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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."
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.
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.
According to the wikipedia article that was linked, a Golomb ruler is a set of numbers where no two pairs of numbers have the same distance. The "order" is how many numbers are in it, and the "optimal" ruler for an order is the one that ends on the lowest number.
So what they've found which set of 25 numbers - where the distance between any possible pair among them is unique - ends on the lowest number.
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.
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.
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.