's place in mathematics is contradicted by this answer, which is a self referential demonstration that the Wolfram axiomatic system (both the person and Alpha) cannot produce the genius of Godel, and is thus incomplete. Thus, Wolfram merely proves Godel's genius, via the original form of Godel's genius in the first place. Basically, Wolfram is ingenious at proving his disingenuity.
- TriinT 17y agoUnlike Wolfram, Gödel did groundbreaking work. Gödel was revolutionary. Wolfram is quite smart, but other than Mathematica, I don't really think he has achieved much at all. Any comparison between the two men is ridiculous. They are in entirely different leagues.
- DannoHung 17y agoShameless self promotion has gotten him pretty far, so I can at least see why he'd not stop. I mean, hell, he's better off than Godel ended up, right?
- TriinT 17y ago"I mean, hell, he's better off than Godel ended up, right?" So far, at least. In 20 or 30 years we will know the answer to that...
- fiaz 17y agoI really don't understand the purpose of this article. Sure, Wolfram has a super huge (and possibly fragile) ego...does that in some way make the author feel less secure such that he has to invest time in trying to convince the world that Wolfram "ain't all that"? I really feel compelled to point this out because as of now, this headline is #2.
- HSO 17y agoThis comment has a certain irony to it... do you feel "compelled to point this out" because the article "in some way make[s you] feel less secure such that [you have] to invest time in trying to convince the world that [the article] "ain't all that"?" Or why don't you just ignore it if it is so off?
- fiaz 17y agoand there you have it...the redditization of HN... edit: I should add that yes, this article does make me feel less secure about the quality of articles making it to the top of HN (hence the very last statement in the original comment).
- HSO 17y agoFair enough. but then you should push for HN letting us downvote articles too, not only comments. I don't know how much impact one comment will have on whether an article (or class of articles) makes the frontpage. And by the way, please don't be prissy, I was just making a little fun.
- DanielBMarkham 17y agoSo this post was about how Wolfram has a big ego? That's it? Nothing wrong with a big ego, is there? Self-promotion is still okay in the world? We're still free to toot our own horn? Write our own resumes, pitch our own products, spin our own political ideas, sell our own worldviews? And what, exactly, does Godel have to do with any of that? I take it the idea is that Godel was the real genius? If we're going to be measuring who's really smart, maybe we'd want to wait a few hundred years. I admire people with big egos and positive attitudes. We could use more of them in the world. I don't buy into their self-image, but I admire it. Positive mental attitude -- the idea that you're capable of making something really big -- is what's going to keep you hacking on that startup long after others would have quit. Arrogance, on the other hand, is a different matter. But this post had nothing to say about arrogance. Just wondering how it got so many upvotes. I guess Wolfram must have a natural ability to tick people off?
- deleted 17y ago[deleted]
- michael_dorfman 17y agoThere's a line between "big ego" and "delusion", and it appears that Wolfram has crossed it. Innovation requires big ego and positive attitude, but it also requires some contact with reality, and the ability to appreciate with humility the achievements of others.
- DanielBMarkham 17y agoinnovation, in your opinion requires those things. I'll use musicians as an example because they're most fresh in my mind. Good grief, take a look at some of the people we all acknowledge as being innovators: Motzart, who said he wrote great music like cows pee -- it was just his thing. Beethoven, who used to play performances that would make people cry -- and then would yell at the crowd for being such naves. Berlioz -- "At least I have the modesty to admit that lack of modesty is one of my failings." Delusion is one of those things, especially with really smart people, that's easy to assume and hard to prove. Humility and all of that are wonderful social skills, but they are by no means a prerequisite for being a paradigm-changing person or leaving great innovations to society. The lack of them just makes one unpleasant, and I never said Wolfram was a pleasant person to be around. And the kicker is -- their degree of popularity or acceptance by their peers in their own time was no indication of the contribution they eventually made. Their popularity and acceptance waxed and waned just like everyone else's: based on a bunch of social factors.
- chanux 17y agohttp://virl.com/2f0b5/ http://virl.com/2f0b5/
- WilliamLP 17y agoIn all but a few situations (for example learning something completely new) being modest is simply a waste of time. I have come to believe that the effects of "overconfidence" are almost overwhelmingly positive. If I look at almost anyone I admire, I see that they have, and have probably had for a long time, a very high sense of their own worth. (For example, look at Paul Graham. Did it take audacity to say he was working on a "100 year language"?) The reason why this took a long time for me to learn, is that being confident triggers an instinct in people to knock that person down and challenge them. See, for example, these comments. Nietzsche described this very well. It makes sense because there can only be a few leaders. Personally, I'm trying to get back a sort of youthful impudence I used to have. It's a personality trait that is awakened when reading about how Wolfram, when he was a university student, in a debate, pointed to a stack of CS books including TAoCP and the Dragon book and said something like "I'm going to read these and then soon I will know all that you know". It's arrogant beyond belief but it also makes me think "fuck yeah". I think that part of me is far more valuable than the part that just wants to behave, be nice, and get upmodded in places like this for going along with a crowd and making sure that everything is said in veneered careful way that will be approved by elders in suits.
- sqs 17y agoMaybe overconfidence gives you a slightly higher likelihood of success. But I couldn't live with myself acting like that, and I wouldn't want the success that would come with it. I will settle for perhaps a slightly lower chance of success, but I'll feel better about it knowing I am being myself and treating others well.
- dinkumthinkum 17y agoI totally disagree. Saying you are working on a 100 year language, ie being openly ambitiousis not the same thing as saying "I'm one of the most important scientists today. I'm really one of a kind." it seems silly to equate the two. And I don't think great scientists typically do that. They usually talk of standing on the shoulders of giants or being humble programmers.
- WilliamLP 17y ago
- req2 17y agoThose aren't adjectives.
- ivom 17y agoThere is another blog entry about Wolfram's ego, where the guy goes even further and proposes that the unit of "ego" be called Wolfram: http://www.aleph.se/andart/archives/2009/04/monumental_egos.html http://www.aleph.se/andart/archives/2009/04/monumental_egos....
- frazerb 17y agoSuch a huge ego, and I see that Wolfram is still at Alpha. Shouldn't we at least wait for WolframBeta ? Maybe he will have been able to iron out these ego discrepancies by then. ;)
- philelly 17y agothis is an amusing article that points out some of the more classic examples of wolfram's risible self-promotion. it's odd, however, that this critique comes from someone whose own webpage offers 3 headshots of himself, including one at the astronomic resolution of 1650x2135. (http://chrishecker.com/Image:Checker-headshot-closed.png http://chrishecker.com/Image:Checker-headshot-closed.png)
- cturner 17y agoThis is quite genuine. I don't particularly care about advanced maths and don't have any interesting questions to ask when faced with Alpha. It's getting mentioned all the time. I've now seen may mentions of ways that it fails. Is there anything that it is actually notably good at? People are obviously excited enough to be giving grief - is there a type of problem at which it is strong in a way that hasn't yet been done on the web? It's quite cool to be able to type in 'sin 5' and the like but google does that already.
- arakyd 17y agoI can't think of much to use Alpha for yet either, but I think it represents a significant accomplishment nevertheless, in a frontiers of knowledge representation/interaction sort of way. Doug Lenat describes it as halfway between Google and his Cyc project on the generality <-> sophistication spectrum (see link), which is a fairly impressive accomplishment (it can do a lot more than just 'sin 5'). It may not end up being much more useful than Cyc is at the moment, but it's still an advance. This stuff will get better, but we still have to go through the intermediate steps. http://www.semanticuniverse.com/blogs-i-was-positively-impressed-wolfram-alpha.html http://www.semanticuniverse.com/blogs-i-was-positively-impre...
- callmeed 17y ago"Anders Sandberg wrote a wonderful article proposing the Wolfram as the unit of ego measurement." I put my own ego at 74 milliwolframs ...
- quizzical 17y agoThe most perplexing thing for me is that Stephen Wolfram's kind of hyperbolic self promotion is something I normally see coming from companies that are trying to mask their lack of success. I actually think that Mathematica is an interesting and educational tool to use. Too bad it is a failure at affordability. Wolfram Alpha is not much to boast about in my opinion, but certainly an "answer engine" is a great goal and I would love to see more innovation here.