You might counter that if both balls of mud have the same mass (i.e. 1 kg), then the total will have 2 kg of weight. Fine. Then I can point you to the Banach Tarski paradox ( http://en.wikipedia.org/wiki/Banach_Tarski_paradox ) which shows that it should be possible to cut a two kilogram ball into finite number of non-overlapping pieces and put together to give two two kilogram balls, so 2=2+2.
You might counter that you can't divide a real world solid the way you can divide a mathematical solid. But in that case, you've shown that the real world is not 100% mathematical in every sense, so all the free variable are interchangeable without consequence.
That's not what you've shown at all. If physics is to be believed then the balls can't be divided past the level of elementary particles, so the "measure" (i.e. the mass) of any real-world object such as these balls is always a well-defined, existing quantity. We've assigned this measure to the real world, and real objects in it such as these balls are always measurable because they are finite unions of elementary particles.
The Banach-Tarski paradox, on the other hand, uses the fact that there exist non-measurable subsets of R^n with the Lebesgue measure. It's a completely different measure than the one we're using in this real world analogy, so it doesn't make the real world any less mathematical because it's not supposed to describe the real world. The real world is still 100% mathematically consistent when you apply the right laws to it -- if I developed a mathematical theory around the law F=ma^2 and then noticed it wasn't like that in the real world, would it make the real world inconsistent or would it mean I'm using the wrong mathematical framework?
No, that AC is right. You can order a finite field (say Z/pZ) in some trivial way. But if c is the minimal element in this ordering, then any time you have an inequality a<b it won't be true that a+(c-b) < b+(c-b), so it's not an ordered field (which is an actual meaningful term). You clearly have no clue what you're talking about.
Reading some articles on Wikipedia doesn't make you an expert.
1. The "prime ideals in that field" refers to the prime ideals in the *ring of integers* in a number field, but people who actually know what they're talking about (not you) don't waste each other's time with those extra few words.
2. The line Re(s)=1/2 is a line in the complex plane, which is where the Riemann zeta function (you know, the zeta function for the field of rational numbers) is defined. The fact that it relates to the rationals and encodes some information about them doesn't change the fact that it's a function from the complex numbers to itself.
No, you're wrong because you have no idea what you're talking about. Every number field has its own zeta function which roughly describes the distribution of prime ideals in that field, and the Riemann zeta function is the one corresponding to the rational field. The Riemann hypothesis states that the Riemann zeta function (that is, the one for the field of rational numbers) has no zeros whatsover, rational or otherwise, on the critical strip 0 < Re(s) < 1 except along the line Re(s) = 1/2, and this is exactly the statement he's claiming to have proved.
You don't know nearly as many of the answers as you think.
The Secret Service isn't just a security force -- it used to be part of the Treasury Department before getting moved to Homeland Security, and one of its responsibilities is investigating fraud. You, as a US taxpayer, are paying to have them assist in a fraud investigation (and one that happens to be dangerous as well) to protect US taxpayers such as yourself.
Re:Math is "Free", MY LILY-WHITE ASS.
on
Open Source Math
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· Score: 4, Informative
There's a growing trend in math (and maybe other disciplines, for all I know) away from non-free publishing.
Prominent mathematicians have been complainingforyears (more links here) about overpriced journals, and entire editorial boards of some journals have resigned in protest (see a list of mass resignations and similar changes here). There are now plenty of entirely free journals in combinatorics, topology, and other fields, and pretty much everything that gets published these days is either available on the author's website or on the arXiv.
So modern research tends to be free, but what about all the books you need to read before you understand this research? Sure, a copy of Rudin may be expensive and there's not much we can do about that, but maybe you can learn from the free analysis course notes at MIT's OCW site. You complain that EGA is out of print, but basically everything Grothendieck wrote is available for free, and you can even get them along with tons of other old French publications through NUMDAM. (There's even a project to transcribe SGA into LaTeX.) Lots of other books are free to download legally (and this is by no means a complete list), even though many are commercially published as well.
Finally, you can complain all you want about university tuition, but I really doubt that free tuition is going to open up mathematics to the masses. Ultimately the very top students who can't afford it are getting scholarships and grants to cover their education (and I do know some people who got free rides at Princeton because they couldn't afford it -- that school is definitely more generous than most), and since most other people couldn't get into Princeton anyway the tuition is never even an issue for them. The best way to make mathematics more accessible is to give everyone access to free textbooks and current research, and the "marxist university professors" you deride have been gradually moving in that direction for years now.
By the way, what do you think has been done to damage the Princeton math department's reputation? Whatever you think Shapiro and Tilghman have done to the university, nobody in their right mind would deny that it's one of the top few in the world and I doubt most people would openly proclaim any one department to be the best anyway.
Re:Majored in math, away from it for a year
on
Prime Obsession
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· Score: 1
Actually, I've read this book. I've also taken a graduate class in analytic number theory at MIT. Sure, a bunch of the math was stuff I already knew, but there's a lot of really well-written history in there that makes the book worthwhile on its own, and it can only be better if you haven't taken all of the prerequisites.
That may be, but I believe the system currently in use was first used at the IOI in 2001 after a year or two of development and testing in the US online competitions.
I'm pretty sure adding a timer was and is still standard practice (or at least I did it) for contestants who didn't expect their solution to be fast enough, though...
It's not at all true. (I should know, since I was a competitor at IOI 2001, when the automated grading system was first introduced.) The only measure of "elegance" that can be used is runtime, since submitted programs generally get no more than a second to produce output, and chances are that if you don't design an efficient enough algorithm to solve a task you'll almost certainly time out on a whole bunch of data sets.
"Nova" does not mean "new" -- the word you're looking for is "nueva", which no Spanish speaker would confuse with "no va." Snopes agrees that this is an urban legend, but the name isn't positive or negative in Spanish and it certainly wouldn't translate as "new."
Tech Talk, the original source of the article, is the MIT newspaper aimed at an administrative audience (as opposed to the student-run Tech). "Famous professors" sounds really good to admins.
Of course, what it doesn't mention is that the professors selected to teach introductory courses like 6.002 are chosen because they're really good at teaching...
I just took 6.002 (the standard version) at MIT this spring; it's a required class for all EECS students, even if they're just studying CS (like me). I had lots of electronics experience from high school, so I didn't mind it, but a lot of CS students (that's "Course 6-3" in MIT parlance) truly hate this class because they don't understand it very well and they know the only EE class they'll ever take again is a required signal processing class which is more math than EE.
I don't know if this is what the administration intended when they approved 6.002x, but I think the course could be a great thing for some of the more hardcore CS types who hate the more standard 6.002. If people complain about there being too much theory that, in the end, just reduces to solving one second-order differential equation after another, maybe they would benefit from learning how some of it works in practice. And maybe these CS people will still never take another EE class, but at least they'll know something practical instead of feeling that they've wasted a semester on this, and they'll still have covered the same curriculum as the normal 6.002 students.
If you want a real teaching controversy at MIT, though, go search the Tech's archives (the MIT student newspaper - http://www-tech.mit.edu/) for the words 8.02 TEAL. They've totally replaced the standard (and required for all students who can't handle the significantly harder, much more mathematically-oriented alternative) electricity and magnetism class with a much more participation-intensive format which has the student body largely up in arms; I won't get into it here, but it's a lot more controversial than teaching a self-chosen group of MIT students electronics with real-world examples.
All the SATs test is your ability to do well on the SATs.
Actually, college admissions types say that they correspond very well to your performance as a college freshman. Beyond that first year, though, everything's up in the air...
Aside from the content of the Boucher-Doolittle bill, this C|NET article mentioned something else important about it: Rep. Boucher had it introduced not in the House Judiciary Committee, where Intellectual Property subcommittee chairman Howard Coble would be a fierce opponent to it, but in the friendlier world of the Commerce Committee. Whether or not you like what the bill actually says - and that doesn't even matter, since it won't happen this year - Boucher's strategical move is an extremely useful tactic in getting such legislation passed (or, for that matter, even acknowledged) in the future.
One thing to remeber is that ashcroft is an appointed law enforcement official. What this basically means is that it is his job to enforce the law, even when he dislikes it.
So when Ashcroft ignores California's legalization of medicinal marijuana or Oregon's legalization of euthanasia by sending in federal agents to stop it, is he doing his job? I realize these may be contradicted by existing federal laws, but you can't ignore his comments when the Supreme Court overturned the ban on virtual child pornography - he basically said he was going to ignore the decision, constitutionality be damned. If Ashcroft really dislikes a law (or lack thereof), he will ignore it because nobody with enough power is telling him to do otherwise.
Let me point out that this guy traded warez on DRM-free machines. He has not seen Intel's forthcoming Palladium implementation, any plans for Microsoft's DRM operating system beyond maybe the patent for it, or anything else related, and since he does not work for Intel, Athlon, or MS he probably doesn't know anything about it beyond the pure (often baseless) speculation people have thrown around since it was first announced. Given that this is the case, any answer he'd provide should be just as baseless. (For those of you familiar with the legend where all the inhabitants of a kingdom were asked for the length of the emperor's nose and the averaged answer was meaningless, compare this question to a survey of all the rhinologists in the land who still have never seen the emperor or anyone related to him.)
Here's a slightly more appropriate question: If you were still free when the first DRM systems were released, knowing that you would now have to evade hardware protection, to what lengths would you be willing to go to continue pirating new software? Given that we on Slashdot don't yet know your motivations for your piracy (or else there wouldn't be so many questions about it), how much would you work on cracking the latest release of, say, Photoshop, before it's no longer worth the effort?
Okay, so downloading music from your preferred P2P service isn't theft. But unless you've purchased the same songs you're downloading, it's copyright infringement, and if you've actually read the text of the NET Act (same link as posted in the article), it deals with infringement rather than theft. The congresscritters behind the law just called it that because it's a much better name than the "NECI Act" would be...
To mikeee, re: "hiaku"
on
Haiku vs Spam
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· Score: 1
You spelling nazis
Should hit the "Preview" button
Lest you seem foolish.
Read the announcement again... they said that people who connect and then attempt to illegally access the network will be banned. They won't blacklist you unless you try to DoS or crack them afterward, since that's what will distinguish the RIAA and its minions from normal users.
I'll freely admit that I dislike Palladium as much as the next Linux user, but here's something to consider:
Microsoft has said that there will be multiple authorities with the ability to sign programs. Imagine that somehow, through a very sudden change of heart, Bill Gates decides to give a company (or a whole bunch of people) such as Red Hat the ability to sign all ELF binaries regardless of content. This won't hurt the Windows users, since they can't handle ELF, so at least their virus protection isn't compromised.
Would you be more willing to trust Palladium if Red Hat or someone like that could sign anything you wanted to compile? Or would you still expect Microsoft to eventually withdraw their support, make the cost of it prohibitive, or pull a Hotmail on the Linux community?
Slashdot Mirror
You might counter that if both balls of mud have the same mass (i.e. 1 kg), then the total will have 2 kg of weight. Fine. Then I can point you to the Banach Tarski paradox ( http://en.wikipedia.org/wiki/Banach_Tarski_paradox ) which shows that it should be possible to cut a two kilogram ball into finite number of non-overlapping pieces and put together to give two two kilogram balls, so 2=2+2.
You might counter that you can't divide a real world solid the way you can divide a mathematical solid. But in that case, you've shown that the real world is not 100% mathematical in every sense, so all the free variable are interchangeable without consequence.
That's not what you've shown at all. If physics is to be believed then the balls can't be divided past the level of elementary particles, so the "measure" (i.e. the mass) of any real-world object such as these balls is always a well-defined, existing quantity. We've assigned this measure to the real world, and real objects in it such as these balls are always measurable because they are finite unions of elementary particles.
The Banach-Tarski paradox, on the other hand, uses the fact that there exist non-measurable subsets of R^n with the Lebesgue measure. It's a completely different measure than the one we're using in this real world analogy, so it doesn't make the real world any less mathematical because it's not supposed to describe the real world. The real world is still 100% mathematically consistent when you apply the right laws to it -- if I developed a mathematical theory around the law F=ma^2 and then noticed it wasn't like that in the real world, would it make the real world inconsistent or would it mean I'm using the wrong mathematical framework?
No, that AC is right. You can order a finite field (say Z/pZ) in some trivial way. But if c is the minimal element in this ordering, then any time you have an inequality a<b it won't be true that a+(c-b) < b+(c-b), so it's not an ordered field (which is an actual meaningful term). You clearly have no clue what you're talking about.
Reading some articles on Wikipedia doesn't make you an expert.
1. The "prime ideals in that field" refers to the prime ideals in the *ring of integers* in a number field, but people who actually know what they're talking about (not you) don't waste each other's time with those extra few words.
2. The line Re(s)=1/2 is a line in the complex plane, which is where the Riemann zeta function (you know, the zeta function for the field of rational numbers) is defined. The fact that it relates to the rationals and encodes some information about them doesn't change the fact that it's a function from the complex numbers to itself.
No, you're wrong because you have no idea what you're talking about. Every number field has its own zeta function which roughly describes the distribution of prime ideals in that field, and the Riemann zeta function is the one corresponding to the rational field. The Riemann hypothesis states that the Riemann zeta function (that is, the one for the field of rational numbers) has no zeros whatsover, rational or otherwise, on the critical strip 0 < Re(s) < 1 except along the line Re(s) = 1/2, and this is exactly the statement he's claiming to have proved.
You don't know nearly as many of the answers as you think. The Secret Service isn't just a security force -- it used to be part of the Treasury Department before getting moved to Homeland Security, and one of its responsibilities is investigating fraud. You, as a US taxpayer, are paying to have them assist in a fraud investigation (and one that happens to be dangerous as well) to protect US taxpayers such as yourself.
There's a growing trend in math (and maybe other disciplines, for all I know) away from non-free publishing.
Prominent mathematicians have been complaining for years (more links here) about overpriced journals, and entire editorial boards of some journals have resigned in protest (see a list of mass resignations and similar changes here). There are now plenty of entirely free journals in combinatorics, topology, and other fields, and pretty much everything that gets published these days is either available on the author's website or on the arXiv.
So modern research tends to be free, but what about all the books you need to read before you understand this research? Sure, a copy of Rudin may be expensive and there's not much we can do about that, but maybe you can learn from the free analysis course notes at MIT's OCW site. You complain that EGA is out of print, but basically everything Grothendieck wrote is available for free, and you can even get them along with tons of other old French publications through NUMDAM. (There's even a project to transcribe SGA into LaTeX.) Lots of other books are free to download legally (and this is by no means a complete list), even though many are commercially published as well.
Finally, you can complain all you want about university tuition, but I really doubt that free tuition is going to open up mathematics to the masses. Ultimately the very top students who can't afford it are getting scholarships and grants to cover their education (and I do know some people who got free rides at Princeton because they couldn't afford it -- that school is definitely more generous than most), and since most other people couldn't get into Princeton anyway the tuition is never even an issue for them. The best way to make mathematics more accessible is to give everyone access to free textbooks and current research, and the "marxist university professors" you deride have been gradually moving in that direction for years now.
By the way, what do you think has been done to damage the Princeton math department's reputation? Whatever you think Shapiro and Tilghman have done to the university, nobody in their right mind would deny that it's one of the top few in the world and I doubt most people would openly proclaim any one department to be the best anyway.
Actually, I've read this book. I've also taken a graduate class in analytic number theory at MIT. Sure, a bunch of the math was stuff I already knew, but there's a lot of really well-written history in there that makes the book worthwhile on its own, and it can only be better if you haven't taken all of the prerequisites.
That may be, but I believe the system currently in use was first used at the IOI in 2001 after a year or two of development and testing in the US online competitions.
I'm pretty sure adding a timer was and is still standard practice (or at least I did it) for contestants who didn't expect their solution to be fast enough, though...
It's not at all true. (I should know, since I was a competitor at IOI 2001, when the automated grading system was first introduced.) The only measure of "elegance" that can be used is runtime, since submitted programs generally get no more than a second to produce output, and chances are that if you don't design an efficient enough algorithm to solve a task you'll almost certainly time out on a whole bunch of data sets.
"Nova" does not mean "new" -- the word you're looking for is "nueva", which no Spanish speaker would confuse with "no va." Snopes agrees that this is an urban legend, but the name isn't positive or negative in Spanish and it certainly wouldn't translate as "new."
Try ^W ^T in pico. It looks like a perfectly good "Goto Line" to me...
From that page:
You know, some of us just don't need to be "audio engineers" or to stare at his "waveforms" and "clipping" to understand that phenomenon...
IIRC, the open source community doesn't need to hire Linus an instructor - his wife was the Finnish national women's karate champion several times.
So what qualifications does Mrs. Darl McBride (if there is one) have, anyway?
How about a daily "SCOreboard" to keep us informed?
I don't know about you, but I like lOX best on bAGELS...
Tech Talk, the original source of the article, is the MIT newspaper aimed at an administrative audience (as opposed to the student-run Tech). "Famous professors" sounds really good to admins.
Of course, what it doesn't mention is that the professors selected to teach introductory courses like 6.002 are chosen because they're really good at teaching...
I just took 6.002 (the standard version) at MIT this spring; it's a required class for all EECS students, even if they're just studying CS (like me). I had lots of electronics experience from high school, so I didn't mind it, but a lot of CS students (that's "Course 6-3" in MIT parlance) truly hate this class because they don't understand it very well and they know the only EE class they'll ever take again is a required signal processing class which is more math than EE.
I don't know if this is what the administration intended when they approved 6.002x, but I think the course could be a great thing for some of the more hardcore CS types who hate the more standard 6.002. If people complain about there being too much theory that, in the end, just reduces to solving one second-order differential equation after another, maybe they would benefit from learning how some of it works in practice. And maybe these CS people will still never take another EE class, but at least they'll know something practical instead of feeling that they've wasted a semester on this, and they'll still have covered the same curriculum as the normal 6.002 students.
If you want a real teaching controversy at MIT, though, go search the Tech's archives (the MIT student newspaper - http://www-tech.mit.edu/) for the words 8.02 TEAL. They've totally replaced the standard (and required for all students who can't handle the significantly harder, much more mathematically-oriented alternative) electricity and magnetism class with a much more participation-intensive format which has the student body largely up in arms; I won't get into it here, but it's a lot more controversial than teaching a self-chosen group of MIT students electronics with real-world examples.
Aside from the content of the Boucher-Doolittle bill, this C|NET article mentioned something else important about it: Rep. Boucher had it introduced not in the House Judiciary Committee, where Intellectual Property subcommittee chairman Howard Coble would be a fierce opponent to it, but in the friendlier world of the Commerce Committee. Whether or not you like what the bill actually says - and that doesn't even matter, since it won't happen this year - Boucher's strategical move is an extremely useful tactic in getting such legislation passed (or, for that matter, even acknowledged) in the future.
Let me point out that this guy traded warez on DRM-free machines. He has not seen Intel's forthcoming Palladium implementation, any plans for Microsoft's DRM operating system beyond maybe the patent for it, or anything else related, and since he does not work for Intel, Athlon, or MS he probably doesn't know anything about it beyond the pure (often baseless) speculation people have thrown around since it was first announced. Given that this is the case, any answer he'd provide should be just as baseless. (For those of you familiar with the legend where all the inhabitants of a kingdom were asked for the length of the emperor's nose and the averaged answer was meaningless, compare this question to a survey of all the rhinologists in the land who still have never seen the emperor or anyone related to him.)
Here's a slightly more appropriate question: If you were still free when the first DRM systems were released, knowing that you would now have to evade hardware protection, to what lengths would you be willing to go to continue pirating new software? Given that we on Slashdot don't yet know your motivations for your piracy (or else there wouldn't be so many questions about it), how much would you work on cracking the latest release of, say, Photoshop, before it's no longer worth the effort?
Okay, so downloading music from your preferred P2P service isn't theft. But unless you've purchased the same songs you're downloading, it's copyright infringement, and if you've actually read the text of the NET Act (same link as posted in the article), it deals with infringement rather than theft. The congresscritters behind the law just called it that because it's a much better name than the "NECI Act" would be...
You spelling nazis
Should hit the "Preview" button
Lest you seem foolish.
Read the announcement again... they said that people who connect and then attempt to illegally access the network will be banned. They won't blacklist you unless you try to DoS or crack them afterward, since that's what will distinguish the RIAA and its minions from normal users.
I'll freely admit that I dislike Palladium as much as the next Linux user, but here's something to consider:
Microsoft has said that there will be multiple authorities with the ability to sign programs. Imagine that somehow, through a very sudden change of heart, Bill Gates decides to give a company (or a whole bunch of people) such as Red Hat the ability to sign all ELF binaries regardless of content. This won't hurt the Windows users, since they can't handle ELF, so at least their virus protection isn't compromised.
Would you be more willing to trust Palladium if Red Hat or someone like that could sign anything you wanted to compile? Or would you still expect Microsoft to eventually withdraw their support, make the cost of it prohibitive, or pull a Hotmail on the Linux community?