It doesn't look like it--they would have to occur in vast quantities within galaxies and they just don't seem to.
If they did, it would be great, because it would mean that would be lots of planets between here and nearby stars. That would make interstellar travel considerably easier because humanity could move outwards very gradually.
Sorry, but that's just wrong. Correct mathematical proofs aren't something informal or vague, they are a well-defined reduction of theorems to axioms.
Mathematical proofs as written up in the literature are usually merely an informal notation, but this informality is only permitted because there is an implicit assumption that a competent reader can fill in all the missing steps. If a published mathematical proof is of the form where competent readers can't fill in the missing steps, then the author hasn't published a proof at all.
So, either you need to publish a complete, formally verifiable proof, or you publish a proof where other competent mathematicians can fill in the missing pieces themselves. If you do neither, you haven't proven anything.
No, the problem is simply that you have a simplistic model of how budget deficits come about. In the end, it's immaterial who "controls the purse strings"; when expenditures are necessary, Congress needs to approve them, no matter how much they may detest it.
The most important factors affecting deficits are economic performance, foreign trade, monetary policy, and military expenditures. Those factors are largely determined by the administration; Congress has just been reacting to them, at least over the last several decades.
There was a budget surplus during the Clinton years because Clinton got those things right, and there have been budget deficits during the Bush years because Bush got those things completely wrong.
If the thing is properly constructed, the effect of a micrometeorite is no worse than with other constructions. Basically, don't think of an elastic skin that snaps, but something more akin to airtight canvas. If you punch a hole in that, you just get a small hole, nothing more. If anything, inflatable space stations are easier to repair than other constructions.
No. The one who proves get credit for the proof. Nobody else.
Geez, talk about circular definitions.
His proof was basically non-readable and some Russians showed that his proof was indeed correct.
By that reasoning, Poincare proved the Poincare conjecture, because he provided a single-step proof (the statement of the conjecture itself), and any subsequent work only filled in a bunch of missing steps.
In real life, there is some threshold above which a sequence of statements constitutes a proof and below which it doesn't. There is no a priori reason to draw it such that Perelman's sequence of statements constitutes a "proof".
Ultimately, mathematics and science is not about people figuring things out for themselves, it's about communicating results. If you don't communicate, you shouldn't get credit.
Claiming the proof in such a case is just academic theft.
Claiming credit for a result without delivering a clear, readable, and understandable explanation of your results is academic theft as well.
According to Congressional Budget Office (reported by Reuters in 2004, you can probably find the graph if you search for it), the only president that has had any significant budget surplus since 1963 was Bill Clinton. And if you want to argue that Clinton's budget surplus wasn't real, then the figures for the Republican presidents are even more disastrous than they were reported to be.
The Republican pattern of fiscal irresponsibility and anti-growth policies is also illustrated at the state level: there is a huge net flow of funds from Democratic states to Republican states.
Republicans like to talk a lot about growth and fiscal responsibility, but in reality, what Republicans primarily deliver is handouts to the rich, bloated government, and restrictions on personal freedoms.
It would be nice to have true conservative government: government that is frugal, government that respects traditional liberties, and government that limits its own size and scope; unfortunately, Republicans are the antithesis of that. The problem with Republican rhetoric isn't even that their criticism of Democrats is wrong, it's that they themselves are even worse.
It's a good thing that the Democrats are "loyal to the dollar" because they have delivered economic growth and budget surplusses over the last 100 years, while Republicans pretty consistently delivered huge budget deficits and economic decline.
For the people doing it, it's fun. It's no different from playing games, playing the piano, or posting on/.
For humanity, understanding low-dimensional spaces better is important: we apparently live in a 3+1D world, and there may well be fundamental mathematical reasons for that.
I can't see why Perelman would share the credit. If his results are right, he proved it first.
You haven't "proved" something until you have written it down in a form in which it convinces at least other specialists in your field. The fact that nobody knows for certain "if his results are right" is tantamount to the statement that he hasn't proven it yet.
So, I suggest a simple rule: whichever of the two proof attempts will be verified first by at least a dozen other mathematicians or by a mechanical device, its author(s) should get recognized as the people to prove the conjecture.
The purpose of a proof is to communicate a sequence of statements such that each and every individual step is easily derivable from axioms or well-known theorems. Let me emphasize this again: a proof is about communication, not merely about making true statements.
Perelman apparently failed to do this: he may have produced a sequence of true statements that could somehow form a subsequence of a complete proof, but he has apparently not supplied enough detail to demonstrate his point to even specialists in his area. The fact that he may have done "the heavy lifting" or that he may have provided the key ideas doesn't change that.
I think it is valid to give all three mathematicians equal credit. And, strictly speaking, the people who actually have done the proof are the ones who "dotted the i's" because that's what ultimately constitutes a proof.
Serious errors in mathematical papers are so common that I wouldn't put any trust in this until the proof has been around for a decade or two; even if Cao and Zhu did everything correctly, there's a good chance that something they relied on turns out not to be true after all.
In the long run, mathematics really needs considerably more formality than it is using now, as well as mechanical support for the bookkeeping necessary for long and involved proofs. Actually, the tools already exist, it's just that working mathematicians usually don't use them.
When I saw all this waste, I was gonna say "Think of the starving children in Africa", but then I remembered that it was Diet Coke and Mentos, two substances that may have the appearance of food but are pretty close to having to carry warning labels about their health risks.
This video content doesn't really fall under "science" (white labcoats don't mean it's "science").
It really is more an example of the kind of new business models for video: low cost productions, free distribution, and web supported advertising. And the content is of a form where nobody really would want to bother redistributing it without advertising.
It's actually not all that different from the original business model of network television, although it is arguably a more "creative" and "innovative" than a lot of what we get on television today.
I find it a little disturbing that this mess of Javascript and HTML is referred to as "innovation". Web 2.0 really is little more than what RPC, DisplayPostscript, NeWS, X11, or Java promised to deliver in the past. There are some good things about it: Web 2.0 is text-based protocols (UNIX influence), it's more open, and it's easier to throw together something in it than in previous standards. On the other hand, Web 2.0 is also a big mess: HTML, DOM, and JavaScript have bloated out of any proportion to the very limited funcitonality they actually provide.
Re:Mac OS X is *much* more common than Linux
on
Lenovo To Shun Linux
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· Score: 1
All those statistics likely tell you is that OS X has a larger share of the home market, which I think few people would dispute. But the home market isn't the same as the desktop market: corporate desktops, retail, data entry, research, engineering, and computer labs just don't generate a lot of hits, but they are clearly desktop usage.
What about printers? Do the cheap color printers you can buy at any electronics store for windows machines work with Linux yet? How about scanners?
Yes, many printers and scanners work with Linux, including cheap ones.
I'm not saying it's the distros fault, but it is their problem.
It's not a problem; there is more than enough supported hardware available for Linux.
What the distros need to provide is compatibility lists; and, guess what, they do.
Re:more proof the RIAA/MPAA are insane
on
Death By DMCA
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· Score: 3, Insightful
If the networks can no longer count on people watching at least some ads, how are they to pay for content?
They aren't; they should go out of business if they can't figure out a new business model under changing market conditions. In fact, advertising supported network television is obsolete.
but you need to put down emotion and maybe start coming up with reasonable alternative business models
Why do I have to figure out a new business model for them? Or why should Congress artificially limit technology just so that outdated business models continue to work?
Do you want Congress to pass laws against combustion engines so that the business model of hay producers and blacksmiths continues to work?
Which part of I think the Bible cannot be banned, and most criminals would be criminal with or without it. did you fail to understand?
No, the way to deal with the harm the Bible and Christianity have been causing to humanity over the past two millennia is to expose the Bible and Christian history for all to see and to make sure the wars, the torture, the genocides, the murders, and the corruption that Christianity has been responsible for are never forgotten. People need to realize that Christianity, far from offering salvation and hope, is about controlling people through shame, ignorance, and fear.
Themeing can be useful (low vision users, low performance machines, etc.). And some of the eye candy (animation, color, transparency, etc.) does actually improve task performance.
The nice thing is that X11, Xgl, and Gnome/KDE support these capabilities architecturally so well that developers and users can explore the utility of these features and users can pick and choose; Apple and Microsoft, in contrast, really are just treating them as marketing and sales tools.
I'm not after "complexity" and neither are the Linux GUI developers; historically, UNIX and Linux GUIs have been clean and minimalistic.
Linux GUIs are getting complex because that's what users coming from Windows and Macintosh expect. If you want Linux GUIs to get better, get Apple and Microsoft to clean up their shitty user interfaces so that Linux doesn't have to keep supporting that kind of mess.
The "practical" truth is, however, when I wanted to buy a printer or a camera, I couldn't just go to Staples or Best Buy and pick the best deal, I had to do some research.
Actually, for both printers and cameras, the protocols and formats are so well standardized now that if Linux doesn't support it, you probably don't want to be using it even on Windows. In different words, if something is really cheap at Staples, the reason is likely that it sucks on all platforms and you don't want it.
Incidentally, for printers, Macintosh is now using the same software and many of the same drivers that Linux has been using for years, and for cameras, both platforms rely on the USB mass storage and PTP standards. So, when it comes to printers and cameras, Linux is actually no worse than Macintosh (and actually a little better, since it has some extra drivers that Macs don't get).
I think the claim that Linux has more presence on the desktop that MacOS [X], requires some evidence.
Linux is enormously widely used at universities, in research labs, in retail desktop applications, and on corporate desktops (and that's not even counting all the embedded consumer applications). The presence of OS X in all those areas is at best modest.
Just about the only area where OS X may be ahead of Linux on the desktop is among home users, but frankly, even there, it's far from clear whether there are more geeky Linux users or more Apple fashion victims.
So, I think the assertion that OS X is more widely used on the desktop than Linux is implausible; if you want to make that claim, why don't you supply some evidence?
The experience was enough to keep me away from Linux as a desktop until the situation has *dramatically* improved.
The situation doesn't need to "improve" any further. If you buy your Linux hardware from a Linux vendor, you won't have any problems. I mean, in addition to many smaller vendors, even Sun and Dell ship preinstalled desktop Linux machines with all the necessary drivers--what more do you want?
Of course, if you buy hardware for Windows and then try to install Linux on it, it may be painful and some hardware may not work, but that's your own f*cking stupidity.
Maybe if your idea of a [Windows install being a] "major undertaking" is hitting [Enter] half a dozen times.
If you think that installing Windows on PC hardware is as simple as "hitting [Enter] half a dozen times", you haven't installed Windows much. Maybe you're thinking of a system restore from manufacturer's disks, but a real from-scratch Windows install on recent hardware requires that you track down drivers for many different pieces of hardware, followed by hours of re-installing applications to get back to a fairly complete, working system. And that's if you're lucky and if your machine doesn't get infected by a virus before you have managed to protect it.
My job is adminning unix machines (amongst others).
This is not a problem with X11 or Ubuntu. X11 has excellent multi-monitor support, and excellent support for changing resolutions on the fly. The reason why you can't do it with your hardware is because your vendor didn't supply a driver for Linux. There is nothing anybody other than the vendor can do about this.
Now, I'll give you this much: Gnome still lacks a good GUI for configuring multiple monitors. The reason it's not there yet is probably because there hasn't been a big need for it in the past: most vendors didn't make drivers available, and the few people for whom this mattered spent the 30 minutes to figure it out.
When you want to configure a GUI like X, you should be able to use the damn GUI to configure it. Apparently, those working on Linux distributions don't get this.
You're confused because you apparently have only seen Windows pre-installed. Installing it by hand is a major undertaking that involves significant text-mode interactions.
Conversely, if you install SuSE, or install Ubuntu from a Live CD, your entire installation process will take place in a graphical environment. Furthermore, almost all X11 server changes can be carried out on the fly these days.
Microsoft is entirely capable of producing a next-generation OS with lots of new, innovative technology. Vist isn't it.
Microsoft has some of the smartest CS researchers in the industry But that is neither necessary nor sufficient for producing a commercial next-generation OS. "Innovation" in a commercial OS doesn't mean inventing new stuff, it means being able to sell stuff that was invented 20 years ago but hasn't made it to market yet.
Slashdot Mirror
It doesn't look like it--they would have to occur in vast quantities within galaxies and they just don't seem to.
If they did, it would be great, because it would mean that would be lots of planets between here and nearby stars. That would make interstellar travel considerably easier because humanity could move outwards very gradually.
Sorry, but that's just wrong. Correct mathematical proofs aren't something informal or vague, they are a well-defined reduction of theorems to axioms.
Mathematical proofs as written up in the literature are usually merely an informal notation, but this informality is only permitted because there is an implicit assumption that a competent reader can fill in all the missing steps. If a published mathematical proof is of the form where competent readers can't fill in the missing steps, then the author hasn't published a proof at all.
So, either you need to publish a complete, formally verifiable proof, or you publish a proof where other competent mathematicians can fill in the missing pieces themselves. If you do neither, you haven't proven anything.
No, the problem is simply that you have a simplistic model of how budget deficits come about. In the end, it's immaterial who "controls the purse strings"; when expenditures are necessary, Congress needs to approve them, no matter how much they may detest it.
The most important factors affecting deficits are economic performance, foreign trade, monetary policy, and military expenditures. Those factors are largely determined by the administration; Congress has just been reacting to them, at least over the last several decades.
There was a budget surplus during the Clinton years because Clinton got those things right, and there have been budget deficits during the Bush years because Bush got those things completely wrong.
If the thing is properly constructed, the effect of a micrometeorite is no worse than with other constructions. Basically, don't think of an elastic skin that snaps, but something more akin to airtight canvas. If you punch a hole in that, you just get a small hole, nothing more. If anything, inflatable space stations are easier to repair than other constructions.
No. The one who proves get credit for the proof. Nobody else.
Geez, talk about circular definitions.
His proof was basically non-readable and some Russians showed that his proof was indeed correct.
By that reasoning, Poincare proved the Poincare conjecture, because he provided a single-step proof (the statement of the conjecture itself), and any subsequent work only filled in a bunch of missing steps.
In real life, there is some threshold above which a sequence of statements constitutes a proof and below which it doesn't. There is no a priori reason to draw it such that Perelman's sequence of statements constitutes a "proof".
Ultimately, mathematics and science is not about people figuring things out for themselves, it's about communicating results. If you don't communicate, you shouldn't get credit.
Claiming the proof in such a case is just academic theft.
Claiming credit for a result without delivering a clear, readable, and understandable explanation of your results is academic theft as well.
According to Congressional Budget Office (reported by Reuters in 2004, you can probably find the graph if you search for it), the only president that has had any significant budget surplus since 1963 was Bill Clinton. And if you want to argue that Clinton's budget surplus wasn't real, then the figures for the Republican presidents are even more disastrous than they were reported to be.
The Republican pattern of fiscal irresponsibility and anti-growth policies is also illustrated at the state level: there is a huge net flow of funds from Democratic states to Republican states.
Republicans like to talk a lot about growth and fiscal responsibility, but in reality, what Republicans primarily deliver is handouts to the rich, bloated government, and restrictions on personal freedoms.
It would be nice to have true conservative government: government that is frugal, government that respects traditional liberties, and government that limits its own size and scope; unfortunately, Republicans are the antithesis of that. The problem with Republican rhetoric isn't even that their criticism of Democrats is wrong, it's that they themselves are even worse.
It's a good thing that the Democrats are "loyal to the dollar" because they have delivered economic growth and budget surplusses over the last 100 years, while Republicans pretty consistently delivered huge budget deficits and economic decline.
For the people doing it, it's fun. It's no different from playing games, playing the piano, or posting on /.
For humanity, understanding low-dimensional spaces better is important: we apparently live in a 3+1D world, and there may well be fundamental mathematical reasons for that.
I can't see why Perelman would share the credit. If his results are right, he proved it first.
You haven't "proved" something until you have written it down in a form in which it convinces at least other specialists in your field. The fact that nobody knows for certain "if his results are right" is tantamount to the statement that he hasn't proven it yet.
So, I suggest a simple rule: whichever of the two proof attempts will be verified first by at least a dozen other mathematicians or by a mechanical device, its author(s) should get recognized as the people to prove the conjecture.
The purpose of a proof is to communicate a sequence of statements such that each and every individual step is easily derivable from axioms or well-known theorems. Let me emphasize this again: a proof is about communication, not merely about making true statements.
Perelman apparently failed to do this: he may have produced a sequence of true statements that could somehow form a subsequence of a complete proof, but he has apparently not supplied enough detail to demonstrate his point to even specialists in his area. The fact that he may have done "the heavy lifting" or that he may have provided the key ideas doesn't change that.
I think it is valid to give all three mathematicians equal credit. And, strictly speaking, the people who actually have done the proof are the ones who "dotted the i's" because that's what ultimately constitutes a proof.
Serious errors in mathematical papers are so common that I wouldn't put any trust in this until the proof has been around for a decade or two; even if Cao and Zhu did everything correctly, there's a good chance that something they relied on turns out not to be true after all.
In the long run, mathematics really needs considerably more formality than it is using now, as well as mechanical support for the bookkeeping necessary for long and involved proofs. Actually, the tools already exist, it's just that working mathematicians usually don't use them.
When I saw all this waste, I was gonna say "Think of the starving children in Africa", but then I remembered that it was Diet Coke and Mentos, two substances that may have the appearance of food but are pretty close to having to carry warning labels about their health risks.
This video content doesn't really fall under "science" (white labcoats don't mean it's "science").
It really is more an example of the kind of new business models for video: low cost productions, free distribution, and web supported advertising. And the content is of a form where nobody really would want to bother redistributing it without advertising.
It's actually not all that different from the original business model of network television, although it is arguably a more "creative" and "innovative" than a lot of what we get on television today.
I find it a little disturbing that this mess of Javascript and HTML is referred to as "innovation". Web 2.0 really is little more than what RPC, DisplayPostscript, NeWS, X11, or Java promised to deliver in the past. There are some good things about it: Web 2.0 is text-based protocols (UNIX influence), it's more open, and it's easier to throw together something in it than in previous standards. On the other hand, Web 2.0 is also a big mess: HTML, DOM, and JavaScript have bloated out of any proportion to the very limited funcitonality they actually provide.
All those statistics likely tell you is that OS X has a larger share of the home market, which I think few people would dispute. But the home market isn't the same as the desktop market: corporate desktops, retail, data entry, research, engineering, and computer labs just don't generate a lot of hits, but they are clearly desktop usage.
What about printers? Do the cheap color printers you can buy at any electronics store for windows machines work with Linux yet? How about scanners?
Yes, many printers and scanners work with Linux, including cheap ones.
I'm not saying it's the distros fault, but it is their problem.
It's not a problem; there is more than enough supported hardware available for Linux.
What the distros need to provide is compatibility lists; and, guess what, they do.
If the networks can no longer count on people watching at least some ads, how are they to pay for content?
They aren't; they should go out of business if they can't figure out a new business model under changing market conditions. In fact, advertising supported network television is obsolete.
but you need to put down emotion and maybe start coming up with reasonable alternative business models
Why do I have to figure out a new business model for them? Or why should Congress artificially limit technology just so that outdated business models continue to work?
Do you want Congress to pass laws against combustion engines so that the business model of hay producers and blacksmiths continues to work?
Which part of I think the Bible cannot be banned, and most criminals would be criminal with or without it. did you fail to understand?
No, the way to deal with the harm the Bible and Christianity have been causing to humanity over the past two millennia is to expose the Bible and Christian history for all to see and to make sure the wars, the torture, the genocides, the murders, and the corruption that Christianity has been responsible for are never forgotten. People need to realize that Christianity, far from offering salvation and hope, is about controlling people through shame, ignorance, and fear.
Themeing can be useful (low vision users, low performance machines, etc.). And some of the eye candy (animation, color, transparency, etc.) does actually improve task performance.
The nice thing is that X11, Xgl, and Gnome/KDE support these capabilities architecturally so well that developers and users can explore the utility of these features and users can pick and choose; Apple and Microsoft, in contrast, really are just treating them as marketing and sales tools.
I'm not after "complexity" and neither are the Linux GUI developers; historically, UNIX and Linux GUIs have been clean and minimalistic.
Linux GUIs are getting complex because that's what users coming from Windows and Macintosh expect. If you want Linux GUIs to get better, get Apple and Microsoft to clean up their shitty user interfaces so that Linux doesn't have to keep supporting that kind of mess.
The "practical" truth is, however, when I wanted to buy a printer or a camera, I couldn't just go to Staples or Best Buy and pick the best deal, I had to do some research.
Actually, for both printers and cameras, the protocols and formats are so well standardized now that if Linux doesn't support it, you probably don't want to be using it even on Windows. In different words, if something is really cheap at Staples, the reason is likely that it sucks on all platforms and you don't want it.
Incidentally, for printers, Macintosh is now using the same software and many of the same drivers that Linux has been using for years, and for cameras, both platforms rely on the USB mass storage and PTP standards. So, when it comes to printers and cameras, Linux is actually no worse than Macintosh (and actually a little better, since it has some extra drivers that Macs don't get).
I think the claim that Linux has more presence on the desktop that MacOS [X], requires some evidence.
Linux is enormously widely used at universities, in research labs, in retail desktop applications, and on corporate desktops (and that's not even counting all the embedded consumer applications). The presence of OS X in all those areas is at best modest.
Just about the only area where OS X may be ahead of Linux on the desktop is among home users, but frankly, even there, it's far from clear whether there are more geeky Linux users or more Apple fashion victims.
So, I think the assertion that OS X is more widely used on the desktop than Linux is implausible; if you want to make that claim, why don't you supply some evidence?
The experience was enough to keep me away from Linux as a desktop until the situation has *dramatically* improved.
The situation doesn't need to "improve" any further. If you buy your Linux hardware from a Linux vendor, you won't have any problems. I mean, in addition to many smaller vendors, even Sun and Dell ship preinstalled desktop Linux machines with all the necessary drivers--what more do you want?
Of course, if you buy hardware for Windows and then try to install Linux on it, it may be painful and some hardware may not work, but that's your own f*cking stupidity.
Maybe if your idea of a [Windows install being a] "major undertaking" is hitting [Enter] half a dozen times.
If you think that installing Windows on PC hardware is as simple as "hitting [Enter] half a dozen times", you haven't installed Windows much. Maybe you're thinking of a system restore from manufacturer's disks, but a real from-scratch Windows install on recent hardware requires that you track down drivers for many different pieces of hardware, followed by hours of re-installing applications to get back to a fairly complete, working system. And that's if you're lucky and if your machine doesn't get infected by a virus before you have managed to protect it.
My job is adminning unix machines (amongst others).
I pity your users.
This is not a problem with X11 or Ubuntu. X11 has excellent multi-monitor support, and excellent support for changing resolutions on the fly. The reason why you can't do it with your hardware is because your vendor didn't supply a driver for Linux. There is nothing anybody other than the vendor can do about this.
Now, I'll give you this much: Gnome still lacks a good GUI for configuring multiple monitors. The reason it's not there yet is probably because there hasn't been a big need for it in the past: most vendors didn't make drivers available, and the few people for whom this mattered spent the 30 minutes to figure it out.
When you want to configure a GUI like X, you should be able to use the damn GUI to configure it. Apparently, those working on Linux distributions don't get this.
You're confused because you apparently have only seen Windows pre-installed. Installing it by hand is a major undertaking that involves significant text-mode interactions.
Conversely, if you install SuSE, or install Ubuntu from a Live CD, your entire installation process will take place in a graphical environment. Furthermore, almost all X11 server changes can be carried out on the fly these days.
Microsoft is entirely capable of producing a next-generation OS with lots of new, innovative technology. Vist isn't it.
Microsoft has some of the smartest CS researchers in the industry But that is neither necessary nor sufficient for producing a commercial next-generation OS. "Innovation" in a commercial OS doesn't mean inventing new stuff, it means being able to sell stuff that was invented 20 years ago but hasn't made it to market yet.