No, I agree with you -- there seems to be a lot of hype mixed with misunderstandings in the article.
(But at least these days we don't see the "test all the possibilities and find the right one instantly" nonsense that was very common a few years ago, so I guess that's an improvement:))
Large scale quantum computers could easily factor large numbers thus rendering perhaps all of our current encryption systems obsolete. I have no idea what they would be replaced with but it seems at least possible that anyone who wanted to communicate securely would need to use a quantum computer.
I don't think that it's likely that quantum computers (if built) will be necessary for secure communication. There are cryptosystems (check out McEliece) that can be run relatively fast in classical computers and are based on the difficulty of solving NP-hard problems. Quantum computers would not offer exponential speedups for these kinds of problems (that's not actually proved, but it's even more certain than P!=NP, I think).
So does that mean that some time in the next 50 years, we'll have quantum computers crunching massively paprallel problems, such as decrypting all our previously secure communications, manipulating all the pixels of a video feed in real-time, right off the sensor or even with an entanglement USB peripheral that takes the place of all our networking and communications systems - providing instantaneous point-to-point links between pairs of chips?
I think you're expecting way too much from quantum computing:
In 50 years we'll probably be able to decrypt all our (current) secure communications anyway, with or without quantum computers. Of course, by then we'll be using larger keys (or probably better algorithms that provide better security with smaller keys). And if quantum computers start to become feasible, we can start moving to encryption systems that cannot be broken by quantum computers (the McEliece cryptosystem is one candidate).
About "manipulating all the pixels of a video feed in real-time", I don't think quantum computers would be incredibly useful for that, at least not in the way you seem to expect it. To get a quantum speedup, you must have a very specific algorithm that computes what you want and, at the same time, makes the correct answer come out with high probability. It's certainly not a magic thing that allows you to massively parallelize any algorithm: for search, for example, it's proven that the quantum speedup is at most sqrt(n), and that's not even counting the time it takes to encode whatever data you want to search in the necessary entangled state.
The "instantaneous point-to-point link" is even worse: quantum mechanics can most certainly not transmit information instantly. Entanglement can't be directly used to transmit information; the (theoretical) best you can do is to double the capacity of a classical channel while "spending" entanglement, and that doesn't seem to be terrible useful for your example.
Quantum computers only offer better speeds; a quantum computer can always be simulated by a classical computer. However, storage and run time of the simulation grows exponentially with the size of the quantum computer being simulated, so this is not feasible in practice.
The reverse is also true. A quantum computer (when/if built) will be able to run any classical algorithm, since it's possible to implement a classical NAND gate using quantum gates. It'd be a huge waste, however, to use quantum gates this way.
You're forgetting that the volume is proportional to the cube of the radius, while gravity is proportional to the inverse square of the radius. So, while gravity doesn't increase linearly with mass, it's not constant either:
Your argument seems to be this (please correct me if I'm misrepresenting it):
Take the formal system of the "theory of everything", call it TOE. By Godel's theorem, there exists a certain arithmetic statement (G) that is independent of TOE. Because the universe is Turing complete, it's possible to physically build a Turing machine (M) whose output (or, even better, whether it halts or not) depends on the truth value of G. Since G is undecidable in TOE, the "theory of everything" can't predict what would physically happen if we actually build M in the physical world. So, this means that the "theory of everything" can't actually predict everything.
One possible objection is the following:
When you follow Godel's proof, you notice that the arithmetic statement that the proof constructs involves huge numbers, and that the more axioms you put on your system, the larger the numbers involved must be (if you don't remember just how huge the numbers are, go back and check it: it's mind boggling, even for the relatively simple formal system used by Godel).
That in itself would not be a problem, since we're only talking about the theoretical possibility of the existence of the "theory of everything". But, it turns out that it's possible (and even probable) that our universe is not actually Turing complete because there's a limit to how much computation is possible even in principle. That is, it's possible that the formal system of the "theory of everything" is complex enough that in order to build the Turing machine that would be unpredictable, you'd either have put so much in too little space that it would become a black hole, or you'd have to spread it out so much (in order to prevent the black hole) that the universe expansion would make one end of the Turing machine inaccessible to the other end, and so the machine wouldn't be able to compute anymore.
In case that last point is not too clear, you can find a much better explanation in this lecture (search for "So what does any of this have to do with computation?").
I'm not saying that this is the case, but it's certainly a possibility that has not been ruled out (and maybe it's even true).
It is, for example, possibly that the scalability (given the need for error correction, e.g.) is so bad, that using all what is available still is not enough for a meaningful size. (By meaningful, I mean here performing far better that a conventional computer built with about the same effort.)
OK, but if that's the case, there has to be a reason why scalability is that bad. Shor's algorithm can factor n-bit numbers with ~4n qubits. Laflamme's error correction works by encoding each qubit as 5. So, to factor a 2048-bit number in polynomial time, we "only" need about 40000 qubits. We currently know nothing in nature that prevents us to achieve that in principle.
The problem is entanglement. (...) With a quantum computer, you always have to look at the whole, due to entanglement, hence all known to work design principles do not apply anymore.
Sure, designing and building quantum computers is very different (much harder!) than designing and building current computers. That shouldn't be a great surprise, I think. Still, I can't see how that's an argument for saying things like "it will take 100 years" or "maybe it's impossible in principle".
Yes, and they are now where, 20? After 10 Years? And keep in mind that these are not "CPU", but "Storage", which is fundamentally easy in comparison.
The result I mentioned was done in 2008, not 10 years ago. Hey, 20 years ago we didn't even have Shor's algorithm, so most people doubted that quantum computers could be useful even in theory (and so, there were very few people studying it).
In addition to all this, there is a real risk that all the projected gains will vanish into, for example, a noise problem or the like. For current quantum devices, the internal state-model of the particles does not have to be very complex. It is quite possible that it turns out that the computing power and storage capability of a single, say electron, is limited to something a $4 MSP430 MCU can do. We would not have noticed that yet as no sufficiently complex computations have been done.
Sure, and if that were indeed true, it would be very exciting for theoretical quantum physics. It would mean that the evolution of a quantum system is not linear, so the Schrodinger's equation is not quite right, and everything after that would have to be changed. It would also probably mean that the state space is not really a Hilbert space, which would have very weird implications that would depend on the geometry of whatever replaced the Hilbert space. The point is, nothing in our current understanding even slightly suggests that. See for instance this.
Also remember that physics regularly adjusts its world model, when more experimental data becomes available. Quantum theory is a theory, the actual physical object may still behave differently in the real-world. And, as far as I know, Quantum Theory still does not mesh with Relativity, so there is a very big "this theory is incomplete or faulty" hint right there.
Sure, and gravity is also a theory, but it would be strange to bet in the 1950's that maybe making something orbit the Earth is impossible, because there may be things we still don't know about gravity (for all we knew, it could have been so). Even Newton's gravity, which is not quite right, is enough to make satellites orbit the earth.
Quantum mechanics seems to work *extremely* well, at least for the energy levels we're trying to make quantum computers work. Quantum Electrodynamics (the part of QM that's has to be right to build a quantum computer) is the most tested theory in human history, its predictions (which of course turned out to be right) are the most accurate ever made, even more than General Relativity.
It's true that it is incomplete -- it says nothing about gravity, and it's not
(...) it is quite possible that quantum computers of meaningful power are fundamentally infeasible in this universe.
That's true, but in order for quantum computers to be fundamentally impossible, there must exist something in the laws of nature that we haven't observed yet. Quantum computers being possible is actually the most boring thing that can happen from the point of view of theoretical physics (i.e., if there are no surprises and what we currently know is pretty much the way things are).
As for a quantum computer not being made of sub-components, I don't quite understand what you mean. From what we currently understand about Quantum Mechanics, it's possible in principle to entangle the spin of, say, 1000 electrons (each spin would count as a qubit). A quantum gate could in principle be implemented by applying a certain magnetic field to individual or small groups of electrons.
This is all in principle, of course. If we ever want to implement a quantum computer, we have to think in more practical terms. There are several schemes proposed (e.g, ion trapping and liquid NMR), but I know almost nothing about them, except that entanglement of 8 atoms has actually been done a few years ago with ion traps.
Why is this modded troll? Anyone who follows the Wii homebrew scene knows Waninkoko has been very disruptive to people who want to write and run homebrew code without having anything to do with piracy.
See also for example this post from another Homebrew Channel developer. And this from marcan (presumably the parent) about how he wrote an USB loader in 6 hours just to show it's no big deal, given everything other people had already done.
What you're describing is a NP-complete problem -- assuming P != BQP != NP. But I'm guessing that you already know that:)
Still, it's still very hard to build a cryptosystem that exploits the hardness of solving NP-complete problems. The main problem is, NP-completeness only guarantees that some instance of the problem is hard, it says nothing about a specific instance. So, for instance, if you have a specific 3-SAT formula, there's no guarantee someone can't come up with a solution for it in polynomial time.
That being said, there are some candidates for a cryptosystem based on NP-completeness. Check for example the McEliece cryptosystem.
I am curious about your claim for "tail call support". Mostly, compilers are smart enough to replace a pure tail call with a simple transfer, and the run-time doesn't have to be aware. If the optimization is contemplated, there cannot be any partial results needed, and this must be maintained through the entire recursive sequence (direct tail call, or through another function). How does the run-time itself assist with this?
I'm guessing that if the transformation (from a tail call to a branch) is done by the compiler, then the generated bytecode loses nice properties used by the checker to ensure it's well formed. If you do it like CLR (with a "tail" modifier to a call), the checker can verify it's a simple method call (and not a branch to some place outside the current method, which might or might not be valid) and then the JIT, seeing the "tail" marker, ensures the proper semantics for the tail call (stack doesn't grow, etc.).
There might be other reasons, like performance: it's very likely that the JIT can do a much better job at optimizing a tail call (when it knows it's a tail call) than optimizing the tail call bytecode generated by the bytecode compiler.
Mod parent up, please (I'd do it if I had mod points).
People talk about "transforming mass into energy" in nuclear reactions, but they almost never say that it's actually much more mundane than that. You don't need nuclear reactions (or even chemical reactions): a sinning top, for example, has more mass than one that's standing still. Here is a somewhat known physicist talking about that, if you don't want to believe a random person on Slashdot.
This question has been considered by quite a few different people; search google for P vs NP independent ("independent" meaning independent from the usual accepted axioms for mathematics, i.e., can't be proven using the currently accepted axioms).
There's a nice survey paper about this question that's very readable if you're willing to invest some time: Is P Versus NP Formally Independent?.
"QP" doesn't mean what you think it means: it actually means "quasi-polynomial time" (basically, worse than polynomial but better than exponential, with nothing to do with "quantum").
I think you mean BQP (bounded-error quantum polynomial time), which is the class that contains Shor's algorithm (the one you mentioned that factors integers in polynomial time).
BQP != NP is actually still unproven (but most people believe it -- if false, quantum computers would be way too powerful). Even BQP != P is unproven (but also mostly believed -- if false, it would render quantum computers largely useless, and would be surprising from what we know about Physics).
As a side note, the direct quantum analog of P is actually EQP (exact quantum polynomial time, i.e., quantum algorithms that run in polynomial time and are right with probability 1). EQP is not known to contain many interesting problems (the only one I know is Deutsch-Jozsa, which is mostly useless), so most quantum algorithms you'll likely hear about are in BQP. BQP is actually the quantum analog of BPP (bounded-error probabilistic polynomial time, which is increasingly believed to be equal to P, especially after "primes in P" -- but there are still problems in BPP that are not known to be in P). BQP, on the other hand, is not largely believed to be equal to EQP.
One user may install and use copies of the software to design, develop, test and demonstrate your programs. You may not use the software on a device or server in a production environment.
Your GP said "I like to play video games, windows has more of them", so it seems obvious that he's installing Windows to play games he's not developing, clearly contradicting section 2.a of the license you linked.
The second link you didn't "delve too closely into" makes section 2.a more explicit: it says you can only use the MSDN-licensed software for development (and testing, etc.). No other uses are allowed, like reading email, playing games, etc.
I'm the last person wanting to force a MS contract on someone else, but in this case it seems obvious that your GP is using the MSDN license irregularly (not that it's any of my business). Unless I completely misunderstood what he meant with "I like to play video games, windows has more of them [...]".
That makes it pretty difficult to develop software for an OS if you're not allowed to use the OS.
Indeed.
But that's beside the point. If you want to use the MSDN subscription license, you must follow its rules (as stupid as they might be), or convince MS to change them. Otherwise, just pay for the full license or simply don't use Windows.
Well, if someone can inject source code during compilation, they can obviously add malicious code to the final executable.
But in this particular instance, there would be no added include directories to the compilation process, since the source code is just one file. So, to do anything bad, the attacker would have to be able to screw the compilation (by changing the command line, environment or whatever other means he has to trick or change the compiler). If they can do that, they can also do any number of things that go way beyond simply overriding the search path of include files.
The file inclusion is done at compile time. Presumably, whoever is compiling the code has a good system (otherwise, the possibilities much worse that what you describe: the compiler might be hacked, for example).
Moreover, in this particular instance, the file is included with '#include <stdio.h>' (as opposed to '#include "stdio.h"'), which means the compiler will look for it first in the system include directories (e.g,/usr/include). This means that, if whoever compiles the code is being attacked this way, their system is already compromised.
You're right, I had missed that. The whole article 107 (the one Doctorow quoted) says, among other things:
you can't "change, suppress, modify or disable" any technical device meant to restrict copy
you can't hinder or prevent the uses allowed by the articles that rule fair use (46, 47 and 48) -- this is what Doctorow is pointing at, I think.
item 1 doesn't apply if you're trying to use something in accord to the articles that rule fair use
It's interesting that a lot of the proposed article 46 is already crossed out (but not the part I mentioned earlier about "ensuring its portability or interoperability"). Still, it's unlikely that article 107 will be approved as it stands. If it was, it would render DRM useless, as you say: you can encrypt, but anyone must be able to decrypt the whole thing (to allow fair use). This clearly will not happen, because it would make it illegal to import all sorts of things (DVDs, for example).
I think you're confusing the technical ability to break encryption with its legality. It seems that the new proposed legislation would allow you to legally break the DRM encryption to use something under fair use. It doesn't say that whoever put DRM must tell you how to break it or give you keys.
Besides, I don't see the point of your scheme. According to Article 46, paragraph II of the proposed law, fair use allows you to make a whole copy of a protected work to "ensure its portability or interoperability", so you wouldn't even need a lot of people, you could do the whole thing yourself (say, to encode in a different format).
Interesting comments. I disagree in one (fundamental, I think) point:
The real question is will piracy have a net positive or a net negative effect on the revenue generated by a popular, successful product.
That's the real question from the point of view of the producer of said product. In a more general (more relevant, in my opinion) point of view, the real question is: Will piracy have a net positive effect on society?
You have to remember that copyright is a (relatively new) artificial right that was created to encourage the development of "the useful arts". Product revenue is not the end, just the means to encourage production. So, if piracy's net effect on revenue is negative while having a positive net effect on the "development of the useful arts", in theory it should be encouraged. Of course, if that's the case, the right thing to do would be to change the laws so that (some controlled form of) "piracy" is not a crime anymore.
So far, for an introduction, there's no bad explanation. But it seems they're promising to explain a lot more that is reasonable to expect: are they really planning to go all the way up to relativistic QM without math? If not, why bring up relativity at all?
There's a lot of QM to explain before getting into that: superposition, entanglement, Bell states (to see what's really weird with entanglement), measurement, uncertainty principle, etc. And that's just the foundation, then (based on Lesson 1) it seems they'll explain photons, electrons and maybe other fundamental particles. That's really hard to explain right (and with simple math!) in only 9 lessons. I don't see how you can do that and still squeeze in the relation of QM with relativity.
Slashdot Mirror
No, I agree with you -- there seems to be a lot of hype mixed with misunderstandings in the article.
(But at least these days we don't see the "test all the possibilities and find the right one instantly" nonsense that was very common a few years ago, so I guess that's an improvement :))
Large scale quantum computers could easily factor large numbers thus rendering perhaps all of our current encryption systems obsolete. I have no idea what they would be replaced with but it seems at least possible that anyone who wanted to communicate securely would need to use a quantum computer.
I don't think that it's likely that quantum computers (if built) will be necessary for secure communication. There are cryptosystems (check out McEliece) that can be run relatively fast in classical computers and are based on the difficulty of solving NP-hard problems. Quantum computers would not offer exponential speedups for these kinds of problems (that's not actually proved, but it's even more certain than P!=NP, I think).
So does that mean that some time in the next 50 years, we'll have quantum computers crunching massively paprallel problems, such as decrypting all our previously secure communications, manipulating all the pixels of a video feed in real-time, right off the sensor or even with an entanglement USB peripheral that takes the place of all our networking and communications systems - providing instantaneous point-to-point links between pairs of chips?
I think you're expecting way too much from quantum computing:
In 50 years we'll probably be able to decrypt all our (current) secure communications anyway, with or without quantum computers. Of course, by then we'll be using larger keys (or probably better algorithms that provide better security with smaller keys). And if quantum computers start to become feasible, we can start moving to encryption systems that cannot be broken by quantum computers (the McEliece cryptosystem is one candidate).
About "manipulating all the pixels of a video feed in real-time", I don't think quantum computers would be incredibly useful for that, at least not in the way you seem to expect it. To get a quantum speedup, you must have a very specific algorithm that computes what you want and, at the same time, makes the correct answer come out with high probability. It's certainly not a magic thing that allows you to massively parallelize any algorithm: for search, for example, it's proven that the quantum speedup is at most sqrt(n), and that's not even counting the time it takes to encode whatever data you want to search in the necessary entangled state.
The "instantaneous point-to-point link" is even worse: quantum mechanics can most certainly not transmit information instantly. Entanglement can't be directly used to transmit information; the (theoretical) best you can do is to double the capacity of a classical channel while "spending" entanglement, and that doesn't seem to be terrible useful for your example.
Quantum computers only offer better speeds; a quantum computer can always be simulated by a classical computer. However, storage and run time of the simulation grows exponentially with the size of the quantum computer being simulated, so this is not feasible in practice.
The reverse is also true. A quantum computer (when/if built) will be able to run any classical algorithm, since it's possible to implement a classical NAND gate using quantum gates. It'd be a huge waste, however, to use quantum gates this way.
You're forgetting that the volume is proportional to the cube of the radius, while gravity is proportional to the inverse square of the radius. So, while gravity doesn't increase linearly with mass, it's not constant either:
4x mass -> 4x volume -> 4^(1/3)x radius -> 4/4^(2/3)x gravity
So, gravity would be increased about 1.6 times. You should apologize to him if he weighs 380 pounds, not 500. :)
Here is a way it could possibly not apply.
Your argument seems to be this (please correct me if I'm misrepresenting it):
Take the formal system of the "theory of everything", call it TOE. By Godel's theorem, there exists a certain arithmetic statement (G) that is independent of TOE. Because the universe is Turing complete, it's possible to physically build a Turing machine (M) whose output (or, even better, whether it halts or not) depends on the truth value of G. Since G is undecidable in TOE, the "theory of everything" can't predict what would physically happen if we actually build M in the physical world. So, this means that the "theory of everything" can't actually predict everything.
One possible objection is the following:
When you follow Godel's proof, you notice that the arithmetic statement that the proof constructs involves huge numbers, and that the more axioms you put on your system, the larger the numbers involved must be (if you don't remember just how huge the numbers are, go back and check it: it's mind boggling, even for the relatively simple formal system used by Godel).
That in itself would not be a problem, since we're only talking about the theoretical possibility of the existence of the "theory of everything". But, it turns out that it's possible (and even probable) that our universe is not actually Turing complete because there's a limit to how much computation is possible even in principle. That is, it's possible that the formal system of the "theory of everything" is complex enough that in order to build the Turing machine that would be unpredictable, you'd either have put so much in too little space that it would become a black hole, or you'd have to spread it out so much (in order to prevent the black hole) that the universe expansion would make one end of the Turing machine inaccessible to the other end, and so the machine wouldn't be able to compute anymore.
In case that last point is not too clear, you can find a much better explanation in this lecture (search for "So what does any of this have to do with computation?").
I'm not saying that this is the case, but it's certainly a possibility that has not been ruled out (and maybe it's even true).
It is, for example, possibly that the scalability (given the need for error correction, e.g.) is so bad, that using all what is available still is not enough for a meaningful size. (By meaningful, I mean here performing far better that a conventional computer built with about the same effort.)
OK, but if that's the case, there has to be a reason why scalability is that bad. Shor's algorithm can factor n-bit numbers with ~4n qubits. Laflamme's error correction works by encoding each qubit as 5. So, to factor a 2048-bit number in polynomial time, we "only" need about 40000 qubits. We currently know nothing in nature that prevents us to achieve that in principle.
Sure, designing and building quantum computers is very different (much harder!) than designing and building current computers. That shouldn't be a great surprise, I think. Still, I can't see how that's an argument for saying things like "it will take 100 years" or "maybe it's impossible in principle".
The result I mentioned was done in 2008, not 10 years ago. Hey, 20 years ago we didn't even have Shor's algorithm, so most people doubted that quantum computers could be useful even in theory (and so, there were very few people studying it).
Sure, and if that were indeed true, it would be very exciting for theoretical quantum physics. It would mean that the evolution of a quantum system is not linear, so the Schrodinger's equation is not quite right, and everything after that would have to be changed. It would also probably mean that the state space is not really a Hilbert space, which would have very weird implications that would depend on the geometry of whatever replaced the Hilbert space. The point is, nothing in our current understanding even slightly suggests that. See for instance this.
Sure, and gravity is also a theory, but it would be strange to bet in the 1950's that maybe making something orbit the Earth is impossible, because there may be things we still don't know about gravity (for all we knew, it could have been so). Even Newton's gravity, which is not quite right, is enough to make satellites orbit the earth.
Quantum mechanics seems to work *extremely* well, at least for the energy levels we're trying to make quantum computers work. Quantum Electrodynamics (the part of QM that's has to be right to build a quantum computer) is the most tested theory in human history, its predictions (which of course turned out to be right) are the most accurate ever made, even more than General Relativity.
It's true that it is incomplete -- it says nothing about gravity, and it's not
(...) it is quite possible that quantum computers of meaningful power are fundamentally infeasible in this universe.
That's true, but in order for quantum computers to be fundamentally impossible, there must exist something in the laws of nature that we haven't observed yet. Quantum computers being possible is actually the most boring thing that can happen from the point of view of theoretical physics (i.e., if there are no surprises and what we currently know is pretty much the way things are).
As for a quantum computer not being made of sub-components, I don't quite understand what you mean. From what we currently understand about Quantum Mechanics, it's possible in principle to entangle the spin of, say, 1000 electrons (each spin would count as a qubit). A quantum gate could in principle be implemented by applying a certain magnetic field to individual or small groups of electrons.
This is all in principle, of course. If we ever want to implement a quantum computer, we have to think in more practical terms. There are several schemes proposed (e.g, ion trapping and liquid NMR), but I know almost nothing about them, except that entanglement of 8 atoms has actually been done a few years ago with ion traps.
Why is this modded troll? Anyone who follows the Wii homebrew scene knows Waninkoko has been very disruptive to people who want to write and run homebrew code without having anything to do with piracy.
See also for example this post from another Homebrew Channel developer. And this from marcan (presumably the parent) about how he wrote an USB loader in 6 hours just to show it's no big deal, given everything other people had already done.
What you're describing is a NP-complete problem -- assuming P != BQP != NP. But I'm guessing that you already know that :)
Still, it's still very hard to build a cryptosystem that exploits the hardness of solving NP-complete problems. The main problem is, NP-completeness only guarantees that some instance of the problem is hard, it says nothing about a specific instance. So, for instance, if you have a specific 3-SAT formula, there's no guarantee someone can't come up with a solution for it in polynomial time.
That being said, there are some candidates for a cryptosystem based on NP-completeness. Check for example the McEliece cryptosystem.
I am curious about your claim for "tail call support". Mostly, compilers are smart enough to replace a pure tail call with a simple transfer, and the run-time doesn't have to be aware. If the optimization is contemplated, there cannot be any partial results needed, and this must be maintained through the entire recursive sequence (direct tail call, or through another function). How does the run-time itself assist with this?
I'm guessing that if the transformation (from a tail call to a branch) is done by the compiler, then the generated bytecode loses nice properties used by the checker to ensure it's well formed. If you do it like CLR (with a "tail" modifier to a call), the checker can verify it's a simple method call (and not a branch to some place outside the current method, which might or might not be valid) and then the JIT, seeing the "tail" marker, ensures the proper semantics for the tail call (stack doesn't grow, etc.).
There might be other reasons, like performance: it's very likely that the JIT can do a much better job at optimizing a tail call (when it knows it's a tail call) than optimizing the tail call bytecode generated by the bytecode compiler.
Heh. I meant a spinning top, of course :)
Mod parent up, please (I'd do it if I had mod points).
People talk about "transforming mass into energy" in nuclear reactions, but they almost never say that it's actually much more mundane than that. You don't need nuclear reactions (or even chemical reactions): a sinning top, for example, has more mass than one that's standing still. Here is a somewhat known physicist talking about that, if you don't want to believe a random person on Slashdot.
This question has been considered by quite a few different people; search google for P vs NP independent ("independent" meaning independent from the usual accepted axioms for mathematics, i.e., can't be proven using the currently accepted axioms).
There's a nice survey paper about this question that's very readable if you're willing to invest some time: Is P Versus NP Formally Independent?.
"QP" doesn't mean what you think it means: it actually means "quasi-polynomial time" (basically, worse than polynomial but better than exponential, with nothing to do with "quantum").
I think you mean BQP (bounded-error quantum polynomial time), which is the class that contains Shor's algorithm (the one you mentioned that factors integers in polynomial time).
BQP != NP is actually still unproven (but most people believe it -- if false, quantum computers would be way too powerful). Even BQP != P is unproven (but also mostly believed -- if false, it would render quantum computers largely useless, and would be surprising from what we know about Physics).
As a side note, the direct quantum analog of P is actually EQP (exact quantum polynomial time, i.e., quantum algorithms that run in polynomial time and are right with probability 1). EQP is not known to contain many interesting problems (the only one I know is Deutsch-Jozsa, which is mostly useless), so most quantum algorithms you'll likely hear about are in BQP. BQP is actually the quantum analog of BPP (bounded-error probabilistic polynomial time, which is increasingly believed to be equal to P, especially after "primes in P" -- but there are still problems in BPP that are not known to be in P). BQP, on the other hand, is not largely believed to be equal to EQP.
What did I miss?
Well, apparently, section 2.a:
Your GP said "I like to play video games, windows has more of them", so it seems obvious that he's installing Windows to play games he's not developing, clearly contradicting section 2.a of the license you linked.
The second link you didn't "delve too closely into" makes section 2.a more explicit: it says you can only use the MSDN-licensed software for development (and testing, etc.). No other uses are allowed, like reading email, playing games, etc.
I'm the last person wanting to force a MS contract on someone else, but in this case it seems obvious that your GP is using the MSDN license irregularly (not that it's any of my business). Unless I completely misunderstood what he meant with "I like to play video games, windows has more of them [...]".
That makes it pretty difficult to develop software for an OS if you're not allowed to use the OS.
Indeed.
But that's beside the point. If you want to use the MSDN subscription license, you must follow its rules (as stupid as they might be), or convince MS to change them. Otherwise, just pay for the full license or simply don't use Windows.
Well, if someone can inject source code during compilation, they can obviously add malicious code to the final executable.
But in this particular instance, there would be no added include directories to the compilation process, since the source code is just one file. So, to do anything bad, the attacker would have to be able to screw the compilation (by changing the command line, environment or whatever other means he has to trick or change the compiler). If they can do that, they can also do any number of things that go way beyond simply overriding the search path of include files.
More information, please? According to Wikipedia (referencing a NIST publication from 2007):
and (referencing VISA):
The file inclusion is done at compile time. Presumably, whoever is compiling the code has a good system (otherwise, the possibilities much worse that what you describe: the compiler might be hacked, for example).
Moreover, in this particular instance, the file is included with '#include <stdio.h>' (as opposed to '#include "stdio.h"'), which means the compiler will look for it first in the system include directories (e.g, /usr/include). This means that, if whoever compiles the code is being attacked this way, their system is already compromised.
You're right, I had missed that. The whole article 107 (the one Doctorow quoted) says, among other things:
It's interesting that a lot of the proposed article 46 is already crossed out (but not the part I mentioned earlier about "ensuring its portability or interoperability"). Still, it's unlikely that article 107 will be approved as it stands. If it was, it would render DRM useless, as you say: you can encrypt, but anyone must be able to decrypt the whole thing (to allow fair use). This clearly will not happen, because it would make it illegal to import all sorts of things (DVDs, for example).
I think you're confusing the technical ability to break encryption with its legality. It seems that the new proposed legislation would allow you to legally break the DRM encryption to use something under fair use. It doesn't say that whoever put DRM must tell you how to break it or give you keys.
Besides, I don't see the point of your scheme. According to Article 46, paragraph II of the proposed law, fair use allows you to make a whole copy of a protected work to "ensure its portability or interoperability", so you wouldn't even need a lot of people, you could do the whole thing yourself (say, to encode in a different format).
Interesting comments. I disagree in one (fundamental, I think) point:
The real question is will piracy have a net positive or a net negative effect on the revenue generated by a popular, successful product.
That's the real question from the point of view of the producer of said product. In a more general (more relevant, in my opinion) point of view, the real question is: Will piracy have a net positive effect on society?
You have to remember that copyright is a (relatively new) artificial right that was created to encourage the development of "the useful arts". Product revenue is not the end, just the means to encourage production. So, if piracy's net effect on revenue is negative while having a positive net effect on the "development of the useful arts", in theory it should be encouraged. Of course, if that's the case, the right thing to do would be to change the laws so that (some controlled form of) "piracy" is not a crime anymore.
This already exists.
So far, for an introduction, there's no bad explanation. But it seems they're promising to explain a lot more that is reasonable to expect: are they really planning to go all the way up to relativistic QM without math? If not, why bring up relativity at all?
There's a lot of QM to explain before getting into that: superposition, entanglement, Bell states (to see what's really weird with entanglement), measurement, uncertainty principle, etc. And that's just the foundation, then (based on Lesson 1) it seems they'll explain photons, electrons and maybe other fundamental particles. That's really hard to explain right (and with simple math!) in only 9 lessons. I don't see how you can do that and still squeeze in the relation of QM with relativity.