Verification of mathematical proofs is left up to the referees of a paper. No one (at the moment) is suggesting that computers are able to perform the verification job of the referees; all the computer was able to do in this case was essentially trot out a (big) number of cases and verify certain computable propositions. It was the checking of those verifications that stumped the referees, but, as those verifications formed an essential part of the proof of Kepler's Conjecture itself, their removal made the proof incomplete. Perhaps an even more appropriate title would be "Are Computers Ready to Assist in Proving Mathematical Theorems?"
It turns out that one of the natural Riemannian structures to put on a torus is a flat metric, coming from the flat metric on Euclidean space modulo a lattice. That this has the topology of a torus you can see by gluing pairs of opposite sides of a "fundamental domain" for the lattice (a square). This corresponds to an embedding of the torus in 4-space (S^1 x S^1 into R^2 x R^2) which you can't really visualize but which avoids the messy curvature of the torus embedded in 3-space.
Those of us who aren't very fond of Bush's push to war with Iraq will be happy to know that moveon.org will be putting out an ad in the Washington DC area. The ad is inspired by Lyndon Johnson's "Daisy" ad from 1964, and makes the (similar) point that catastrophic things can happen when war is prosecuted irresponsibly. The hope is that it will inspire Congress and the Bush administration to think twice before blustering into this planned wholly unnecessary bloodshed. The press release is here.
You seem to be unfamiliar with mathematical proofs.
Whether or not the previous poster knew what he was talking about, the fact is that the Four-Color Theorem has been rigorously proven. The problem with the proof is that a computer was used to check a great (finite) number of cases that were found using traditional mathematics. The general case was logically reduced to a large, finite number of special cases and then checked by computer, since to check by hand would be unwieldy.
Seeing as computers are basically big, fast logic engines, this is a reasonable use, so long as the cases checked were finite in number, and were arrived at by sound mathematics. The paper was published in a peer-reviewed journal, and has been accepted by the mathematical community, so it certainly should be accepted by you.
In the future, you probably shouldn't go accusing fellow geeks of ignorance of basic concepts (like mathematical proof). It's just rude.;-)
This supposed quark star is 450 light years away, and ultracompact, which according to NASA's site would allow light to orbit. So here's an idea: Concoct a message for future human societies (probably not too different from the messages now designed for extraterrestrial civilizations), and send it in a wad towards RX J185635-375, so that it might get there, orbit a few times, then come shooting back to earth 900 years from now to be picked up by whatever remnants of our civilization are still around.
Of course, the chances of this working are a million to one, and the arrival date might be off by a few hundred years, but if it did work I think it would be an great archeological find for the 4th millenium or so.
btw, anyone else read Interstellar Pig back in the day? William Sleator is a GOD.
Re:The worst part about this story
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Stopping Light
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· Score: 1
The problem is that nothing in quantum physics really "exists" per se. Quantum physics is a mathematical system for describing the bizarre things that have been observed in experiment, such as how photons act like particles in some experiments and like waves (less definite objects) in others. If two photons have the same quantum properties (frequency, direction) then according to theory, they might as well be the same photon, for quantum physics has no way to distinguish two such similar photons. The point being, if the photons look the same, they are the same (in theory).
Anyone remember that episode of the Tick where some supervillian halfway puts his name on the moon with a giant laser? And then this half of his name stays on the face of the moon, besmirching its image for the remainder of the series? The far side of the Moon offers innumerable possibilities for settlement which does not alter Luna's earthly appearance. It seems like putting probes/telescopes/colonies on the far side would be much more admissible to the gazing public, in addition to allowing for wonderful views of the outer universe, to the attendant eyes. Of course, this would eliminate views of the earth from lunar installations, but our orbitting satellites see this planet well enough as it is, I think.
I don't see what's so confusing about it. This black hole was part of a binary system, with a star progressively feeding a black hole. It is an example of a relatively small phenomenon. Supermassive black holes, on the other hand, represent the cores of galaxies, and are incomparable to these "small" black holes for any number of reasons. This 14-sol black hole is new because we never knew small black holes could be so large.
The problem with your argument is that Communism never made anybody rich. The forces that caused the collapse of the USSR were economic more than political; they were just bankrupted by their "business model" of oppressive centralized control.
</i><p>
But this is exactly my point. Microsoft exercises oppressive control over the programming powers of its employees, and when the computer industry becomes conscious of the fact that the bubble has burst, Microsoft won't make anyone else rich. Microsoft is well on its way to being the AT&T of computer software, only without the scarcity of resources. Eventually programmers will realize that working on contract for corporations (like a mechanic) will be the option offering them the most money, more money than central software houses like Microsoft. To put it another way, Microsoft will eventually be revealed to be the inefficient middleman that it really is, and then its fall will not be far behind.
The book was written at the same time as the movie was being made, and the two works were released pretty much simultaneously. I remember this from the foreward to Clarke's book. Clarke and Kubrick were collaborating throughout the project, and I think both works should rightfully be considered joint creations.
This idea is neat to me: it seems to imply that the production of a certain sort of technology will liberate mankind from manmade organisms like monolithic corporations which now are engaged in sucking mankind dry.
I pray for the day when we first create our own kind of life, a microscopic but fantastically complex artificial organism, a computer, hopefully tested in a closed lab by the professionals who created it, designed to be a benefit to mankind. It is then when mankind will realize that progress is only an illusion, the cascading, arbitrary process of evolution. Worship of technology by introverts like you and I will disappear into an adolescent fad, a reflection of youth. When control of matter becomes the real science it deserves to be, its practice will be limited to scientists, and humans will be left to do other, more human things.
I guess what I imagine is a sort of coupled system, as in engineering. Expression in computer programming could be showcased and copyrighted (and bartered over, as the case may be) in an academic setting, perhaps in a variety of online journals of sorts (more organized than slashdot, i'd hope). Work that is functional (that is, intended for distribution) could be distributed via a patent system. I suppose then an academic publication would often come with a patent (or patent pending) to protect the code in the paper, but the ideas would be disseminated.
The original poster was saying that copyright, in its defense of computer code, is being improperly used. Computer code is functional speech, and so is SUPPOSED to be widely, freely disseminated! That's part of the whole purpose of patents, anyway, to have a system of both exclusivising rights to a method and publicizing that method for use whenever it may be needed in the future (e.g. after the patent has expired.) Using copyright to control these nonexpressive works is a destruction of the ideal of freedom of information embodied in the U.S. patent system. DeCSS was being distributed freely, but the DMCA would (under the guise of protecting someone else's copyright) strip technicians of the rights afforded them by their trade, specifically the right to communicate in the language of computer programmers.
This is a bit of a tangent, but I think it would be a natural extension of the U.S. patent system if the agency were to accept computer source code as a patentable process (just as it accepts engineering methods now as patentable processes). The code would be made public. For a limited time (say 5 years) the code would be usable for profit only under contract with the patent holder. Microsoft might release its code on a license basis, GNU under a GPL-like contract. In any case, this would drive competition, for all competitors could examine the code of others and create their own workalikes. It would eliminate concerns about back-doors and privacy, for all the source code would be available to all. It would also, of course, allow Microsoft and other closed software manufacturers to make money for a limited time. But most importantly in my opinion, it would force media companies to open their methods, so that they may be examined by their consumers. Code, being offered no more protection under copyright, could only turn a profit if it were patented, and that would immediately make the method public.
There's a small ambiguity with this idea, that is in how to define when code has been used by another party. There ought to be ample work done in this area in patent law, though, I would think, and I'd guess there would be appropriate analogies to be made there. All this hinges on the idea that software code is functional speech, which I think is quite arguable in court. This is a scheme, I believe, which would successfully bring pre-PC ideas of a patent system into the information age.
I think the reason that the popular media has been so obsessive about cloning while respectable journals avoid the issue is that the popular notion of "cloning" and the scientific notion are so very different. "Cloning" just happened to be the word used to describe the process of producing an intentional genetic twin to an adult mammal. The popular version has very little to do with emulating genes, and everything to do with emulating personality, which is something from which we are thankfully quite far away.
Politicians have been adamant about banning human cloning because it throws a bone to the anti-abortion crowd, who object not to the prospect of a perfect twin but to the production and killing of embryos in the process of creating a successful twin. I think this should be seen for what it is: political jerrymandering, basically idiotic. The issue of whether an embryo should be regarded as a human being is, of course, a different discussion.
In actuality I think cloning by itself will be little more than a proverbial footnote in scientific history. It was a great step, and indicates that we are developing the techniques to manipulate stem cells, which will afford us such things as manufactured organs, a step which I would argue is much more important than any sort of human cloning. Probably the only real effect of human cloning itself will be the marginalization of infertility (perhaps a problem in and of itself, but that's yet another discussion:P).
I feel this is one more way in which the popular media exaggerates a meaningless detail while ignoring the big picture.
Every revolution in personal computing has been heralded by a killer app, an application that cannot be achieved in any other way. Now that Napster has been accepted as the norm for years by college students across the country, I think that if Windows XP in fact keeps people from playing protected media, young people will flock to free software in droves. The next Napster-style program will necessarily be based on free software, and one will need free software to properly take advantage of the music it provides.
So I was looking at Colormax's website, and apparently they have "proprietary technology" which will "enhance color discrimination" in color-blind people. My question is, could this technology be modified so as to provide someone like me (non-colorblind) with tetrachromatic vision, or even pentachromatic vision? I can see it now: "Geordi La forge glasses sold here!" I'd buy it.
The rest of your comments aside (I feel they've been spoken to by the other responders), what I meant by mob rule is that the dynamics of American democracy resemble more the dynamics of a mob than anything else. Small concerns get heavily magnified, and visibility of the candidates is paramount. Therefore, the corporate media (which has a propensity to magnify certain small concerns while ignoring others as well as limit visibility of certain individuals and focus on the two major parties) effectively controls the system in this country. To summarize, corporate influence + mob rule = corporate control. Not quite 1984, but it works to minimize criticism of our corporate system.
The system is (almost) perfect. Vote for who you want. The person with the most votes gets in.
More precisely, you're saying that the American system is a "perfect" democracy. Well, I'm not really sure that's true in any sense of the word, but let's just assume that it is. I think that democracy in the form it is practiced in this country is terribly harmful to every sort of non-moneyed minority, precisely because majority rules. This is confounded by the fact that the corporate media controls the information delivered to a large majority of the people, not to mention more subtle subconscious tricks (like giving W. perpetual lip service and thence lending him credibility as a presidential candidate, when in fact his history as governor of Texas reveals a frighteningly corporate-focused platform). In addition, the entertainment industries have been corporatized to the extent that it is well within their interest to restrict political entertainment which speaks ill of the American corporate system. Who's the Bob Dylan of our times, anyway? If he exists, he certainly isn't signed.
It`d be nice if people went `wait a minute, i dont like (for example) the `war on drugs`, lets vote for someone who`ll dump it and spend the money saved on free health insurance`. As soon as they do, the war on drugs will go away.
This country is run by mob rule. Rumors and misconceptions have this way of spreading like wildfire, especially when endorsed by the major media. As long as the alcohol and pharmeceutical companies keep their influence, legalization of marijuana (arguably the most benign illegal drug, less harmful than alcohol) will not enter into any presidential platform. Tax cuts and abortion rights (or lack thereof) will always be bankable as campaign platforms, and will suffice to cloud the masses from the truth.
Bleh, I could continue, but this is getting depressing.
The line people would always give when some corporate entity decided to try and introduce a "secure" music format was "pshah, people will still use MP3's." Well, so pshah, people will still use an old version of Winamp if it isn't crippled like AOL seems to want to make it.
Right now I think it's reasonable to say that given a choice, people would prefer Napster to work and Winamp to not (as opposed to the other way around). If Winamp suddenly becomes copy-protected, it'll be abandoned for a more free player (like freeamp or older versions of Winamp) overnight.
I was in a video store yesterday and came across a video (2 hours? how many cartoon videos do you know that are two hours?) of "The Maxx," a very very strange MTV animated show from five or six years ago featuring this big purple ogre with large teeth who is a nothing in real life but who is a superhero in his lush fantasy world (which dominates half the show)...it comes from the same era of MTV creativity that produced Aeon Flux...really funny too, as i recall, with decent animation...
What the IETF is now proposing, is an "official" definition of what can go into this "open" data field. Of course, the new specification will define the data field in such a way that Microsoft's current "implimentation" of Kerberos will no longer conform to the specification. The IETF can only do this because it is completely in control of the Kerberos specification already.
This is sorta ironic, given that this was precisely the strategy first exercised by Microsoft to keep Samba incompatible (and thus out of the replacing-NT-business). They changed the SMB standard and had a few precious months (weeks? days?) of "innovation" before the changes were reverse-engineered and incorporated into Samba.
Of course, the only thing the IETF is trying to protect is the equivalence of the terms "Kerberos compliant" and "Kerberos interoperable." Seems to make a lot more sense than Microsoft's attempt to make the terms "Microsoft compatible" and "Microsoft owned" indistinguishable...
Slashdot Mirror
Verification of mathematical proofs is left up to the referees of a paper. No one (at the moment) is suggesting that computers are able to perform the verification job of the referees; all the computer was able to do in this case was essentially trot out a (big) number of cases and verify certain computable propositions. It was the checking of those verifications that stumped the referees, but, as those verifications formed an essential part of the proof of Kepler's Conjecture itself, their removal made the proof incomplete. Perhaps an even more appropriate title would be "Are Computers Ready to Assist in Proving Mathematical Theorems?"
Was I the only person who saw this as a reference to Rick Moranis (as Vince Clortho, Keymaster of Gozer) in Ghostbusters? I am such a dork.
It turns out that one of the natural Riemannian structures to put on a torus is a flat metric, coming from the flat metric on Euclidean space modulo a lattice. That this has the topology of a torus you can see by gluing pairs of opposite sides of a "fundamental domain" for the lattice (a square). This corresponds to an embedding of the torus in 4-space (S^1 x S^1 into R^2 x R^2) which you can't really visualize but which avoids the messy curvature of the torus embedded in 3-space.
Those of us who aren't very fond of Bush's push to war with Iraq will be happy to know that moveon.org will be putting out an ad in the Washington DC area. The ad is inspired by Lyndon Johnson's "Daisy" ad from 1964, and makes the (similar) point that catastrophic things can happen when war is prosecuted irresponsibly. The hope is that it will inspire Congress and the Bush administration to think twice before blustering into this planned wholly unnecessary bloodshed. The press release is here.
Next time, listen to Ray, or get your own lawyer.
Whether or not the previous poster knew what he was talking about, the fact is that the Four-Color Theorem has been rigorously proven. The problem with the proof is that a computer was used to check a great (finite) number of cases that were found using traditional mathematics. The general case was logically reduced to a large, finite number of special cases and then checked by computer, since to check by hand would be unwieldy.
Seeing as computers are basically big, fast logic engines, this is a reasonable use, so long as the cases checked were finite in number, and were arrived at by sound mathematics. The paper was published in a peer-reviewed journal, and has been accepted by the mathematical community, so it certainly should be accepted by you.
In the future, you probably shouldn't go accusing fellow geeks of ignorance of basic concepts (like mathematical proof). It's just rude. ;-)
Of course, the chances of this working are a million to one, and the arrival date might be off by a few hundred years, but if it did work I think it would be an great archeological find for the 4th millenium or so.
btw, anyone else read Interstellar Pig back in the day? William Sleator is a GOD.
The problem is that nothing in quantum physics really "exists" per se. Quantum physics is a mathematical system for describing the bizarre things that have been observed in experiment, such as how photons act like particles in some experiments and like waves (less definite objects) in others. If two photons have the same quantum properties (frequency, direction) then according to theory, they might as well be the same photon, for quantum physics has no way to distinguish two such similar photons. The point being, if the photons look the same, they are the same (in theory).
Seems like the department really should be "justice plugged." Justice was well unplugged before this, no?
Anyone remember that episode of the Tick where some supervillian halfway puts his name on the moon with a giant laser? And then this half of his name stays on the face of the moon, besmirching its image for the remainder of the series? The far side of the Moon offers innumerable possibilities for settlement which does not alter Luna's earthly appearance. It seems like putting probes/telescopes/colonies on the far side would be much more admissible to the gazing public, in addition to allowing for wonderful views of the outer universe, to the attendant eyes. Of course, this would eliminate views of the earth from lunar installations, but our orbitting satellites see this planet well enough as it is, I think.
I don't see what's so confusing about it. This black hole was part of a binary system, with a star progressively feeding a black hole. It is an example of a relatively small phenomenon. Supermassive black holes, on the other hand, represent the cores of galaxies, and are incomparable to these "small" black holes for any number of reasons. This 14-sol black hole is new because we never knew small black holes could be so large.
The problem with your argument is that Communism never made anybody rich. The forces that caused the collapse of the USSR were economic more than political; they were just bankrupted by their "business model" of oppressive centralized control.
</i><p>
But this is exactly my point. Microsoft exercises oppressive control over the programming powers of its employees, and when the computer industry becomes conscious of the fact that the bubble has burst, Microsoft won't make anyone else rich. Microsoft is well on its way to being the AT&T of computer software, only without the scarcity of resources. Eventually programmers will realize that working on contract for corporations (like a mechanic) will be the option offering them the most money, more money than central software houses like Microsoft. To put it another way, Microsoft will eventually be revealed to be the inefficient middleman that it really is, and then its fall will not be far behind.
The book was written at the same time as the movie was being made, and the two works were released pretty much simultaneously. I remember this from the foreward to Clarke's book. Clarke and Kubrick were collaborating throughout the project, and I think both works should rightfully be considered joint creations.
I pray for the day when we first create our own kind of life, a microscopic but fantastically complex artificial organism, a computer, hopefully tested in a closed lab by the professionals who created it, designed to be a benefit to mankind. It is then when mankind will realize that progress is only an illusion, the cascading, arbitrary process of evolution. Worship of technology by introverts like you and I will disappear into an adolescent fad, a reflection of youth. When control of matter becomes the real science it deserves to be, its practice will be limited to scientists, and humans will be left to do other, more human things.
I guess what I imagine is a sort of coupled system, as in engineering. Expression in computer programming could be showcased and copyrighted (and bartered over, as the case may be) in an academic setting, perhaps in a variety of online journals of sorts (more organized than slashdot, i'd hope). Work that is functional (that is, intended for distribution) could be distributed via a patent system. I suppose then an academic publication would often come with a patent (or patent pending) to protect the code in the paper, but the ideas would be disseminated.
This is a bit of a tangent, but I think it would be a natural extension of the U.S. patent system if the agency were to accept computer source code as a patentable process (just as it accepts engineering methods now as patentable processes). The code would be made public. For a limited time (say 5 years) the code would be usable for profit only under contract with the patent holder. Microsoft might release its code on a license basis, GNU under a GPL-like contract. In any case, this would drive competition, for all competitors could examine the code of others and create their own workalikes. It would eliminate concerns about back-doors and privacy, for all the source code would be available to all. It would also, of course, allow Microsoft and other closed software manufacturers to make money for a limited time. But most importantly in my opinion, it would force media companies to open their methods, so that they may be examined by their consumers. Code, being offered no more protection under copyright, could only turn a profit if it were patented, and that would immediately make the method public.
There's a small ambiguity with this idea, that is in how to define when code has been used by another party. There ought to be ample work done in this area in patent law, though, I would think, and I'd guess there would be appropriate analogies to be made there. All this hinges on the idea that software code is functional speech, which I think is quite arguable in court. This is a scheme, I believe, which would successfully bring pre-PC ideas of a patent system into the information age.
Politicians have been adamant about banning human cloning because it throws a bone to the anti-abortion crowd, who object not to the prospect of a perfect twin but to the production and killing of embryos in the process of creating a successful twin. I think this should be seen for what it is: political jerrymandering, basically idiotic. The issue of whether an embryo should be regarded as a human being is, of course, a different discussion.
In actuality I think cloning by itself will be little more than a proverbial footnote in scientific history. It was a great step, and indicates that we are developing the techniques to manipulate stem cells, which will afford us such things as manufactured organs, a step which I would argue is much more important than any sort of human cloning. Probably the only real effect of human cloning itself will be the marginalization of infertility (perhaps a problem in and of itself, but that's yet another discussion :P).
I feel this is one more way in which the popular media exaggerates a meaningless detail while ignoring the big picture.
Every revolution in personal computing has been heralded by a killer app, an application that cannot be achieved in any other way. Now that Napster has been accepted as the norm for years by college students across the country, I think that if Windows XP in fact keeps people from playing protected media, young people will flock to free software in droves. The next Napster-style program will necessarily be based on free software, and one will need free software to properly take advantage of the music it provides.
Wow. This is making me all tingly :)
So I was looking at Colormax's website, and apparently they have "proprietary technology" which will "enhance color discrimination" in color-blind people. My question is, could this technology be modified so as to provide someone like me (non-colorblind) with tetrachromatic vision, or even pentachromatic vision? I can see it now: "Geordi La forge glasses sold here!" I'd buy it.
The rest of your comments aside (I feel they've been spoken to by the other responders), what I meant by mob rule is that the dynamics of American democracy resemble more the dynamics of a mob than anything else. Small concerns get heavily magnified, and visibility of the candidates is paramount. Therefore, the corporate media (which has a propensity to magnify certain small concerns while ignoring others as well as limit visibility of certain individuals and focus on the two major parties) effectively controls the system in this country. To summarize, corporate influence + mob rule = corporate control. Not quite 1984, but it works to minimize criticism of our corporate system.
More precisely, you're saying that the American system is a "perfect" democracy. Well, I'm not really sure that's true in any sense of the word, but let's just assume that it is. I think that democracy in the form it is practiced in this country is terribly harmful to every sort of non-moneyed minority, precisely because majority rules. This is confounded by the fact that the corporate media controls the information delivered to a large majority of the people, not to mention more subtle subconscious tricks (like giving W. perpetual lip service and thence lending him credibility as a presidential candidate, when in fact his history as governor of Texas reveals a frighteningly corporate-focused platform). In addition, the entertainment industries have been corporatized to the extent that it is well within their interest to restrict political entertainment which speaks ill of the American corporate system. Who's the Bob Dylan of our times, anyway? If he exists, he certainly isn't signed.
It`d be nice if people went `wait a minute, i dont like (for example) the `war on drugs`, lets vote for someone who`ll dump it and spend the money saved on free health insurance`. As soon as they do, the war on drugs will go away.
This country is run by mob rule. Rumors and misconceptions have this way of spreading like wildfire, especially when endorsed by the major media. As long as the alcohol and pharmeceutical companies keep their influence, legalization of marijuana (arguably the most benign illegal drug, less harmful than alcohol) will not enter into any presidential platform. Tax cuts and abortion rights (or lack thereof) will always be bankable as campaign platforms, and will suffice to cloud the masses from the truth.
Bleh, I could continue, but this is getting depressing.
Right now I think it's reasonable to say that given a choice, people would prefer Napster to work and Winamp to not (as opposed to the other way around). If Winamp suddenly becomes copy-protected, it'll be abandoned for a more free player (like freeamp or older versions of Winamp) overnight.
Every time I start playing peekaboo by myself, my folks give me more ritalin.
I was in a video store yesterday and came across a video (2 hours? how many cartoon videos do you know that are two hours?) of "The Maxx," a very very strange MTV animated show from five or six years ago featuring this big purple ogre with large teeth who is a nothing in real life but who is a superhero in his lush fantasy world (which dominates half the show)...it comes from the same era of MTV creativity that produced Aeon Flux...really funny too, as i recall, with decent animation...
This is sorta ironic, given that this was precisely the strategy first exercised by Microsoft to keep Samba incompatible (and thus out of the replacing-NT-business). They changed the SMB standard and had a few precious months (weeks? days?) of "innovation" before the changes were reverse-engineered and incorporated into Samba.
Of course, the only thing the IETF is trying to protect is the equivalence of the terms "Kerberos compliant" and "Kerberos interoperable." Seems to make a lot more sense than Microsoft's attempt to make the terms "Microsoft compatible" and "Microsoft owned" indistinguishable...