Really? Well, I guess my English friends inadequately explained to me how the system worked when I lived over there. They had told me that a proportional representation scheme was how someone from the racist, nationalist party (whose name escapes me) had won a seat in parliament. The fact that he actually won a plurality of the votes somewhere scares me.
Re:is there any other way to prevent crowd dispers
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Revisiting DIY HERF Guns
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If you truly believe that the two parties are roughly equivalent and that both candidates are equally bad for the job, then, at least in Britain, you aren't throwing your vote away by choosing a third party candidate. No, you're not going to win the entire government, but you will end up with at least some representation. In the U.S., if a national third party were to get 25% of the vote in a years worth of Senate races, spread out roughly equally all across the country, absolutely nothing would come of it. If that happened in England, the third party would have a decent representation in parliament. So while it is very difficult in England for a third party to gain significant power, it is absolutely impossible in America (unless winning the presidency but having no support in congress counts as significant power, which would require a well funded, well connected, and charasmatic candidate, in addition to miraculous circumstances).
Why do you feel that anecdotal evidence has no value at all? Without anecdotal evidence, we wouldn't have theories to try to prove/disprove with real data. And while anecdotes can record statistically improbable events (with no way of discerning that the results are improbable), they do, at the very least, show what is possible. Additionally, for things you know nothing about, anecdotal evidence can be a useful way to form your initial opinions. Furthermore, for things that aren't scientific in nature (e.g., is the movie/restaurant any good?) anecdotal evidence can be invaluable.
While I am sure that many of the claims of chiropractors are bunk, I am also confident that the basic claims have at least some merit (realigning your back can relieve back pain but cannot cure ear infections or cancer). I accept or reject anecdotal evidence according to my own personal biases, so I agree that anecdotes are of little use for changing my opinions, but to say that anecdotal evidence has no particular value is dangerous. In fact, a friend of mine spoke out against anecdotal evidence, and then he died of cancer.
The people who argue that viruses aren't alive are almost inevitably non-biologists or biologists who don't work with viruses.
And the people who argue that HTML isn't computer code aren't web designers. And the people who argue that slashdot isn't interesting aren't slashdot readers. Ok, well, maybe not on the second point, but of course people who work with viruses are going to view their work differently than others will. It makes it sound better from the outside if they could convince people that viruses are alive. I bet you could find robot designers who would try to argue that their creations are alive too. As long as we insist on using vague human languages which have definitions that break down in corner cases (What is alive? Red? Funny?), we're going to have disagreements like this. In the end, it doesn't matter except for people's egos.
Well, I'm not exactly sure what you mean by "for profit", but there is a lot more than just the lectures that goes on at decent universities, and it doesn't come cheap.
Universities (which, for the sake of this discussion, are places where there are graduate studies and research being done, which we contrast with colleges, where there is just teaching and undergraduates) have several costs. Labs are expensive. And I don't mean the labs that students practice using pipettes in. The places where basic research occurs need equipment. And they don't run themselves. While grad students can do some of the work (and can be payed relatively cheaply), you need actual research level scientists too. They get paid less than they would in an industrial job, AND they have to teach. If you cut their budgets too much, they can't do their work, and if you cut their salaries too much, they would do much better to abandon ship. And while some of the money comes from tuition, a lot comes from both public and private sources who either have interests in education or interests in the research.
The upshot of this is that we are taught by experienced practitioners in our field of interest who have not only experience and perspective, but also keen insight into how the state of the art is changing.
Additionally, these people can offer unique guidance to those students who have true potential. They can help them get involved with ongoing research. They can guide them towards graduate level classes. Of course, talking about education for the best and the brightest might be completely antithetical to this discussion.
But given the number of people who go to college because it gives them better job prospects, is it that wrong that people pay to invest in their future?
Of course, my perspective here is from that of the sciences. I don't appreciate the benefit of being taught English by a professional literary critic or what benefit a university would offer a liberal arts student over a college. It also doesn't apply to people who are only going to college to party or to broaden their mind in an intangible sense. However, for the sciences or engineering disciplines*, it does seem reasonable that getting the education that we want requires money.
*And I'm not counting basic IT or programming in this. Computer science, yes. Something where an MSCE might matter? No.
I once had a conversation with a department head at Caltech who told me that, thanks to their endowments, they could easily afford to charge a much smaller tuition, and that like 70% of their students were given fairly good financial packages, but if they lowered their base price and charged less than other universities, people would assume that they were of lesser quality. Since the value of a degree (not of an education) is in how other people view it, cutting their prices would be a great detriment to their graduates.
As long as the system is in place, and as long as there are more people who want to go to good schools than those schools can accommodate, it is in their best interests to keep their sticker prices high. They only have reason to show you the price you will pay if nobody is considering them because they are too expensive.
Of course you have to allow people to say things you disagree with to be able to call it free speech. But we don't allow people to shout "Fire!" in a crowded theater when there is none, and threats of bodily harm can construe assault. It is clear that society appreciates that speech has power and consequences, and the question is, where do we draw the line on what should be allowed in the name of free speech versus what should be disallowed for the sake of a calm and peaceable society?
Should we allow to call for the assassination of abortion doctors? What about when the people who listen to them actually commit murder? Should there be culpability?
What about verbal bullying? If someone kills themselves because you repeatedly put them down, do you not bear some responsibility, even if you didn't pull the trigger?
Of course, in both these cases, the blame can't be placed entirely with the speaker, as others had to decide what to do with the words (nor should placing any blame on the speaker be seen as a lessening of the blame on the actor), but when words have a direct impact on whether someone lives or dies, I don't think it is as easy to dismiss them as just words. Of course, it is much harder to judge intent of words, it is harder to judge what the reasonable expectation of the consequences of words should be, and it may well be that there is no way to prosecute this kind of speech without creating a system that is rife for abuse and which undesirably suppresses other kinds of free speech, but the issue isn't so clear cut that it can be put to rest by a few choice quotes.
An iPhone may not be a necessity, but if you ALREADY HAVE ONE and you drop AT&T as your carrier, you are essentially throwing away money and converting it to an iPod. If this was about what carrier to choose if you were just starting out, or if smart phones didn't exist and all cell phones were roughly equivalent, you might have a point. As it stands, I honestly have no clue how what you are saying is relevant.
Maybe there are other phone companies, but I'm pretty sure that horribly unfair contracts are the norm (with terms like required arbitration and that the terms of the contract can be changed at any time without notice). Additionally, without jail breaking (which might be undone the next software upgrade), you can't switch if you are an iPhone user. To say "just use someone else, competition solves everything" is a bit glib and shortsighted, if not downright disingenuous.
Why do people think that CO2 = bad? There is a natural carbon cycle. CO2 goes into the air, plants breath it in and breath out O2 while turning the carbon into sugar. Animals eat the plants (and other animals) and use the bonds in molecules containing carbon as a storage for energy. As they use the energy, the carbon goes back into the atmosphere. When things are in relative equilibrium, everything is fine.
The problem with fossil fuels is that there used to be a lot more carbon in the atmosphere, which was absorbed by plants which died and took the carbon with them. When we burn fossil fuels, we are re-releasing this carbon into the atmosphere, changing the balance of things. Except for deforestation and burning of fossil fuels, most other CO2 related activities don't actually change the overall amount of carbon in play. There is no need to be alarmist about this.
First, the distribution of the primes is not an observation, it's a proven mathematical fact that took many smart people a long time to fully establish.
Second, knowing the distribution of the primes has direct applications to things like the security of encryption methods (if large primes were significantly more sparse than they are, then factoring numbers which are the product of two large primes would be much easier than it is).
But the difference in the distribution of the primes versus the distribution of their leading digits is akin to a shoe manufacturer knowing how many shoes of each size to make versus a shoe manufacturer knowing the distribution of the third digit of the number of atoms in the human foot. Yes, they are both observations of a sort, but only one of them has useful information.
Actually, the result is more that the prime numbers don't obey Benford's law, but obey a generalized version of it having to do with the specifics of the distribution of prime numbers. However, a list of numbers doesn't have to be random to obey Benford's law.
The reason the discovery isn't useful is because, while there is use in knowing the distribution of the primes, there is little use in knowing the probabilities of the leading digits of primes. The only application I could think of is if someone gave you a list that they claimed to be all the primes up to 10^100, and you wanted a quick sanity check on whether it might be it. Of course, adding 1 to every number would make nothing (but 2) prime and change almost none of the leading digits.
But in any case, since numbers on income tax statements or stock prices are not required to be prime numbers, and since the leading digit of a number has very little mathematical use, there is little in terms of applications of this observation, mathematical or otherwise.
Companies seem to think that the IT dept is the most expendable for some reason.
You say this as if it is a mystery why a company would feel this way. But regardless of whether IT is as expendable as some companies may treat it, I think it is important to understand why things are the way they are.
To any large company, there are essentially two parts. First, there is the part of the company devoted to whatever the company sells. This will include engineering and design, product, sales and marketing, and perhaps some portion of management.
On there other side, there is the part of the company that is there so that the company runs smoothly. This is the part of the company that is there to facilitate and support the first part of the company. IT is in this group (in a non-IT company), as are janitorial staff, a certain other amount of management, and other random departments which might vary from company to company.
There is, of course, some overlap between the two sides. For example, while you might consider the running of the website an IT role, it is also essential to sales. Still, viewing a company as having the two sides is helpful for understanding why companies see IT the way they do.
When money is tight, and a person needs to decide where to cut money, they cut the things they deem less important to their survival. They can refuse to buy a new stereo or new underwear, but they can't refuse to buy any more food.
Similarly, when money is tight and a company needs to decide what to cut, they get rid of what they deem to be the least important to their survival. From upper management's point of view, they see what the impact of laying off staff in their core business will be, and will be less likely to view management as just support. However, it is harder for them to see why they can't just halve their IT staff or janitorial staff. Maybe the floors will get vacuumed less often or it will take slightly longer to deploy Windows 7, but the company will still do what it does roughly as well as it currently does, right? (That is not to say that IT isn't crucial to a company's success, just that it is much harder for upper management to appreciate the relative worth of IT staff).
It's much harder to appreciate exactly how expendable support staff is, but it isn't that hard to see why management would view support staff as more expendable than others.
Benford's law works by the observation that, when numbers come up in certain real world contexts, the fluctuations you get in numbers should be proportional to the numbers themselves. Phrased differently, variations tend to be relative, not absolute. Because of this, if you have a very large range of random numbers from many real world measurements, then you would expect the number between t and t*(1.0001) not to vary too much for small changes in t. Let us try to use this observation very coarsely. Among the numbers with 6 digits, the number that look like 1xxxxxx (those between 100000 and 200000) should be about the same the number between 200000 and 400000. The same thing happens with the numbers with 5 digits or 7 digits or n digits (assuming that you have a wide range of random numbers, and the numbers are the kind that come from certain sorts of real world measurements). Additionally, you can get distributions for the first two digits, the first three digits, etc.
This observation doesn't depend on the base that you're working with.
Now, with the prime numbers, they have a distribution that is different from a lot of real world measurement data. The number of primes between n and n+d is approximately d/ln(n), where ln is the log with base e and d is small compared to n. So the number of primes between 500000 and 600000 is about 100000/ln(500000), and the number of primes between 500000 and 600000 is about 100000/ln(600000). By using this, and being slightly more careful, one can determine fairly easily the distribution of the leading terms of the prime numbers.
This is not a hard result. I would say that any professional mathematician who knew about the basic distribution of the primes could derive the distribution of the leading digis of the prime numbers fairly easily if anybody actually asked them to. The reason nobody mentioned this before is that nobody actually cares. While Benford's law does have applications to fraud detection, this new result does not. It's one of those things that makes people say "ooh, a pattern!" but which is just an easy and somewhat mundane corollary to a well known theorem.
Yes, it is conceivable that standing up to Amazon will cause them to back down. They might feel that this is a fight they won't win and that isn't worth the bad press. Then again, they might not. Best case scenario is that the site owner (who might just be running the site as a hobby, and who may currently be in a less than stellar financial situation) spends a few hundred dollars and kills his relationship with Amazon, which he might view as important given the content of the website. Still, no legal precedent is set.
Worst case scenario is that Amazon views this as a legitimate matter that is too important to drop, it goes to trial, he is out thousands of dollars and a lot of time, and even if he wins, he has still lost. Additionally, I think you far overestimate how much publicity this will get. Odds are good that, even if the mainstream media picks up the story, it will only be a brief blurb. Most people who hear it won't care, and many who do will go, "Oh wow, that's a nice ebook reader!" While slashdot probably has a higher percentage of people would would buy portable ebook readers than in the general public, a boycott by all slashdot/digg/reddit/etc readers would still probably not persuade amazon to stop, if they are that concerned about piracy and the device really is a loss leader.
I would love to see him fight and win. I hate bullies, I hate people who abuse the system, and I feel that one should be able to use hardware however one sees fit. However, I honestly cannot fault him for choosing not to fight. If you want to teach them a lesson, go ahead and pick a fight. But remember, not everybody has the luxury of being able to stand on their principles (and even fewer still have the luxury of standing on yours).
Just because you run and hide from a pack of wolves doesn't mean you are a sheep. While you might wish them to martyr themselves for your principles, if they don't have the resources to fight, or if a win would not accomplish anything for anybody else, why shouldn't they act in their own best interests?
Yes, and no. While copyright is a right to control as opposed to a right to profit, it is also supposed to be a limited monopoly which gives creators an incentive to create before turning their creation over to the public domain. The question that must be asked is, "What is the purpose of allowing this control, and under what circumstances is it ethical to ignore a valid copyright?"
To my understanding, there are three fundamental rights (beyond the pragmatic benefits) which justify the existence of copyright: 1) The right to attempt to benefit from one's work 2) The right to not have others unfairly benefit from one's work 3) The right not to suffer from a misappropriation of one's work. (e.g., if someone is making shoddy knockoffs of your creation and attributing it to you, or if someone takes and shares a work that you did not want to publish because you felt it was sub par.)
If a book is no longer in print, it is reasonable to assume that the first right has been exercised. To proceed ethically, one must make sure not to violate the other rights. Buying or selling pirated copies of the book would be in violation, but merely obtaining a pirated copy for personal use would not. Redistributing the pirated copy without charging for it may be viewed as a violation, but merely using the book would not.
To be ethical with piracy, one must understand the spirit of the law. Copyright is a simple codification of an agreement between creators and the public. If the spirit of the agreement is upheld, the rest is just details.
According to an econ professor I had, those groups of "intelligent" people who think that the tax rate is higher than the optimal value are not economists. He also said that it is generally accepted that the optimal rate is probably somewhere between 60% and 80% for the United States.
The Laffer curve is an interesting economic idea, but it has only really been used as a poor political idea. Additionally, since there is so much more that goes into the health of a country than just government revenues, the Laffer curve is only a reasonable thing to be looking at when the tax rate is higher than optimal, and it is only reasonable then in the sense that you couldn't have optimized the correct thing if you are too far to the right on the Laffer curve.
You are right that it is not inherently idiotic to imagine how tax cuts could increase revenue (if people were actively saying, "What's the point of working hard? The government is just going to take it. Therefore, I won't try to work."), but the problems with the Laffer curve are manifold, and its misapplication by policy makers against the recommendations of economists only goes to show that, in a democracy, the people get the government that they deserve.
I recommend "Mathematical Methods of Classical Mechanics" by V.I. Arnold for the classical mechanics side of things. I am not sure what to read for general relativity. The bit that I know I learned from "Semi-Riemannian Geometry" by Barret O'neil, but I don't feel that the book is a good place to learn general relativity unless you already have a very strong background in differential geometry. I hope this helps.
"Now, what's the difference between an invisible, incorporeal, floating dragon who spits heatless fire and no dragon at all?"
I don't know. What's the difference between a universe full of other races that we've never heard from and a universe inhabited solely by us.
While I suspect that this is a troll, and while there is a quick one sentence response (God can never be proven or disproven, but if there is intelligent life out there, we have a chance of finding it) I'll bite.
The difference of what we currently know in the two universes is small, but the difference between what we could realistically know is huge. Given that life evolved on earth to the point that intergalactic travel seems like a real future possibility, and given the vastly huge number of solar systems, it stands to reason that there is a decent chance that we aren't alone in the universe and that if there are others out there like us, they have the potential to meet us. If such a meeting did occur, it could have amazing consequences.
Now, if you contrast that with the dragon situation, the dragon is by definition unknowable. There is no way he could ever have an impact on our daily lives. In fact, even if we knew for sure that he existed, the only way that would possibly affect our lives is if we chose to devote time and thought to the dragon.
There is a difference between what there is no evidence for and what there is no direct evidence for, and there is a difference between what we can never show and what we have not yet shown. I mean, until we had particle colliders, we didn't have any evidence for quarks, but we had reason to look for them, and after we had particle colliders we had an idea of how to use experimental data to determine indirectly if quarks existed. With the dragon, there is no conceivable experiment that could be done to determine if the dragon existed.
While SETI is more like anthropology than science (as there is no falsifiable premise that they are working with), it is not like god or the dragon (as there is at least a verifiable premise they are working with). When you go into the realm of what can neither be proved nor disproved, you have left the realm of science and reality. There is use in life for things beyond science, such as art, imagination, and even faith. However, it is sad when one cannot tell the difference between the realms.
If I'm not mistaken, this is a large part of why Sun has both open office and star office. If you ignore the issue of support (which could be purchased separately from OO.o), businesses were skeptical of a product that was just being given away, and so they added a few minor proprietary things (clip art, etc) and slapped a price tag on it to make it more appealing to businesses. Kinda funny, actually.
The joy of being a mathematician is that I got to have this debate with a few of my friends a week ago.
Quite frankly, I am torn. On one hand, wikipedia is supposed to be an encyclopedia, and this is not the kind of thing that would generally make it in an encyclopedia. Even though wikipedia doesn't have the space concerns that regular encyclopedias have, there are issues of aesthetics and flow, as well as not cluttering up what the user wants to find with too much noise (which many proofs will be to many people).
On the other hand, there isn't an a priori reason why wikipedia should be bound by any of the limitations of a regular encyclopedia, and most of the problems mentioned above can be solved by creating appendices for any proofs that cannot be tastefully inserted into the text, either at the bottom, in a collapsible section, or on another page.
However, it can be argued that even this leads to clutter, or that certain proofs do not meet relevancy or quality standards. Wikipedia is not, and should not be a general storehouse for everything that happens to be true. It might be appropriate to have a proof of the Pythagorean theorem but not appropriate to have a proof that a fibration leads to a long exact sequence of homotopy groups. In fact, for some things, it is probably for the best if no more than a sketch of a proof and a reference to an edited book/paper are given.
Personally, I would like to see a companion site, wikimath or some such, that integrates well with wikipedia but contains the things that wikipedia should not. I envision a site which subsumes the content planetmath.org but is closer to the style of wikipedia, both editorially and aesthetically. With enough interlinking between the two sites, it could easily serve as an appendix to wikipedia, placating both the people who wish to add proofs and the people who wish to keep wikipedia pure and relevant.
In any case, I don't believe that the issue is as clear cut as many people want to claim, and I don't think that a completely satisfactory solution will be simple and easy.
Slashdot Mirror
Really? Well, I guess my English friends inadequately explained to me how the system worked when I lived over there. They had told me that a proportional representation scheme was how someone from the racist, nationalist party (whose name escapes me) had won a seat in parliament. The fact that he actually won a plurality of the votes somewhere scares me.
If you truly believe that the two parties are roughly equivalent and that both candidates are equally bad for the job, then, at least in Britain, you aren't throwing your vote away by choosing a third party candidate. No, you're not going to win the entire government, but you will end up with at least some representation. In the U.S., if a national third party were to get 25% of the vote in a years worth of Senate races, spread out roughly equally all across the country, absolutely nothing would come of it. If that happened in England, the third party would have a decent representation in parliament. So while it is very difficult in England for a third party to gain significant power, it is absolutely impossible in America (unless winning the presidency but having no support in congress counts as significant power, which would require a well funded, well connected, and charasmatic candidate, in addition to miraculous circumstances).
Why do you feel that anecdotal evidence has no value at all? Without anecdotal evidence, we wouldn't have theories to try to prove/disprove with real data. And while anecdotes can record statistically improbable events (with no way of discerning that the results are improbable), they do, at the very least, show what is possible. Additionally, for things you know nothing about, anecdotal evidence can be a useful way to form your initial opinions. Furthermore, for things that aren't scientific in nature (e.g., is the movie/restaurant any good?) anecdotal evidence can be invaluable.
While I am sure that many of the claims of chiropractors are bunk, I am also confident that the basic claims have at least some merit (realigning your back can relieve back pain but cannot cure ear infections or cancer). I accept or reject anecdotal evidence according to my own personal biases, so I agree that anecdotes are of little use for changing my opinions, but to say that anecdotal evidence has no particular value is dangerous. In fact, a friend of mine spoke out against anecdotal evidence, and then he died of cancer.
The people who argue that viruses aren't alive are almost inevitably non-biologists or biologists who don't work with viruses.
And the people who argue that HTML isn't computer code aren't web designers. And the people who argue that slashdot isn't interesting aren't slashdot readers. Ok, well, maybe not on the second point, but of course people who work with viruses are going to view their work differently than others will. It makes it sound better from the outside if they could convince people that viruses are alive. I bet you could find robot designers who would try to argue that their creations are alive too. As long as we insist on using vague human languages which have definitions that break down in corner cases (What is alive? Red? Funny?), we're going to have disagreements like this. In the end, it doesn't matter except for people's egos.
Well, I'm not exactly sure what you mean by "for profit", but there is a lot more than just the lectures that goes on at decent universities, and it doesn't come cheap.
Universities (which, for the sake of this discussion, are places where there are graduate studies and research being done, which we contrast with colleges, where there is just teaching and undergraduates) have several costs. Labs are expensive. And I don't mean the labs that students practice using pipettes in. The places where basic research occurs need equipment. And they don't run themselves. While grad students can do some of the work (and can be payed relatively cheaply), you need actual research level scientists too. They get paid less than they would in an industrial job, AND they have to teach. If you cut their budgets too much, they can't do their work, and if you cut their salaries too much, they would do much better to abandon ship. And while some of the money comes from tuition, a lot comes from both public and private sources who either have interests in education or interests in the research.
The upshot of this is that we are taught by experienced practitioners in our field of interest who have not only experience and perspective, but also keen insight into how the state of the art is changing.
Additionally, these people can offer unique guidance to those students who have true potential. They can help them get involved with ongoing research. They can guide them towards graduate level classes. Of course, talking about education for the best and the brightest might be completely antithetical to this discussion.
But given the number of people who go to college because it gives them better job prospects, is it that wrong that people pay to invest in their future?
Of course, my perspective here is from that of the sciences. I don't appreciate the benefit of being taught English by a professional literary critic or what benefit a university would offer a liberal arts student over a college. It also doesn't apply to people who are only going to college to party or to broaden their mind in an intangible sense. However, for the sciences or engineering disciplines*, it does seem reasonable that getting the education that we want requires money.
*And I'm not counting basic IT or programming in this. Computer science, yes. Something where an MSCE might matter? No.
I once had a conversation with a department head at Caltech who told me that, thanks to their endowments, they could easily afford to charge a much smaller tuition, and that like 70% of their students were given fairly good financial packages, but if they lowered their base price and charged less than other universities, people would assume that they were of lesser quality. Since the value of a degree (not of an education) is in how other people view it, cutting their prices would be a great detriment to their graduates.
As long as the system is in place, and as long as there are more people who want to go to good schools than those schools can accommodate, it is in their best interests to keep their sticker prices high. They only have reason to show you the price you will pay if nobody is considering them because they are too expensive.
Of course you have to allow people to say things you disagree with to be able to call it free speech. But we don't allow people to shout "Fire!" in a crowded theater when there is none, and threats of bodily harm can construe assault. It is clear that society appreciates that speech has power and consequences, and the question is, where do we draw the line on what should be allowed in the name of free speech versus what should be disallowed for the sake of a calm and peaceable society?
Should we allow to call for the assassination of abortion doctors? What about when the people who listen to them actually commit murder? Should there be culpability?
What about verbal bullying? If someone kills themselves because you repeatedly put them down, do you not bear some responsibility, even if you didn't pull the trigger?
Of course, in both these cases, the blame can't be placed entirely with the speaker, as others had to decide what to do with the words (nor should placing any blame on the speaker be seen as a lessening of the blame on the actor), but when words have a direct impact on whether someone lives or dies, I don't think it is as easy to dismiss them as just words. Of course, it is much harder to judge intent of words, it is harder to judge what the reasonable expectation of the consequences of words should be, and it may well be that there is no way to prosecute this kind of speech without creating a system that is rife for abuse and which undesirably suppresses other kinds of free speech, but the issue isn't so clear cut that it can be put to rest by a few choice quotes.
An iPhone may not be a necessity, but if you ALREADY HAVE ONE and you drop AT&T as your carrier, you are essentially throwing away money and converting it to an iPod. If this was about what carrier to choose if you were just starting out, or if smart phones didn't exist and all cell phones were roughly equivalent, you might have a point. As it stands, I honestly have no clue how what you are saying is relevant.
Maybe there are other phone companies, but I'm pretty sure that horribly unfair contracts are the norm (with terms like required arbitration and that the terms of the contract can be changed at any time without notice). Additionally, without jail breaking (which might be undone the next software upgrade), you can't switch if you are an iPhone user. To say "just use someone else, competition solves everything" is a bit glib and shortsighted, if not downright disingenuous.
Why do people think that CO2 = bad? There is a natural carbon cycle. CO2 goes into the air, plants breath it in and breath out O2 while turning the carbon into sugar. Animals eat the plants (and other animals) and use the bonds in molecules containing carbon as a storage for energy. As they use the energy, the carbon goes back into the atmosphere. When things are in relative equilibrium, everything is fine.
The problem with fossil fuels is that there used to be a lot more carbon in the atmosphere, which was absorbed by plants which died and took the carbon with them. When we burn fossil fuels, we are re-releasing this carbon into the atmosphere, changing the balance of things. Except for deforestation and burning of fossil fuels, most other CO2 related activities don't actually change the overall amount of carbon in play. There is no need to be alarmist about this.
I'm afraid I have to disagree with you.
First, the distribution of the primes is not an observation, it's a proven mathematical fact that took many smart people a long time to fully establish.
Second, knowing the distribution of the primes has direct applications to things like the security of encryption methods (if large primes were significantly more sparse than they are, then factoring numbers which are the product of two large primes would be much easier than it is).
But the difference in the distribution of the primes versus the distribution of their leading digits is akin to a shoe manufacturer knowing how many shoes of each size to make versus a shoe manufacturer knowing the distribution of the third digit of the number of atoms in the human foot. Yes, they are both observations of a sort, but only one of them has useful information.
Actually, the result is more that the prime numbers don't obey Benford's law, but obey a generalized version of it having to do with the specifics of the distribution of prime numbers. However, a list of numbers doesn't have to be random to obey Benford's law.
The reason the discovery isn't useful is because, while there is use in knowing the distribution of the primes, there is little use in knowing the probabilities of the leading digits of primes. The only application I could think of is if someone gave you a list that they claimed to be all the primes up to 10^100, and you wanted a quick sanity check on whether it might be it. Of course, adding 1 to every number would make nothing (but 2) prime and change almost none of the leading digits.
But in any case, since numbers on income tax statements or stock prices are not required to be prime numbers, and since the leading digit of a number has very little mathematical use, there is little in terms of applications of this observation, mathematical or otherwise.
Companies seem to think that the IT dept is the most expendable for some reason.
You say this as if it is a mystery why a company would feel this way. But regardless of whether IT is as expendable as some companies may treat it, I think it is important to understand why things are the way they are.
To any large company, there are essentially two parts. First, there is the part of the company devoted to whatever the company sells. This will include engineering and design, product, sales and marketing, and perhaps some portion of management.
On there other side, there is the part of the company that is there so that the company runs smoothly. This is the part of the company that is there to facilitate and support the first part of the company. IT is in this group (in a non-IT company), as are janitorial staff, a certain other amount of management, and other random departments which might vary from company to company.
There is, of course, some overlap between the two sides. For example, while you might consider the running of the website an IT role, it is also essential to sales. Still, viewing a company as having the two sides is helpful for understanding why companies see IT the way they do.
When money is tight, and a person needs to decide where to cut money, they cut the things they deem less important to their survival. They can refuse to buy a new stereo or new underwear, but they can't refuse to buy any more food.
Similarly, when money is tight and a company needs to decide what to cut, they get rid of what they deem to be the least important to their survival. From upper management's point of view, they see what the impact of laying off staff in their core business will be, and will be less likely to view management as just support. However, it is harder for them to see why they can't just halve their IT staff or janitorial staff. Maybe the floors will get vacuumed less often or it will take slightly longer to deploy Windows 7, but the company will still do what it does roughly as well as it currently does, right? (That is not to say that IT isn't crucial to a company's success, just that it is much harder for upper management to appreciate the relative worth of IT staff).
It's much harder to appreciate exactly how expendable support staff is, but it isn't that hard to see why management would view support staff as more expendable than others.
Benford's law works by the observation that, when numbers come up in certain real world contexts, the fluctuations you get in numbers should be proportional to the numbers themselves. Phrased differently, variations tend to be relative, not absolute. Because of this, if you have a very large range of random numbers from many real world measurements, then you would expect the number between t and t*(1.0001) not to vary too much for small changes in t. Let us try to use this observation very coarsely. Among the numbers with 6 digits, the number that look like 1xxxxxx (those between 100000 and 200000) should be about the same the number between 200000 and 400000. The same thing happens with the numbers with 5 digits or 7 digits or n digits (assuming that you have a wide range of random numbers, and the numbers are the kind that come from certain sorts of real world measurements). Additionally, you can get distributions for the first two digits, the first three digits, etc.
This observation doesn't depend on the base that you're working with.
Now, with the prime numbers, they have a distribution that is different from a lot of real world measurement data. The number of primes between n and n+d is approximately d/ln(n), where ln is the log with base e and d is small compared to n. So the number of primes between 500000 and 600000 is about 100000/ln(500000), and the number of primes between 500000 and 600000 is about 100000/ln(600000). By using this, and being slightly more careful, one can determine fairly easily the distribution of the leading terms of the prime numbers.
This is not a hard result. I would say that any professional mathematician who knew about the basic distribution of the primes could derive the distribution of the leading digis of the prime numbers fairly easily if anybody actually asked them to. The reason nobody mentioned this before is that nobody actually cares. While Benford's law does have applications to fraud detection, this new result does not. It's one of those things that makes people say "ooh, a pattern!" but which is just an easy and somewhat mundane corollary to a well known theorem.
A spider monkey inspired car horn set for space? A webkit inspired grapling hook set for space? Oh, the joy of open source browsers.
Yes, it is conceivable that standing up to Amazon will cause them to back down. They might feel that this is a fight they won't win and that isn't worth the bad press. Then again, they might not. Best case scenario is that the site owner (who might just be running the site as a hobby, and who may currently be in a less than stellar financial situation) spends a few hundred dollars and kills his relationship with Amazon, which he might view as important given the content of the website. Still, no legal precedent is set.
Worst case scenario is that Amazon views this as a legitimate matter that is too important to drop, it goes to trial, he is out thousands of dollars and a lot of time, and even if he wins, he has still lost. Additionally, I think you far overestimate how much publicity this will get. Odds are good that, even if the mainstream media picks up the story, it will only be a brief blurb. Most people who hear it won't care, and many who do will go, "Oh wow, that's a nice ebook reader!" While slashdot probably has a higher percentage of people would would buy portable ebook readers than in the general public, a boycott by all slashdot/digg/reddit/etc readers would still probably not persuade amazon to stop, if they are that concerned about piracy and the device really is a loss leader.
I would love to see him fight and win. I hate bullies, I hate people who abuse the system, and I feel that one should be able to use hardware however one sees fit. However, I honestly cannot fault him for choosing not to fight. If you want to teach them a lesson, go ahead and pick a fight. But remember, not everybody has the luxury of being able to stand on their principles (and even fewer still have the luxury of standing on yours).
Just because you run and hide from a pack of wolves doesn't mean you are a sheep. While you might wish them to martyr themselves for your principles, if they don't have the resources to fight, or if a win would not accomplish anything for anybody else, why shouldn't they act in their own best interests?
Yes, and no. While copyright is a right to control as opposed to a right to profit, it is also supposed to be a limited monopoly which gives creators an incentive to create before turning their creation over to the public domain. The question that must be asked is, "What is the purpose of allowing this control, and under what circumstances is it ethical to ignore a valid copyright?"
To my understanding, there are three fundamental rights (beyond the pragmatic benefits) which justify the existence of copyright:
1) The right to attempt to benefit from one's work
2) The right to not have others unfairly benefit from one's work
3) The right not to suffer from a misappropriation of one's work. (e.g., if someone is making shoddy knockoffs of your creation and attributing it to you, or if someone takes and shares a work that you did not want to publish because you felt it was sub par.)
If a book is no longer in print, it is reasonable to assume that the first right has been exercised. To proceed ethically, one must make sure not to violate the other rights. Buying or selling pirated copies of the book would be in violation, but merely obtaining a pirated copy for personal use would not. Redistributing the pirated copy without charging for it may be viewed as a violation, but merely using the book would not.
To be ethical with piracy, one must understand the spirit of the law. Copyright is a simple codification of an agreement between creators and the public. If the spirit of the agreement is upheld, the rest is just details.
That reminds me of a joke:
An engineer, physicist, and a mathematician are sitting at a bar, and the bartender asks, "Can any of you guys think about four dimensions?"
"Sorry, not me," the engineer replies.
The physicist chimes in, "I suppose I can, if the fourth dimension is time."
The mathematician starts laughing. "Oh, you guys, this is easy! Picture n-dimensional space. Now, let n be equal to four..."
According to an econ professor I had, those groups of "intelligent" people who think that the tax rate is higher than the optimal value are not economists. He also said that it is generally accepted that the optimal rate is probably somewhere between 60% and 80% for the United States.
The Laffer curve is an interesting economic idea, but it has only really been used as a poor political idea. Additionally, since there is so much more that goes into the health of a country than just government revenues, the Laffer curve is only a reasonable thing to be looking at when the tax rate is higher than optimal, and it is only reasonable then in the sense that you couldn't have optimized the correct thing if you are too far to the right on the Laffer curve.
You are right that it is not inherently idiotic to imagine how tax cuts could increase revenue (if people were actively saying, "What's the point of working hard? The government is just going to take it. Therefore, I won't try to work."), but the problems with the Laffer curve are manifold, and its misapplication by policy makers against the recommendations of economists only goes to show that, in a democracy, the people get the government that they deserve.
I recommend "Mathematical Methods of Classical Mechanics" by V.I. Arnold for the classical mechanics side of things. I am not sure what to read for general relativity. The bit that I know I learned from "Semi-Riemannian Geometry" by Barret O'neil, but I don't feel that the book is a good place to learn general relativity unless you already have a very strong background in differential geometry. I hope this helps.
I don't know. What's the difference between a universe full of other races that we've never heard from and a universe inhabited solely by us.
While I suspect that this is a troll, and while there is a quick one sentence response (God can never be proven or disproven, but if there is intelligent life out there, we have a chance of finding it) I'll bite.The difference of what we currently know in the two universes is small, but the difference between what we could realistically know is huge. Given that life evolved on earth to the point that intergalactic travel seems like a real future possibility, and given the vastly huge number of solar systems, it stands to reason that there is a decent chance that we aren't alone in the universe and that if there are others out there like us, they have the potential to meet us. If such a meeting did occur, it could have amazing consequences.
Now, if you contrast that with the dragon situation, the dragon is by definition unknowable. There is no way he could ever have an impact on our daily lives. In fact, even if we knew for sure that he existed, the only way that would possibly affect our lives is if we chose to devote time and thought to the dragon.
There is a difference between what there is no evidence for and what there is no direct evidence for, and there is a difference between what we can never show and what we have not yet shown. I mean, until we had particle colliders, we didn't have any evidence for quarks, but we had reason to look for them, and after we had particle colliders we had an idea of how to use experimental data to determine indirectly if quarks existed. With the dragon, there is no conceivable experiment that could be done to determine if the dragon existed.
While SETI is more like anthropology than science (as there is no falsifiable premise that they are working with), it is not like god or the dragon (as there is at least a verifiable premise they are working with). When you go into the realm of what can neither be proved nor disproved, you have left the realm of science and reality. There is use in life for things beyond science, such as art, imagination, and even faith. However, it is sad when one cannot tell the difference between the realms.
If I'm not mistaken, this is a large part of why Sun has both open office and star office. If you ignore the issue of support (which could be purchased separately from OO.o), businesses were skeptical of a product that was just being given away, and so they added a few minor proprietary things (clip art, etc) and slapped a price tag on it to make it more appealing to businesses. Kinda funny, actually.
If they start preventing duplicate posts, do you think that they could prevent duplicate articles too? I might even pay money for that!
The joy of being a mathematician is that I got to have this debate with a few of my friends a week ago.
Quite frankly, I am torn. On one hand, wikipedia is supposed to be an encyclopedia, and this is not the kind of thing that would generally make it in an encyclopedia. Even though wikipedia doesn't have the space concerns that regular encyclopedias have, there are issues of aesthetics and flow, as well as not cluttering up what the user wants to find with too much noise (which many proofs will be to many people).
On the other hand, there isn't an a priori reason why wikipedia should be bound by any of the limitations of a regular encyclopedia, and most of the problems mentioned above can be solved by creating appendices for any proofs that cannot be tastefully inserted into the text, either at the bottom, in a collapsible section, or on another page.
However, it can be argued that even this leads to clutter, or that certain proofs do not meet relevancy or quality standards. Wikipedia is not, and should not be a general storehouse for everything that happens to be true. It might be appropriate to have a proof of the Pythagorean theorem but not appropriate to have a proof that a fibration leads to a long exact sequence of homotopy groups. In fact, for some things, it is probably for the best if no more than a sketch of a proof and a reference to an edited book/paper are given.
Personally, I would like to see a companion site, wikimath or some such, that integrates well with wikipedia but contains the things that wikipedia should not. I envision a site which subsumes the content planetmath.org but is closer to the style of wikipedia, both editorially and aesthetically. With enough interlinking between the two sites, it could easily serve as an appendix to wikipedia, placating both the people who wish to add proofs and the people who wish to keep wikipedia pure and relevant.
In any case, I don't believe that the issue is as clear cut as many people want to claim, and I don't think that a completely satisfactory solution will be simple and easy.