Here are some quotes from the paper I found significant.
File sharing proponents have also suggested that music sales
decreased as consumers substituted into other types of entertainment goods, such
as prerecorded movies and video games. However, Michel (2005) concludes
there is no evidence that CEX [the study that the author is using for data] households' decrease in music purchases
corresponds to an increase in spending on movie tickets, prerecorded movies or
video games.
He also raises the possibility that some of the decrease may be due to legal music downloads, but believes that this is less true for the years covered by his study than in more recent years.
From his conclusion:
Our micro-level data test results suggest that file sharing may have
reduced album sales (between 1999 and 2003) by as much as 13 percent for some
music consumers. At minimum, our test results indicate that the relationship
between computer ownership and music purchases (in the CEX) weakened after
Internet file sharing became a viable option for music purchasers. No similar
negative change exists in the data prior to the initiation of the first file-sharing
service.
After reading his paper, I'm inclined to agree. The data does suggest that there may have been a 13% drop in CD purchases among computer owners who spent more music than the median consumer, but there may be alternate explanations to account for at least some of the drop. However, it seems clear that filesharing did reduce music sales among that population.
Ok, that's true and is a good point. I'm curious as to whether original author covered these issues at all, and, if so, what he had to say about them.
So I did some browsing, and found the abstract and a link where you can view the article: http://www.bepress.com/bejeap/topics/vol6/iss1/art 18/. I'm not sure if you can access the article from anywhere, but if you're on a university network it should be no problem. You can also request guest access, which worked fine for me to see the article in question. I'll read it when I get the chance, and post back if I find anything interesting in how he discusses these issues.
On a side note, it seems the researcher used to work for the Heritage Foundation, and may have a somewhat conservative bias. On the other hand, this is not so uncommon for economists, and doesn't mean his research is without merit.
This would be true - except they aren't charting the expenditures of computer owners vs. non computer owners. They are studying how the expenditures change from year to year, and how those changes correlate with big changes in the ability to get illegal music free over the internet.
According to the study, the average computer owner spent $4.79 less on CDs in 2002 than they did in 2001, and in 2003 they spent $5.55 less than that. This cannot be explained by the fact that computer owners spend more on other forms of entertainment than non-computer owners, since the motivation to buy other things instead of CDs was the same in 2001 as in 2002, but they spent significantly less in 2002.
Economic changes in 2002 might have an impact, as people were less likely to spend money on luxuries. The discrepancy in the decreased spending between those with and without computers could possibly be due to the different impacts on luxury spending between people with more and less money, but it could also be due to easily available free pirated music. Likewise the increase - there could definitely be some sort of global effect unrelated to filesharing that affects those with computers differently than those without. Or it could be the effect of the demise of Napster making filesharing much more difficult.
I imagine the study addresses such issues, although the article did not. Does anyone have a link to the study? Personally, I found the numbers contained in the article fairly convincing, although even in the absence of hard data I would have said it was very likely that filesharing has had a negative impact on music sales, at least prior to online digital music stores.
I can't help but wonder whether you're questioning the validity of the study because you don't like it's methods (by the way, have you actually read the study, or just the linked article) or because you don't like it's results.
We're not saying the system is inefficient. We're saying it plain doesn't work. It purports to do something which, if it actually did it, would violate conservation of momentum, a well-known and accepted part of the physics on which this "invention" purports to be based.
I don't see blind skepticism here. I see informed skepticism from people who have enough foggy memories of freshman physics to realize that the paper invokes relativity to purportedly prove that you can violate conservation of momentum, which is not possible in relativity theory. Blind skepticism would be as bad as blind faith, but well-founded skepticism is the sign of a healthy and alert mind.
No, a solar sail which doesn't reflect is not impossible, merely a terrible idea. If it absorbs the photons instead of reflecting them, then conservation of momentum still says that the momentum of the photons is transferred to the sail, but the force is half as much, since the photons are absorbed rather than bouncing off with the same momentum in the opposite direction. Yes, the sail will heat up, as it is absorbing a lot of energy (unless it converts it into some other form of energy, like electricity). So it will work, but only half as well as a reflective sail. On the other hand, if it converts the energy from the absorbed photons into something worthwhile, it might compensate for the loss of motive force.
Just because an object does not exist in nature does not mean that theories about it cannot be useful for natural science. For example, you will never find imaginary quantities, and yet complex numbers play and important role in quantum mechanics, and make just about any equation involving periodic oscillations more manageable.
No, information still cannot be transmitted, as other posters have mentioned. They can control the spin of one of the entangled electrons, but once they do, the electrons are no longer entangled. Science-fiction authors are fond of using "entanglement" to defeat speed of light limitations on communication, but it doesn't actually work (at least, not according to current theories, which are unchanged by this experiment).
That's not precisely true. Of course, some ways of recording the spin will change it, and there are theoretical restrictions, but in theory it is possible to observe the spin without changing it. For example, measuring the spin in a particular axis as up or down will set the quantum state to a pure state of up or down in that axis. If it was already in that same pure state, observing it wouldn't change it. Of course, observing the spin in a particular axis sets it into a pure state, so if it weren't already in a pure state, or if it were in a pure state along a different axis, then you're right that an observation would change the spin.
I've seen the "proof" of Fermat's Last Theorem on a T-shirt before (it was very very abridged, but was an accurate summary and gave references to where the full proof could be found). I would not be at all surprised if similar T-shirts become available for this in the not-too-distant future.
I really don't know anything specific about Perlman's technique, so I have no idea how effective or abstract it is (i.e. whether a computer could implement it).
As far as object recognition goes, remember that what we mean when we say a 3-dimensional manifold is a space that has three dimensions everywhere, not an object which can be embedded in 3-dimensional space. In fact, a 3-dimensional manifold may require as many as 7 spacial dimensions to be embedded in ordinary euclidean space, and even more may be required if the embedding actually preserves distance, and not just topological properties.
What you seem to be referring to is to have a computer tell what an object is by looking at it's surface, which is a 2-manifold, not a three manifold. There are mathematical programs that can identify the type of a surface, and these use triangulations rather than Ricci Flow, but I'm not sure if such methods have ever been used to identify real-world objects.
If you're looking for real world applications of Ricci Flow or Perlman's surgery methods, I think the closest you'll get for the moment is theoretical physics. Of course, I could be wrong - sometimes seemingly very abstract mathematics has turned out to be very useful.
I'm not a geometer, but here is my understanding of the proof:
The Ricci Flow was defined by Richard Hamilton in 1981 as a step towards classifying topological compact 3-manifolds. Classifying 3-manifolds would certainly decide The Poincare Conjecture, as it states that all simply connected compact 3-manifolds are homeomorphic to the sphere. This is an important special case: most proofs of the classification of compact 2-manifolds start out by proving the an analogous statement for the 2-sphere. The Ricci Flow is a differential equation which defines how the shape of a manifold changes in time: given an arbitrary manifold M(0), you can apply the differential equation to it to get manifolds M(t) for (some) positive t, which gradually change shape. However, the Ricci Flow is not volume preserving, so you "renormalize" so that M(t) has constant volume.
The Ricci Flow has the useful property that it tends to make manifolds smoother and smoother. For example, if you started out with a lumpy ball, you would eventually get a smooth ball. It was hoped that it could be proved that if the initial manifold was a compact simply connected 3-manifold, then as t increased, the manifold would tend towards a 3-sphere. Unfortunately, while locally solutions to differential equations always exist, they don't necessarily exist for all time, and for some starting manifolds, eventually you would get to a road-block: a t for which M(t) could not be defined. What Perlman (hopefully) showed was that all road-blocks were of certain types, and that a surgery could be formed that would modify the manifold but not it's topological nature, and then you could again apply the Ricci Flow, until the manifold became a sphere.
Note that this method is useful beyond proving the Poincare Conjecture, as it (again, hopefully) describes all road blocks to extending the Ricci Flow, so that the same tools can be applied to any 3-manifold, and not just simply connected ones. In this manner, assuming Perlman made no mistakes (or that any mistakes can be corrected), it is possible to apply the same arguments to prove the Geometrization Conjecture of Thurston, which classifies 3-manifolds.
Remember, the proofs that appear in textbooks are very polished, and use many lemmas that were proved earlier. The 1000 page proof includes proofs of all lemmas needed to complete the full proof, and there may be some redundancy as multiple lemmas may have similar proofs. Compare this to the classification of finite simple groups, which is tens of thousands of pages, and known as "the enormous theorem" (although that proof is needfully more complex, as there are many special cases that need to be dealt with).
However, there is definitely some cause for skepticism, as such a long proof is very hard to check, and other similar announcements in the past have had later holes found (such as Andrew Wiles first announcement of the proof of Fermat's Last Theorem, and the above mentions Enormous Theorem.) On the other hand, bost of those proofs have had (in the case of the enormous theorem, probably had) the holes plugged, and I feel confident that if a gap is found in this proof, it will also be bridged.
"If you had ever studied special relativity, you would know that it's possible to have momentum without mass, and the momentum of a photon is defined as P=E/c, or h*v/c."
This is completely true, although I'm not quite sure who you say "is defined". Momentum is a defined quantity (albeit one with a natural definition, just like mass and energy), but once you have defined what is meant by momentum in general, the momentum of a photon is not "defined" but rather a consequence of conservation of momentum. (Although I suppose you could say that massless particle momentum is defined, and conservation of momentum is a consequence if you wanted to.)
For a concrete example of the momentum of photons, consider solar sail craft, which accelerate by recieving the momentum of impacting photons. (Yes, this is concrete. Solar sails have been launched, although their success has been limited.)
I can't imagine what would provoke a researcher to ever write such a paper. I cannot imagine a single good use that this research could be put too, and there are myriad evil uses possible. If I were the researcher, and someone used my research to actually create such a virus, I would have trouble looking at myself in the mirror.
It's like the atomic bomb project - it took a World War to cause scientists to put their research energy into an invention that was so single-mindedly and frighteningly destructive, and many of them regretted helping to invent it afterwards, despite the fact that it may have helped end the war. (Ok, I admit that this is debatable, but let's please not do it here.)
Slashdot Mirror
From his conclusion: After reading his paper, I'm inclined to agree. The data does suggest that there may have been a 13% drop in CD purchases among computer owners who spent more music than the median consumer, but there may be alternate explanations to account for at least some of the drop. However, it seems clear that filesharing did reduce music sales among that population.
Ok, that's true and is a good point. I'm curious as to whether original author covered these issues at all, and, if so, what he had to say about them.
t 18/. I'm not sure if you can access the article from anywhere, but if you're on a university network it should be no problem. You can also request guest access, which worked fine for me to see the article in question. I'll read it when I get the chance, and post back if I find anything interesting in how he discusses these issues.
So I did some browsing, and found the abstract and a link where you can view the article: http://www.bepress.com/bejeap/topics/vol6/iss1/ar
On a side note, it seems the researcher used to work for the Heritage Foundation, and may have a somewhat conservative bias. On the other hand, this is not so uncommon for economists, and doesn't mean his research is without merit.
This would be true - except they aren't charting the expenditures of computer owners vs. non computer owners. They are studying how the expenditures change from year to year, and how those changes correlate with big changes in the ability to get illegal music free over the internet.
According to the study, the average computer owner spent $4.79 less on CDs in 2002 than they did in 2001, and in 2003 they spent $5.55 less than that. This cannot be explained by the fact that computer owners spend more on other forms of entertainment than non-computer owners, since the motivation to buy other things instead of CDs was the same in 2001 as in 2002, but they spent significantly less in 2002.
Economic changes in 2002 might have an impact, as people were less likely to spend money on luxuries. The discrepancy in the decreased spending between those with and without computers could possibly be due to the different impacts on luxury spending between people with more and less money, but it could also be due to easily available free pirated music. Likewise the increase - there could definitely be some sort of global effect unrelated to filesharing that affects those with computers differently than those without. Or it could be the effect of the demise of Napster making filesharing much more difficult.
I imagine the study addresses such issues, although the article did not. Does anyone have a link to the study? Personally, I found the numbers contained in the article fairly convincing, although even in the absence of hard data I would have said it was very likely that filesharing has had a negative impact on music sales, at least prior to online digital music stores.
I can't help but wonder whether you're questioning the validity of the study because you don't like it's methods (by the way, have you actually read the study, or just the linked article) or because you don't like it's results.
We're not saying the system is inefficient. We're saying it plain doesn't work. It purports to do something which, if it actually did it, would violate conservation of momentum, a well-known and accepted part of the physics on which this "invention" purports to be based.
I don't see blind skepticism here. I see informed skepticism from people who have enough foggy memories of freshman physics to realize that the paper invokes relativity to purportedly prove that you can violate conservation of momentum, which is not possible in relativity theory. Blind skepticism would be as bad as blind faith, but well-founded skepticism is the sign of a healthy and alert mind.
No, a solar sail which doesn't reflect is not impossible, merely a terrible idea. If it absorbs the photons instead of reflecting them, then conservation of momentum still says that the momentum of the photons is transferred to the sail, but the force is half as much, since the photons are absorbed rather than bouncing off with the same momentum in the opposite direction. Yes, the sail will heat up, as it is absorbing a lot of energy (unless it converts it into some other form of energy, like electricity). So it will work, but only half as well as a reflective sail. On the other hand, if it converts the energy from the absorbed photons into something worthwhile, it might compensate for the loss of motive force.
Just because an object does not exist in nature does not mean that theories about it cannot be useful for natural science. For example, you will never find imaginary quantities, and yet complex numbers play and important role in quantum mechanics, and make just about any equation involving periodic oscillations more manageable.
No, information still cannot be transmitted, as other posters have mentioned. They can control the spin of one of the entangled electrons, but once they do, the electrons are no longer entangled. Science-fiction authors are fond of using "entanglement" to defeat speed of light limitations on communication, but it doesn't actually work (at least, not according to current theories, which are unchanged by this experiment).
That's not precisely true. Of course, some ways of recording the spin will change it, and there are theoretical restrictions, but in theory it is possible to observe the spin without changing it. For example, measuring the spin in a particular axis as up or down will set the quantum state to a pure state of up or down in that axis. If it was already in that same pure state, observing it wouldn't change it. Of course, observing the spin in a particular axis sets it into a pure state, so if it weren't already in a pure state, or if it were in a pure state along a different axis, then you're right that an observation would change the spin.
I've seen the "proof" of Fermat's Last Theorem on a T-shirt before (it was very very abridged, but was an accurate summary and gave references to where the full proof could be found). I would not be at all surprised if similar T-shirts become available for this in the not-too-distant future.
Oops, I meant 6 dimensions, not 7. See the Whitney Embedding Theorem.
I really don't know anything specific about Perlman's technique, so I have no idea how effective or abstract it is (i.e. whether a computer could implement it).
As far as object recognition goes, remember that what we mean when we say a 3-dimensional manifold is a space that has three dimensions everywhere, not an object which can be embedded in 3-dimensional space. In fact, a 3-dimensional manifold may require as many as 7 spacial dimensions to be embedded in ordinary euclidean space, and even more may be required if the embedding actually preserves distance, and not just topological properties.
What you seem to be referring to is to have a computer tell what an object is by looking at it's surface, which is a 2-manifold, not a three manifold. There are mathematical programs that can identify the type of a surface, and these use triangulations rather than Ricci Flow, but I'm not sure if such methods have ever been used to identify real-world objects.
If you're looking for real world applications of Ricci Flow or Perlman's surgery methods, I think the closest you'll get for the moment is theoretical physics. Of course, I could be wrong - sometimes seemingly very abstract mathematics has turned out to be very useful.
I'm not a geometer, but here is my understanding of the proof:
The Ricci Flow was defined by Richard Hamilton in 1981 as a step towards classifying topological compact 3-manifolds. Classifying 3-manifolds would certainly decide The Poincare Conjecture, as it states that all simply connected compact 3-manifolds are homeomorphic to the sphere. This is an important special case: most proofs of the classification of compact 2-manifolds start out by proving the an analogous statement for the 2-sphere. The Ricci Flow is a differential equation which defines how the shape of a manifold changes in time: given an arbitrary manifold M(0), you can apply the differential equation to it to get manifolds M(t) for (some) positive t, which gradually change shape. However, the Ricci Flow is not volume preserving, so you "renormalize" so that M(t) has constant volume.
The Ricci Flow has the useful property that it tends to make manifolds smoother and smoother. For example, if you started out with a lumpy ball, you would eventually get a smooth ball. It was hoped that it could be proved that if the initial manifold was a compact simply connected 3-manifold, then as t increased, the manifold would tend towards a 3-sphere. Unfortunately, while locally solutions to differential equations always exist, they don't necessarily exist for all time, and for some starting manifolds, eventually you would get to a road-block: a t for which M(t) could not be defined. What Perlman (hopefully) showed was that all road-blocks were of certain types, and that a surgery could be formed that would modify the manifold but not it's topological nature, and then you could again apply the Ricci Flow, until the manifold became a sphere.
Note that this method is useful beyond proving the Poincare Conjecture, as it (again, hopefully) describes all road blocks to extending the Ricci Flow, so that the same tools can be applied to any 3-manifold, and not just simply connected ones. In this manner, assuming Perlman made no mistakes (or that any mistakes can be corrected), it is possible to apply the same arguments to prove the Geometrization Conjecture of Thurston, which classifies 3-manifolds.
Remember, the proofs that appear in textbooks are very polished, and use many lemmas that were proved earlier. The 1000 page proof includes proofs of all lemmas needed to complete the full proof, and there may be some redundancy as multiple lemmas may have similar proofs. Compare this to the classification of finite simple groups, which is tens of thousands of pages, and known as "the enormous theorem" (although that proof is needfully more complex, as there are many special cases that need to be dealt with).
However, there is definitely some cause for skepticism, as such a long proof is very hard to check, and other similar announcements in the past have had later holes found (such as Andrew Wiles first announcement of the proof of Fermat's Last Theorem, and the above mentions Enormous Theorem.) On the other hand, bost of those proofs have had (in the case of the enormous theorem, probably had) the holes plugged, and I feel confident that if a gap is found in this proof, it will also be bridged.
"If you had ever studied special relativity, you would know that it's possible to have momentum without mass, and the momentum of a photon is defined as P=E/c, or h*v/c." This is completely true, although I'm not quite sure who you say "is defined". Momentum is a defined quantity (albeit one with a natural definition, just like mass and energy), but once you have defined what is meant by momentum in general, the momentum of a photon is not "defined" but rather a consequence of conservation of momentum. (Although I suppose you could say that massless particle momentum is defined, and conservation of momentum is a consequence if you wanted to.) For a concrete example of the momentum of photons, consider solar sail craft, which accelerate by recieving the momentum of impacting photons. (Yes, this is concrete. Solar sails have been launched, although their success has been limited.)
I can't imagine what would provoke a researcher to ever write such a paper. I cannot imagine a single good use that this research could be put too, and there are myriad evil uses possible. If I were the researcher, and someone used my research to actually create such a virus, I would have trouble looking at myself in the mirror. It's like the atomic bomb project - it took a World War to cause scientists to put their research energy into an invention that was so single-mindedly and frighteningly destructive, and many of them regretted helping to invent it afterwards, despite the fact that it may have helped end the war. (Ok, I admit that this is debatable, but let's please not do it here.)