The really great part about Roland Piquepaille's posts is that the sites he mirrors seem never to have any trouble staying up. Perhaps it's just me, but I'd think he could help out more by mirroring some of the sites that appear in other stories?
Well, I guess he still does a service by bringing these stories to attention.
Not that I really care, I don't own an iPod, but these "killer" headlines are starting to sound like the "BSD is dead" troll.
Using my iPod, I can transfer 17MB of data from my right pocket to my left pocket in just a couple of seconds. How long would it take with one of these Rio Carbons, hmmmm?
How the hell is Amtrak a drain on taxpayers's liberty?
I would also be dubious of the claim that it's bloated and inefficient, but on those counts I must admit I don't really know the basic facts. Still, some serious evidence would be needed to justify such an assertion.
The solution of a celebrated problem creates a disturbance in the otherwise quiet flow of mathematical events. The solution escapes the planning of committees. Colleagues are unprepared because the possibility of a solution has not been included in their research proposals. Students have avoided related thesis topics because of the risk that the work will not be welcome to a prospective employer. Friends are discouraged from research activity by the demands of the situation created by the solution. The manuscript, which is necessarily written at the highest research level, is readable only to a limited audience. An introduction is therefore needed which makes available the opportunities created by the solution.
He's really sorry that he disturbed the otherwise quiet flow of our pathetic lives. Also, since we are complete idiots, he will patiently tell us about the opportunities created by the solution. Isn't he nice?
I may be talking out my ass here, but the habit of modern scientists in all branches seems to be to avoid unseemly self-promotion. This is why papers say things like "WE" or "ONE" instead of "I". It is also why scientists usually don't issue a press release of their research before publishing it. LdB is not displaying any sort of modesty or humility here... I don't think he's defending his proof. In his mind, his proof is right. He's apologizing for solving it before the rest of us.
I'm sure experts in complex analysis know the names of the Russian students who rewrote his proof; I just took a complex analysis class once upon a time.
But you're right: proving things in an unusual manner is not at all a problem.
Provided they are actually proofs. Nash may have been off his rocker, but his proofs were solid. Wiles's proof of Fermat's Last Theorem was up in the stratosphere (for such a concrete statement, the methods are insanely abstract)---but the proof is appropriate and carefully done and all that good stuff. Didn't hurt that people expected that sort of method, either.
LdB's proofs, both for Bieberbach and RH, have been unnecessarily wacky. The RH proof has been decisively discredited. Not just the specific proof, but the whole method of proof----we're not talking about a typo on line 17, or a lemma that needs to be rewritten. No, the whole idea he uses has been shown mathematically to be inadequate to proving RH.
Yet he still claims to have a proof. This is insane: putting out the same proof and thinking this time it'll be accepted.
Whatever. This guy is annoying, but fortunately it's easy to ignore him...
It is not proved; he is not at the top of his field; this "paper" will be quickly forgotten among professional mathematicians; and I doubt any professional mathematician is going over the proof with any sort of comb.
L. de Branges first achieved fame for proving the Bieberbach conjecture. His proof went through strange and abstract methods. He went on the road to present his proof at various seminars in France, Russia, etc; IIRC a bunch of Russian students got very excited and basically rewrote his proof. Their new proof was much shorter and avoided the use of strange methods. Nowadays, their proof is remembered and his is not, but the proof still bears his name, since after all he was the first to come up with *some* kind of proof, and their proof did more or less come out of his.
So he deserves credit for that, and it was quite an achievement to prove the Bieberbach conjecture. But even then he was using unwieldy proofs with unnecessarily abstract methods.
For many years he has been claiming to have a proof of the Riemann Hypothesis. Professional mathematicians stopped listening a long time ago.
This guy is washed-up.
I whole-heartedly agree that this short article is hilarious, but I would like to add the adjective condescending. What kind of asshole apologizes for solving a problem? Does he think he lives on some higher plane, and therefore must take direct, personal responsibility for every aspect of our lives?
Look at how G. Perelman submitted his ideas on proving the Poincare conjecture just a little while ago. He didn't waste anyone's time by rehashing the already-available history of the problem or its wider context in mathematics. Nor did he apologize for having an idea. Rather, he submitted his ideas for consideration, with the full awareness that there may have been a mistake..... Now, this is where I admit that I do not really understand that area of math, and have not been closely following the status of (alliteration alert) Perelman's proposed proof. Still, Perelman is a real mathematician, and even if the proof is (was?) wrong, it has real ideas of value in it.
chgros's reply is right---you should really look at a book on abstract algebra, such as the books of Fraleigh, Gallian, or Dummitt & Foote. But for some reason I feel like chipping in (to hear my own voice, most likely), so here goes.
4 = 1 (mod 3)
so
4*4 = 1*1 (mod 3)
which is to say that 4^2 = 1^2 (mod 3)
Similarly, 4^3 = 1^3 (mod 3), and 4^4 = 1^4 (mod 3), and so on. At this point you could write down an induction if you want (given 4^p = 1^p (mod 3), multiply the left hand side by 4 and the right hand side by 1; these are equal). Really it should just be direct.
The idea is that, for cripe's sake, 4 = 1. So 4+73 = 1+73, and whatever other operations you want to do. For example, 4^p = 1^p. Mod 3.
HTH
zach (ps. Too bad there's no TeX posting option:-) )
Well, $a,b,c,\dots$ have to be specified before $p$ or $q$ or whatever. So there can't be any requirement that $a,b,c,\dots < p$, and if setting $q = a/2 = b/4 = \dots$ doesn't work then you'll just have to try some other value of $q$.
As has been pointed out in another post, some tuples such as $(a,b)=(2,4)$ have finitely many solutions (for that example, one solution, given by $p=3$). This is because $(0,2,4)$ is a complete set of residues mod 3. More information about this can be found at
(Thanks to another poster for posting a pointer to primepages.org.)
The $k$-tuple article may not be crystal clear in every way, but it makes it pretty clear that this problem of tuples has been studied, and there is a fairly simple criterion which is believed to ensure that a given pattern $(a,b,c,\dots)$ will have infinitely many "solutions". Do the ones that don't meet the criterion still have at least one solution? Hmm, not necessarily. For a silly example, $(2,4,6)$ doesn't have any solutions.
Addresses an issue in which scheduled items, such as automated backups or Software Update checks, may not work if the computer is asleep at the scheduled time. With this update, the schedule will run once the computer wakes from sleep.
What about the periodic scripts (daily, weekly, monthly)? Is anacron now unnecessary?
Welllll.... They are not trying to do a substitution cypher or anything. The idea is that the letters are a sequence of initials for words in some quotation or something.
There can't be all that many quotations, or even meaningful phrases, with two consecutive words that start with V (and three out of four contiguous words), can there? Witness the incredibly awkward attempts to come up with "joke" answers in other posts on this page. And the line of poetry is pretty awkward, too. So those V's would seem to impose some pretty strong conditions after all---giving hope that there might be a unique meaningful answer. Not much hope, though. (Still, as mentioned elsewhere, there's a lot of "side" info: the painting, etc.) We'll see.
Scroll down to April 9th and listen in Real Player (sorry). The relevant bit starts at the 32:00 mark. (Yeah, the whole thing is an hour long... sorry.)
Anyway, this report was produced locally here in Ann Arbor, by a friend of mine who interviewed Dr. Miller in person. The whole point is that the dwarf/long-lived mutation is in fact naturally occuring, **not** the result of genetic engineering.
(Also, the audio report suggests that the colony is much larger, but perhaps the older mice are sequestered from the rest of the colony, so the AP report might have that right; hard to say.)
Were you deliberately misunderstanding what I said? I have nothing against his claim that 500 watts is a lot. In fact, it seems rather a lot to me, too. But why can't he just say watts? Why say "kilowatt-hours per hour"? That's just silly.
There are efforts underway to collect and streamline the (alleged?) proof of the classification of finite simple groups. See, for example, http://www.ams.org/online_bks/surv40-1/. I am not a group theorist (IANAGT:-) ), only a mere algebraic geometer, so I'm definitely not current on this issue, but I think everyone, and especially group theorists, are painfully aware of this huge steaming mess of a proof. They are working to bring it into a better shape.
There won't be any announcement; there'll just be books like the above-linked one that quietly turn up in mathematical catalogs.
It's not clear that any similar effort could even possibly be undertaken with a computer proof. You type in "RUN" and it spits out a long-ass proof. What are you supposed to do with that? Write a "elegant( )" function that makes proofs elegant?
This does not mean that computer proofs are bad. I guess my point is that a good, human proof brings greater understanding, which can lead to improved proofs, or better results, etc. Computer proofs seem to lack this feature of greater understanding. You get a result, and that's about it.
At least, that's the impression I've received over the years...
As a calculus and pre-calculus teacher, I have found that students will call *any* concave-up graph a parabola. x^4, definitely a parabola, if you're a pre-calc student. I could draw a graph of e^x for x > 0 and some of them would still say it was a parabola.
There's been a lot of talk to the effect that Apple is not likely to abandon the catchy-sounding "OS X" name. ("O S X I" doesn't sound as cool as "O S X"....) So will they call it "OS X Eleven" or "OS X Two point Oh" or what? Who knows?! As much as the OS might deserve a full new version number, the marketing aspect of it definitely pulls in the direction of keeping "OS X" as long as possible.
zach
Re:Fellow Slashdotters, prepare to be dazzled!
on
The Zenith Angle
·
· Score: 1
Nothing wrong with TeX as a word processor replacement. Or, not much, anyway. As a math grad student, I use TeX a fair amount, and word processors next to never.
As a spreadsheet, though, TeX is a little awkward...
Perhaps they are hoping to get a variety of examples so newbies can see more than one implementation? Also, perhaps they want to give their readers something "fun" to do... I can see how some people would enjoy having a little mini-challenge every now and then, and they will enter the contest; and other people are too busy or would rather spend their free time in other ways, and so they won't enter the contest... And that's fine.
Slashdot Mirror
The really great part about Roland Piquepaille's posts is that the sites he mirrors seem never to have any trouble staying up. Perhaps it's just me, but I'd think he could help out more by mirroring some of the sites that appear in other stories?
Well, I guess he still does a service by bringing these stories to attention.
-zach
Not that I really care, I don't own an iPod, but these "killer" headlines are starting to sound like the "BSD is dead" troll.
Using my iPod, I can transfer 17MB of data from my right pocket to my left pocket in just a couple of seconds. How long would it take with one of these Rio Carbons, hmmmm?
How the hell is Amtrak a drain on taxpayers's liberty?
I would also be dubious of the claim that it's bloated and inefficient, but on those counts I must admit I don't really know the basic facts. Still, some serious evidence would be needed to justify such an assertion.
The bit about drain on wallets.... eh, well....
zach
... to move a 17 MB file from one folder to another?
Thank you! Thank you! Thank you! Thank you! Thank you!
Hmmm, that's not the impression I got.
The solution of a celebrated problem creates a disturbance in the otherwise quiet flow of mathematical events. The solution escapes the planning of committees. Colleagues are unprepared because the possibility of a solution has not been included in their research proposals. Students have avoided related thesis topics because of the risk that the work will not be welcome to a prospective employer. Friends are discouraged from research activity by the demands of the situation created by the solution. The manuscript, which is necessarily written at the highest research level, is readable only to a limited audience. An introduction is therefore needed which makes available the opportunities created by the solution.
He's really sorry that he disturbed the otherwise quiet flow of our pathetic lives. Also, since we are complete idiots, he will patiently tell us about the opportunities created by the solution. Isn't he nice?
I may be talking out my ass here, but the habit of modern scientists in all branches seems to be to avoid unseemly self-promotion. This is why papers say things like "WE" or "ONE" instead of "I". It is also why scientists usually don't issue a press release of their research before publishing it. LdB is not displaying any sort of modesty or humility here... I don't think he's defending his proof. In his mind, his proof is right. He's apologizing for solving it before the rest of us.
Good point. Maybe I went a little too far.
I'm sure experts in complex analysis know the names of the Russian students who rewrote his proof; I just took a complex analysis class once upon a time.
But you're right: proving things in an unusual manner is not at all a problem.
Provided they are actually proofs. Nash may have been off his rocker, but his proofs were solid. Wiles's proof of Fermat's Last Theorem was up in the stratosphere (for such a concrete statement, the methods are insanely abstract)---but the proof is appropriate and carefully done and all that good stuff. Didn't hurt that people expected that sort of method, either.
LdB's proofs, both for Bieberbach and RH, have been unnecessarily wacky. The RH proof has been decisively discredited. Not just the specific proof, but the whole method of proof----we're not talking about a typo on line 17, or a lemma that needs to be rewritten. No, the whole idea he uses has been shown mathematically to be inadequate to proving RH.
Yet he still claims to have a proof. This is insane: putting out the same proof and thinking this time it'll be accepted.
Whatever. This guy is annoying, but fortunately it's easy to ignore him...
Sorry, but...
.... Now, this is where I admit that I do not really understand that area of math, and have not been closely following the status of (alliteration alert) Perelman's proposed proof. Still, Perelman is a real mathematician, and even if the proof is (was?) wrong, it has real ideas of value in it.
It is not proved; he is not at the top of his field; this "paper" will be quickly forgotten among professional mathematicians; and I doubt any professional mathematician is going over the proof with any sort of comb.
L. de Branges first achieved fame for proving the Bieberbach conjecture. His proof went through strange and abstract methods. He went on the road to present his proof at various seminars in France, Russia, etc; IIRC a bunch of Russian students got very excited and basically rewrote his proof. Their new proof was much shorter and avoided the use of strange methods. Nowadays, their proof is remembered and his is not, but the proof still bears his name, since after all he was the first to come up with *some* kind of proof, and their proof did more or less come out of his.
So he deserves credit for that, and it was quite an achievement to prove the Bieberbach conjecture. But even then he was using unwieldy proofs with unnecessarily abstract methods.
For many years he has been claiming to have a proof of the Riemann Hypothesis. Professional mathematicians stopped listening a long time ago.
This guy is washed-up.
I whole-heartedly agree that this short article is hilarious, but I would like to add the adjective condescending. What kind of asshole apologizes for solving a problem? Does he think he lives on some higher plane, and therefore must take direct, personal responsibility for every aspect of our lives?
Look at how G. Perelman submitted his ideas on proving the Poincare conjecture just a little while ago. He didn't waste anyone's time by rehashing the already-available history of the problem or its wider context in mathematics. Nor did he apologize for having an idea. Rather, he submitted his ideas for consideration, with the full awareness that there may have been a mistake.
de Branges is so full of crap, it makes me sick.
zach
Not-for-profit, eh? Underpants throughout the land breath a sigh of relief!
zach
main() { ;
;
;
int last_digit
if( is_even(last_digit) ) {
poster_is_wrong()
}
return 0
}
/* please don't mock my style */
chgros's reply is right---you should really look at a book on abstract algebra, such as the books of Fraleigh, Gallian, or Dummitt & Foote. But for some reason I feel like chipping in (to hear my own voice, most likely), so here goes.
:-) )
4 = 1 (mod 3)
so
4*4 = 1*1 (mod 3)
which is to say that 4^2 = 1^2 (mod 3)
Similarly, 4^3 = 1^3 (mod 3), and 4^4 = 1^4 (mod 3), and so on. At this point you could write down an induction if you want (given 4^p = 1^p (mod 3), multiply the left hand side by 4 and the right hand side by 1; these are equal). Really it should just be direct.
The idea is that, for cripe's sake, 4 = 1. So 4+73 = 1+73, and whatever other operations you want to do. For example, 4^p = 1^p. Mod 3.
HTH
zach
(ps. Too bad there's no TeX posting option
Well, $a,b,c,\dots$ have to be specified before $p$ or $q$ or whatever. So there can't be any requirement that $a,b,c,\dots < p$, and if setting $q = a/2 = b/4 = \dots$ doesn't work then you'll just have to try some other value of $q$.
f ile=ktuple.html
As has been pointed out in another post, some tuples such as $(a,b)=(2,4)$ have finitely many solutions (for that example, one solution, given by $p=3$). This is because $(0,2,4)$ is a complete set of residues mod 3. More information about this can be found at
http://primes.utm.edu/glossary/includes/file.php?
(Thanks to another poster for posting a pointer to primepages.org.)
The $k$-tuple article may not be crystal clear in every way, but it makes it pretty clear that this problem of tuples has been studied, and there is a fairly simple criterion which is believed to ensure that a given pattern $(a,b,c,\dots)$ will have infinitely many "solutions". Do the ones that don't meet the criterion still have at least one solution? Hmm, not necessarily. For a silly example, $(2,4,6)$ doesn't have any solutions.
zach
Addresses an issue in which scheduled items, such as automated backups or Software Update checks, may not work if the computer is asleep at the scheduled time. With this update, the schedule will run once the computer wakes from sleep.
What about the periodic scripts (daily, weekly, monthly)? Is anacron now unnecessary?
zach
Welllll.... They are not trying to do a substitution cypher or anything. The idea is that the letters are a sequence of initials for words in some quotation or something.
There can't be all that many quotations, or even meaningful phrases, with two consecutive words that start with V (and three out of four contiguous words), can there? Witness the incredibly awkward attempts to come up with "joke" answers in other posts on this page. And the line of poetry is pretty awkward, too. So those V's would seem to impose some pretty strong conditions after all---giving hope that there might be a unique meaningful answer. Not much hope, though. (Still, as mentioned elsewhere, there's a lot of "side" info: the painting, etc.) We'll see.
zach
The page no longer says "proton" anywhere on it: it's all been changed to photons!
Obviously this is pretty low-quality writing, and the fact that changes were made without any kind of little note or anything just adds to that.
zach
Does that mean step **four** is profit?
Audio report on this story (produced for Michigan Radio's Stateside program):
http://www.michiganradio.org/stateside.asp
Scroll down to April 9th and listen in Real Player (sorry). The relevant bit starts at the 32:00 mark. (Yeah, the whole thing is an hour long... sorry.)
Anyway, this report was produced locally here in Ann Arbor, by a friend of mine who interviewed Dr. Miller in person. The whole point is that the dwarf/long-lived mutation is in fact naturally occuring, **not** the result of genetic engineering.
(Also, the audio report suggests that the colony is much larger, but perhaps the older mice are sequestered from the rest of the colony, so the AP report might have that right; hard to say.)
zach
Were you deliberately misunderstanding what I said? I have nothing against his claim that 500 watts is a lot. In fact, it seems rather a lot to me, too. But why can't he just say watts? Why say "kilowatt-hours per hour"? That's just silly.
"12 kWh/day". Whatever.
A refrigerator is usually around 1000. That's a little less than 3 kWh a day, or 0.125 kWh (period... in an hour).
0.125 kWh per hour is equal to 0.125 kilowatts, or 12.5 Watts.
Over what period of time?
Oh my. "Watts" don't go over a period of time; the OP was perfectly fine.
zach
There are efforts underway to collect and streamline the (alleged?) proof of the classification of finite simple groups. See, for example, http://www.ams.org/online_bks/surv40-1/. I am not a group theorist (IANAGT :-) ), only a mere algebraic geometer, so I'm definitely not current on this issue, but I think everyone, and especially group theorists, are painfully aware of this huge steaming mess of a proof. They are working to bring it into a better shape.
There won't be any announcement; there'll just be books like the above-linked one that quietly turn up in mathematical catalogs.
It's not clear that any similar effort could even possibly be undertaken with a computer proof. You type in "RUN" and it spits out a long-ass proof. What are you supposed to do with that? Write a "elegant( )" function that makes proofs elegant?
This does not mean that computer proofs are bad. I guess my point is that a good, human proof brings greater understanding, which can lead to improved proofs, or better results, etc. Computer proofs seem to lack this feature of greater understanding. You get a result, and that's about it.
At least, that's the impression I've received over the years...
zach
As a calculus and pre-calculus teacher, I have found that students will call *any* concave-up graph a parabola. x^4, definitely a parabola, if you're a pre-calc student. I could draw a graph of e^x for x > 0 and some of them would still say it was a parabola.
zach
I would think by then it would get bumped to XI.
There's been a lot of talk to the effect that Apple is not likely to abandon the catchy-sounding "OS X" name. ("O S X I" doesn't sound as cool as "O S X"....) So will they call it "OS X Eleven" or "OS X Two point Oh" or what? Who knows?! As much as the OS might deserve a full new version number, the marketing aspect of it definitely pulls in the direction of keeping "OS X" as long as possible.
zach
It's Long John Silver!
Nothing wrong with TeX as a word processor replacement. Or, not much, anyway. As a math grad student, I use TeX a fair amount, and word processors next to never.
As a spreadsheet, though, TeX is a little awkward...
zach
Perhaps they are hoping to get a variety of examples so newbies can see more than one implementation? Also, perhaps they want to give their readers something "fun" to do... I can see how some people would enjoy having a little mini-challenge every now and then, and they will enter the contest; and other people are too busy or would rather spend their free time in other ways, and so they won't enter the contest... And that's fine.
zach