From the paper, it looks like that is a confidence interval - see the first full paragraph on page 12. I think it means that the most likely estimate is 39M, and with some confidence they put the range at 22M to 40M.
Mod parent up. It says a lot about math education that this discussion has focused on whether or not programmers ever implement routines related to calculus. Math is as much a way of thinking, solving problems and making useful definitions as it is about specific techniques or computations. To quote Wigner:
In fact, the definition of these concepts, with a realization that interesting and ingenious considerations could be applied to them, is the first demonstration of the ingeniousness of the mathematician who defines them. The depth of thought which goes into the formulation of the mathematical concepts is later justified by the skill with which these concepts are used.
Within computer programming alone, topics as diverse as decidability and Turing completeness, computational complexity, discrete probability, number theory for cryptography, calculus for almost any optimization problem, geometry not only for graphics but also for information theory, which is necessary for compression and coding - show that math is the heart and soul of all of these concepts! Beyond that, so many of the operations that computers are actually useful for carrying out are inherently mathematical.
I get why so many people are dismissive of "higher" math - there is no shortage of lousy teachers or rote arithmetic in early education, boring classes and an overall negative reinforcement that can leave people jaded and scornful. But I've learned from experience that it IS possible to get young kids interested in real math, mostly by knowing some of the relationships to fascinating phenomena. Regardless, I think it is tragic to see such disparaging opinions of mathematics.
But let's be honest: Most of the time, watching sports is very boring... Most of the time, it's arduous, painfully slow, occasionally expensive, and often humbling.
I agree with your post - I think the relatively minor point I was trying to make was interpreted as a condemnation of any post-Renaissance art, which it was not. My point was that work which is driven by a gimmick is often overtaken by the gimmick. My evidence in this case was that the artists talk much more about "hacking" and "glitches" than showing what they do. Although this could be the fault of the filmmaker, imagine Rothko dwelling on how his collaboration with the books of DJ Nietzsche inspired him to paint squares instead of faces, without any exhibition of his work. The demonstrations by Pollock of his techniques were always focused on the final work. I can imagine how exploiting some unintentional features of commercial products could lead to quite interesting art - some of the Machinima with grenades from the first Halo game could show in most New York galleries. However, from the video, it seems the potential is not quite being reached...
It now means dabbling in an engineering discipline... poorly. The nouveau team could probably exploit glitches to interesting effect. Although the video does an impressively bad job of conveying what these "artists" do, mostly they are shorting or breaking various connections on video cards to mess up the graphics.
Alarming pessimism is the defining trait of Slashdot culture... Science is like any field, and the majority of scientists are like the majority of other professionals - there is plenty to complain about, and plenty to be thankful for. If you want to see how it really works, I suggest trying to attend a small conference or summer school. The Les Houches schools are very good if you can go abroad, otherwise a school which is at least two weeks and has fewer than one hundred participants, mostly students, is ideal. You will meet people doing similar things to what you will be doing in the near future if you stay in physics, and you will learn a lot about the field beyond the textbook and canonical examples level of undergraduate studies. Which is not to disparage the textbooks - if you don't have Altland and Simons' book you should get it, it's fantastic.
From your post, it seems the assignation of the asshole title should not be exclusive... A grammarian would point out several errors in your post (mostly subject-verb agreements), and some of these even vary between British and American English. I'm sure everyone who read your post, or the post above it, understood what both of you were trying to say, so most of your arguments do not apply in this case. While I agree that abandoning grammatical rules can make communication very difficult, I also think some grammatical rules have been detrimental to clarity. Some rules are not even agreed upon - see ending a sentence with a preposition, where to put the punctuation with respect to the closing quotation mark, whether "everybody" can be plural, etc. Syntax is important, but a lot of language is like white-space, and languages that rigidly interpret white-space are a pain in the ass, just like grammarians.
Terribly insightful post - I wish that every parent who hated school thought about this. This force-feeding may be one small reason why the brightest kids tend to gravitate toward careers in IT or finance over science and math - every decent first course in programming shows a kid how to do or learn to do almost anything he or she can imagine doing, and with no oversight from the teacher. It's rare that a math or science teacher has the expertise to guide a student through any interesting independent project, and this is neglected in most curricula anyway. Instead you learn adding and subtraction for 5 years or more, then multiplication tables, then long division, and eventually basic algebra for word problems and differential calculus in the form of tables, again, if you are "advanced". On the other hand, once you've learned to program, especially with a computational bent, the jobs in finance and IT pay more and require less training that an academic job in math or science. It's silly to separate fundamental disciplines in such an artificial way, and it leads to exactly the symptoms described here.
It depends on the Hamiltonian. But, you can calculate it in the following way for some systems you are familiar with:
Let a+ and a be creation/annihilation operators for your (non-Majorana) fermion. You can define new operators, which obey the commutation relation for fermions: b = (a+ + a)/2 and b' = (a+ - a)/2i. But both of these operators satisfy bi = bi+, so the quasiparticles on which these operators act are Majorana fermions. If you want the position representation for b or b', you just need the position representations of the underlying ladder operators a+ and a.
For fermions, the canonical commutation relations must use the anticommutator: {a,b} = ab + ba. The Majorana fermion is a fermion. But, that doesn't completely answer your question, since you could correctly apply your reasoning to bosons which are their own antiparticle, like the photon, to claim that [a,a+]=0. But you have to keep in mind that the antiparticle of a photon is time-reversed compared to that photon - a+ and a are still distinct.
The point of distinguishing the two complexity classes is that the required steps scale differently. In most cases the scaling is the important issue, since for fixed N, 2^N is always larger than N^x for large enough N. For most algorithms, x is small (2.373 for matrix multiplication, 1.465 or smaller for multiplication, etc.), so the difference between exponential time and polynomial time becomes significant at reasonable values of N. There's no special value of N to expand around - it's asymptotics that matter.
Besides, you can't Taylor expand around a discontinuity. At all.
Since this is the FBI, we can assume there will never be ANY oversight or transparency regarding what they do. For now, they support the program by citing terrorism and national security, claimed goals which were OBVIOUSLY never used to restrict our freedoms... But what's worse, access to this type of data (everyone's private data, for all time), combined with the government's authority, can very quickly lead to a fascist state. Just add to that list of trigger words "intellectual", "liberal", "rebel", not to mention religion and ethnicity. Of course individually these data are easy to gather, but consider the methods of inference which are possible from this type of data - for example, the MIT project "Gaydar". It's only a matter of time before someone tries to use this type of inference in court, to prove ties to terrorism or tendencies of pedophilia. At that point, the government will be able to decide legally all kinds of categories to put you in from just a crawl.
There's a documentary called "The City Dark" which is all about light pollution. Some people claim that excess nighttime light plays a role in the development of cancer, and disrupts the seaward migration of just hatched sea turtles. These ideas are discussed in the film, but in a more humorous than preachy way. I'd be interested to see what the Slashdot community has to say about the movie, since I screened it with a crowd of mostly artists.
Well, the post was titled "Ask Slashdot: how do you view the Wall Street protests?" and my answer was that they are inspiring, more relevant than indicated by the media, and if they grew in size they could really get the attention of a congress which is otherwise dumb deaf and blind towards its electorate. What I find hilarious, but also pathetic, about your post, is that by demanding I address issues which are not essential to the discussion at hand, you are able to determine that I am uneducated politically, and the same as the Chinese cultural revolution, the Hitler Youth Brigade, etc. I wonder what information you use in general to reach conclusions, and how this determines your political ideas?
As I indicated in my post, there are a variety of problems that most people can see. Some that I think are especially important are overturning the Citizens United decision, eliminating tax loopholes for the wealthy (capital gains, etc.), shifting education funding away from local property taxes and towards taxes collected at the state or federal level, establishing a cabinet secretary dedicated to the quality of life and political representation of the citizen, limiting more stringently the leverage ratio of banks while increasing their liquidity and capital requirements, funding research and development for sustainable energy, and nationalizing health care. I'm sure there are important issues that others see as more problematic. I think unifying dissatisfaction over several topics, by highlighting the disproportionate political power of corporations, and banks in particular, can strengthen the movement politically.
I notice that you are quick and severe in your attack, but you yourself say nothing about your political beliefs while condemning me for not being more specific about mine. Do you support the status quo, or do you have a superior protest I can join?
I went down to Zuccotti Park to protest yesterday and it was really inspiring. Considering how screwed up our political system is right now, I think what it really takes to raise awareness is dedication and bravery rather than carefully planned bullet points. Sure, to the average IT guy there are new hairstyles, clothing styles, odors, financial backgrounds, employment statuses etc. represented, but if you want homogeneity you can go to North Korea, and besides, you can find something to criticize about ANY large group of people. What these protesters are doing should be celebrated, and everyone who thinks our government needs to stop weighting decisions by dollars needs to join. The Wall Street protests could easily be ten times the size, and you can always say "no one will listen to them anyway" but at some point you must have your say in whatever way you can. This is a good way.
As a PhD student in the best funded field of science in the US, I have to ask about the supposed spectre of outsourcing. If developing countries are better funding these fields, why not pursue a faculty position in one of these countries?
The point is that the sensor in this telescope is curved, so that the curve of focus coincides with the sensor making it possible to create aberration free images. I tried to find a description of the sensor in the SST but was unsuccessful. I think the Kepler telescope's sensor approximates this technique by tiling 42 flat CCDs along a parabolic surface. I'm not sure if SST does the same thing or actually managed to manufacture a curved individual CCD like this one, although presumably much larger:
eye shaped camera is shaped like an eye (engadget article)
Slashdot Mirror
From the paper, it looks like that is a confidence interval - see the first full paragraph on page 12. I think it means that the most likely estimate is 39M, and with some confidence they put the range at 22M to 40M.
In fact, the definition of these concepts, with a realization that interesting and ingenious considerations could be applied to them, is the first demonstration of the ingeniousness of the mathematician who defines them. The depth of thought which goes into the formulation of the mathematical concepts is later justified by the skill with which these concepts are used.
Within computer programming alone, topics as diverse as decidability and Turing completeness, computational complexity, discrete probability, number theory for cryptography, calculus for almost any optimization problem, geometry not only for graphics but also for information theory, which is necessary for compression and coding - show that math is the heart and soul of all of these concepts! Beyond that, so many of the operations that computers are actually useful for carrying out are inherently mathematical. I get why so many people are dismissive of "higher" math - there is no shortage of lousy teachers or rote arithmetic in early education, boring classes and an overall negative reinforcement that can leave people jaded and scornful. But I've learned from experience that it IS possible to get young kids interested in real math, mostly by knowing some of the relationships to fascinating phenomena. Regardless, I think it is tragic to see such disparaging opinions of mathematics.
But let's be honest: Most of the time, watching sports is very boring... Most of the time, it's arduous, painfully slow, occasionally expensive, and often humbling.
FTFY
I agree with your post - I think the relatively minor point I was trying to make was interpreted as a condemnation of any post-Renaissance art, which it was not. My point was that work which is driven by a gimmick is often overtaken by the gimmick. My evidence in this case was that the artists talk much more about "hacking" and "glitches" than showing what they do. Although this could be the fault of the filmmaker, imagine Rothko dwelling on how his collaboration with the books of DJ Nietzsche inspired him to paint squares instead of faces, without any exhibition of his work. The demonstrations by Pollock of his techniques were always focused on the final work. I can imagine how exploiting some unintentional features of commercial products could lead to quite interesting art - some of the Machinima with grenades from the first Halo game could show in most New York galleries. However, from the video, it seems the potential is not quite being reached...
It now means dabbling in an engineering discipline... poorly. The nouveau team could probably exploit glitches to interesting effect. Although the video does an impressively bad job of conveying what these "artists" do, mostly they are shorting or breaking various connections on video cards to mess up the graphics.
Alarming pessimism is the defining trait of Slashdot culture... Science is like any field, and the majority of scientists are like the majority of other professionals - there is plenty to complain about, and plenty to be thankful for. If you want to see how it really works, I suggest trying to attend a small conference or summer school. The Les Houches schools are very good if you can go abroad, otherwise a school which is at least two weeks and has fewer than one hundred participants, mostly students, is ideal. You will meet people doing similar things to what you will be doing in the near future if you stay in physics, and you will learn a lot about the field beyond the textbook and canonical examples level of undergraduate studies. Which is not to disparage the textbooks - if you don't have Altland and Simons' book you should get it, it's fantastic.
From your post, it seems the assignation of the asshole title should not be exclusive... A grammarian would point out several errors in your post (mostly subject-verb agreements), and some of these even vary between British and American English. I'm sure everyone who read your post, or the post above it, understood what both of you were trying to say, so most of your arguments do not apply in this case. While I agree that abandoning grammatical rules can make communication very difficult, I also think some grammatical rules have been detrimental to clarity. Some rules are not even agreed upon - see ending a sentence with a preposition, where to put the punctuation with respect to the closing quotation mark, whether "everybody" can be plural, etc. Syntax is important, but a lot of language is like white-space, and languages that rigidly interpret white-space are a pain in the ass, just like grammarians.
Terribly insightful post - I wish that every parent who hated school thought about this. This force-feeding may be one small reason why the brightest kids tend to gravitate toward careers in IT or finance over science and math - every decent first course in programming shows a kid how to do or learn to do almost anything he or she can imagine doing, and with no oversight from the teacher. It's rare that a math or science teacher has the expertise to guide a student through any interesting independent project, and this is neglected in most curricula anyway. Instead you learn adding and subtraction for 5 years or more, then multiplication tables, then long division, and eventually basic algebra for word problems and differential calculus in the form of tables, again, if you are "advanced". On the other hand, once you've learned to program, especially with a computational bent, the jobs in finance and IT pay more and require less training that an academic job in math or science. It's silly to separate fundamental disciplines in such an artificial way, and it leads to exactly the symptoms described here.
It depends on the Hamiltonian. But, you can calculate it in the following way for some systems you are familiar with: Let a+ and a be creation/annihilation operators for your (non-Majorana) fermion. You can define new operators, which obey the commutation relation for fermions: b = (a+ + a)/2 and b' = (a+ - a)/2i. But both of these operators satisfy bi = bi+, so the quasiparticles on which these operators act are Majorana fermions. If you want the position representation for b or b', you just need the position representations of the underlying ladder operators a+ and a.
For fermions, the canonical commutation relations must use the anticommutator: {a,b} = ab + ba. The Majorana fermion is a fermion. But, that doesn't completely answer your question, since you could correctly apply your reasoning to bosons which are their own antiparticle, like the photon, to claim that [a,a+]=0. But you have to keep in mind that the antiparticle of a photon is time-reversed compared to that photon - a+ and a are still distinct.
should have been fixed x
The point of distinguishing the two complexity classes is that the required steps scale differently. In most cases the scaling is the important issue, since for fixed N, 2^N is always larger than N^x for large enough N. For most algorithms, x is small (2.373 for matrix multiplication, 1.465 or smaller for multiplication, etc.), so the difference between exponential time and polynomial time becomes significant at reasonable values of N. There's no special value of N to expand around - it's asymptotics that matter. Besides, you can't Taylor expand around a discontinuity. At all.
Since this is the FBI, we can assume there will never be ANY oversight or transparency regarding what they do. For now, they support the program by citing terrorism and national security, claimed goals which were OBVIOUSLY never used to restrict our freedoms... But what's worse, access to this type of data (everyone's private data, for all time), combined with the government's authority, can very quickly lead to a fascist state. Just add to that list of trigger words "intellectual", "liberal", "rebel", not to mention religion and ethnicity. Of course individually these data are easy to gather, but consider the methods of inference which are possible from this type of data - for example, the MIT project "Gaydar". It's only a matter of time before someone tries to use this type of inference in court, to prove ties to terrorism or tendencies of pedophilia. At that point, the government will be able to decide legally all kinds of categories to put you in from just a crawl.
There's a documentary called "The City Dark" which is all about light pollution. Some people claim that excess nighttime light plays a role in the development of cancer, and disrupts the seaward migration of just hatched sea turtles. These ideas are discussed in the film, but in a more humorous than preachy way. I'd be interested to see what the Slashdot community has to say about the movie, since I screened it with a crowd of mostly artists.
I think a portion of Slashdotters would appreciate Ishiguro - Never Let Me Go is a bit like Aldous Huxley with a heart. His other books are great too.
Well, the post was titled "Ask Slashdot: how do you view the Wall Street protests?" and my answer was that they are inspiring, more relevant than indicated by the media, and if they grew in size they could really get the attention of a congress which is otherwise dumb deaf and blind towards its electorate. What I find hilarious, but also pathetic, about your post, is that by demanding I address issues which are not essential to the discussion at hand, you are able to determine that I am uneducated politically, and the same as the Chinese cultural revolution, the Hitler Youth Brigade, etc. I wonder what information you use in general to reach conclusions, and how this determines your political ideas? As I indicated in my post, there are a variety of problems that most people can see. Some that I think are especially important are overturning the Citizens United decision, eliminating tax loopholes for the wealthy (capital gains, etc.), shifting education funding away from local property taxes and towards taxes collected at the state or federal level, establishing a cabinet secretary dedicated to the quality of life and political representation of the citizen, limiting more stringently the leverage ratio of banks while increasing their liquidity and capital requirements, funding research and development for sustainable energy, and nationalizing health care. I'm sure there are important issues that others see as more problematic. I think unifying dissatisfaction over several topics, by highlighting the disproportionate political power of corporations, and banks in particular, can strengthen the movement politically. I notice that you are quick and severe in your attack, but you yourself say nothing about your political beliefs while condemning me for not being more specific about mine. Do you support the status quo, or do you have a superior protest I can join?
I went down to Zuccotti Park to protest yesterday and it was really inspiring. Considering how screwed up our political system is right now, I think what it really takes to raise awareness is dedication and bravery rather than carefully planned bullet points. Sure, to the average IT guy there are new hairstyles, clothing styles, odors, financial backgrounds, employment statuses etc. represented, but if you want homogeneity you can go to North Korea, and besides, you can find something to criticize about ANY large group of people. What these protesters are doing should be celebrated, and everyone who thinks our government needs to stop weighting decisions by dollars needs to join. The Wall Street protests could easily be ten times the size, and you can always say "no one will listen to them anyway" but at some point you must have your say in whatever way you can. This is a good way.
As a PhD student in the best funded field of science in the US, I have to ask about the supposed spectre of outsourcing. If developing countries are better funding these fields, why not pursue a faculty position in one of these countries?
The point is that the sensor in this telescope is curved, so that the curve of focus coincides with the sensor making it possible to create aberration free images. I tried to find a description of the sensor in the SST but was unsuccessful. I think the Kepler telescope's sensor approximates this technique by tiling 42 flat CCDs along a parabolic surface. I'm not sure if SST does the same thing or actually managed to manufacture a curved individual CCD like this one, although presumably much larger: eye shaped camera is shaped like an eye (engadget article)