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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.
The Wikipedia page says One practical use of Golomb rulers is in the design of phased array radio antennas such as radio telescopes. Antennas in an [0,1,4,6] Golomb ruler configuration can often be seen at cell sites. Does this mean we can now construct larger antennas with greater sensing power, using fewer materials, due to knowing a larger optimal configuration than previously?
-Clio
Karma: Bad (mostly from not giving a fuck)
Blog: http://clintjcl.wordpress.com
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.
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...
A few lines of Python suggests that there are 180 numbers that can't be measured, starting with 81, 90, 93, 103, 110...
Obviously the 11 numbers preceding 480 can't be measured, for example.
Well, 25 choose 2 is 300 so presumably 180 numbers must be missing.
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?
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.
You are confused - there are no assumptions in mathematics because mathematics does not deal with any real entities. There are only definitions and what you are talking about applies to them: depending on your definitions properties of defined entities will differ. Quite a trivial conclusion most sane people already realize.
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?
the application has to do with harmonics. For example the classic problem is that bridge that collapsed under wind load in the 40's. It collapsed partly because harmonics from the wind, just like a whistle, built up. Part of breaking harmonics is having a quick list of numbers that you can be sure won't duplicate. In a bridge you might pick your structural members to be just a little "off" using proportions from this list so that no two pieces were identical, one way of reducing vibrations in the structure.
Each length appears exactly once on the list and they can never be repeated unless you pick the exact same line segment.
I was expecting you to measure the shit with a Golomb ruler. Oh well.
Hasn't GÃdel done pretty much exactly that?
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."
> You are confused - there are no assumptions in mathematics because mathematics does not deal with any real entities. There are only definitions and what you are talking about applies to them: depending on your definitions properties of defined entities will differ. Quite a trivial conclusion most sane people already realize.
*You* are confused and are mixing definitions and axioms. There are assumptions in mathematics, they are called axioms.
http://en.wikipedia.org/wiki/Axiom
116 comments and none have yet explained what the article is actually talking about. Thanx for nothing /.
All I want is a little clarity plz. =)
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
#!/usr/bin/python
marks = [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]
unmeasurable = set(range(1, 481))
for i in range(1, len(marks)):
for j in range(i):
unmeasurable.discard(marks[i] - marks[j])
print sorted(unmeasurable)
Output:
[81, 90, 93, 103, 110, 111, 120, 139, 153, 171, 172, 174, 176, 183, 184, 192, 196, 198, 200, 204, 210, 213, 216, 220, 221, 223, 227, 231, 232, 238, 241, 242, 243, 247, 249, 254, 255, 256, 257, 259, 262, 264, 267, 269, 272, 275, 279, 280, 283, 284, 286, 288, 291, 292, 294, 295, 296, 297, 308, 309, 311, 312, 317, 318, 326, 327, 328, 329, 330, 331, 332, 335, 336, 337, 338, 339, 341, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 356, 358, 361, 362, 363, 364, 366, 369, 370, 371, 373, 374, 375, 377, 378, 379, 380, 381, 383, 385, 386, 388, 390, 391, 393, 397, 398, 399, 400, 401, 403, 404, 405, 406, 407, 409, 410, 411, 412, 413, 414, 415, 416, 417, 418, 421, 422, 423, 424, 425, 426, 427, 429, 432, 433, 434, 435, 436, 437, 439, 440, 442, 443, 444, 445, 446, 448, 449, 450, 452, 453, 454, 456, 457, 458, 460, 461, 462, 463, 464, 465, 466, 469, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479]
Exactly... I participated in RC5-64, but RC5-72 just seems pointless to me. It's the exact same problem, just 256 times harder.
Furthermore, these encryption challenges are not actually discovering anything. They're essentially brute-forcing a random number which another computer chose.
Contrast this with distributed computing challenges about mathematics (such as OGR-25 which is being discussed here), health or other issues where the result is something meaningful and potentially useful about the world.
The AACS key is NOT 0xF606EEFD628B1CA427BEA93A9CA9773F
Let's assume the project will terminate when 50% of the keyspace has been searched. That's 2^71 keys to search.
A E6600 Core 2 Duo PC calculates about 17M keys per second according to a quick google search. This means around 1.4e14 computer-seconds to search 50% of the keyspace, or 3.85e10 hours.
A PC like this one uses around 150 watts, so it would consume 5,775,000,000 KWh of energy to search that keyspace.
Some different ways of visualizing this amount of energy:
This of course doesn't take into account future improvements in CPU efficiency.
The AACS key is NOT 0xF606EEFD628B1CA427BEA93A9CA9773F
I for one welcome our new Golomb Ruler!
The difference is of course, that Apple and MS are not people.
Corporations are investment vehicles for people. They represent the interests of people. These people are called "stockholders." This is how the average Joe (70% of US equities are held by the small investor) can pool his resources with other people and get part of the Dream. Like my parents. My dad is a former middle class salesman who was "retired" early due to an on-the-job disability. Thankfully, my parents got into Apple at a good price, and the stock has been a stellar performer for their golden years.
Although personally, I'm not particularly statist about Apple and Microsoft. I just wish they would stop being cunts.
Now, if only other people like yourself would understand that corporations are not, in fact, entities in and of themselves, but represent the interests of stockholders. Not employees, not customers, not Slashdotters who don't believe in patent or copyright, but the interests of those who entrusted their money to the corporation. So keep your hands and laws and regulations off of other peoples' money, if you please. If you don't like the iTunes DRM, don't buy an iPod.
You are entitled to your opinion, but at least understand why Apple does the things it does - to increase shareholder value. And they do it well. So please don't tell other people how their business should be run. Go invest your money with Red Hat or something, or buy an open-source media player. But disparaging Apple because it doesn't do what you want is like being mad at your neighbor's wife because she doesn't make you dinner at night. It's not her job. And if she makes your neighbor great dinners that you have to smell every night, don't be a hater; congratulate your neighbor on finding a great wife. Then go find one that meets your needs. Because the relationship between your neighbor and his wife is none of your goddamned business!
Slashdot "libertarians": Small government for me, big government for those I disagree with. -1, I disagree with you