And you've explained exactly how it's at least a better analogue, if not a good one. Facebook isn't likely to disappear any time soon, so backing up my pictures likely won't even matter, but if it does, I'll be glad I did back up my pictures. (Though, actually, I couldn't care less about mine, so I don't back mine up, but that's not the point.)
That's a terrible analogue, more akin to swapping out your power supply. For a better analogy, it's more like getting your fluids checked regularly: everyone born in the modern age *should* know to do this, but somehow some people manage to miss this lesson.
Their terminology is obviously off, but their intention is clear. During the election the private key is split into chunks that are distributed among different people and they delete (securely, I hope) the pieced together version. Thus, in order to use said private key you (theoretically) either need to make a mathematical breakthrough or get all of those guys to give up their piece. After the election, these guys get together and put the private key back together. Assuming they don't screw up the implementation or leave other glaring holes elsewhere, this is an entirely reasonable scheme.
Your naïveté is cute if you actually think your average voter has done legitimate research. I will grant you that low turnout means only people who care (either about a position or about voting in general will show up, and most of them will have a strong opinion one way or another, but the level of research doesn't tend to be beyond party lines or media favourites.
Did I ever say that Watson was going to be a doctor? So much of modern diagnosis beyond the really common diagnoses is basically doing what Watson does that a doctor armed with a Watson derivative will be far stronger than either a human doctor or Watson alone. He doesn't need to deduce, infer, learn, plan, or resolve; the doctor can do that using the information that Watson can provide, and Watson can provide that information much faster than a human trying to do a lookup, and, since he doesn't need to stop looking as soon as he finds something that kinda fits. We're still many years off from replacing doctors, but Watson will make for an/impressive/ supplement.
You and the anonymous coward are both worng. Considering there is so many version of "japanese", there is a direct way to converting "some" Japanese to roman letter.
Okay, perhaps we are lacking some mutual clarity in what we consider a direct romanisation. If you simply want a mapping from Japanese onto roman characters, then Nippon-shiki will grant that. However, I consider this lacking because, if you follow its pronunciation you will be mispronouncing a lot of things in any dialect I've heard. This is how we run into the Nippon->Japan problem. Hepburn, which would probably be my romaji of choice if I wanted to present to an primarily-English-speaking audience, is actually a pretty good transliteration of pronunciation, but otherwise it's pretty much impossible, and it doesn't really do much of a mapping. This is the dichotomy that I call problematic to declaring a "direct translation": you can have good mapping or good transliteration, but not both. In this manner, there is no direct mapping, but we have agreed on a handful of romaji, chiefly Nippon-shiki and Hepburn, and called them "good enough". But even note here we come up with multiple ways to write the same thing. Now, Arabic script has its romanisations, too, each with their own issues. We've agreed on more than a handful of these, however, and everybody seems to have chosen different ones, hence all of the different ways listed above of writing just one name.
You clearly don't understand what Watson's achieved. Clearly, we don't have much use for a Jeopardy-playing computer, but that was never the real point. The point is we have a system with reasonable natural language processing skills combined with it's lookup/association capabilities and its learning system. this can be repurposed in a number of actually useful applications, and they're starting with the medical field. Something like this could potentially revolutionise medical diagnosis, and that's just the _start_.
The most difficult part, something touched on by the concurrent RPI lectures / commentary, was sorting out the right word from the resulting search context.
Going backwards in time is really easy. The most difficult part, something touched on by science fiction novels, was exceeding the speed of light.
Seriously, that problem is much more difficult than you are making it out to be. Also, the fill-in-the-blank style questions actually used to be a weak point of Watson's that has obviously now become a strong point. I don't remember where I read it, but apparently they chose the questions in the same manner they normally do, less the audio/video questions, so I wouldn't say they are geared toward Watson at all. In fact, I remember at least two categories where Watson didn't provide a single answer!
What controversy? The only person bitching about this "controversy" is you. Originally Watson didn't even have a trigger finger until the Jeopardy guys bitched and insisted it needed one. If they thought that OCR was necessary, they would have bitched about that, too. Otherwise, it's an entirely unnecessary expense in terms of hardware, software, and testing for a problem they're not even trying to solve and all it really does is open up an irrelevant point of failure. Consider this in more scientific terms: they're isolating variables.
Uh, what are you going on about? Watson could only buzz in after he decided on an answer, and it is impossible to buzz in before Alex finishes reading the question (indeed, attempting to do so locks the buzzer out). The humans were basically playing a different game, where they were racing to buzz in first, then figure out the answer, since they were screwed if they gave Watson a chance.
No, we merely needed to see if Watson could answer questions *as well as a human*. The other two players are assumed to know the answer to anything Watson buzzed into first and, for the most part, that's a correct assumption. The competition format was simply publicity for the main challenge of showing that Watson can interpret Jeopardy answers and provide the correct questions, which it did _beautifully_. This was never about fairness, this was about innovation and achievement. Now that it's been proven, this tech is going to be used for actually _useful_ applications.
Actually, Watson got totally owned on "ALSO ON YOUR COMPUTER KEYS". Somebody, please inform me if there's actual information about this (as if I have to say that on/.), but this further cements my belief that Watson doesn't take the category much into consideration. This makes some good sense since misparsing a category that was used as a strong filter could be disastrous, but it did result in some silliness (2003 being a decade, IIRC, Toronto being a U.S. City, chemise being a key, etc). Intuitively, this seemed to be an obvious area for improvement, but I can imagine that the people on the Watson project can spot the obvious at least well as I can given what they've accomplished.
Might I suggest reading the books? Stephen Fry reads them very well if you don't have the time to use your own eyes and they are far superior to the movies.
While I don't agree with most of what GP said, wouldn't everything you said just be a factor of 'costs' that must be considered against the revenues gained from it? Your post reads more or less as "comparing revenue v. cost is short term thinking because you don't take into effect this and that cost" which... doesn't make much sense.
Clever, except that I can name at least four different methods of romaji, each of which have their own deep flaws and a lot of areas where they simply don't agree. This is how we got "Japan" out of "Nippon", after all.
Even if you do select a particular romaji method, you're still without a way to properly translate moras, pitch, and some of the subtly different sounds (like the "r" people so love to make fun of). Which brings us to the GPs point: there is no way to directly translate Japanese, but we have agreed on a handful of systems that we consider "good enough".
Who said I was doing anything more than a rebuke? It is clear that you don't understand the nature of real numbers, nor the nature of infinity. This left me with three choices: Be the one to try to teach you these fundamental concepts, don't comment at all, or take my time to poke some fun. By the way I derided constructionists at the end, I thought it would be clear that I was just being an ass.
Though, if you seriously do want some education, here's a few things to think about:
* 0.999... is not a process. It is simply a number.
* While it is just a number, 0.999... can be constructed from a process. Specifically, \sum_{i=0}^\infty 9/10^i.
* There is no analogous process for producing what you call "0.000..0001", nor does this concept mathematically make sense. The closest concept is lim_{n\rightarrow\infty} 1/10^n, but this is 0, not some mystical 0.000..0001.
The point is, as I've said multiple times already, a number is not a process. This is key to understanding why.999... and 1 are not distinct.
Another important thing to understand is that any numerical representation must have multiple representations for the same number. It is no stranger that.999...=1 than it is that 1 = 1.0 = 1.00...
Finally, one last thought to leave you with: you are proposing a number that would necessarily be the smallest possible positive real number. However, it would immediately follow that the real numbers would be countable, via an obvious bijection with the natural numbers (specifically, your 0.00...001 would match 1, 0.00...002 would be 2, and, in general, you would match n with 0.00...001 * n). However, it's already been proven to death that the real numbers are uncountable. Therefore your number cannot exist.
Honestly, though, when it comes to it, I can prove it rigorously many different ways, most of which you likely don't have the mathematical background for if you still believe.999... != 1, and you're going to continue to trust your intuition, thinking that we must be tricking you or something. Which is why I didn't even bother the first time around.
You're forgetting the second part of this: because NP-completeness proofs have formed a chain of reductions, finding an algorithm for one of them is the last step to finding an algorithm for all NP-complete problems that we have found (and any others we manage to reduce later).
It's actually much less complicated than that. The process you're proposing can't actually be done. Not only that, but 0.999999... is *not* a process; it simply is. I understand that infinity is hard to wrap your head around, but the first thing you need to understand is that there is simply no process here. That's one of the things that really pisses constructionists off, which just means it amuses me more.
And you're wrong in a very obvious way: 0.999.... is every bit as static and stable as 1, even if they were not equal (the same way that 0.333... is static and has a stable meaning). The fact that we are using an infinite number of digits to represent it in decimal does not change this fact. Numbers are not processes. If they were, then in order to cut.333... of a cake I'd need to go 3/10 from my first cut, then 3/100, then 3/1000, etc forever. You can do that if you want, but I''ll just go.333... from the outset and be done with it.
NOTE: Yes, I use a few simplifications and a lot of non-rigorous language. This should still be good enough to give the basic idea to people who don't study complexity.
What other option is there? It's either polynomial (P) or not polynomial (NP), isn't it?
Your first problem: NP does *not* mean "not polynomial" or even anything remotely like that. It means "non-deterministic polynomial time", which essentially means we can verify the answer in polynomial time. All P algorithms are inherently also NP. NP-complete problems, like 3-SAT, are problems such that it is easy (i.e. doable in polynomial time) to turn any other NP problem into them. That's why being able to solve an NP-complete problem in polynomial time means we can solve all NP problems in polynomial time. NP-hard is another class that only partially overlaps NP, and it means that the problem is at least as hard as the hardest problem in NP (i.e. it may or may not be in NP, but it's at least as hard as an NP-complete problem).
Note, there are many, many more complexity classes than just these, also. NP is just the set of yes/no problems that can be verified in polynomial time. One thing you'll note is that integer factorization isn't in NP. Or, more accurately, integer factorization as you usually think about it isn't in NP. The "decision version" (i.e. NP version) of the problem is, essentially, "Is there a non-trivial factor of a given number?" The analogous "function version" is much more what you probably consider to be integer factorization: "Is there a non-trivial factor? If so, give me one." Function problems exist in a different class: FNP, which has FP as the counterpart to P. However, FNP=FP if and only if NP=P.
And, just for your edumacation, a small sampling of other complexity classes:
* PSPACE (doesn't care about time; it's the set of problems that can be solved with polynomial _space_; note that we've already proven that the analogous "NPSPACE" is equivalent to PSPACE; we've also shown that NP is entirely contained within, but not equivalent to PSPACE)
* BQP (similar to P, except with quantum computers and a hint of uncertainty; in particular, it's the set of decision problems solvable on a quantum computer in polynomial time with the kicker that it allows for a limited probability of error; we don't know how this relates to NP, other than that all P problems are BQP)
There are many, many others, covering far more things than you can probably imagine without a background in complexity.
Anyway, that was a bit more teach-y than I had expected, but complexity is one of those topics that I adore too much to pass up such an opportunity.
The #1 reason I avoid pirated software is because more often than not, they contain malware and viruses.
Not that you aren't right to avoid pirated software, but I'd love to see your data on this. As it turns out, the pirate scene is big on reputation and cred, which can only be obtained with quick, clean releases. Anyone spreading malware with their cracks is basically done before they start.
I agree with you almost entirely, but there is a wide difference between "you should at least carefully consider what you are doing" and "we should eliminate all of culture".
Slashdot Mirror
And you've explained exactly how it's at least a better analogue, if not a good one. Facebook isn't likely to disappear any time soon, so backing up my pictures likely won't even matter, but if it does, I'll be glad I did back up my pictures. (Though, actually, I couldn't care less about mine, so I don't back mine up, but that's not the point.)
That's a terrible analogue, more akin to swapping out your power supply. For a better analogy, it's more like getting your fluids checked regularly: everyone born in the modern age *should* know to do this, but somehow some people manage to miss this lesson.
this is how real socialism works
Everybody keeps using that word. I do not think it means what they think it means.
Their terminology is obviously off, but their intention is clear. During the election the private key is split into chunks that are distributed among different people and they delete (securely, I hope) the pieced together version. Thus, in order to use said private key you (theoretically) either need to make a mathematical breakthrough or get all of those guys to give up their piece. After the election, these guys get together and put the private key back together. Assuming they don't screw up the implementation or leave other glaring holes elsewhere, this is an entirely reasonable scheme.
Your naïveté is cute if you actually think your average voter has done legitimate research. I will grant you that low turnout means only people who care (either about a position or about voting in general will show up, and most of them will have a strong opinion one way or another, but the level of research doesn't tend to be beyond party lines or media favourites.
Did I ever say that Watson was going to be a doctor? So much of modern diagnosis beyond the really common diagnoses is basically doing what Watson does that a doctor armed with a Watson derivative will be far stronger than either a human doctor or Watson alone. He doesn't need to deduce, infer, learn, plan, or resolve; the doctor can do that using the information that Watson can provide, and Watson can provide that information much faster than a human trying to do a lookup, and, since he doesn't need to stop looking as soon as he finds something that kinda fits. We're still many years off from replacing doctors, but Watson will make for an /impressive/ supplement.
You and the anonymous coward are both worng. Considering there is so many version of "japanese", there is a direct way to converting "some" Japanese to roman letter.
Okay, perhaps we are lacking some mutual clarity in what we consider a direct romanisation. If you simply want a mapping from Japanese onto roman characters, then Nippon-shiki will grant that. However, I consider this lacking because, if you follow its pronunciation you will be mispronouncing a lot of things in any dialect I've heard. This is how we run into the Nippon->Japan problem. Hepburn, which would probably be my romaji of choice if I wanted to present to an primarily-English-speaking audience, is actually a pretty good transliteration of pronunciation, but otherwise it's pretty much impossible, and it doesn't really do much of a mapping. This is the dichotomy that I call problematic to declaring a "direct translation": you can have good mapping or good transliteration, but not both. In this manner, there is no direct mapping, but we have agreed on a handful of romaji, chiefly Nippon-shiki and Hepburn, and called them "good enough". But even note here we come up with multiple ways to write the same thing. Now, Arabic script has its romanisations, too, each with their own issues. We've agreed on more than a handful of these, however, and everybody seems to have chosen different ones, hence all of the different ways listed above of writing just one name.
You clearly don't understand what Watson's achieved. Clearly, we don't have much use for a Jeopardy-playing computer, but that was never the real point. The point is we have a system with reasonable natural language processing skills combined with it's lookup/association capabilities and its learning system. this can be repurposed in a number of actually useful applications, and they're starting with the medical field. Something like this could potentially revolutionise medical diagnosis, and that's just the _start_.
The most difficult part, something touched on by the concurrent RPI lectures / commentary, was sorting out the right word from the resulting search context.
Going backwards in time is really easy. The most difficult part, something touched on by science fiction novels, was exceeding the speed of light.
Seriously, that problem is much more difficult than you are making it out to be. Also, the fill-in-the-blank style questions actually used to be a weak point of Watson's that has obviously now become a strong point. I don't remember where I read it, but apparently they chose the questions in the same manner they normally do, less the audio/video questions, so I wouldn't say they are geared toward Watson at all. In fact, I remember at least two categories where Watson didn't provide a single answer!
What controversy? The only person bitching about this "controversy" is you. Originally Watson didn't even have a trigger finger until the Jeopardy guys bitched and insisted it needed one. If they thought that OCR was necessary, they would have bitched about that, too. Otherwise, it's an entirely unnecessary expense in terms of hardware, software, and testing for a problem they're not even trying to solve and all it really does is open up an irrelevant point of failure. Consider this in more scientific terms: they're isolating variables.
Uh, what are you going on about? Watson could only buzz in after he decided on an answer, and it is impossible to buzz in before Alex finishes reading the question (indeed, attempting to do so locks the buzzer out). The humans were basically playing a different game, where they were racing to buzz in first, then figure out the answer, since they were screwed if they gave Watson a chance.
No, we merely needed to see if Watson could answer questions *as well as a human*. The other two players are assumed to know the answer to anything Watson buzzed into first and, for the most part, that's a correct assumption. The competition format was simply publicity for the main challenge of showing that Watson can interpret Jeopardy answers and provide the correct questions, which it did _beautifully_. This was never about fairness, this was about innovation and achievement. Now that it's been proven, this tech is going to be used for actually _useful_ applications.
Actually, Watson got totally owned on "ALSO ON YOUR COMPUTER KEYS". Somebody, please inform me if there's actual information about this (as if I have to say that on /.), but this further cements my belief that Watson doesn't take the category much into consideration. This makes some good sense since misparsing a category that was used as a strong filter could be disastrous, but it did result in some silliness (2003 being a decade, IIRC, Toronto being a U.S. City, chemise being a key, etc). Intuitively, this seemed to be an obvious area for improvement, but I can imagine that the people on the Watson project can spot the obvious at least well as I can given what they've accomplished.
Personally, I really liked Watson's voice and I'd be really happy if IBM released his synthesizer. I find it strangely soothing.
Might I suggest reading the books? Stephen Fry reads them very well if you don't have the time to use your own eyes and they are far superior to the movies.
But we're talking about Snape, who is not dead as of the first Deathly Hallows movie.
While I don't agree with most of what GP said, wouldn't everything you said just be a factor of 'costs' that must be considered against the revenues gained from it? Your post reads more or less as "comparing revenue v. cost is short term thinking because you don't take into effect this and that cost" which... doesn't make much sense.
Clever, except that I can name at least four different methods of romaji, each of which have their own deep flaws and a lot of areas where they simply don't agree. This is how we got "Japan" out of "Nippon", after all.
Even if you do select a particular romaji method, you're still without a way to properly translate moras, pitch, and some of the subtly different sounds (like the "r" people so love to make fun of). Which brings us to the GPs point: there is no way to directly translate Japanese, but we have agreed on a handful of systems that we consider "good enough".
Though, if you seriously do want some education, here's a few things to think about:
* 0.999... is not a process. It is simply a number.
* While it is just a number, 0.999... can be constructed from a process. Specifically, \sum_{i=0}^\infty 9/10^i.
* There is no analogous process for producing what you call "0.000..0001", nor does this concept mathematically make sense. The closest concept is lim_{n\rightarrow\infty} 1/10^n, but this is 0, not some mystical 0.000..0001.
The point is, as I've said multiple times already, a number is not a process. This is key to understanding why .999... and 1 are not distinct.
Another important thing to understand is that any numerical representation must have multiple representations for the same number. It is no stranger that .999...=1 than it is that 1 = 1.0 = 1.00...
Finally, one last thought to leave you with: you are proposing a number that would necessarily be the smallest possible positive real number. However, it would immediately follow that the real numbers would be countable, via an obvious bijection with the natural numbers (specifically, your 0.00...001 would match 1, 0.00...002 would be 2, and, in general, you would match n with 0.00...001 * n). However, it's already been proven to death that the real numbers are uncountable. Therefore your number cannot exist.
Honestly, though, when it comes to it, I can prove it rigorously many different ways, most of which you likely don't have the mathematical background for if you still believe .999... != 1, and you're going to continue to trust your intuition, thinking that we must be tricking you or something. Which is why I didn't even bother the first time around.
You're forgetting the second part of this: because NP-completeness proofs have formed a chain of reductions, finding an algorithm for one of them is the last step to finding an algorithm for all NP-complete problems that we have found (and any others we manage to reduce later).
It's actually much less complicated than that. The process you're proposing can't actually be done. Not only that, but 0.999999... is *not* a process; it simply is. I understand that infinity is hard to wrap your head around, but the first thing you need to understand is that there is simply no process here. That's one of the things that really pisses constructionists off, which just means it amuses me more.
And you're wrong in a very obvious way: 0.999.... is every bit as static and stable as 1, even if they were not equal (the same way that 0.333... is static and has a stable meaning). The fact that we are using an infinite number of digits to represent it in decimal does not change this fact. Numbers are not processes. If they were, then in order to cut .333... of a cake I'd need to go 3/10 from my first cut, then 3/100, then 3/1000, etc forever. You can do that if you want, but I''ll just go .333... from the outset and be done with it.
What other option is there? It's either polynomial (P) or not polynomial (NP), isn't it?
Your first problem: NP does *not* mean "not polynomial" or even anything remotely like that. It means "non-deterministic polynomial time", which essentially means we can verify the answer in polynomial time. All P algorithms are inherently also NP. NP-complete problems, like 3-SAT, are problems such that it is easy (i.e. doable in polynomial time) to turn any other NP problem into them. That's why being able to solve an NP-complete problem in polynomial time means we can solve all NP problems in polynomial time. NP-hard is another class that only partially overlaps NP, and it means that the problem is at least as hard as the hardest problem in NP (i.e. it may or may not be in NP, but it's at least as hard as an NP-complete problem).
Note, there are many, many more complexity classes than just these, also. NP is just the set of yes/no problems that can be verified in polynomial time. One thing you'll note is that integer factorization isn't in NP. Or, more accurately, integer factorization as you usually think about it isn't in NP. The "decision version" (i.e. NP version) of the problem is, essentially, "Is there a non-trivial factor of a given number?" The analogous "function version" is much more what you probably consider to be integer factorization: "Is there a non-trivial factor? If so, give me one." Function problems exist in a different class: FNP, which has FP as the counterpart to P. However, FNP=FP if and only if NP=P.
And, just for your edumacation, a small sampling of other complexity classes:
* PSPACE (doesn't care about time; it's the set of problems that can be solved with polynomial _space_; note that we've already proven that the analogous "NPSPACE" is equivalent to PSPACE; we've also shown that NP is entirely contained within, but not equivalent to PSPACE)
* BQP (similar to P, except with quantum computers and a hint of uncertainty; in particular, it's the set of decision problems solvable on a quantum computer in polynomial time with the kicker that it allows for a limited probability of error; we don't know how this relates to NP, other than that all P problems are BQP)
There are many, many others, covering far more things than you can probably imagine without a background in complexity.
Anyway, that was a bit more teach-y than I had expected, but complexity is one of those topics that I adore too much to pass up such an opportunity.
The #1 reason I avoid pirated software is because more often than not, they contain malware and viruses.
Not that you aren't right to avoid pirated software, but I'd love to see your data on this. As it turns out, the pirate scene is big on reputation and cred, which can only be obtained with quick, clean releases. Anyone spreading malware with their cracks is basically done before they start.
I agree with you almost entirely, but there is a wide difference between "you should at least carefully consider what you are doing" and "we should eliminate all of culture".