Comments on: A SAT Attack on the Erdos Discrepancy Conjecture
http://www.metafilter.com/138247/A-SAT-Attack-on-the-Erdos-Discrepancy-Conjecture/
Comments on MetaFilter post A SAT Attack on the Erdos Discrepancy ConjectureSat, 12 Apr 2014 09:07:23 -0800Sat, 12 Apr 2014 09:07:23 -0800en-ushttp://blogs.law.harvard.edu/tech/rss60A SAT Attack on the Erdos Discrepancy Conjecture
http://www.metafilter.com/138247/A-SAT-Attack-on-the-Erdos-Discrepancy-Conjecture
<a href="http://io9.com/computers-are-providing-solutions-to-math-problems-that-1525261141">Computers are providing solutions to math problems that we can't check</a> - "A computer has solved the longstanding <a href="http://arxiv.org/abs/1402.2184">Erdős discrepancy</a> problem! Trouble is, we have no idea what it's talking about — because the solution, which is <a href="http://www.newscientist.com/article/dn25068-wikipediasize-maths-proof-too-big-for-humans-to-check.html">as long as all of Wikipedia</a>'s pages combined, is far too <a href="http://mathbabe.org/2013/07/30/the-stacks-project-gets-ever-awesomer-with-new-viz/">voluminous</a> for us <a href="http://oliviacaramello.com/Unification/Unification.htm">puny humans</a> to confirm." (<a href="http://marginalrevolution.com/marginalrevolution/2014/04/are-computer-coming-up-with-answers-we-cannot-understand.html">via</a>; <a href="http://www.metafilter.com/126041/Computerized-Math-Formal-Proofs-andamp-Alternative-Logic">previously</a> ;)post:www.metafilter.com,2014:site.138247Sat, 12 Apr 2014 08:55:27 -0800kliulessmathmathsmathematicsalgorithmalgorithmsprogramprogrammingprooflogictheorycodecomputationcomplexityuniversalityphilosophyresearchscienceBy: Tell Me No Lies
http://www.metafilter.com/138247/A-SAT-Attack-on-the-Erdos-Discrepancy-Conjecture#5502752
The singularity has arrived! Huzzah!
Actually this is an interesting problem. About the best you could do is have independent parties create proof checkers that walked through the solution. Which when you get down to it may have a higher accuracy rate for less voluminous proofs as well.comment:www.metafilter.com,2014:site.138247-5502752Sat, 12 Apr 2014 09:07:23 -0800Tell Me No LiesBy: three blind mice
http://www.metafilter.com/138247/A-SAT-Attack-on-the-Erdos-Discrepancy-Conjecture#5502760
There is absolutely elegance in the brute force solution. It's just not as pretty on paper.comment:www.metafilter.com,2014:site.138247-5502760Sat, 12 Apr 2014 09:18:39 -0800three blind miceBy: symbioid
http://www.metafilter.com/138247/A-SAT-Attack-on-the-Erdos-Discrepancy-Conjecture#5502763
Now, here's a question.
Would it be possible to create a sort of AI conjecture-maker entity? An AI that knows how all these various parts relate, and then can create conjectures, and the put them up for proof to a proof-checking algo/AI?
I don't think we'd still be able to create AIs that would be able to create new forms of mathematics, at least not yet, but surely there must be a way to combine formal statements of patterns in a given constrained domain along with the condition for truth or falseness?
I'm sure more complicated conjectures might not be able to be made at this point, but surely there must be a way for conjectures to be created by machine?comment:www.metafilter.com,2014:site.138247-5502763Sat, 12 Apr 2014 09:21:02 -0800symbioidBy: Tell Me No Lies
http://www.metafilter.com/138247/A-SAT-Attack-on-the-Erdos-Discrepancy-Conjecture#5502764
Oh, and speaking as someone who watches things go wrong with software a lot I would be leery of accepting a solution by a computer "using a different approach" as proof. The programmer's intent might be different but it would not surprise me a whit to see the computer end up largely copying the first proof.
If you want to know that things went right you want to forget the content and hammer on the form. We can't understand the overall proof but we should be able to understand each individual step quite clearly.comment:www.metafilter.com,2014:site.138247-5502764Sat, 12 Apr 2014 09:21:24 -0800Tell Me No LiesBy: save alive nothing that breatheth
http://www.metafilter.com/138247/A-SAT-Attack-on-the-Erdos-Discrepancy-Conjecture#5502769
Meh. Work is fine, articles overblown. The work here was encoding the conjecture into an instance of the well-studied SAT problem. Solvers for SAT problems have been around...comment:www.metafilter.com,2014:site.138247-5502769Sat, 12 Apr 2014 09:27:08 -0800save alive nothing that breathethBy: Chocolate Pickle
http://www.metafilter.com/138247/A-SAT-Attack-on-the-Erdos-Discrepancy-Conjecture#5502810
I've heard that the computer-proof of Fermat's Last Theorem was so long and complicated that no one actually knows if it is correct.comment:www.metafilter.com,2014:site.138247-5502810Sat, 12 Apr 2014 10:04:40 -0800Chocolate PickleBy: dilaudid
http://www.metafilter.com/138247/A-SAT-Attack-on-the-Erdos-Discrepancy-Conjecture#5502844
There is no computer proof of Fermat's last theorem.comment:www.metafilter.com,2014:site.138247-5502844Sat, 12 Apr 2014 10:35:54 -0800dilaudidBy: escabeche
http://www.metafilter.com/138247/A-SAT-Attack-on-the-Erdos-Discrepancy-Conjecture#5502867
There's also no computer proof -- or any proof, yet -- of the Erdos discrepancy conjecture, despite the linked article incorrectly saying so.comment:www.metafilter.com,2014:site.138247-5502867Sat, 12 Apr 2014 10:53:16 -0800escabecheBy: Tell Me No Lies
http://www.metafilter.com/138247/A-SAT-Attack-on-the-Erdos-Discrepancy-Conjecture#5502886
<i>There's also no computer proof -- or any proof, yet -- of the Erdos discrepancy conjecture, despite the linked article incorrectly saying so.</i>
Could you expand on that a bit?comment:www.metafilter.com,2014:site.138247-5502886Sat, 12 Apr 2014 11:08:15 -0800Tell Me No LiesBy: escabeche
http://www.metafilter.com/138247/A-SAT-Attack-on-the-Erdos-Discrepancy-Conjecture#5502907
The conjecture says that, for every C, every sufficiently long sequence has a subsequence with discrepancy at least C. The new proof shows that this is true for C = 2. They are working on proving it for C = 3 along similar lines. But this is well short of proving it's true for ALL C, which is what the conjecture proposes.comment:www.metafilter.com,2014:site.138247-5502907Sat, 12 Apr 2014 11:24:20 -0800escabecheBy: benito.strauss
http://www.metafilter.com/138247/A-SAT-Attack-on-the-Erdos-Discrepancy-Conjecture#5502964
C'mon, escabeche, you know that the only important numbers are 0, 1, and ∞. 2 is practically the same thing as ∞.
<small>/<em>L<sup>p</sup></em>-space joke.</small>comment:www.metafilter.com,2014:site.138247-5502964Sat, 12 Apr 2014 12:25:34 -0800benito.straussBy: jamjam
http://www.metafilter.com/138247/A-SAT-Attack-on-the-Erdos-Discrepancy-Conjecture#5502980
I think the real problem will come not when we can't follow the proof of a conjecture, but when we can't grasp the computer-made conjecture itself.comment:www.metafilter.com,2014:site.138247-5502980Sat, 12 Apr 2014 12:37:09 -0800jamjamBy: blue_beetle
http://www.metafilter.com/138247/A-SAT-Attack-on-the-Erdos-Discrepancy-Conjecture#5503036
Who computes the computers?comment:www.metafilter.com,2014:site.138247-5503036Sat, 12 Apr 2014 13:38:32 -0800blue_beetleBy: save alive nothing that breatheth
http://www.metafilter.com/138247/A-SAT-Attack-on-the-Erdos-Discrepancy-Conjecture#5503143
I read once to bootstrap Lisp someone wrote a minimal Lisp interpreter in Lisp and compiled it to assembly by hand.comment:www.metafilter.com,2014:site.138247-5503143Sat, 12 Apr 2014 16:06:11 -0800save alive nothing that breathethBy: RobotVoodooPower
http://www.metafilter.com/138247/A-SAT-Attack-on-the-Erdos-Discrepancy-Conjecture#5503155
No one really understands the exact circuit layout on the CPU you're using, which was spat out by a similar SAT solver, but it seems to work just fine.
Pesky humans demanding compact forms for boolean equations, harrumph.comment:www.metafilter.com,2014:site.138247-5503155Sat, 12 Apr 2014 16:20:05 -0800RobotVoodooPowerBy: The Tensor
http://www.metafilter.com/138247/A-SAT-Attack-on-the-Erdos-Discrepancy-Conjecture#5503182
Rather, <i>quis probabit ipsos probatores?</i>comment:www.metafilter.com,2014:site.138247-5503182Sat, 12 Apr 2014 17:17:26 -0800The TensorBy: nevercalm
http://www.metafilter.com/138247/A-SAT-Attack-on-the-Erdos-Discrepancy-Conjecture#5503246
I somehow feel smarter just reading the comments. Please keep it up, you brilliant bastards.
<small><small>not kidding</small></small>comment:www.metafilter.com,2014:site.138247-5503246Sat, 12 Apr 2014 18:29:23 -0800nevercalmBy: spiderskull
http://www.metafilter.com/138247/A-SAT-Attack-on-the-Erdos-Discrepancy-Conjecture#5503364
<i>No one really understands the exact circuit layout on the CPU you're using, which was spat out by a similar SAT solver, but it seems to work just fine.</i>
Well, unless it's an Intel CPU -- they still do everything by hand. Also, there aren't too many SAT-based synthesis packages used for real problems. Logic synthesis is binate, so minimizing SAT has a bad habit of blowing up for anything larger than a trivially sized circuit. It's useful for automated validation, though.comment:www.metafilter.com,2014:site.138247-5503364Sat, 12 Apr 2014 23:21:43 -0800spiderskullBy: drnick
http://www.metafilter.com/138247/A-SAT-Attack-on-the-Erdos-Discrepancy-Conjecture#5503401
So I worked in pure maths for quite some time where I did quite a lot of relatively long proof by hand and later I worked on a automated computer proof system with several others, and both approaches to proving things bothered me for different reasons.
For the hand proof, in some sense you never really prove anything. You give a convincing argument that outlines the major logical steps that a proof of the result would have. But you're still writing most of it in English with a bit of mathematical notation, which while much more structured and precise than most any other language, is still not a formal proof. A formal proof uses axioms, formal rules of inference and basically syntactic transforms of symbolic sentences to establish truth. Maybe a few logicians work this way, but 99% of pure mathematicians don't.
The computer proof has the fundamental problem that from a false statement, anything can be proved. So if your automated math prover has a software flaw (who ever heard of code having bugs?) that means that occasionally it can generate the sentence "false" without good reason, perhaps buried very deeply within very large proof, then it'll be able to get any result you like proved.
Neither approach is ideal. But in both cases it's sensible to get someone or something to independently check the working.comment:www.metafilter.com,2014:site.138247-5503401Sun, 13 Apr 2014 01:15:05 -0800drnickBy: 1367
http://www.metafilter.com/138247/A-SAT-Attack-on-the-Erdos-Discrepancy-Conjecture#5503647
<a href="http://www.bbc.co.uk/cult/hitchhikers/guide/deepthought.shtml">Didn't Douglas Adams already describe how to deal with a computer coming up with an answer beyond our ability to understand?</a>comment:www.metafilter.com,2014:site.138247-5503647Sun, 13 Apr 2014 10:18:44 -08001367By: escabeche
http://www.metafilter.com/138247/A-SAT-Attack-on-the-Erdos-Discrepancy-Conjecture#5504024
<em>2 is practically the same thing as ∞.</em>
You say so, but I just came back from a conference where one of the speakers had a good L_2 bound but the L_∞ bound seems totally out of reach, and I'm all, you should do L_4, that's what you do when you can't get an L_∞ bound but you don't want to just give up, and he was all, good point, 4 isn't ∞ but it sure isn't 2. In conclusion, harmonic analysis is a land of contrasts.comment:www.metafilter.com,2014:site.138247-5504024Sun, 13 Apr 2014 18:11:27 -0800escabecheBy: radwolf76
http://www.metafilter.com/138247/A-SAT-Attack-on-the-Erdos-Discrepancy-Conjecture#5504695
I knew no good would come from letting COLOSSUS have a data link to GUARDIAN.comment:www.metafilter.com,2014:site.138247-5504695Mon, 14 Apr 2014 08:34:02 -0800radwolf76By: atbash
http://www.metafilter.com/138247/A-SAT-Attack-on-the-Erdos-Discrepancy-Conjecture#5506267
<i>Well, unless it's an Intel CPU -- they still do everything by hand. Also, there aren't too many SAT-based synthesis packages used for real problems.</i>
I was just going to make a similar comment — but I don't think it's strictly true any more. As I understand it, they currently do the largest scale layout by hand, but many of the portions that go into it are laid out with SAT solvers with constraints to make the results something humans can reasonably stitch together.
Also I seem to recall AMD CPUs and most ARM IP modules are built with automated layout.
Alas, I'm having difficulty finding solid references to back my understanding up.comment:www.metafilter.com,2014:site.138247-5506267Tue, 15 Apr 2014 11:21:39 -0800atbashBy: kliuless
http://www.metafilter.com/138247/A-SAT-Attack-on-the-Erdos-Discrepancy-Conjecture#5507007
<i>I knew no good would come from letting COLOSSUS have a data link to GUARDIAN.</i>
<a href="http://www.metafilter.com/83367/a-pink-sliver-of-rat-brain-sat-in-a-beaker#2657079">THERE IS ANOTHER SYSTEM</a>.comment:www.metafilter.com,2014:site.138247-5507007Tue, 15 Apr 2014 20:11:27 -0800kliuless