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Wiki to Help Solve Millennium Problems?
Posted by
CowboyNeal
on Sat Apr 15, 2006 11:07 AM
from the np-complete dept.
from the np-complete dept.
MattWhitworth writes "A new wiki has been set up over at QEDen to try to gather a community to solve the Millennium Problems. The problems are seven as yet unsolved mathematical problems that continue to vex researchers today. What do you think of this effort? Will gathering a community of people help solve problems such as P=NP, or do you think it requires a lot more than a semi-qualified community to approach the problem?"
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Please. . . (Score:5, Insightful)
Re:Please. . . (Score:5, Insightful)
GIGO.
The quantity of GI does not effect the reality of GO.
The very few people who actually do understand the problems and the underlying issues will eventually stop trying to explain what the real issue is.
One very quickly learns the pointlessness of trying to explain to the Unskilled and Unaware of It that it would take about two years of education for them to even understand that they don't understand the issue.
And it only annoys the pig.
KFG
Re:Please. . . (Score:3, Insightful)
Re:Please. . . (Score:3, Interesting)
Re:Please. . . (Score:2)
3/4 of the people will argue about their misunderstanding of the problems involved, the other won't even know what the problems are but think they do. The very few people who actually do understand the problems and the underlying issues will eventually st
Re:Please. . . (Score:5, Insightful)
--Kurt Vonnegut in Cat's Cradle
Would you not say there is quite a difference from explaining what you are doing to an 8 year old child and giving sufficient information to expect that child to contribute to the work?
For example, I study reaction dynamics and intramolecular energy flow during 'fast' reactions. It is pretty easy for me to explain to children that I study chemical reactions - how things are changed from one thing to another. I could even do some demo's and talk about them in some detail.
But that's a far cry from expecting those children from being able to help me solve Navier-Stokes equations, apply classical thermodynamics, statistical mechanics and quantum mechanics to arrive at quantitative models of deflagration explosions.
Re:Please. . . (Score:5, Funny)
Aha! A charlatan!
Re:Please. . . (Score:2)
As an
Re:Please. . . (Score:3, Insightful)
Have you ever seen any of the threads which pop up on some forums now and again attempting to convince people that 0.9 recurring is equ
Re:Please. . . (Score:2, Informative)
A scientist's work needs to touch on reality at some point. If a scientist doesn't understand why he's doing what he's doing clearly enough to tell an eight year
Re:Please. . . (Score:3, Funny)
nowadays that restriction has been relaxed, and the official requirement for grant proposals in the UK is that it should be able to be understood by "an interested 1
Re:Please. . . (Score:2)
Meanwhile... (Score:4, Funny)
Re:Meanwhile... (Score:2)
...and BBSpot [bbspot.com] will set up a Wiki to solve the Y2K problem. 85% of this Wiki will consist of suggestions from people who don't know what the problem was, and think it sill exists. The other 15% will consist of people asking Brian Briggs [bbspot.com] how to contact Ens [bbspot.com]
Re: Meanwhile... (Score:3, Insightful)
This analogy is quite flawed. Whereas discussion of theoretical problems can lead to the solution itself, discussion of practical issues can only be a small part
well, (Score:3, Interesting)
(sorry about the bad spelling)
well I'm completely unqualified in every sense for these things, but being a political scientist I should be able to have a stab at the last question... Concordat's jury theorum suggests that with more people your chance of getting a right answer increases, say if everyone has about 60% chance of getting it right for example then with a few hundered people that chance should have increased to over 80%... which would lead me to believe yes it will work, still, i tend to think that the more people you have the less productive you are capable of being as people will disagree, and if the two most experienced people disagree then it could polarise the views of the less experienced people and split the project... so basically, it could go either way...
Re:well, (Score:3, Insightful)
I would think, and this is just a guess, that the qualified pool of people working on those problems is already nearly maxed out. Adding a bu
Re:well, (Score:2)
If you look through history you will find that the established scientists were often preventing the release of new ideas. Whether this be from their younger colleagues or from amateurs.
That said,
In related news... (Score:5, Insightful)
Lets put it this way, if there was a Wiki on solving complex DNA evolution problems, 50%+ of the posts would be from wackos talking about ID and Creationism.
I hate to break it to people, but Maths and Physics make computing look like a liberal arts degree.
Re:In related news... (Score:2)
[Insert rant about the diminishing frontiers between maths and computer science here]
Re:In related news... (Score:2)
Let's see... The entire computer department was gutted out this Spring Semester due to low enrollment. The only class I was able to pick up was statistics math. An obvi
Mass Gap in the Yang-Mills equestion... (Score:5, Funny)
Monkeys (Score:3, Interesting)
Monkeys Are Now Code Monkeys... (Score:2)
Motivation? (Score:3, Insightful)
Noble endavor (Score:2, Insightful)
I doubt it will work (Score:5, Insightful)
But then, more people working on it doesn't necessarily improve things. For one, you will expect a very bad noise to signal ratio, where there would be a bunch of smart ass ideas that have already been disproved decades ago, or ideas which are so obviously wrong that no academic would even think of writing a paper for.
Basically the whole thing is based on the assumption that "monkeys banging on typewriters will eventually produce all the works of shakespear". It works in theory, but remember that it takes either an infinite number of monkeys, or infinite time -- whereas you could find a group of talented people to do the same job more effectively.
Expect a dozen claims of "TSP solved in P time!" from this site within a month, and nothing more afterwards.
I don't think so, no.. (Score:3, Insightful)
Will gathering a community of people help solve problems such as P=NP, or do you think it requires a lot more than a semi-qualified community to approach the problem?
Proofs are not really found by committee. This Wiki might be a good way to share research and in that sense it may aid the effort but above and beyond that it's not going to contribute much.
It will take a unique insight and a particularly sharp mind to get to the bottom of these problems.
Simon
solid approach (Score:5, Insightful)
Re:solid approach (Score:5, Informative)
This is going to become an instructional site to teach people (hopefully correctly) what is going on in these fields, nothing more.
IQ is not cumulative (Score:2)
GJC
Not a unique idea... (Score:5, Insightful)
The important difference there was that this project was only open to those actually actively involved in working on this problem. A public wiki will likely be bogged down by people who don't truly understand the problem or the approaches used to solve them - instead of everyone being able to contribute a little (as is possible in Wikipedia, which effectively just requires a transcription of information) the vast majority of people won't have anything to offer at all. And of course, those that are actively involved in working on these projects and want to share their work are in all likihood already doing so - with other people in the same field.
This project will likely attract those who do not have the particlar interest, time or background to work in a focused fashion on the problem, and consequently I'd be surprised if anything really unique or surprising came out of the project.
Re:Not a unique idea... (Score:5, Interesting)
I'd agree, with two caveats: this project might attract some math prodigy that isn't working on these problems (Ramanujan, anyone?). Also, this project will help a lot of people learn how to think about the most abstract parts of mathematics.
The possibility of either result would justify this project in my eyes.
Not gonna find any new genius here... (Score:2)
They could contribute (Score:5, Insightful)
Real researchers are familiar with cranks on newsgroups (James S Harris on sci.math for example) who year in year out claim to have proved this or that famous conjecture. Or, these people send proofs to real researchers, expecting attention when page one of their "proof" contains an error. So my hopes are not high that a community of semi-qualified people could solve the problems, but....
Suppose that this community set about collating and putting in context all of the material related to those problems that exists in the **research level** literature and **expounding** it in an extremely clear way. And suppose that real researchers were interested and joined the effort. This resource could be a HUGE contribution to the effort.
Unfortunately, the only joint efforts in mathematics on the web so far, do not deal seriously with the literature, but approach mathematics at a level of understanding of a first year graduate student. Problems that are well understood by the most brilliant minds on the planet are not going to be solved by people with an understanding as limited as that. It isn't as though some tough problems haven't been solved with elementary methods (the Kayal-Agrawal-Saxena result being a case in point), nor is it true that cranks do not occasionally come up with the goods (de Branges proof of the Bieberbach conjecture being a case in point), but the fact is, these are exceptions to the rule and the vast majority of difficult problems had immensely difficult solutions which took new developments in mathematics over periods of many years before they could be solved. Will a community of non-researchers make developments in modern mathematics? Personally I doubt it.
But, this is a new idea, hasn't been tried, so who knows where it will lead. As a research mathematician, the idea intrests me, and I would be involved if it headed in the right direction and didn't become a place for cranks to meet and fiddle with polynomials over an unspecified ring.
Re:They could contribute (Score:3, Interesting)
That's an excellent idea, and I can s
WikiCaps (Score:2, Funny)
"The title of this article is incorrect..."
-merv.
Why share the credit? (Score:3, Insightful)
Personally, I don't think the wiki will do any good. Good collaboration requires face-to-face contact. Anything else is really equivalent to the modern email/conference/preprint system in math. After all, who wants to share their million-dollar insight on a wiki only to get scooped? Double-plus-ungood: how do you decide which researcher did the critical part of the problem? It's tough to say now (and mostly irrelevant, but intellectual pissing matches have been with math since at leave Liebnitz vs. Newton), and it would be harder to decide in the mixed-up collaborative world of the wiki.
While there are critics (Score:3, Insightful)
So, jokes and criticism aside, the OST (open source thinking) is a good plan. Execution may have some drawbacks, but it has goodness in it.
Solutions (Score:5, Funny)
How about monkeys? (Score:3, Funny)
Ramanujan (Score:5, Insightful)
A lot of people on Slashdot are degree-obsessed; at an early age they have bought into the idea that everybody who does not have a formal academic education to at least PhD level is necessarily unable to contribute anything to research. (This is not just the chip on my shoulder talking, but as someone with a degree from Fen Poly who has recruited a fair number of graduates over the years, I know it takes far more than a degree or two to make a scientist, mathematician or even a developer. Curiosity, persistence, the ability to see connections are all important.) Although this Wiki may well fail, it might just bring to light a few more Ramanujans. The world does not consist solely of North Americans, and there are doubtless plenty of educated people in other cultures who do not have access to the networks that bring some people to the fore while others, equally well endowed, may never get an opportunity.
Re:Ramanujan (Score:4, Interesting)
P vs NP Question (Score:2)
Re:P vs NP Question (Score:5, Informative)
What makes a problem NP is not whether it's solvable but rather how long it takes to solve. The algorithm you propose is a search algorithm. Consider what would happen if your list of incompatible students was so large that within the group of 100 students you randomly choose, there is not a single possible arrangement of pairs. This means you would have to choose another group of 100 students. It's a minor refinement but an important one.
Now consider if that list was so large that there was only a single possible group of 100 that contains an arrangement of pairs that worked. Now consider that within that group of 100, there was only one good possible arrangement. If you're very unlucky, and you choose these set of 100 and arrangement of pairs last, you have to try every possible combination before finding the right one. Okay, so what?
Lets see how many possible answers you'd have to try. Within a group of 100 students, there are 100 choose 2 possible arrangements. There are 400 choose 100 possible choices of 100 students. n choose k is really n! / (k! (n-k)!) where n! is n * (n - 1) *
[400! / (100! 300!)] * [100! / (2! 98!)]
Your standard calculator is not going to be able to solve this one but if you have an arbitrary precision calculator (like bc), you get:
1109718121819397093151989141664840784648478532850
Which is an awfully large number. That number is so large, in fact, that even if you have a computer that could check one possible solution with every electron in the universe, until the Sun supernova's, you'd still not find the answer.
Now, that depends on really bad luck. You can construct problems though that given average luck, you would not find the solution in the lifetime of the universe. This is what cryptography is based on.
Compare this to a standard sorting algorithm. To sort the list [3, 4, 5, 6, 7, 8, 9, 2, 1, 0] given a crappy algorithm like bubble sort requires n*n = 100 computations. You can solve this problem the same way using search though. You merely have to randomly arrange the list in every possible way and check to see if your random arrangement is sorted. There are n! possible arrangements of a list of n elements so there are 10! = 3628800 possible answers to search. You can see that even a crappy algorithm like bubble sort is much better than search.
The difference is even greater with larger lists. A problem that is only solvable via search is considered NP. A problem that is solvable with an algorithm in polynomial time (n*n is a polynomial) is considered P. The N in NP stands for non-polynomial.
So the problem here is whether there exists a polynomial solution for these set of problems that we've labelled NP. What makes this even more significant is that it has been proven that if we find a polynomial solution for one NP problem, we can create solutions for any NP problem. A lot is riding on the lack of existence of a polynomail solution for NP problems. If someone where to prove that there are indeed polynomial solutions to NP problems it would be earth-shattering. After the initial shock, it would also open up a whole new world of mathematics since a lot of things we didn't think were possible to do efficiently became possible.
Online Encyclopedia of Integer Sequences (Score:3, Informative)
With over 100,000 web pages, searchable, with posters' email addresses given, and both internal and external hotlinks and citations to hardcopy literature, this has been the leading collaborationware in Mathematics. The Online Encyclopedia of Integer Sequences (or OEIS) recently faced a problem with increasing numbers of clueless postings.
The distinguished panel of editors, under Dr. Neil J. A. Sloane, first added a keyword of "probation." Submissions so tagged, unless okayed by an editor, are deleted after a reasonable time. At my urging, citing the history of Slashdot, they even more recently adopted the keyword "less" -- meaning less than interesting, but better than probation. "Less" sequences stay in the database, but are given minimum priority in searches.
Similarly, MathWorld [wolfram.com] is a form of collaborationware or pseudowiki. Although edited by Dr. Eric W. Weisstein and his staff, it encourages submission by form from anyone, and posts attribution to such submissions, and lists of contributors.
I contend that web-based systems have substantially affected the practice of Mathematics. Social mechanisms such as pioneered by Slashdot contribute to weeding out useless from interesting contributions. As with Wikipedia, one's academic credentials mean nothing here. What matters is the quality of one's submissions, as evaluated by one's online peers.
There also many fine Math blogs, but that's another topic.
-- Jonathan Vos Post [livejournal.com]
Insight Required (Score:5, Insightful)
These problems are all incredibly difficult. A lot of very good mathematicians have thought about them, in some cases for over a hundred years. In some cases, even understanding the problem requires an advanced mathematical education. If there was anything approaching an easy solution, it would have been found already. That said
Problems like these always require some insight. Typically, either a way to relate the problem to some other unexpected area, or some new kind of machinery that creates a leverage against the problem.
Personally, I wouldn't expect that from such an effort.
I remember... (Score:5, Interesting)
He told me that if he he solved the problem by showing P=NP (instead of P!=NP, which "most mathematicians believe"), he wouldn't publish his proof. Instead, he would setup a website that would take credit card payments to solve problems quickly (for example, packing boxes into the back of a UPS truck, or various traveling salesman problems). At the time, I though this was a little antisocial, but not much more.
Later, when I had more mathematical training, I looked back on this and realized how revealing this attitude was: of course, if someone proves P=NP, the proof will almost certainly not be accompanied by practical algorithms which are significantly better than those used already for problems on most scales. Of course, the idea that he was going to solve this problem without any collaboration or formal education in logic or complexity theory demonstrated the arrogance typical of many super-successful business-people. I can't help but remark that for all the stupid patents on software "ideas" and sometimes algorithms, we're lucky that, most of the time, theoretical advances are made not by people like this... and and so people publish their results, and are rewarded with respect rather than dollars.
Imagine the state of our theoretical knowledge in mathematics and computer science if, even in Academia, every discovery of a new algorithm or idea resulted in a patent application, and was jealously guarded as a secret which could produce profit. Unfortunately, this is already largely the state of things in the wet sciences (unnecessarily so, I would argue, and point to mathematics as my evidence).
As for the wiki thing: I don't think most ordinary people are like this guy, so hey, good for the wiki. (I think this attitude is taught by the business world, and not somehow the other way around). Unfortunately, I fear that the millenium problems are deep enough that amateurs will have trouble making a big impact. There are a few amateur contributions to mathematics occasionally, but there hasn't been a significant one in a long time. (The last was arguably by Marjorie Rice, a housewife who essentially resolved the question of the number of different ways to tile the plane with convex pentagons). Astronomy is probably the last big field where amateurs play a really significant role.
Re:I remember... (Score:3, Insightful)
And your entire post underlines one for me. Believe it or not, the academic world is full of plenty of people just like your friend. Just a
Re:Unsolved Problem (Score:2)