The nice thing about patents is that they eventually expire, GPL doesn't.
That isn't quite right. The GPL is a way to license a copyrighted piece of software, and as such, is meaningless when the copyright expires. Now I know that congress keeps on extending copyright every time steamboat willy is about to come due, and I know that the time for a copyright to expire is more time than we can possibly conceive as useful, but the GPL does expire. Patents last an extraordinarily long time for the computer industry, and if enough things end up getting patented, it will make life extremely painful for everybody but the large patent holders. It is very easy not to steal someone else's implementation of an idea, but when the idea itself is patented, your own implementation is not enough. In short, it is hard to conceive of viral GPL license issues being anywhere near the problem that patents are unless Microsoft decides they can't do it better themselves and that they are above the law. Moreover, they would have to be wrong on the second count. Frankly, I just don't see it happening.
The most open state for a wiki, fundamentally, is to allow, and immediately publish, all edits. If Wikipedia is backing away from that, that's not becoming "more of a wiki".
Yes, the most open state for a wiki is when anybody can do anything, and so the more things people can do, the more "wiki" the site is (that has to be the stupidest sounding adjective I have ever heard, but I digress). Changing protected or semi-protected pages over to the new system means that more people can now do more things, and while the changes people make might not immediately show up to those who are not logged in, they are still there for anybody to see. One might argue that this is less open than semi-protected, but it is certainly more open than protected.
Of course, the question is, will they use the new flag in place of protected/semi-protected, or will they use it everywhere? In the former case, wikipedia seems more open. In the latter, it does not. My understanding is that we will be in the former case. Wikipedia might work better if the tag is applied everywhere, but I do not believe that is the plan. In any event, since this is only a small scale test, if it does not work out the way people imagine, we won't have to worry about it.
Don't worry, the grown meat will be labeled. Of course, not in the US.
In Europe, all genetically modified crops must be labeled as such. People aren't positive about the long term effects of GMO foods, and so they are given a chance to opt out and to vote with their euros. In America, people are not given that choice. Whether it be modified crops, milk from cows treated with BGH, or vat grown beef, labeling in the US is comparatively lax. I suppose the fear is that if we knew what we were eating, we wouldn't buy it. To some people, that is reason enough to label everything. To other people, it is reason enough to label as little as possible. Guess which ones have more influence in Washington.
If you don't know how natural your carrots are, don't expect to know about your beef either.
Re:How about a more qualified reviewer?
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Divine Proportions
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A friend of mine caught wind of the book a few months ago, and because I was his mathematically inclined friend, he asked me what I thought. I haven't read the entire book, but I looked at the sample chapters that he had posted on his website. My partially informed opinion is:
It is an interesting idea which simplifies the calculations in some cases by working only with intermediate values that might otherwise have to be square rooted and re-squared otherwise. However, it is not easier than trig in any real sense (assuming that trig is taught correctly, and not as some black box). Moreover, doing away with trig and replacing it with rational trig would be detrimental. Rational trig is at best a complement to normal trigonometry.
I should add that you'd be hard pressed to people both qualified to review the book for its mathematical content and interested in reading it. If he really included a section on field theory, it would require someone with the background of a decent undergraduate math curriculum, and the majority of the book would be so uninteresting and uninspired (just a reworking of how to solve trig problems using intermediate results to see that most problems actually are still solvable) that they would fall asleep. Most people at that level wouldn't want to review a standard trig textbook, and if you were at that stage, this would not be substantially different enough to change this fact.
I'm curious, how do you know about fields of characteristic 2 but not feel you are qualified to critique the book?
Fields (warning, this post contains math)
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Divine Proportions
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There is so much wrong with the review that I don't know quite where to begin. However, the one thing that nobody seems to have to responded to is
However, you don't have to read between the lines to see on page 21 that Wildberger excludes 'characteristic two fields.' Although I am not versed in Field Theory, I opine that such an exclusion does not apply to classical geometry and/or trigonometry, otherwise he would have said so. So, he is already implicitly confessing, to a failure of Rational Geometry in the global sense.
I opine that if one does not know field theory, one should not comment on how it relates to classical geometry. For the sake of being more enlightening than the review, I will try to explain fields and how they relate to geometry (classical and otherwise). Before I begin, I want to note that classical geometry has no relation to fields of nonzero characteristic, so the complaint is completely off base.
A field is a mathematical object that contains the same kind of algebraic structure as the real numbers, the complex numbers, and the rational numbers. Namely, we have two commutative operations (+ and *), identity elements for each operation (0+k=k, 1*k=k), every number has a negative (k+(-k)=0), every nonzero number has a reciprocal (k*(1/k)=1), and multiplication distributes over addition (a*(b+c)=(a*b)+(a*c)).
For a field to be nontrivial, we must have that 1!=0. However, it is still possible to have that 1+1+1+...+1=0 in our field, for some number of 1's. The smallest number of 1's required is called the characteristic of the field. If there is no nonzero amount of 1's that work, the field is said to have characteristic 0. Most people only deal with fields of characteristic 0, but fields of characteristic 2 and useful for cryptography, and other fields pop up in random places.
Fields have a lot of structure, and give you just the right amount of generality for doing a lot of math. In particular, most linear algebra can be done over arbitrary fields, and a lot more math is done over fields with some additional restrictions (e.g algebraic closure: every polynomial factors).
While the Cartesian plane is generally though of as ordered pairs of real numbers, you can have a Cartesian plane over arbitrary fields. There is actually a good use of this (in my opinion):
(skip this paragraph if you don't like details) If you start with a line segment that you say is of length 1, then with straight edge alone, you can make all the rational numbers, it is straight forward to add two numbers or divide two numbers, and a compass allows you to multiply two numbers. However, it is easy to construct non-rational numbers: a right triangle with sides of length 1 has a hypotenuse of sqrt(2). If you look at the equations that you use when you intersect lines and circles, the length of any new line segment you can make comes from a finite number of additions, subtractions, multiplications, divisions, and square roots. We say that a field is constructable if it is the smallest field containing all lengths of line segments generated in the process of a ruler-compass construction. Basic field theory and the above observation shows that any constructable field is a vector space over the rational numbers of dimension 2^n for some n. Since cos(20) has a minimal polynomial of degree 3, and since we can construct equilateral triangles little more field theory tells us:
We cannot trisect a 60 degree angle, and therefore we cannot trisect arbitrary angles.
Greeks (and then non-Greeks) tried for a long time to prove or disprove that one could trisect an angle. It took field theory to give a proof.
There are more links between geometry and fields. For instance, transporting the dot product to arbitrary Cartesian planes, can can define cosines of angles by analogy (although not the angles themselves), and then try to do trigonometry. This approach sort of works if the field is nice, but fields of characteristic 2 are
I'm not sure what he means by a common API, but maybe he wants binary compatibility? If the state wants to deploy a new program but different distros are compiled with different versions of GCC and include different versions of the standard libraries (or even different subsets of the standard libraries), they can't just distribute a single binary. Depending on what the app is, they could give all of the district admins the source and say "compile this for your system and make it work" but that would be at least slightly annoying. Also, if they wanted to distribute some proprietary closed source program, that would not be an option.
Asking for a common installer is lunacy, but asking for a common way to install a single binary program across the state isn't.
Yes, it is all well and good that hardware virtualization gives you tools that allow you to do virtualization more efficiently. The problem is, why in these tests did software virtualization come out ahead of hardware virtualization? You can dispute the methodology as giving misleading or inappropriate results, but unless they are lying (which is not impossible), you still have the issue that software virtualization performed better.
Imagine a man with a computer and a man with a pen and paper both tasked with performing a complex calculation. The man with the computer can do everything that the man with just pen and paper can, and more. The man with the computer should be able to perform the calculation faster. If he does, you are happy. However, if he is slower, saying, "No, note really, because he has better tools, he wasn't actually slower" isn't going to change the results.
So, argue about the way the test was performed, or argue about why the results are the way they are, but don't try to explain why hardware virtualization is unequivocally better when experiment disagrees.
Haha, yes, for some reason, instead of thinking I had made a population of 200m, I thought it was 200m men and 200m women. Oops. I'm a mathematician, not a statistician, so I'm not used to working with actual numbers.
Besides, who conducts a survey comparing the preferences of men and women with a sample set of one group (men, in this case) half the size of the other. While I am by no means a statistician, it seems to me that you would use equally sized data samples, or at least weight the sample sizes based on the percentage of the population as a whole.
I'm not a statistician, but I have taken enough statistics classes to know that this kind of sampling still works. The rough idea is that, while there might be different results for men and women, and while these differences mean that you can't get infer population average by merely taking the average over the entire group, you can get plenty of information from this kind of data, and with knowledge of the population, you can infer population averages.
Really, as long as you isolate the variables you want to look at and take enough people from each group, it really doesn't matter if your sample set looks anything like the population. Mathematics allows you to adjust this data easily.
Just as a quick example, assume that 10% of a million men and 20% of two million women sampled love popcorn. If there are 100 million men and 100 million women in your country, you can assume that 10 million men and 20 million women love popcorn, or 7.5% of the population. Of course, if there was some other significant factor that was ignored, like they only asked people from California, and Californians happen to not like popcorn as much as other people, then the statistics will less useful. That is why it is important to take large samples, so that the things you don't control for end up looking approximately like they do in the general population.
You would be surprised at what you can do to kill a tree. Most of a tree is not alive, only near the outside is, and so stripping bark or cutting slightly into the tree is all that it takes to kill it. People did this for "slash and burn agriculture" where they stripped bark or cut trees, left them to die and dry out, and then burned away what remained. You don't have to cut down a tree to kill it.
Actually, if you check the dictionary, you will see that what I claim *is* in fact an accepted definition of anti-social. Someone even put a link to a definition somewhere else in the comments. I made sure to add the group of friends specificly to point out that you don't have to be alone to be doing something anti-social.
You don't need to criminalize pissing people off for the legal system to deal with anti-social behavior. Most anti-social behavior would be criminal if it were of a greater scope or severity. All you need to do is set up a system of warnings so that repeat violations can accumulate. If someone smashes your mailbox once, it might not warrant jail time, but if someone smashes your mailbox repeatedly, in part because they feel that there will be no serious consequences, something needs to be done. For some people, fear of punishment is the only thing that deters them from committing acts like this, and so some sort of punishment needs to exist so that society as a whole can function properly.
I think that you misunderstand the meaning of anti-social in this context. Yes, if you sit in your room all day, not interacting with other people, that can be called anti-social, or perhaps more descriptively unsocial or not social. However, anti-social is broader than that. If you and a group of friends were to go around your neighborhood egging people's houses, throwing small rocks at passers-by, breaking the limbs of public trees, bullying people, shooting people on the street with water guns (not necessarily filled with water) or a number of other similar acts, that would be anti-social. Anti-social behavior is often behavior which is disruptive to society in one form or another.
Unfortunately, when a particular behavior is referred to as anti-social, it is usually because it is not severe enough to call it by greater term such as assault or vandalism. Anti-social behaviors are things which might not warrant jail, and which many people might try to ignore because they don't want to merely escalate things, but are acts which normal, functioning members of a civil and polite society do not do. Anti-social behaviors are the things that you say, "it might not technically be illegal, but I won't do it because it will accomplish nothing but pissing other people off." Generally, people who engage in anti-social behavior are jackasses, and the only legal way to stop them (if they aren't being carried out by children whose parents are willing to step up) is to call the cops.
I have a very small nitpick about one of your nitpicks. "it has led to me getting" does seem like a better way to phrase what he wrote, but you are incorrect in your lament that the correction contains a split infinitive. The "to" converts the latter half of the sentence into a prepositional phrase, and is not used as part of an infinitive. Also, while split infinitives should be avoided when they confuse the action of a sentence or detach it from its object, if no such confusion arises, then they can improve sentence flow and meter. Teachers say that one should strive to never split infinitives, but they only say this because so many people split them poorly.
My bigger concern with the grandparent is not a grammatical concern, but rather a logical one. Even if the SAT test did the slightest bit to test grammar, the gp asserts that using AIM and IRC exclusively are the cause of his success. Even if this were a true statement, and even if anecdotal evidence were statistically significant, the sample is still bad writing in the context of this discussion. A better way to phrase the argument is as follows:
"I do not think that IRC and AIM damage one's grammar skills. I have been using both media almost exclusively for my writing over the past few years, yet I was still able to score well on my SAT's. I think that communication, in all forms, helps to improve grammar."
Of course, if the grandparent did intend to say that exclusivity use of his AIM and IRC was what led to his SAT scores, then I also have to question his intelligence and logic skills in addition to his writing skills.
Yes, research is required for conclusive evidence, but at this point all we have are preliminary results and a (perhaps overblown) sense of optimism. If science operated in a vacuum, the logical thing would be to follow the initial results with more research. However, enough people have concerns that we can't just do science for science's sake, and we can't even do science for humanity's sake. Unfortunately, before many people will give the go ahead for embryonic stem cell research, they have to know how the story ends, and we can't honestly tell them yet because there is no sure way to know.
Actually, I think that all we need to do is to make everybody understand that the embryonic stem cells that we harvest are the leftovers from in vitro fertilization. No embryos are created specifically to be harvested. Rather, the embryos can either be used in science, or they can just be disposed of. The political argument from opponents of embryonic stem cell research has been "I am against killing." I know that I would feel more comfortable with the argument if it were shifted to "I believes that it is better for an embryo to die than to be used without consent in scientific research." Of course, such a change in debate might not sway anybody, but if the debate is more intellectually honest, I think that a lot of scientists would feel a lot better about having the argument.
Of course, on the other side of things, I have not heard conclusive evidence that embryonic stem cells are the miracle cure that some people laud them as, nor have I see evidence that future cures involving embryonic stem cells will not be feasible with other types of stem cells. However, I don't think that you can have a fair debate on the necessity of embryonic stem cells until the other side of the discussion is more honest. There are moral questions about the research, to be sure, and perhaps we should not engage in immoral science, but we cannot answer those moral questions until we can agree upon what they are.
This may be hard for you to accept, but in war people die. Their language may be crude, but either way I'm sure it makes no difference to the dead insurgent and all the difference in the world to our guys who live to fight another day.
I think the problem is that you are implicitly assuming that they would not be firing on innocent people. I have heard of slaughters in this war. The killing of women and children. The killing of all "military aged" men in a town. If we had a guarantee that all the people who were killed were guilty of trying to attack soldiers or other Iraqis first, the language would not matter. However, if innocents are dying (and they are), then to kill so lightheartedly and to speak the way they do is a travesty. Killing at a distance is one thing, but to be so detached and jovial about it, even if they do follow strict ROE, is highly disturbing. I suppose that the world if full of less than stellar people, and that the military is no exception, but I am sure that if the innocent people who are gunned down like animals knew the way their killers laughed when they pressed the trigger, they would wish that they hadn't been so innocent.
I don't think I've ever met someone who said "The space under my desk is at such a premium, I would gladly pay another $300 for something smaller than my dell. There might be good reasons to choose a mac over a dell, but I don't know many people for whom that would be a compelling argument. I think some benefits are only convincing once you've made up your mind.
I'm sorry, but what? In what geometries (where betweenness has an actual significance) which contain the integers in their natural ordering have five between three and four? I have studied quite a lot of math, including at the graduate level, and I have come across nothing that leads me to believe that your comment is any more that pseudo-intellectual gibberish intended to sound insightful but which is actually devoid of any real meaning. What vies on infinity could impact the discussion at all? Do you mean that if we view the number line as a giant circle which loops back upon itself that five is between four and three? If this is the case, I contend that betweenness is meaningless, as any number is then "between" any other two numbers.
There is a time and a place for mathematics to be deep and mysterious. If you throw around comments like this, nobody will care when we reach one of those times.
Of course, if this was just an attempt at humor, forgive me. My anger should be directed at the moderators!
If 10 billion euros were spent on developing solar, wind, and other (currently known) renewable energies, we would probably have a lot more windmills that are only slightly more efficient than current ones. Environmentalists, at least the ones on the fringe who are making noise, are against a lot of things. They don't like coal plants because of the obvious pollution. They don't like fission plants because of the radiation and risk of meltdown. They don't like windmills because of the dangers they pose to birds. I have even heard stories of environmentalists opposing coastal wave plants.
Fusion is our best hope for a high yield power source that doesn't pollute, doesn't radiate, and doesn't have a risk of meltdown (although I don't know how viable and useful something like geothermal would be). With each larger plant, and with each new design, we understand more and get closer to break even. If we can achieve a sustained reaction, it will be the biggest thing that has happened for the environment in a long while.
If we can replace all coal with fusion, then the energy required to make solar cells, electricity for electric cars, and hydrogen fuel cells won't be coming from sources that pollute. A lot of technologies that only appeared to be environmentally friendly finally would be. Fusion would help make cars that don't run on petroleum products a lot more viable. Cheap, clean, bountiful energy will do a lot to help the world, and even if this particular reactor doesn't achieve break-even, the science conducted there will help us to eventually reach that point. We might have better uses for the money in the short term, but not in the long term.
There are a lot of times when I sympathize or even completely agree with environmentalists. However, since there is almost no way that fusion is not in their best interests, this cannot be one of those times.
The Feynman lectures are great. They are fun to read and help to make the material understandable. They are also long winded, sometimes lacking in mathematics or examples, and are definitely not best used as a single source of information (or even as a reference). I think that everybody taking physics should read them, but they do not serve to replace a traditional textbook, but rather to complement one. They should be recommended reading everywhere. However, I can't fault textbook companies for presenting other options.
I'm sorry, but your arguments don't really convince me of anything.
So what if a general audience hardback costs $20? When a textbook costs $150 (and I have had some that were that much), and people are complaining about the cost of textbooks, general audience books don't really factor into it.
So what if a really good $80 book ended up being worth it when you worked in computers? That is a very different situation than a poor college student buying an expensive book for a required class that will not do him much good after he graduates.
Writers might need to be paid, but my understanding of textbook publishing, at least in mathematics, is that the writers will have funding to write the book (either via NSF or because they have tenure), writers are expected to write, typeset, and edit the book without great assistance from the publisher (although this was not the case 50 years ago), and that the vast majority of the profits from the book do not go to the authors. Publishers are not going out and fronting vast sums of money for people to write textbooks.
Now, here is the rub. College textbooks are not necessarily that expensive. As has mentioned, at least some of the books can be bought used and sold, which means that any one book, at least at the lower levels, is unlikely going to cost more than $50. Second, books can be shared. Find someone in to go halfsies. And third, I had very few professors that actually demanded and checked we had the most recent version of the book.
Except in my humanities classes where we had to buy 6 $20 books (which were not actually textbooks), my textbooks were all really expensive. Nothing was ever less than $50. Several were two or three times that. And when publishers make small changes and release a new edition, many bookstores will not buy back the old editions. My campus bookstore would not. Sharing of books is more than inconvenient unless you have a roommate or a neighbor taking the same class as you. If you are doing the homework and need the book, and so does the other person, what do you do? What if one of you has to go out of town? Finally, even though professors might not personally check that you own the most current edition of the text, having an older edition (or nothing at all) can cause problems depending on how things have changed between editions, what the prof is doing for problem sets, and other factors. In short, not having the current edition of the textbook for yourself can easily be a big gamble.
In short, textbooks actually are expensive, there isn't always a good reason for it, the "easy" ways to pay less have their costs, and the tactics that publishers use to keep prices high do work. If you can't understand why people complain about textbook costs, you aren't trying very hard.
Some people also call the zeros of a function its roots. A lot of important information can be determined about a function by studying its roots, which is why we bother to give them a name (whether roots or zeros). However, the places where a function takes the value one are less obviously important. In particular, they change if you multiply your function by a constant or by another continuous function. The roots do not. The 'ones' of a function are only important when the function f(x)-1 is important to study.
The point of all this is that terms in mathematics, whether they sound silly to a layman or not, generally have conceptual power associated with them. Language is incredibly powerful at dictating thought, and having the right words to refer to things is an important part of having frameworks to think about things. I know that calling the zeros of a function zeros doesn't seem very profound, but it is more important than you might think.
Slashdot Mirror
That isn't quite right. The GPL is a way to license a copyrighted piece of software, and as such, is meaningless when the copyright expires. Now I know that congress keeps on extending copyright every time steamboat willy is about to come due, and I know that the time for a copyright to expire is more time than we can possibly conceive as useful, but the GPL does expire. Patents last an extraordinarily long time for the computer industry, and if enough things end up getting patented, it will make life extremely painful for everybody but the large patent holders. It is very easy not to steal someone else's implementation of an idea, but when the idea itself is patented, your own implementation is not enough. In short, it is hard to conceive of viral GPL license issues being anywhere near the problem that patents are unless Microsoft decides they can't do it better themselves and that they are above the law. Moreover, they would have to be wrong on the second count. Frankly, I just don't see it happening.
Yes, the most open state for a wiki is when anybody can do anything, and so the more things people can do, the more "wiki" the site is (that has to be the stupidest sounding adjective I have ever heard, but I digress). Changing protected or semi-protected pages over to the new system means that more people can now do more things, and while the changes people make might not immediately show up to those who are not logged in, they are still there for anybody to see. One might argue that this is less open than semi-protected, but it is certainly more open than protected.
Of course, the question is, will they use the new flag in place of protected/semi-protected, or will they use it everywhere? In the former case, wikipedia seems more open. In the latter, it does not. My understanding is that we will be in the former case. Wikipedia might work better if the tag is applied everywhere, but I do not believe that is the plan. In any event, since this is only a small scale test, if it does not work out the way people imagine, we won't have to worry about it.
Don't worry, the grown meat will be labeled. Of course, not in the US.
In Europe, all genetically modified crops must be labeled as such. People aren't positive about the long term effects of GMO foods, and so they are given a chance to opt out and to vote with their euros. In America, people are not given that choice. Whether it be modified crops, milk from cows treated with BGH, or vat grown beef, labeling in the US is comparatively lax. I suppose the fear is that if we knew what we were eating, we wouldn't buy it. To some people, that is reason enough to label everything. To other people, it is reason enough to label as little as possible. Guess which ones have more influence in Washington.
If you don't know how natural your carrots are, don't expect to know about your beef either.
A friend of mine caught wind of the book a few months ago, and because I was his mathematically inclined friend, he asked me what I thought. I haven't read the entire book, but I looked at the sample chapters that he had posted on his website. My partially informed opinion is:
It is an interesting idea which simplifies the calculations in some cases by working only with intermediate values that might otherwise have to be square rooted and re-squared otherwise. However, it is not easier than trig in any real sense (assuming that trig is taught correctly, and not as some black box). Moreover, doing away with trig and replacing it with rational trig would be detrimental. Rational trig is at best a complement to normal trigonometry.
I should add that you'd be hard pressed to people both qualified to review the book for its mathematical content and interested in reading it. If he really included a section on field theory, it would require someone with the background of a decent undergraduate math curriculum, and the majority of the book would be so uninteresting and uninspired (just a reworking of how to solve trig problems using intermediate results to see that most problems actually are still solvable) that they would fall asleep. Most people at that level wouldn't want to review a standard trig textbook, and if you were at that stage, this would not be substantially different enough to change this fact.
I'm curious, how do you know about fields of characteristic 2 but not feel you are qualified to critique the book?
I opine that if one does not know field theory, one should not comment on how it relates to classical geometry. For the sake of being more enlightening than the review, I will try to explain fields and how they relate to geometry (classical and otherwise). Before I begin, I want to note that classical geometry has no relation to fields of nonzero characteristic, so the complaint is completely off base.
A field is a mathematical object that contains the same kind of algebraic structure as the real numbers, the complex numbers, and the rational numbers. Namely, we have two commutative operations (+ and *), identity elements for each operation (0+k=k, 1*k=k), every number has a negative (k+(-k)=0), every nonzero number has a reciprocal (k*(1/k)=1), and multiplication distributes over addition (a*(b+c)=(a*b)+(a*c)).
For a field to be nontrivial, we must have that 1!=0. However, it is still possible to have that 1+1+1+...+1=0 in our field, for some number of 1's. The smallest number of 1's required is called the characteristic of the field. If there is no nonzero amount of 1's that work, the field is said to have characteristic 0. Most people only deal with fields of characteristic 0, but fields of characteristic 2 and useful for cryptography, and other fields pop up in random places.
Fields have a lot of structure, and give you just the right amount of generality for doing a lot of math. In particular, most linear algebra can be done over arbitrary fields, and a lot more math is done over fields with some additional restrictions (e.g algebraic closure: every polynomial factors).
While the Cartesian plane is generally though of as ordered pairs of real numbers, you can have a Cartesian plane over arbitrary fields. There is actually a good use of this (in my opinion):
(skip this paragraph if you don't like details) If you start with a line segment that you say is of length 1, then with straight edge alone, you can make all the rational numbers, it is straight forward to add two numbers or divide two numbers, and a compass allows you to multiply two numbers. However, it is easy to construct non-rational numbers: a right triangle with sides of length 1 has a hypotenuse of sqrt(2). If you look at the equations that you use when you intersect lines and circles, the length of any new line segment you can make comes from a finite number of additions, subtractions, multiplications, divisions, and square roots. We say that a field is constructable if it is the smallest field containing all lengths of line segments generated in the process of a ruler-compass construction. Basic field theory and the above observation shows that any constructable field is a vector space over the rational numbers of dimension 2^n for some n. Since cos(20) has a minimal polynomial of degree 3, and since we can construct equilateral triangles little more field theory tells us:
We cannot trisect a 60 degree angle, and therefore we cannot trisect arbitrary angles.
Greeks (and then non-Greeks) tried for a long time to prove or disprove that one could trisect an angle. It took field theory to give a proof.
There are more links between geometry and fields. For instance, transporting the dot product to arbitrary Cartesian planes, can can define cosines of angles by analogy (although not the angles themselves), and then try to do trigonometry. This approach sort of works if the field is nice, but fields of characteristic 2 are
I'm not sure what he means by a common API, but maybe he wants binary compatibility? If the state wants to deploy a new program but different distros are compiled with different versions of GCC and include different versions of the standard libraries (or even different subsets of the standard libraries), they can't just distribute a single binary. Depending on what the app is, they could give all of the district admins the source and say "compile this for your system and make it work" but that would be at least slightly annoying. Also, if they wanted to distribute some proprietary closed source program, that would not be an option.
Asking for a common installer is lunacy, but asking for a common way to install a single binary program across the state isn't.
Yes, it is all well and good that hardware virtualization gives you tools that allow you to do virtualization more efficiently. The problem is, why in these tests did software virtualization come out ahead of hardware virtualization? You can dispute the methodology as giving misleading or inappropriate results, but unless they are lying (which is not impossible), you still have the issue that software virtualization performed better.
Imagine a man with a computer and a man with a pen and paper both tasked with performing a complex calculation. The man with the computer can do everything that the man with just pen and paper can, and more. The man with the computer should be able to perform the calculation faster. If he does, you are happy. However, if he is slower, saying, "No, note really, because he has better tools, he wasn't actually slower" isn't going to change the results.
So, argue about the way the test was performed, or argue about why the results are the way they are, but don't try to explain why hardware virtualization is unequivocally better when experiment disagrees.
Haha, yes, for some reason, instead of thinking I had made a population of 200m, I thought it was 200m men and 200m women. Oops. I'm a mathematician, not a statistician, so I'm not used to working with actual numbers.
I'm not a statistician, but I have taken enough statistics classes to know that this kind of sampling still works. The rough idea is that, while there might be different results for men and women, and while these differences mean that you can't get infer population average by merely taking the average over the entire group, you can get plenty of information from this kind of data, and with knowledge of the population, you can infer population averages.
Really, as long as you isolate the variables you want to look at and take enough people from each group, it really doesn't matter if your sample set looks anything like the population. Mathematics allows you to adjust this data easily.
Just as a quick example, assume that 10% of a million men and 20% of two million women sampled love popcorn. If there are 100 million men and 100 million women in your country, you can assume that 10 million men and 20 million women love popcorn, or 7.5% of the population. Of course, if there was some other significant factor that was ignored, like they only asked people from California, and Californians happen to not like popcorn as much as other people, then the statistics will less useful. That is why it is important to take large samples, so that the things you don't control for end up looking approximately like they do in the general population.
You would be surprised at what you can do to kill a tree. Most of a tree is not alive, only near the outside is, and so stripping bark or cutting slightly into the tree is all that it takes to kill it. People did this for "slash and burn agriculture" where they stripped bark or cut trees, left them to die and dry out, and then burned away what remained. You don't have to cut down a tree to kill it.
Actually, if you check the dictionary, you will see that what I claim *is* in fact an accepted definition of anti-social. Someone even put a link to a definition somewhere else in the comments. I made sure to add the group of friends specificly to point out that you don't have to be alone to be doing something anti-social.
You don't need to criminalize pissing people off for the legal system to deal with anti-social behavior. Most anti-social behavior would be criminal if it were of a greater scope or severity. All you need to do is set up a system of warnings so that repeat violations can accumulate. If someone smashes your mailbox once, it might not warrant jail time, but if someone smashes your mailbox repeatedly, in part because they feel that there will be no serious consequences, something needs to be done. For some people, fear of punishment is the only thing that deters them from committing acts like this, and so some sort of punishment needs to exist so that society as a whole can function properly.
I think that you misunderstand the meaning of anti-social in this context. Yes, if you sit in your room all day, not interacting with other people, that can be called anti-social, or perhaps more descriptively unsocial or not social. However, anti-social is broader than that. If you and a group of friends were to go around your neighborhood egging people's houses, throwing small rocks at passers-by, breaking the limbs of public trees, bullying people, shooting people on the street with water guns (not necessarily filled with water) or a number of other similar acts, that would be anti-social. Anti-social behavior is often behavior which is disruptive to society in one form or another.
Unfortunately, when a particular behavior is referred to as anti-social, it is usually because it is not severe enough to call it by greater term such as assault or vandalism. Anti-social behaviors are things which might not warrant jail, and which many people might try to ignore because they don't want to merely escalate things, but are acts which normal, functioning members of a civil and polite society do not do. Anti-social behaviors are the things that you say, "it might not technically be illegal, but I won't do it because it will accomplish nothing but pissing other people off." Generally, people who engage in anti-social behavior are jackasses, and the only legal way to stop them (if they aren't being carried out by children whose parents are willing to step up) is to call the cops.
I have a very small nitpick about one of your nitpicks. "it has led to me getting" does seem like a better way to phrase what he wrote, but you are incorrect in your lament that the correction contains a split infinitive. The "to" converts the latter half of the sentence into a prepositional phrase, and is not used as part of an infinitive. Also, while split infinitives should be avoided when they confuse the action of a sentence or detach it from its object, if no such confusion arises, then they can improve sentence flow and meter. Teachers say that one should strive to never split infinitives, but they only say this because so many people split them poorly.
My bigger concern with the grandparent is not a grammatical concern, but rather a logical one. Even if the SAT test did the slightest bit to test grammar, the gp asserts that using AIM and IRC exclusively are the cause of his success. Even if this were a true statement, and even if anecdotal evidence were statistically significant, the sample is still bad writing in the context of this discussion. A better way to phrase the argument is as follows:
"I do not think that IRC and AIM damage one's grammar skills. I have been using both media almost exclusively for my writing over the past few years, yet I was still able to score well on my SAT's. I think that communication, in all forms, helps to improve grammar."
Of course, if the grandparent did intend to say that exclusivity use of his AIM and IRC was what led to his SAT scores, then I also have to question his intelligence and logic skills in addition to his writing skills.
Yes, research is required for conclusive evidence, but at this point all we have are preliminary results and a (perhaps overblown) sense of optimism. If science operated in a vacuum, the logical thing would be to follow the initial results with more research. However, enough people have concerns that we can't just do science for science's sake, and we can't even do science for humanity's sake. Unfortunately, before many people will give the go ahead for embryonic stem cell research, they have to know how the story ends, and we can't honestly tell them yet because there is no sure way to know.
Actually, I think that all we need to do is to make everybody understand that the embryonic stem cells that we harvest are the leftovers from in vitro fertilization. No embryos are created specifically to be harvested. Rather, the embryos can either be used in science, or they can just be disposed of. The political argument from opponents of embryonic stem cell research has been "I am against killing." I know that I would feel more comfortable with the argument if it were shifted to "I believes that it is better for an embryo to die than to be used without consent in scientific research." Of course, such a change in debate might not sway anybody, but if the debate is more intellectually honest, I think that a lot of scientists would feel a lot better about having the argument.
Of course, on the other side of things, I have not heard conclusive evidence that embryonic stem cells are the miracle cure that some people laud them as, nor have I see evidence that future cures involving embryonic stem cells will not be feasible with other types of stem cells. However, I don't think that you can have a fair debate on the necessity of embryonic stem cells until the other side of the discussion is more honest. There are moral questions about the research, to be sure, and perhaps we should not engage in immoral science, but we cannot answer those moral questions until we can agree upon what they are.
Oh, these are laptops we're talking about? Oops!
I think the problem is that you are implicitly assuming that they would not be firing on innocent people. I have heard of slaughters in this war. The killing of women and children. The killing of all "military aged" men in a town. If we had a guarantee that all the people who were killed were guilty of trying to attack soldiers or other Iraqis first, the language would not matter. However, if innocents are dying (and they are), then to kill so lightheartedly and to speak the way they do is a travesty. Killing at a distance is one thing, but to be so detached and jovial about it, even if they do follow strict ROE, is highly disturbing. I suppose that the world if full of less than stellar people, and that the military is no exception, but I am sure that if the innocent people who are gunned down like animals knew the way their killers laughed when they pressed the trigger, they would wish that they hadn't been so innocent.
I don't think I've ever met someone who said "The space under my desk is at such a premium, I would gladly pay another $300 for something smaller than my dell. There might be good reasons to choose a mac over a dell, but I don't know many people for whom that would be a compelling argument. I think some benefits are only convincing once you've made up your mind.
Yes, but only because it has been under constant development.
I'm sorry, but what? In what geometries (where betweenness has an actual significance) which contain the integers in their natural ordering have five between three and four? I have studied quite a lot of math, including at the graduate level, and I have come across nothing that leads me to believe that your comment is any more that pseudo-intellectual gibberish intended to sound insightful but which is actually devoid of any real meaning. What vies on infinity could impact the discussion at all? Do you mean that if we view the number line as a giant circle which loops back upon itself that five is between four and three? If this is the case, I contend that betweenness is meaningless, as any number is then "between" any other two numbers.
There is a time and a place for mathematics to be deep and mysterious. If you throw around comments like this, nobody will care when we reach one of those times.
Of course, if this was just an attempt at humor, forgive me. My anger should be directed at the moderators!
If 10 billion euros were spent on developing solar, wind, and other (currently known) renewable energies, we would probably have a lot more windmills that are only slightly more efficient than current ones. Environmentalists, at least the ones on the fringe who are making noise, are against a lot of things. They don't like coal plants because of the obvious pollution. They don't like fission plants because of the radiation and risk of meltdown. They don't like windmills because of the dangers they pose to birds. I have even heard stories of environmentalists opposing coastal wave plants.
Fusion is our best hope for a high yield power source that doesn't pollute, doesn't radiate, and doesn't have a risk of meltdown (although I don't know how viable and useful something like geothermal would be). With each larger plant, and with each new design, we understand more and get closer to break even. If we can achieve a sustained reaction, it will be the biggest thing that has happened for the environment in a long while.
If we can replace all coal with fusion, then the energy required to make solar cells, electricity for electric cars, and hydrogen fuel cells won't be coming from sources that pollute. A lot of technologies that only appeared to be environmentally friendly finally would be. Fusion would help make cars that don't run on petroleum products a lot more viable. Cheap, clean, bountiful energy will do a lot to help the world, and even if this particular reactor doesn't achieve break-even, the science conducted there will help us to eventually reach that point. We might have better uses for the money in the short term, but not in the long term.
There are a lot of times when I sympathize or even completely agree with environmentalists. However, since there is almost no way that fusion is not in their best interests, this cannot be one of those times.
The Feynman lectures are great. They are fun to read and help to make the material understandable. They are also long winded, sometimes lacking in mathematics or examples, and are definitely not best used as a single source of information (or even as a reference). I think that everybody taking physics should read them, but they do not serve to replace a traditional textbook, but rather to complement one. They should be recommended reading everywhere. However, I can't fault textbook companies for presenting other options.
I'm sorry, but your arguments don't really convince me of anything.
So what if a general audience hardback costs $20? When a textbook costs $150 (and I have had some that were that much), and people are complaining about the cost of textbooks, general audience books don't really factor into it.
So what if a really good $80 book ended up being worth it when you worked in computers? That is a very different situation than a poor college student buying an expensive book for a required class that will not do him much good after he graduates.
Writers might need to be paid, but my understanding of textbook publishing, at least in mathematics, is that the writers will have funding to write the book (either via NSF or because they have tenure), writers are expected to write, typeset, and edit the book without great assistance from the publisher (although this was not the case 50 years ago), and that the vast majority of the profits from the book do not go to the authors. Publishers are not going out and fronting vast sums of money for people to write textbooks.
Now, here is the rub. College textbooks are not necessarily that expensive. As has mentioned, at least some of the books can be bought used and sold, which means that any one book, at least at the lower levels, is unlikely going to cost more than $50. Second, books can be shared. Find someone in to go halfsies. And third, I had very few professors that actually demanded and checked we had the most recent version of the book.
Except in my humanities classes where we had to buy 6 $20 books (which were not actually textbooks), my textbooks were all really expensive. Nothing was ever less than $50. Several were two or three times that. And when publishers make small changes and release a new edition, many bookstores will not buy back the old editions. My campus bookstore would not. Sharing of books is more than inconvenient unless you have a roommate or a neighbor taking the same class as you. If you are doing the homework and need the book, and so does the other person, what do you do? What if one of you has to go out of town? Finally, even though professors might not personally check that you own the most current edition of the text, having an older edition (or nothing at all) can cause problems depending on how things have changed between editions, what the prof is doing for problem sets, and other factors. In short, not having the current edition of the textbook for yourself can easily be a big gamble.
In short, textbooks actually are expensive, there isn't always a good reason for it, the "easy" ways to pay less have their costs, and the tactics that publishers use to keep prices high do work. If you can't understand why people complain about textbook costs, you aren't trying very hard.
Some people also call the zeros of a function its roots. A lot of important information can be determined about a function by studying its roots, which is why we bother to give them a name (whether roots or zeros). However, the places where a function takes the value one are less obviously important. In particular, they change if you multiply your function by a constant or by another continuous function. The roots do not. The 'ones' of a function are only important when the function f(x)-1 is important to study.
The point of all this is that terms in mathematics, whether they sound silly to a layman or not, generally have conceptual power associated with them. Language is incredibly powerful at dictating thought, and having the right words to refer to things is an important part of having frameworks to think about things. I know that calling the zeros of a function zeros doesn't seem very profound, but it is more important than you might think.