I know this is slashdot but that is the single most ridiculous analogy I have ever seen in my life. Are you implying in any way that the possibility of P turning out to be same as NP or factorization being in P after all is the same as possibility of dragons existing?
While dragons are not proven to not exist, one can make reasonably good plausibility arguments about their non-existence depending on what characteristics your dragon has, whereas these big questions have no plausibility arguments for settling either way. But that is not even an issue here.
How many times does reality offer you a surprise? Not many I would guess. Mathematicians on the other hand frequently come up with very surprising results. And if you were basing your analogy on the assumption that there is a consensus about the status of these big problems, then you are mistaken.
Ummm.. when you are discussing whether a problem is in NP and/or in coNP you normally have a decision problem in mind. So the problem here is not "What are the prime factors of n?" but rather "Does n have a non-trivial factor less than m?"
By repeatedly asking this question you can eventually get the prime factors of any number.
Of course you can make the decision problem "Does n have a prime factor less than m?" in which case you would indeed need the AKS result, but I believe the former variant is more common since talking about primality of factors (like in the latter variant) only complicates the issue without changing the complexity of factorization (the usual "give me prime factors of n").
...that testing for primality is P. As a result factorization is NP because we can check if a given factorization is correct in polynomial time.
Factorization is in NP irrespective of whether primality testing is in P or not. You can check whether a given factorization is correct or not by simply multiplying the claimed factors. The result you cite proves that factorization is in coNP (the complement of NP).
Let me see: On one hand I have a disease that gives me a rather quick (even though painful) death, and on other I have something that slowly turns me into a vegetable. Tough choice? I think not.
If I was forced to pick one (without a hope for cure once I made my choice) I would pick Ebola any day of the week. Thank you very much.
No. Just that the story caught the fancy of not just your usual slashdotter but our intergalactic overlords too.
(And they are probably pissed because rumor has it that google is thinking of a partnership with virgin galactic and mount a camera on top of the galactic bus. And sure as hell they will ignore all those galactic "no trespassing" signs.)
Also, what's up with that "exposed" in the subject of the story? I don't see any sort of conclusion about the quality of curriculum (good or bad) to justify that sensational title.
The only thing "exposed" here are slashdot editors napping while selecting what "stories" go on the front page!
As a rule of thumb, if you problem requires solving many instances of one simple subproblem which are independent of each other then a gpu helps. A gpu is like a cpu with many many cores where each cpu is not as general purpose as your intel, rather each core is optimized for some solving small problem (without optimizing for frequent load/store/switching operations etc that a general cpu can handle quite well).
So if you see an easy parallelization of your problem, you might think of using a gpu. There are problems that are believed to not be efficiently parallelizable (Linear Programming is one such problem). Also, even if your problem can be easily made parallel it might be tricky to benefit from a gpu as each subroutines might be too complex.
I don't program but my guess would be that if you can see the solution to your problem consisting of a few lines of codes running on many processors and gaining anything, a gpu might be the way to go.
It's too bad the article that Yahoo! had failed to mention that he got to spend a day with the Pittsburgh Steelers and their wide receiver, Hines Ward. While he didn't actually play in the NFL, I imagine he came as close as he was going to get.
Which article are you talking about? The linked article on abcnews.go.com does mention this on the last page. From TFA:
But even though he had enabled the dreams of so many others, we couldn't help but notice that there was one dream Pausch had never been able to fulfill -- playing in the NFL.
So ABC News made a couple of phone calls, and in October, Pausch took the field with the Pittsburgh Steelers. He was wearing the jersey of his favorite player: wide receiver Heinz Ward.
Moments later he was catching balls thrown by Ward.
He caught every pass -- and even kicked a field goal, on his first attempt.
If you follow the link in the story, you would see that the poster claims the following:
1) Foxconn advertises its motherboard as ACPI compliant thus potentially misleading people into thinking that linux should be able to handle the board. The company does nothing to counter such possible misunderstandings. One could argue that Foxconn is not obliged to do anything of that sort but for customers it is not as simple as "doing homework" as you suggest. Foxconn doesn't say that things break on linux. They only say "works with windows" and "ACPI compliant". The only way to check is to buy and use (at least until this story).
2) The BIOS actively looks for the OS and passes a modified table to linux. It does not even ask the OS to identify itself and go along with that identification. It rather keeps on having random checks to ensure it is running on windows. I can't think of any good reason why they need to do that unless they want to actively break things for linux.
3) The poster smells something fishy in Foxconn's behavior. Right or wrong, I don't know. But if the poster is right in his suspicion (which s/he must believe), it would be a natural, rational and justified behavior to bitch and moan about it rather than just return the board for a refund. Society owes a lot to such "troublemakers".
Well, in my case even disabling the network adapter altogether didn't change a thing. Hangs with a different network adapter type, hangs with no network adapter.
Just to verify, the same virtual machine (with the same configuration) has DesktopBSD (another FreeBSD variant) already installed, and that boots up just fine. Even though the network in DesktopBSD doesn't work, it at least boots up without hanging. No such luck with DragonFly.
Did anyone manage to get the live cd work on VirtualBox? On my Ubuntu box it seems to hang once I get to the screen with various options of booting DragonFly.:|
But with your data encrypted, why do you need to trust anyone? For you it is the state of your browser, passwords etc, but for anyone else it is random bits.
Doesn't Browser sync already supports encrypting your data? Even if it doesn't I am sure this capability can be added now that it is open-source.
Perhaps what the OP meant was that as producing corn becomes more profitable, farmers will switch to producing corn instead of other crops, thus creating a scarcity of *those* grains and raising the price of food in general. A big chunk of world already finds it hard to afford food and hence the conclusion of people starving if prices rose further.
For the longest time I thought this was psychological, but I've played both kinds of violins to friends and family with no music knowledge, and almost always, people say that the older violin just sounds richer.
Perhaps you should try a double-blind experiment? I am not saying that claim is wrong, just that a single-blind experiment like yours still leaves room for psychological bias. Maybe *you* played it better when you knew you were playing a "better" instrument?:-)
The Continuum Hypothesis is known to be neither provable nor disprovable in the standard axiomatic set theory ZF, enriched with the axiom of choice (ZFC). So I wouldn't really count on someone settling that one either way any time soon. Of course one could come up with a new set of axioms for the set theory and *then* prove or disprove CH but you would be hardpressed to find anyone showing interest in that result. After all, I could just add CH or not(CH) to ZFC and trivially prove or disprove it. So anything in that line first needs to even define what a sensible problem is.
For those who have no clue what I said above:
Continuum hypothesis: There is no set strictly larger than the set of natural numbers and at the same time strictly smaller than the set of real numbers. The size of a set in relation to other is defined in terms of mapping. Positive integers are the same number as even numbers because you can define a bijection between the two. Reals are strictly more than naturals.
ZF: Set theory made axiomatic. Few axioms (like empty set exists, supersets are larger than original sets etc) that you need to believe and most of the set theory believed to follow.
Axiom of Choice: Given a set of sets, one can make a set containing one element from each set. Looks obviously true but in some equivalent but different sounding formulations looks obviously false. Known to be independent to ZF.
Y Independent to axioms X: Believing that Y is true does not yield contradiction together with X unless X itself yield contradictions. Same holds for believing that Y is false.
PS: Apologies for not including links. I am feeling lazy. Wikipedia has nice articles about all of the above. Articles on ZF, CH or Axiom of Choice are the place to start for a fun reading.
Free markets require perfect knowledge. And without that, the invisible hand doesn't work.
I suppose getting everyone to acquire perfect knowledge is going to be pretty tough. So my interpretation of your post is that as an anarchist you propose that somebody should regulate the market. Is that right? I couldn't agree more.
We will need some of us anarchists to join hands and form a regulatory board or such. Naturally the board would not be able to regulate anything unless it can regulate itself and so we will need some sort of hierarchy. Also, the board would need a mandate to regulate anything at all, let alone the market. So we could maybe try to get other people (who are not in the board) to consent to our plan. We could either buy guns and make them agree or we could ask them to pick their favorite among a bunch of us anarchist that are going to be the members of the regulatory body. Either way, it is going to work out easily.
Every sunday we could burn books to emphasize that we are anarchists, so that no one confuses our regulatory board with dictatorship or democracy (depending on how we got the mandate). You know, symbolism and all that!
Slashdot Mirror
I know this is slashdot but that is the single most ridiculous analogy I have ever seen in my life. Are you implying in any way that the possibility of P turning out to be same as NP or factorization being in P after all is the same as possibility of dragons existing?
While dragons are not proven to not exist, one can make reasonably good plausibility arguments about their non-existence depending on what characteristics your dragon has, whereas these big questions have no plausibility arguments for settling either way. But that is not even an issue here.
How many times does reality offer you a surprise? Not many I would guess. Mathematicians on the other hand frequently come up with very surprising results. And if you were basing your analogy on the assumption that there is a consensus about the status of these big problems, then you are mistaken.
Ummm.. when you are discussing whether a problem is in NP and/or in coNP you normally have a decision problem in mind. So the problem here is not "What are the prime factors of n?" but rather "Does n have a non-trivial factor less than m?"
By repeatedly asking this question you can eventually get the prime factors of any number.
Of course you can make the decision problem "Does n have a prime factor less than m?" in which case you would indeed need the AKS result, but I believe the former variant is more common since talking about primality of factors (like in the latter variant) only complicates the issue without changing the complexity of factorization (the usual "give me prime factors of n").
...that testing for primality is P. As a result factorization is NP because we can check if a given factorization is correct in polynomial time.
Factorization is in NP irrespective of whether primality testing is in P or not. You can check whether a given factorization is correct or not by simply multiplying the claimed factors. The result you cite proves that factorization is in coNP (the complement of NP).
Let me see: On one hand I have a disease that gives me a rather quick (even though painful) death, and on other I have something that slowly turns me into a vegetable. Tough choice? I think not.
If I was forced to pick one (without a hope for cure once I made my choice) I would pick Ebola any day of the week. Thank you very much.
I would have given you the answer, but I suppose you would rather that I speak axiomatic set theory or such.
No. Just that the story caught the fancy of not just your usual slashdotter but our intergalactic overlords too.
(And they are probably pissed because rumor has it that google is thinking of a partnership with virgin galactic and mount a camera on top of the galactic bus. And sure as hell they will ignore all those galactic "no trespassing" signs.)
forbidden fruit probably?
1. Create $x
2. Make everyone think that $x is the best thing since sliced bread. (by making it secret)
3. ???
4. Profit
Also, what's up with that "exposed" in the subject of the story? I don't see any sort of conclusion about the quality of curriculum (good or bad) to justify that sensational title.
The only thing "exposed" here are slashdot editors napping while selecting what "stories" go on the front page!
Not really. Not every problem gains from a gpu.
As a rule of thumb, if you problem requires solving many instances of one simple subproblem which are independent of each other then a gpu helps. A gpu is like a cpu with many many cores where each cpu is not as general purpose as your intel, rather each core is optimized for some solving small problem (without optimizing for frequent load/store/switching operations etc that a general cpu can handle quite well).
So if you see an easy parallelization of your problem, you might think of using a gpu. There are problems that are believed to not be efficiently parallelizable (Linear Programming is one such problem). Also, even if your problem can be easily made parallel it might be tricky to benefit from a gpu as each subroutines might be too complex.
I don't program but my guess would be that if you can see the solution to your problem consisting of a few lines of codes running on many processors and gaining anything, a gpu might be the way to go.
Perhaps someone can explain it better.
It's too bad the article that Yahoo! had failed to mention that he got to spend a day with the Pittsburgh Steelers and their wide receiver, Hines Ward. While he didn't actually play in the NFL, I imagine he came as close as he was going to get.
Which article are you talking about? The linked article on abcnews.go.com does mention this on the last page. From TFA:
But even though he had enabled the dreams of so many others, we couldn't help but notice that there was one dream Pausch had never been able to fulfill -- playing in the NFL.
So ABC News made a couple of phone calls, and in October, Pausch took the field with the Pittsburgh Steelers. He was wearing the jersey of his favorite player: wide receiver Heinz Ward.
Moments later he was catching balls thrown by Ward.
He caught every pass -- and even kicked a field goal, on his first attempt.
If you follow the link in the story, you would see that the poster claims the following:
1) Foxconn advertises its motherboard as ACPI compliant thus potentially misleading people into thinking that linux should be able to handle the board. The company does nothing to counter such possible misunderstandings. One could argue that Foxconn is not obliged to do anything of that sort but for customers it is not as simple as "doing homework" as you suggest. Foxconn doesn't say that things break on linux. They only say "works with windows" and "ACPI compliant". The only way to check is to buy and use (at least until this story).
2) The BIOS actively looks for the OS and passes a modified table to linux. It does not even ask the OS to identify itself and go along with that identification. It rather keeps on having random checks to ensure it is running on windows. I can't think of any good reason why they need to do that unless they want to actively break things for linux.
3) The poster smells something fishy in Foxconn's behavior. Right or wrong, I don't know. But if the poster is right in his suspicion (which s/he must believe), it would be a natural, rational and justified behavior to bitch and moan about it rather than just return the board for a refund. Society owes a lot to such "troublemakers".
I was about to call you a grammar nazi, but then I thought that maybe you prefer being called a semantics nazi.
Well, in my case even disabling the network adapter altogether didn't change a thing. Hangs with a different network adapter type, hangs with no network adapter.
Just to verify, the same virtual machine (with the same configuration) has DesktopBSD (another FreeBSD variant) already installed, and that boots up just fine. Even though the network in DesktopBSD doesn't work, it at least boots up without hanging. No such luck with DragonFly.
Did anyone manage to get the live cd work on VirtualBox? On my Ubuntu box it seems to hang once I get to the screen with various options of booting DragonFly. :|
Can you please tell me know to moderate the summary (-1, binspam)?
Yes.
Shouldn't the subject of your post be: "English may once have had grammar" or "English may have had grammar once"?
But with your data encrypted, why do you need to trust anyone? For you it is the state of your browser, passwords etc, but for anyone else it is random bits.
Doesn't Browser sync already supports encrypting your data? Even if it doesn't I am sure this capability can be added now that it is open-source.
It does cost more than Vista. Just that all us commies are unwilling to admit that McBride owns all of linux!!
Perhaps what the OP meant was that as producing corn becomes more profitable, farmers will switch to producing corn instead of other crops, thus creating a scarcity of *those* grains and raising the price of food in general. A big chunk of world already finds it hard to afford food and hence the conclusion of people starving if prices rose further.
Dupe too
For the longest time I thought this was psychological, but I've played both kinds of violins to friends and family with no music knowledge, and almost always, people say that the older violin just sounds richer.
Perhaps you should try a double-blind experiment? I am not saying that claim is wrong, just that a single-blind experiment like yours still leaves room for psychological bias. Maybe *you* played it better when you knew you were playing a "better" instrument? :-)
The Continuum Hypothesis is known to be neither provable nor disprovable in the standard axiomatic set theory ZF, enriched with the axiom of choice (ZFC). So I wouldn't really count on someone settling that one either way any time soon. Of course one could come up with a new set of axioms for the set theory and *then* prove or disprove CH but you would be hardpressed to find anyone showing interest in that result. After all, I could just add CH or not(CH) to ZFC and trivially prove or disprove it. So anything in that line first needs to even define what a sensible problem is.
For those who have no clue what I said above:
Continuum hypothesis: There is no set strictly larger than the set of natural numbers and at the same time strictly smaller than the set of real numbers. The size of a set in relation to other is defined in terms of mapping. Positive integers are the same number as even numbers because you can define a bijection between the two. Reals are strictly more than naturals.
ZF: Set theory made axiomatic. Few axioms (like empty set exists, supersets are larger than original sets etc) that you need to believe and most of the set theory believed to follow.
Axiom of Choice: Given a set of sets, one can make a set containing one element from each set. Looks obviously true but in some equivalent but different sounding formulations looks obviously false. Known to be independent to ZF.
Y Independent to axioms X: Believing that Y is true does not yield contradiction together with X unless X itself yield contradictions. Same holds for believing that Y is false.
PS: Apologies for not including links. I am feeling lazy. Wikipedia has nice articles about all of the above. Articles on ZF, CH or Axiom of Choice are the place to start for a fun reading.
Free markets require perfect knowledge. And without that, the invisible hand doesn't work.
I suppose getting everyone to acquire perfect knowledge is going to be pretty tough. So my interpretation of your post is that as an anarchist you propose that somebody should regulate the market. Is that right? I couldn't agree more.
We will need some of us anarchists to join hands and form a regulatory board or such. Naturally the board would not be able to regulate anything unless it can regulate itself and so we will need some sort of hierarchy. Also, the board would need a mandate to regulate anything at all, let alone the market. So we could maybe try to get other people (who are not in the board) to consent to our plan. We could either buy guns and make them agree or we could ask them to pick their favorite among a bunch of us anarchist that are going to be the members of the regulatory body. Either way, it is going to work out easily.
Every sunday we could burn books to emphasize that we are anarchists, so that no one confuses our regulatory board with dictatorship or democracy (depending on how we got the mandate). You know, symbolism and all that!
You can try eating a tonne of cyanide today. I am sure you won't be putting on any weight.