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Distributed.net Finds Optimal 25-Mark Golomb Ruler
kpearson writes "Distributed.net's 8-year-old OGR-25 distributed computing project has just proven conclusively that the predicted shortest 25-mark Golomb ruler is optimal. 'The total length of the ruler is 480, with marks at positions: 0 12 29 39 72 91 146 157 160 161 166 191 207 214 258 290 316 354 372 394 396 431 459 467 480. (This ruler may alternatively be expressed in terms of the distance between those positions, which is how dnetc displays them: 12-17-10-33-19-...).' 124,387 people participated in the project and two people found the shortest ruler, one on October 10, 2007 and the other on March 24, 2008."
i know we're all supposed to be nerds here, but this is way left of field. dont supposed you could have included a LITTLE more info in the summary as to what the fuck you're talking about?
It means the optimum ruler is Gollum.
Yes. Yes, you did.
Mathematics may be defined
as the subject in which we
never know what we are talking
about,nor whether what we are
saying is true.
--Bertrand Russell
You're thinking of science. You can only disprove a hypothesis, never prove it true. In math, you can prove or disprove a conjecture.
What a fool believes, he sees, no wise man has the power to reason away.
distributed.net used to have a very vibrant community, with several projects on-going at one time. But lately, things haven't been going so well for them. The prize funds for their RC5-72 challenge were recently yanked. And the only other project they had on-going was this OGR-25 project.
Does anyone know if they'll offer further projects in the near future? Many people I know have moved on to BOINC-based distributed computing projects, instead of sticking with distributed.net.
But you can't prove that, which proves his point.
What most people don't realize is that all of mathematics is based on certain assumptions, alternatively called axioms, postulates or definitions. Do all triangles have interior angles that add up to 180 degrees? Yes, but only if you make certain assumptions. That's called Euclidean geometry. There is also non-Euclidean geometry which is equally valid and is used to describe some systems in reality. Is there no highest prime? Does 2 + 2 = 4? Do parallel lines never intersect? Are no circles square? Yes again on all counts, but only if you make certain assumptions. So when we say that "x is proven" in mathematics then that is really shorthand for "x is proven based on certain assumptions". That doesn't stop some overzealous mathematicians from acting a little bit smug. I would like to point all smug mathematicians to Kurt Godel's incompleteness theorems.
Probably not. The [0,1,4,6] ruler is only order 4; we've previously known optimal rulers up to order 23. If larger configurations can be practically used, I would expect to see order 5 and higher already in use.
why the hell is everything tagged "story"?
I have another question. What happened to the option to turn off tags?
And one more: Is there any forum to discuss Slashdot issues? Seems like the only way is to bitch off-topic in the articles.
Headlines or summaries should be self explanatory.
Only the State obtains its revenue by coercion. - Murray Rothbard
That's got to be the most incomprehensible story summary I've ever seen posted to Slashdot, and that's saying a lot. Seriously. The predicted shortest 25-mark Golomb ruler is optimal? What on earth are you talking about? How about giving us the barest minimum of a context, so we might have some tiny clue what that spew of buzzwords is getting at.
My new yumiz ruler is perfectly calibrated in emh's and is 14.667 long. Now I'm going to go measure something like the how many pins can fit on one you guy's heads...
You just reminded me of......
Ah, Kryten; just thinking. [Rapidly] Assuming of course we're not dealing with five-dimensional objects in a basic Euclidean geometric universe and given the essential premise that all geo-mathematics is based on the hideously limiting notion that one plus one equals two, and not as Astemeyer correctly postulates that one and two are in fact the same thing observed from different precepts, (Pulls a "nerdy" grimace, and loudly exhales through his nose.) the theoretical shape described by Siddus must therefore be a poly-dri-doc-deca-wee-hedron-a-hexa-sexa-hedro-adicon-a-di-bi-dolly-he-deca-dodron. (Pulls the same face, exhales a second time.) Everything else is poppycock. Isn't that so?
it's essentially defines a list of numbers such that if you pick any two segments that are not the same segment they will always have different lengths. This is useful for things that involve harmonics.. radio, buildings, ect. where you need to build "imperfect" shapes. With antennas this is so that they don't interfere with each other in close proximity. With bridges you might need to make each length of bridge section a slightly different length to keep the bridge from vibrating to pieces. It's a list, highly useful to engineers of various types. Not that exciting, unless you really needed to have 25 critical measurements when 24 just wouldn't do.
Yes, people routinely get this wrong. They're not wrong this time.
In this case, the distinction between "it was proven" and "it was shown" is a distinction without a difference. In math, you can "show" something within a restricted domain; for example, that a postulated solution to a given equation really is a solution, without giving a complete family of solutions. One can show it numerically, or show it analytically. Here, a restricted set of postulated solutions over the only available domain (the positive integers) was exhaustively searched for actual solutions, and the set that satisfied the postulates was also shown to be optimal (in a well-defined sense for the problem).
This is no more a "non-proof" than the proof of the 4-color map theorem in two dimensions, which was also "shown" using an exhaustive search.
There is a BIG difference between [proven and shown] as anyone within the Maths and the Sciences can tell you. I'm sorry, but people routinely get this wrong and it gets quite aggravating.
First, there is such a thing as proof by inspection. It may be considered inelegant by certain folks, but it's there nonetheless.
Second, it's just as aggravating (for those in certain fields) that computational results are not more valued. Sure, analytical results provide insight that computational results do not. But if you simply want to know the answer, why not accept a computational result?
Third, anticipating the old "how do we know the computer didn't make a mistake" comment: Theoretical proofs need to be proofread just as code does. So why not accept a computer program (and its verified output, as in the summary) as proof?
I was expecting you to measure the shit with a Golomb ruler. Oh well.
I am sorry, but listing out all possibilities (assuming that's what they did) and showing one is the minimum IS a valid proof for that minimum in that particular case.
For example, to prove "7 is a prime number", listing out 1,2,3,4,5,6 and then showing all are not a factor of 7 is a valid proof that "7 is a prime number". If you think this is not a proof, tell me which step in the proof is wrong.
Of course, whether the proof of Distributed.net is correct depends on how strongly they can prove their program actually covered all possibilities.
Oliver.
The sumbitch spends most of his time in a dark cave.
And what the hell would he measure anyway? Not like he has any windows for drapes, my precious.
Slashdot "libertarians": Small government for me, big government for those I disagree with. -1, I disagree with you
A forum!? You can take your fancy Web 2.0 "community" fad elsewhere. We've got Golomb rulers to discuss here!
--I'm not talking about dance lessons. I'm talking about putting a brick through the other guy's windshield.-
why the hell is everything tagged "story"?
If you mouse over it (and have JavaScript enabled), you'll be informed that it's the "type tag." I assume the concept is that it differentiates between journals, comments, bookmarks, feed entries, and other types of nodes that could, conceptually, appear in the firehose.
I have no idea why Slashdot feels the need to show these on the main page, though, considering that everything that currently shows on the main page is a story. But if you play with the firehose, it's what tells you what "thing" the entry is.
You are in a maze of twisty little relative jumps, all alike.
No, you can directly email them but of course they will only use that as ammunition to be taken out of context and savaged via the poorly conceived "Disagree Mail" "Feature".
I'd leave, but there isn't really an alternative that's better. Instead I use adblock and suck off this teat without providing benefit to the site. (Unless you include this post as "providing benefit" which is dubious since it will almost certainly get modded down.)
LISTER: "Don't give me any of that 'Star Trek' crap. It's too early in the morning."
It's worth calculating the number of gigawatt-hours of electricity is expended on these toy problems. The original goal was to make a political point: we can't assume some of these codes are out of range with present technology. Having made your point, you're just boiling water to arbitrarily make the problem another order of magnitude more expensive to crack.
When did we decide that the major problem facing planet earth was a surplus of electricity we must burn off by any available method?
a few lines from Python would say
Then shalt thou count to three, no more, no less. Three shall be the number thou shalt count, and the number of the counting shall be three. Four shalt thou not count, neither count thou two, excepting that thou then proceed to three. Five is right out.
rewriting history since 2109
If you mouse over it (and have JavaScript enabled), you'll be informed that it's the "type tag."
Actually, when I mouse over tags I get an incomprehensible mess of overlapping elements. It's probably my fault for using something as obscure as Firefox, though; I'm sure it works perfectly on IE6.
sic transit gloria mundi