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:

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.

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.