Why do quantum physical properties come in pairs?

Question: Why do quantum physical properties come in pairs, governed by the
uncertainty principle (that is, position and momentum?)
Why not in groups of three, four, etc.?
Answer: The duality is a duality because of the notion of canonical conjugation in classical mechanics.
The reason people say that they come in pairs has nothing to do with quantum mechanics, but with the structure of classical mechanics. In classical mechanics, to give you the initial conditions for a system, you need to give the initial position of everything, and also the initial momentum. The classical variables come in pairs. These pairs are called canonically conjugate, because they have the property that their time rate of change of one is given by the derivative of the energy with respect to the other one.
The quantum mechanical description is only for wavefunctions which vary over values of one of the two canonically conjugate pairs. The other one is not freely specified, the wavefunction which gives its quantum description can be derived from the first.
People express the failure of classical mechanics by saying that half of all the initial data is related by uncertainty to the other half. This is the quantum duality. This idea was important historically, becuase it could explain how the classical equations could be taken up in quantum mechanics unchanged, while the predictions became probabilistic. People made analogies with the case where you have a classical particle whose position and momentum are unknown, and obey the Heisenberg relation. Quantum mechanics is completely different in that the presence at different position states is parametrized by probability amplitudes, not probabilities. But the description is always on half the phase space variables.
The uncertainty in position/momentum is directly analogous to the uncertainty in angular position/angular momentum, in the uncertainty of phase of a field mode and particle number of that mode, and in every other canonically cojugate pair. States of definite position are also uncertain energy, because energy and position do not commute, but nobody calls this a duality, because energy and position are not canonically conjugate.
I should also point out the energy/time uncertainty principle, which is hard to think of in terms of canonical pairs in the usual formulations of QM, because particles don't have a time associated to them, but all particles have a global time. In Schwinger/Feynman particle formalisms this is taken care of, but the uncertainty relation can be worked out in any formalism of course. This uncertainty relation might not be called a duality by some, I don't know.
Answer: Good question! For the properties related by the uncertainty principle, there are two reasons why they come in pairs:

Intuitively, the uncertainty principle relates the variance of a function to the variance of its Fourier transform. And, up to a couple of numerical factors, the Fourier transform of a Fourier transform is the original function. (Mathematicians will balk at this statement because it's not technically true, but conceptually it's accurate enough for my purposes here.) So the process of Fourier conjugation leads you through a cycle of two functions.
Mathematically, the uncertainty principle is based on commutators, namely that
$$\sigma_A \sigma_B \ge \biggl|\frac{1}{2i}\langle[A,B]\rangle\biggr|$$
and it doesn't really make as much sense to compute the commutator of three or more operators since there are multiple ways in which you can rearrange them.
Comment: indeed. I agree mostly with you, but still one can avoid to think that for instance, we also have vector spaces and their duals, but have not more complex tuples of vector spaces. What is called again an algebraic object with ternary operators beside the usual binary operators that define groups? we don't have it because we don't think in those terms, not necessarily because it might not make sense
Comment: I agree with the first of the arguments. As for the second, one could easily generalize commutators to _n_ tuples of operators in a manner similar to antisymmetric tensors (i.e. sum over all permutations employing permutation sign). See Levi-Civita symbol.
Comment: exactly, maybe there is some generalization out there for 'Lie thing of ternary operators' using such symbols as infinitesimal generators, but maybe such math is too weird to fit in our thinking models
Comment: Yeah, I've seen things like this on occasion (like the Nambu bracket Qmechanic mentioned), but they're not as generally useful as the commutator. Albeit perhaps only because the math is more complicated and less intuitive.
Answer: 1) There are already many good answers explaining the conventional theory and observations. Nevertheless, related to comments by lurscher and  Adam Zalcman, it seems appropriate to mention the Nambu bracket, which is a Poisson-like bracket
$$ \{ f,g,h \} $$
with 3 function entries, originally invented by Nambu in 1973, purportedly in a failed attempt to explain the $SU(3)$ symmetry of quarks. Already Nambu discusses an operator 3-bracket
$$ [\hat{f},\hat{g},\hat{h}], $$
and one can imagine some kind of uncertainty relation associated to this, where canonical variables come in triples. Unfortunately, the subject so far has remained just theoretical speculations. [Authors even don't agree what should replace the Jacobi identity for the Poisson bracket  $\{ f,g\}$, although most think it should be the so-called Filippov fundamental Identity (FI).]
2) Recently in 2008, the Nambu-bracket has been used in the Bagger–Lambert–Gustavsson M2 brane proposal.
3) The exist various generalizations to higher Nambu brackets
$$ \{ f_1,\ldots ,f_n \} $$
with $n$ entries.
4) For more information, see this recent review.
Answer: I think this has to do with the fact that one is the infinitesimal generator of the other (i.e p is the generator of position). If I remember correctly, commutators arise naturally when we generate a Lie Algebra (not entirely sure about this).
Answer: It's because physical observables are operators in quantum mechanics. For two operators $F,G$, one may always compute the commutator
$$ [F,G] = FG-GF $$
which is the simplest quantity that should be zero in classical physics but it is nonzero in quantum mechanics. In general, the commutator is  another observable (it may be a $c$-number, too). In the leading approximation, the commutator is equal to $i\hbar$ times the classical "Poisson bracket" of the classical observables with the same name.
But if you define your classical initial state by the values of observables $Q_i$ (includes both positions and velocities or momenta in the familiar case), you may study configurations close to $Q_i$. In this way, you linearize the phase space and the commutator
$$ [Q_i,Q_j] = \omega_{ij} $$
may be approximated by a constant antisymmetric matrix that I called $\omega$. (It becomes a nonconstant function of $Q_i$ if you allow large deviations from the predetermined point.) It defines the so-called symplectic structure on the phase space. In this linearized approximation where the commutator is constant, the symplectic structure may always be diagonalized by choosing better combinations of $Q_i$, so that $\omega$ becomes a block diagonal matrix composed of
$$ \left ( \begin{array}{rr}0&+1\\-1&0\end{array} \right ) $$
blocks, and these blocks guarantee that the observables defining the initial conditions - coordinates on the phase space - may be divided to pairs. In a simpler way, your question is really "because $\omega_{ij}$ has two indices".
The rearrangement of a larger number of operators, e.g. $XYZT-YTZX$, may always be reduced to transpositions of the neighbors i.e. to commutators of two operators. That's why the ordinary commutators are always more important. In a group-theory context of mathematics, the commutators define the so-called "Lie algebra". Generalizations of commutators with more than 2 objects in the brackets also exist but they seem to be much less relevant physically. In particular, they're not naturally defined for operators - and physical observables become operators in QM.
Answer: [Peter: You asked this some time ago, but it's just too delightful of a question to pass over without adding my two conjugated cents... :) You already have several good answers (I liked David Zaslavsky's in particular), so this one will be concept-heavy and math-light.]
One ways to visualize why quantum uncertainty occurs in pairs is to picture the universe as having two spaces that share a symmetric, two-way relationship.
The first of these spaces is the one we call spacetime, consisting of xyz (space) plus t (time). For brevity I'll call this xyzt space "length space", and will refer to it even more briefly as just x. Length space is of course the space we know best, and is the space in which most classical physics phenomena take place.
The second of spaces is technically an abstraction, but in terms of measurable effects it's about as real of an abstraction as you are likely to encounter. It's called momentum space, and it too has four dimensions: $p_{x}p_{y}p_{z}$, the momentum axes, plus $E$, the energy axis. I'll call $p_{x}p_{y}p_{z}E$ "momentum space," and will also refer to it as just p.
Momentum and energy are of course very much part of classical mechanics. However, in classical mechanics, x dominates over p in much the same way that air dominates over water in a cloud by breaking up the water into many tiny and isolated droplets. This structural domination of x over p means that p shows up mostly in the dynamic properties of how large object move and interact in x, rather than as a space.
However, for objects that are very small, very low in energy, or very low in momentum, that situation changes. For example, there are cases where ordinary matter can "condense" or form fluids that are most easily described as residing in momentum space. You might thing that such bizarre fluids would be rare and exotic, but that's not the case at all. For example, if you look in a mirror or at a shiny piece of metal you are looking directly at the surface of a type of p space condensate called a Fermi sea. The Fermi sea is composed of conduction electrons, and only electrons at the very top of that sea are capable of reflecting light.
It's often useful to think of p as approximately the place where the odd behaviors of quantum mechanics take place. Why that is I'll explain below, since it's directly related to your question about quantum uncertainty.
Now to the meat of your question: For reasons I think is best described as the way our universe happens to works, there exists an extraordinarily deep and mostly symmetric relationship between x and p. I can describe that relationship this way: Each point in each space x and p behaves a tuned radio receiver for some frequency along the equivalent axis in the other space.
For example, picture the $p_x$ axis of p as an old-style analog radio tuner, the kind with a little red dot indicating the frequency you have selected. Sliding the red dot up to the position labeled "103.5 megahertz" would create in a sinusoidal wave with just that frequency over on the $x$ axis of x. That infinitely long sinusoidal wave then becomes another way to "view" the red dot, since each precisely defines the other.
That's all well and good, but it's also important to realize that this works both ways. That is, if you instead decide to select a "dial point" along the length space axis $x$, that too will select a pure frequency along the corresponding axis of the other space, that is, along the $p_x$ of p. That's a nice symmetry!
It's a symmetry with some profound consequences. Remember, if you select a compact point in p you get an very long sinusoidal frequency over in x, and vice-versa. So let's say you don't want to have your particle scattered about so much in x, and you decide to pull it all in to one compact point in x. Oops! The moment you do that, the symmetric relationship causes the particle's representation in p to explode into an indefinitely long sinusoidal wave.
Now, since x corresponds to length (and time) and p to momentum (and energy), what does this curious see-saw relationship remind you of? If you answered quantum uncertainty, you are exactly correct. In fact, that is what quantum uncertainty is, at its deepest levels: the impossibility of representing the same particle compactly in both x and p space at the same time, due to their symmetric "tuning" relationship to each other.
The radio-dial like frequency tuning of these spaces has a more precise name: It's called a Fourier transform. So, if you have an old-style radio receiver and use it to move a dot back and forth along a linear scale, you can correctly say that you are doing a Fourier transform from frequency of the radio wave to the linear position on your radio dial.
So, here at last is the answer to your original question quantum uncertainty always seems to express itself in pairs, rather than in triples or some other combination.
The answer is that uncertainty is defined by pairs of spaces connected in both directions by Fourier transforms, which in turn just seems to be how our universe is constructed. To create a quantum uncertainty triplet, you would need to postulate a new universe in which there was a three-way Fourier-like relationship, presumably extending across three parallel spaces. Ouch! That's not intuitive at all.
But also, it's not necessarily impossible. Some of the most interesting and important insights in both mathematics and physics have come about from people trying to do nominally "impossible" things that turned out to have interesting and non-trivial solutions. Dirac's prediction of antimatter certainly comes to mind, since in that case he dug in and got stubborn about wanting only "linear" solutions for some equations that didn't have linear solutions. By using complex matrix mathematics, he finally found a way to do it -- and simultaneously uncovered one of the deepest equations in physics. His instincts, and his stubborn insistence in following through on them, ended in a unique and spectacular success.
(And warning to the wise: Very few people indeed have physics instincts like Dirac did, and even Dirac got stubborn in some quite wrong-headed ways in his later years. So if anyone wants to try exploring ideas like these for fun, please use a bit of caution on adopting the "stubborn" part of the Dirac insight recipe!)
And finally: I said earlier that x and p are not exactly symmetric. What did I mean by that? The back-and-forth Fourier relationship is exactly symmetric, as best we can tell. So where does the breakdown in symmetry come in?
The main break is this: While adding size or distance costs nothing x (length) space, adding size in p (momentum) space turns out to be very costly. This means that there is no problem with placing a particle very precisely in p, even if it results in an absolutely enormous (e.g. light years across) wave function in ordinary x space. Since adding more size to the x wave function costs nothing, it can just keep spreading until something disrupts it.
If instead you try to stuff the particle into a very precise location in x, the wave function in p again become enormous. However, since momentum cost energy, a large wave function in p quickly becomes hugely expensive in terms of the mass-energy needed to sustain it. That's one reason why particle accelerators have to pile so much energy into their particles. The extra energy expands their energy-intensive p space wave until they are large enough to make their sizes in ordinary x space very small indeed. Such additions of energy can for example be used to locate electrons precisely enough in space for them to "see" the motions of individual quarks inside protons and neutrons.
So, massive overkill, but again: That was a good question. And who knows? Perhaps some clever mathematically inclined person will someday come up with an unexpected n-space generalization of the Fourier 2-space relationship that seems to guide our universe. As the old saying goes, the only sure way to fail is never to try.
Answer: The generalized uncertainty principles relates any two observables (see eg the Schrödinger uncertainty relation).
It probably can be further generalized to more than two observables, possibly by starting from
$$
\langle x,x\rangle\langle y,y\rangle\langle z,z\rangle \geq \frac13 \left(\langle x,x\rangle|\langle y,z\rangle|^2 + \langle y,y\rangle|\langle x,z\rangle|^2 + \langle z,z\rangle|\langle x,y\rangle|^2\right)
$$
instead of straight Cauchy-Schwarz in case of three observables, but this is just a guess on my part - I did not check any literature.
Related to this are canonically conjugate observables like $x,p_x$, for which the classical uncertainty principle holds because they are governed by the commutation relation
$$
[x,p_x]=i\hbar
$$
corresponding to the fundamental Poisson bracket
$$
\{x,p_x\}=1
$$
of classical mechanics.
However, these observables are not ordinary: In particular, the observable $x$ corresponds to a coordinate of the underlying configuration space.
In classical mechanics, the existence of a conjugate momentum follows from the symplectic structure of phase space, in quantum mechanics, it follows from the properties of the Fourier transform on our state space $L^2$.
Answer: That's not necessarily the case. For instance, besides position and momentum, there are also other observables like energy (and no, time is a parameter and not an operator). More strikingly, for spin, there is no natural pair. There is an angular momentum operator corresponding to the component in each spatial direction, but directions don't come naturally in pairs.
Answer: A system is described by variables of our choosing, like $x,y,z$.
They are combined by changes seen as one, defining one system time step.
The reason for conjugate variables is that
the changes of their values happen in the same time step.
As an example,
when the position $x$ changes,
it is accompanied by a change in velocity $ẋ$.
$x$ and $ẋ$ are conjugate.
The Lagrangian $L$ does not yet know whether they are one time step.
Minimizing $∫Ldt$ one gets the Euler-Lagrange equation $∂_x L - d ∂_ẋ L / dt = 0$,
which is $F=ṗ$, by replacing $∂_ẋ L = p$ and $F=∂_x L$.
Since we minimized, we took away the double counting.
Every change is now a physical time step $dI$.
$I = ∫dI$ is the full count, i.e. the full information of the system.
Using an arbitrary time step $dt$
motivates $H = dI/dt$ as comparison between two system times.
The Euler Lagrange Equation corresponds to the Hamilton equations,
which, with the notation here, can be written as:
$$
\frac{dI}{dxdt} = -\frac{dp}{dt} \\
\frac{dI}{dpdt} = \frac{dx}{dt}
$$
We don't need the $dt$.
$$
\frac{dI}{dx} = -dp \\
\frac{dI}{dp} = dx
$$
In other words (and dropping the $-$):
$$
dI = dpdx
$$
Each $dI$ change is represented by a volume element in the phase space $dpdx$.
The information resolution of the physical world has a lower limit $h$.
$$
dI = dpdx ≥ h
$$
$dpdx$ is just an example.
It leads to the Schrödinger equation.
The Dirac equations has more observables
falling into the same system time step
and limited below by $h$.


Is there a definitive reference on Pinball playfield design?

Question: I'm looking at designing tables for Future Pinball but I'm not sure where to start as I've little background in game design per se. I've played scores of pinball tables over the years so I've a fairly good idea of what is "fun" in those terms. However, I'd like to know if there is a definitive "bible" of pinball design as far as layout and scoring/mode design goes. I've looked but there doesn't seem to be anything really coherent that I could find. Is it simply a lost art or am I missing some buried gem?
Answer: This seems akin to asking if there is a definitive "bible" of first-person-shooter design. Pinball is just a genre/type of arcade game which became popular and was copied in the same why fps games were among video games. The design of pinball games was likely more stable than that of video games due to the complexity and inherently higher cost of developing new mechanical game elements vs. digital game elements. Each player has their preferences as to what would qualify as definitive elements of pinball machine design. Some would swear by the early machines with no computerized components, others are going to think the almost seizure-inducing 1992 The Addams Family /// machine was the culmination of pinball design, and I'm sure someone out there at some point swore that adding paddles was heresy and they shouldn't mess with the design of Bagatelle.
The only other element of design is profit. This is likely a stronger influence to pinball design than anything else. It's easier and much more cost effective to use the same mechanical elements in many machines just in different configurations and with different themes/graphics. So once they hit on something that worked it was copied many times over. These common elements are what define "pinball". As for scoring it is mostly just a way to compare relative skill and the particular mechanics of scoring is generally irrelevant as long as a better player scores higher. Scoring systems also has economic implications as well as discussed here: http://cheaptalk.org/2009/11/17/the-economics-of-pinball/
You've played lots of machines, you know what you like, and you know what you find fun, I'd suspect you might also have an idea of what you haven't seen but think might be fun. You know how you define "pinball." Game design, be it classic arcade or modern computer games, is about what is fun, and is always a matter of taste and opinion. Just use your own experience and try to make something you would find fun.
Comment: There is a bible for FPS design, or rather rules to make gameplay more fun and let a level work. I came here (like 16 other upvoters) to search for some design mechanics and possible illuminate pitfalls before spending many hours on 3D models. There is not much  info on this matter it would be nice, if there is any, to put it here.
Answer: There was a program called Pinball Builder where you could build your own pinball games based on different layouts. This would be good for planning and designing ideas. The program is old so it may be hard to find.
I'm not sure if there is a definitive set of rules for designing a pinball game. Flippers, bumpers and ramps are the main things that signify the genre, I guess if you have them you have a pinball game?


Good video on separating eggs

Question: Could anyone point me to a good video on cracking an egg and then separating the white and the yolk?  I need to improve my technique.  For every few eggs that I crack I end up with little bits of egg shell in the white that I then have to pick out.
Answer: I find the site startcooking.com particularly useful for some quick videos that are narrated clearly, photographed neatly, and generally are better in quality than those found on Youtube.
Here is the video at that site: http://startcooking.com/video/295/Crack-and-Separate-an-Egg
That said, there are many such videos on Youtube that might be useful also:

http://www.youtube.com/watch?v=t-OwbEy-Vxk
http://www.youtube.com/watch?v=yAGX-54iR30
http://www.youtube.com/watch?v=04jY7A1yy_g
Answer: Just crack the egg and empty the contents into the slightly closed fingers of your hand. Spread the fingers a little over a bowl, to let the white run out, place the yoke in a separate bowl.
Comment: I don't have edit privileges yet... you definitely want to say "bowl" instead of "bowel." Definitely.
Comment: That's what happens when English is not ones native language. Thanks for the heads-up
Comment: No worries, just wanted to help. :)
Answer: I accidentally found a slick way to separate the egg yolk from the white: before cracking, shake the egg like crazy. I expected the egg to to be scrambled after doing this, but when I cracked it open into the frying pan, the yolk was intact! The yolk just slipped away from the egg white, frying completely separately.

Related trivia: you can use this technique to make an egg stand upright on its own.
Comment: How did you _accidentally_ shake the egg like crazy?
Comment: @Tim: I didn't actually shake the egg^^ I was demonstrating something to my middle-school tutoring student, and he was goofing off with the egg.
Answer: Check THIS one out! It went viral for good reason - I've tried it, it works just like in the video! She slightly squeezes a plastic water bottle and presses the opening against the top of the yolk, then releases the pressure on the bottle. The resulting vacuum sucks the clean yolk (no white at all) into the bottle. Another squeeze and the yolk is deposited in another bowl. She picks up and deposits the same yolk repeatedly. It's headshaking - Why didn't I think of that?! No more eggy fingers.
http://www.youtube.com/watch?v=Uz2Vnp5ZW4c
Comment: @SAJ14SAJ --Done
Comment: You might summarize the technique to add value to the answer...

Good video on separating eggs


Oracle: deleting data from tables leads to data file fragmentation?

Question: When randomly deleting ~5GB from a ~10GB Oracle table, I suspect that disk space is left in fragments.  Is there a way to know about the disk state and any query to defragment or shrink the space?
Answer: Can you explain exactly what problem you are concerned with?  People have come up with lots of different definitions of "fragmentation" some of which are impossible, some of which are possible but don't create any problems, and a few of which might be worth thinking about.
If you delete at random 1 out of every 2 rows in a table, that will generally mean that you'll have lots of half-empty blocks in the table.  That space will be reused by subsequent inserts into the table, though, so it is generally not create any problems unless you are stating that you are permanently reducing the size of the table (i.e. it will never again grow past 5 GB in size) or you have queries that rely on doing full table scans of the table that you want to tune.  Depending on the Oracle version, you can probably do a SHRINK SPACE on the table to reduce the size of the segment in that case.
Answer: Yes, deleting 50% of data from a table leaves it fragmented, and this make two problems:
1) The High Water Mark (which show the max usage of a table) is still at maximum size of table and make worst performance on Full table Scan
2) Space (extents) are not freed.
If you are using Oracle 11g you can run the Segment Advisor (read this) and run ALTER TABLE  SHRINK SPACE CASCADE;
Read warnings for the ALTER command like this one:
"As with other DDL operations, segment shrink causes subsequent SQL statements to be reparsed because of invalidation of cursors unless you specify the COMPACT clause."
Comment: thanks. Is Segment advisor some kind of external tool? Is there any way i can query the table to get this segment information


If mac has the built-in backup tool time machine, why we still need mac data recovery?

Question: I dont know much about computer thing and just knew that mac has a built-in backup called time-machine? what is that? can it help us recover the lost data in my mac. and why people still need some third party mac data recovery tool like minitool mac data recovery software used by my friends for a couple of years?
Answer: Time Machine is a bit different from third party data recovery software. Here's how they work:
When your computer is connected to an external hard drive and Time Machine is turned on, every hour it backs up the files on your computer (or any files changed since the previous backup). In this way, you always have a copy of everything, including versions going back in the past (depending on how large the external hard drive is). Then if you lose a file, you can grab a copy from this backup. (As a side note, the latest version of OS X includes a Versions feature that makes locally stored backups of older versions of files, so if you change a document, you can still see what it used to be.)
Third party data recovery software, on the other hand, is what you use when you do not have an actual backup to rely on. It's also not very reliable. What this does is it tries to scan your Mac's hard drive's empty space for files that were deleted. This sometimes works because even though files are deleted from the hard drive, the hard drive isn't necessarily overwritten, so some deleted files may still be retrievable.
Answer: Time Machine is a tool by Apple that stores incremental backups to an external hard drive. Third party applications may add other functionality your friends may not want. From personal experience, Time Machine has saved me several times & I recommend it. For more info on Time Machine, see this article: http://support.apple.com/kb/HT1427
Answer: From time to time your hard disk might write garbage that results in corrupt files. Time Machine will have no clue that those files are corrupt and will back them up. Hopefully Time Machine will have backed up a good copy at some point in the past.
HFS+ is an old filesystem and doesn't do much to prevent filesystem corruption. That's when a data recovery tool might come in handy.


Sites & Tools for comparing domains

Question: What are some good tools or websites for comparing websites traffic, SEO, and other factors site owners might want to know about their competition.
Answer: Alexa is good for larger websites and for directionally accurate data.  IE, it can help guide you if site A is bigger than site b.
Also, if available, you can use the google doubleclick ad planning tool to compare site traffic.  However, the sites will have to make their sites available to google, but its free so worth a shot.
You can use a paid service like http://www.compete.com/, but i have never used them personally.
If you want to just compare domain registration companies for prices and features, I would use something like http://smallbusiness-domain.com .
Answer: Alexa is a website on which you can compare different websites / domains. The data of alexa isn't the best but it could be interesting for website owners anyhow.
Majestic SEO is a tool which could be interesting for you, too. It let's you compare domains, too.
I hope I could help you :)

Sites & Tools for comparing domains


Inexpensive microphone setup for iPhone video?

Question: I play piano and have a Yamaha C2 grand. I'd like to occasionally record using the video camera on my iPhone 4. I've done a couple of tests using the built-in mike, and also using the little mike on the included white earbuds; these are almost good enough for my purposes, but there's a little distortion, especially on louder passages. (See here for a couple of tests with the earbud mike.)
I'm just looking for something good enough to post on Facebook or YouTube, for the benefit (?) of friends and family who are willing to humor me and my amateurish playing. I'm not looking to become an hobbyist sound engineer. Unfortunately, all of the resources I've found online on recording piano (here, here, here, or here for example) are aimed at the high end and involve hundreds of dollars worth of bulky gear - multiple microphones, preamps and stands and cables and whatnot.
Some other options I've considered and/or tried:

There are a lot of good USB mikes out there; I use the Blue Snowflake for videoconferencing on my computer. Someone suggested that I could use the USB-to-dock-connector adapter that comes with the iPad Camera Connection Kit to connect a USB mike to my iPhone. I've tried this and it doesn't work (accessory not supported message, no signal from the microhone).
The Blue Mikey looks perfect, but alas doesn't work with the iPhone 4.
The AMT M40 also looks like a good solution, but I'm not sure I can justify to my wife spending $500 on this.

So here are my criteria:

I'm not looking for audiophile quality
I'd prefer not to spend over, say, $100
I'd prefer to stick with a single microphone
I'd really prefer something self-contained, e.g. with a built-in preamp
I'd like something that can live unobtrusively in my living room (for example, no floor mounts)
I'd like for everything to be done on my iPhone - i.e. I don't want to record the audio separately on another device or on a computer and then have to combine it with the video.

Any suggestions?
Answer: Have you checked this? And maybe an accessory here.
Also a different alternative is shown here, using the headphone's jack.


Simulating having multiple Control Flows in a SSIS package

Question: I have a SSIS package that in its Control Flow I have quite lot of Data flows. To be able to organise them, I have wrapped the related Data flows into Groups. For example I have 5 groups as below which each one has got on average 8 Data flows. For example:
Students Group (includes a number of Data flows)
Courses Group (includes a number of Data flows)
Institutes Group (includes a number of Data flows)
Enrollments Group (includes a number of Data flows)
...
Now I see the need for adding more and more Data flows to each group is growing! Each of these groups are already big and adding more Data flows only make them more crowded and more difficult to maintain.
Based on my research there is no way to have multiple Control flows in a package, otherwise I would put each of the Data flows above in a Control flow, e.g.: one Control flow for Students, one for Courses, etc.
I know I can create a package for each area, for example one package for Students, etc, but I prefer to avoid adding two many packages as much as possible.
Do you have any idea how I can organise them in a package in a sustainable and clean manner?
Thanks.
Answer: Don't use groups, use Sequence Containers. That way, you can have the ones you want to run in parallel in the same container, and then have a subsequent container kicked off with additional data flows.
You can't have multiple Control Flows, but you can have multiple packages, and you can have a ton of containers to give you more control over the flow.


Properties of a good paella pan

Question: I was bought a paella pan for my birthday. It had a small label on it with only the brand name on, which I've since washed off. It is steel (I think), with rubberised handles and dozens of concentric dimples on the surface. I was wondering what these impressions were for and by extension, what makes a really good pan for making paella in?
Answer: I believe the dimples are for two reasons. One, they possibly help to make the pan, which should be fairly thin, more rigid. Secondly, they are a reminder of the time when these pans were hammered by hand - so, in a way, they make a factory-made pan seem more authentic.
The pan should be fairly thin, yet rigid, and conduct heat well. You don't want localised hot spots, but a strong, even heat.
The pan should probably not be too non-stick - you want to encourage the formation of socarrat - the slightly crusty layer at the base of a good paella.
The "how to cook" series in the Guardian are excellent for researching various recipes and deciding on an evidence-based amalgam - have a look at http://www.guardian.co.uk/lifeandstyle/2011/aug/18/how-to-cook-perfect-paella.
Comment: Thanks for the answer. With @toloco's corroborating it seems the dimples are an historic tradition. I quite like Felicity Cloake's series, but I find some recipes them less authoritative and thorough than others.
Answer: As I ask many times to my grandma dimples are a remain of old pans, now a days it is fancy, so there are a reason apart of this is how paella pans may look.
So remember non-stick surface and gas or barbacue (full power after you drop the stock)

Properties of a good paella pan


Do I need ME2 and all DLCs installed on my PC to transfer my ME2 saves to ME3?

Question: There are have been some speculations that some ME2 saves cannot be imported by ME3 because those saves uses DLCs in ME2 (such as Overlord or Shadow Broker). Will reinstalling ME2 and those DLCs help?
Answer: Having the DLCs installed or not installed should not matter, as Mass Effect 3 only draws from the file directly, and does not actually check your installation.
I have a character file with all the DLCs installed and played and she imports fine (minus her face mesh, for whatever reason) just the same as my current playthrough, my vanguard, who never got around to installing and playing the DLCs before ending his career.
Answer: The only thing that matters is that you have MAss EFfect 2 save files after the "ending" of Mass Effect 2. DLC doesn't matter in any way, you can import any save with/without any DLC as long as you reached the end of ME2.

 It's also important that Shepard didn't die during the ending

The save files should be in  My Documents\Bioware\Mass effect\Save, if they're not in that folder the import won't automatically find them. If you uninstalled Mass EFfect 2 it might have removed the save files (I really don't know) so check and make sure those files exist.


What should I do about my 3 month old baby wanting to nurse all night?

Question: I've been too tired to get up every 2-3 hrs to nurse, so I've been sleeping with him attached to my breast... Unfortunately I can't sleep well. What should I do? He doesn't burp well either, and spits up a lot. I'm afraid of him choking on his spit-up.
Answer: Hate to be that person, but.. Get up every few hours. If it's an option, make sure your partner is getting up with the child, doing the changing, burping, etc so you can focus on feeding and sleeping.
The fact that your child is snacking all night isn't worrying in itself - they'll do that, if the food is available. But if you worry about him spitting up while you sleep or you just aren't sleeping well, changing routine is the only practical answer.
Also, just remember - it gets easier.
Answer: It seems like you have two problems here: having to nurse frequently during the night, and a fear that your child might choke on spit up.
I agree with Saiboogu's answer to the first part.  It's hard, I know.  Try and get naps during the day while he sleeps, and enlist any help you need from your partner.  This phase of his life won't last long.
As far as spitting up goes, if your baby has actually been choking on his spit up, I suggest you talk to a doctor about it, because that could be dangerous.  If you're simply worried that he might choke while he sleeps on his back, then you don't have to worry.  On page 11 of this PDF, the AAP says they didn't see any increased chance of choking on spit-up for babies who slept on their backs vs. babies who slept on their stomachs.
Comment: Attaching a link to the AAP statement would be helpful. :)
Comment: Done!  I couldn't find one at first, and got lazy. ;)
Answer: You acknowledge the problem in the first sentence. Put the baby in the bassinet/crib and then get up to nurse when needed. The first couple of nights are going to be miserable.
When it is time for a feeding, be businesslike and quiet. Rise promptly rather than let the baby cry itself fully awake. Feed, burp, change diaper if needed, back to sleep for both of you.  Don't stimulate the baby with anything other than the feeding. It will soon become a routine that both of you almost sleep through.

You and the baby both will sleep better.
The feedings will be quicker, leading to more sleep.
Answer: Our son was like that for the first several months.
We dealt with this by co-sleeping.  It took several weeks of adjustment, but once we were used to it, my wife could feed him without fully waking up herself, thus felt much better rested in the morning.
I'll also echo what @Saiboogu said: we agreed that I did all the night-time diaper changing to balance the night-time disturbances.


from a share point portal website, how can i tell what version of share point is running?

Question: that is to say if i am browsing around on share point where can i get to a details page to tell me what version of share point it is?
Answer: The only way that I am aware of in the browser, is in Central Administration > Operations > Topology & Services > Servers in Farm.
probably not what you wanted to hear, but else we are talking custom code or PowerShell
Answer: So not from a browser, but from the server, this has been answered before. I think if there were easier it would be obvious. Anders approach is the only browser way that I know how and that requires access to CA.
Answer: You might also try viewing the value of the MicrosoftSharePointTeamServices response header that SharePoint sends with every response. You can view it using the IE Dev Tools, Firebug for Firefox, Fiddler, etc.
Answer: You can also navigate to the site, click Site Actions, Site Settings and look at the Version number.  You can then cross reference that figure to this list to get the product and patch level.  It won't tell you if it's the free version (WSS or Foundations) or a paid for version (Standard or Enterprise) like linked by Neil.


How to generate XML files of various list present in sharepoint?

Question: I want to generate XML files of the lists present inside a sharepoint site. The XML file will contain all the data and folders in a structured way. Is there any tool available to do this?
Has anybody worked on this. Thanks in advance.
Answer: well, if you save the site as a template and include data, the resulting WSP/STP consists of a CAB file with XML data inside, making it machine-readable. I assume that's why you want the XML output? So you can parse it in code?
Answer: Try using content deployment wizard available here: http://spdeploymentwizard.codeplex.com/
Once your lists are exported in .cmp file, you can rename it to .cab and open he cab file and access bunch of XML files.
Answer: Save the list as template and use it as your wish. it will be generated like XML.


System Settings (12.10)

Question: I don't find the control center but only a simple system setting window. How to make it more complete than before? I search for login screen setting, and I don't find it. Someone can help me? I'm still beginner and wanna learn more for Linux especially Ubuntu.
Comment: Ubuntu tweak (http://ubuntu-tweak.com/) has some more options but   if memory serves me well there is no login settings (anymore ;) )
Comment: Nope. it is not an answer @EliahKagan ;) Plus I am sure this has been asked before but I can not seem to find it :D
Comment: i just watching at youtube that there's login screen an showed how to change unity into ubuntu classic, and it's from login screen. The window title bar shows 'control center'. any help? :)
Answer: Changing Your Session Type
To change your session type and get a different GUI, log out. Then you have a login screen. It's not necessary to change anything in your settings, nor is it necessary to disable automatic login (which I presume you have enabled).
To log out, click the Ubuntu logo icon at the upper-right corner of the screen (the same one you click to access System Settings), and click Log Out....
On the login screen, you can select your user and log in (with your password--the one you set up when you installed Ubuntu, the same password you'd use to unlock the screen or install software). You can also select your desktop environment.

Previous versions of Ubuntu hide the menu where you can select your interface in a little square icon (which shows the GUI's logo, which by default is an Ubuntu logo for Unity). But this setting is available right on the login screen before 12.10, too.

Selecting a More "Classic" Session Type
Ubuntu 11.04 was the last version that had GNOME 2. After that, it's been GNOME 3. Ubuntu Classic was a GNOME 2 interface, and thus has not been supported since then.
However, a GNOME Fallback session is in many ways (not all ways) similar to Ubuntu Classic; you might like that interface. You can get this by installing the gnome-session-fallback  package. Then select GNOME Classic for "Desktop environment" on the login screen.
Other alternatives that may interest you are two alternative desktop environments: Xfce [wikipedia] and LXDE [wikipedia].

To get Xfce on Ubuntu, install xubuntu-desktop  and select Xubuntu Desktop as the session type.
To get LXDE on Ubuntu ([wiki]), install lubuntu-desktop  and select Lubuntu Desktop as the session type.

Both desktop environments have traditional design--expanding, nested application menus and a window list embedded in a panel.
Getting More Settings (Like the old "GNOME Control Center.")
The old version GNOME Control Center is no longer available in Ubuntu 12.10. The new System Settings have replaced it (coalescing into its current form over the last few Ubuntu releases).
As Rinzwind suggested, you can use Ubuntu Tweak (more info here) to get a variety of additional handy settings--but as Rinzwind said (and can be confirmed by looking at the categories of settings available), it doesn't add much that's related to user accounts.
Fortunately, the old Users and Groups utility is still available. (This dates back from even before the GNOME Control Center itself was introduced. It's still around because other supported desktop environments--Xfce and LXDE--don't have GNOME's control center.)
The old Users and Groups utility is provided by the gnome-system-tools  package.
To run it, press Alt+F2 and run users-admin. (Do not run it as root, that doesn't work. Instead it calls out to PolicyKit internally, to perform administrative tasks.)

For more information about alternative ways to administering user accounts, see my answer to How to manage users and groups?.

System Settings (12.10)


How to get rid of Xorg from Macports?

Question: I have installed some packages from macports, and nearly all of them required to install Xorg. How can I remove the Xorg packages? Is there a way to reinstall all my Xorg dependant package without Xorg support?
Answer: Many ports have a +nox11 variant, which you can add as a default variant in the variants.conf file that's pointed to in your macports.conf file.  However, in my experience, there are some X11-dependent ports that don't have the +nox11 variant. I believe I've also seen situations in which non-X11-dependet port A depends on port B, and port B is so deeply X11-dependent that it wouldn't even make sense for it to have a +nox11 variant. Overall, in my experience, it's practically impossible to keep Xorg from getting installed. :-(
Answer: There is no need to worry about xorg-* related ports. They provide the client libs for applications using X11 only. You can continue to use the X server shipped with OS X (or XQuartz).
See also the corresponding entry in the MacPorts FAQ.
Answer: To disable X11 variants by default, edit /opt/local/etc/macports/variants.conf and add this line: -x11 +no_x11 +quartz.
If you install a port that requires X11 and doesn't offer a variant without, you'll have to live with it. But this will at least make it harder to accidentally install the X11 libraries when you don't want to.

How to get rid of Xorg from Macports?


How do I deal with the Pack?

Question: By far the type of creature I struggle the most with in Dead Space 2 is the Pack, the gray children who attack you in swarms. Whenever I use Stasis I only seem to hit one or two and the rest end up swarming me, and then I have problems killing them effectively. What's a good strategy for dealing with these little guys?
Answer: Positioning: The Pack are very weak individually and are primarily effective if they can get to you from behind. You want to engage them in a funnel, or with your back against the wall. You are faster than the Pack but if you get trapped, they can very quickly surround you. Know where they spawn and use this to your advantage, for instance stay under balconies if they will drop in front of you. You should not fight other types of enemies in such closed spaces, but the Pack are so weak that you can be approached head-on with little danger unless you need to reload.
Weapons: The Pack will die to one shot of virtually every gun, so firepower isn't an issue. Instead, focus on ammo conservation and reload times, as that is when you are the most vulnerable. The pulse rifle is the best choice, as it works well against individual enemies and groups, but the plasma cutter is also effective. The sawblade is also great, just watch out as it requires being close to the Pack and you can get surrounded. Rather than reload, switch to another weapon, unless it is a particularly long fight or there are only a few enemies remaining (you don't want to waste expensive ammo).
Statis: I rarely used statis for my playthrough, but the idea is to aim at the ground under the Pack. In addition, you may want to circle around as the pack chases you (dangerous), but it will cause them to group up and be susceptible to a group statis or line gun shot.

 The final boss fight involves a ton of the Pack. Ammo is the biggest concern, and you should stick to the outside boundaries and never venture to the middle, keeping on the move.
Comment: Awesome, thanks for the help! I'll give you the bounty when it lets me in 11 hours.
Answer: I used only two weapons to deal with the pack the entire time I played.  The pulse rifle is very good at quickly eliminating many of them, especially if they are near each other.  Even if the pulse rifle is not an option, I actually tend to prefer the other option - use the javelin gun's alt-fire.
Typically whenever they attack, they tend to come from multiple directions.  What I would do when swarmed is to use the pulse rifle to eliminate a few in a single direction.  I would then run that direction, and switch to the javelin gun.  Turn around and fire a javelin into the ground in front of you (but far enough away not to be hit by the alt-fire).  What until the first one runs right by it and trigger the alt fire.  The electric shock will trigger for a few seconds.  During this time, any pack members that run by it will die instantly.  You end up with a pile of bodies and loot.  Any survivors can be mopped up with the weapon of your choice, which can include physical attacks (they die from a hit).
Using this method, I typically wipe out the entire pack with around 10 pulse rifle rounds and 2 javelins (1 to fire it, 1 to trigger alt-fire).

How do I deal with the Pack?


How does one better execute kick then punch combos when the legs are significantly longer than the arms?

Question: I'm one of those tall, lanky people whose legs are much longer than their arms. While this is often advantageous in Taekwondo, our style attempts to integrate punches and kicks. While leading with a punch and then following up with a kick poses little problem, I find that combinations that start with a kick and then lead to a punch result in swinging into thin air. So my question is this: what are some techniques that can help me close the distance/extend my reach when transitioning from a kick to a punch during a combination?
Answer: Personal Style
Taekwondo is a great system, but I believe the essence of martial arts is to develop your own personal art, based on a system. Different body shapes will tend towards different combinations and techniques - it's still Taekwondo, but it's Taekwondo done your way. Be careful though: this is not permission to ignore your instructor. He's there to help you discard the bad, focus on the good, and develop your personal art; he's not there to be ignored because you're "doing it your own way".
Range
Punching and kicking have naturally different ranges for lots of people. Different kicks, and different punches, have their own ranges. One of the key skills you need to develop as a martial artist is the ability to select the right strike for the range, or to control your range to suit your style.
Combo Selection
Combination kicks and punches are key to taekwondo - but you need to adjust the combination to suit your opponent's reaction. If you throw a right-leg front-kick and your opponent slides away to your right, you need to discard the plan to follow up with a left-leg roundhouse. Sparring is very dynamic, and you're constantly adjusting.
Kick-Punch Combinations
Kick-punch combinations aren't likely to work well if your opponent is moving back out of range to avoid your kicks. If you commit, in your head, to a kick-punch and your opponent just steps back out of range of the kick, you're gonna have to close the range as you punch - and in my experience trying to close range with a punch is asking for them to have a go at a quick front-kick as you move in.
When K-P Can Work
All that said, I use kick-punch combinations all the time. Whenever my opponent side-steps a kick and I find them in close, it's much faster to follow up with a few punches than to try to gain enough room to throw a kick. For me, punching is a range-gaining technique - you can certainly land effective hand techniques in sparring, but their main utility to me is to keep my opponent occupied and push them back to bring them in range of a kick.
Other Takes
I know people who do use punches differently - I tend to use kicks to close range, punches to gain them, but I've seen people who can close in with punches. If you want to work that into your own style, ask your instructor to help you work on it. I can offer this advice - your biggest risk is that your opponent will see your ribs as a tempting target as you step in without a kick chambered. The best way to combat this, in my opinion, is to either let your opponent close the range for you (move sideways out of the way of their kick) - you can also just watch for an opening when they're off-balance.
As for the original question, regarding the kick-punch, you can throw a quick kick in as you move out of the way - I often find that if someone's wound up a big kick I can step sideways as I throw a prop kick, and then finish in punch range - or you want wait for the right opening, often if they're off-balance after a missed kick, and then throw in a quick kick while stepping in to punch range.

In summary, what you really need to do is to think about range. Kick-punch combinations are all about using a kick as you close in to punching range, and that just isn't going to work if you're both on balance and your opponent tends to step out of range of kicks.
It's worth noting that it can be a great technique on what I think of as bully sparrers - people who rely less on technique and more on throwing their weight around and forcing you to move. These people tend to step in even with no opening, and rely on the tendency of taekwondo students to want to stay in kicking range. Punish them by stepping off the line of their movement, throwing in a quick prop kick, and following up with a few punches.
Answer: 1 A short good hint that helped me a lot (I am also a 2 m. long guy).
Don't lean backwards when kicking. Many do this to counterweight their legs. From that position it's hard to follow it up by a punch and you are vulnerable for overtakes and even more (if allowed): takedowns and swipes.
It may take some practice.
2 Extend those arms!
I still find so many people who don't fully extend their arms and don't twist their hips enough. This is necessarily to get the speed, reach and power you need.
3 Train with positioning, train with both legs in front (regular and south paw) in other words train footwork a lot!
Answer: I find there's not enough time to change hip position after a kick, so if the combo is kick first then punch, I typically can only make use of a punch with the same side I kicked with.
So if I'm lunging in with a right kick, the punch is also with the right.  It feels a bit weird if you've never tried it that way before, and you have to set up your upper body for the punch as well... you'll need to practice it to figure out when it's most efficient to punch.
Like, if you're doing a roundhouse kick, when you make the kick, bring your knee in straight away... you're kinda folding up or tucking in your kick as soon as you've past the striking point... and at the same time, cock your right arm in a position from where you can punch out and then punch.  It's different from a normal punch and sort of comes out a little sideways, but you can follow up really quickly with your left hand, and then the left leg is ready... turning kick, back kick, sliding side kick, then a fatality.
Answer: Getting a good kick-punch combination relies on where you are moving to, and where your feet are.
The most common use is when a kick is blocked.

If the opponent closes, in which case legs aren't any use any more so can you get a punch or two in?
If they stay their ground, is your body weight moving you forwards such that a punch can be landed without overstretching too much?

Either of these are relatively straightforward, and the punch is often the fastest way to get a point.
Answer: Recoil
Don't leave your left out too long after the kick, you will lose balance and won't be able to put your foot where you want it.
Distance
If you're too far away to punch, don't punch! Keep kicking if you're too far away, and if you're too far away to kick, don't kick at all.
Footwork
Practice footwork drills. These differ between martial arts, so you probably need to talk to your instructor about how they do it.
Answer: Option 1: Lead with closer range kicks - following a crescent kick or an axe kick with a punch will be a lot easier than following a front or side kick with a punch.
Option 2: Instead of returning your feet to the original position after a kick, them fall where they kicked. So after a kick you'd end up in a lunge position (think Yoga's Warrior poses), from which you could follow with a punch.
Option 3:  Make footwork part of your combo. So instead of trying for kick-kick-punch-punch you could do kick-kick-step-punch-punch. There's a pause, but that pause is likely timed with the opponent making a step to the back or to the side.
Option 4: Bait your opponent to come in, your legs are likely longer than your opponent's, so they'll want to close the distance and get inside. Throw a couple of kicks then chamber and have the punch ready for them as they close the distance (if you can do a superman punch this could be a good opportunity to use it).


What is sheaf cohomology intuitively?

Question: What is sheaf cohomology intuitively?
For local systems it is ordinary cohomology with twisted coefficients. But what
if the sheaf in question is far from being constant?
Can one still understand sheaf cohomology in some "geometric" way?
For example I would be very interested in the case of coherent $\mathcal{O}_X$-Modules.
Or even just line bundles.
Comment: I think it is more "intuitive" to think of Cech cohomology with respect to some fixed cover (as opposed to derived functor cohomology). Unfortunately, this is still not inherently geometric. The fact that in simple cases it corresponds to homology (which is very geometric) is a strange but wonderful miracle to me. I think of Cech cohomology is more of a combinatorial game that involves assigning labels to a bunch of things so that they satisfy some (quite intuitive) combinatorial rules. Of course, I'd be only too happy to see a more intuitive explanation, and overjoyed to see a geometric one.
Comment: Nice question. So we ask if $H^n(X,F)$ for a fixed sheaf $F$ on $X$ has a geometric interpretation. Unfortunately, the answers so far only mention the well-known techniques using various cohomology groups, but not tell what infortmation is included in $H^n(X,F)$.
Comment: @ Martin: Would you say that the information depended on whether $F$ was a general sheaf, or some structural sheaf of some nature?
Answer: One way to think about $H^1(A)$ is to use the long exact sequence not as a property of cohomology, but outright as a definition.  That is, given an exact sequence of sheaves,
$$ 0\rightarrow A\rightarrow B\rightarrow C\rightarrow 0$$
then $H^1(A)$ is measuring the obstruction of global sections to be exact:
$$ 0\rightarrow \Gamma(A)\rightarrow \Gamma(B)\rightarrow \Gamma(C)\rightarrow H^1(A)$$
In words, $H^1$ is `measuring the failure of $\Gamma$ to preserve surjectivity'.
If you want this idea to actually define $H^1(A)$, you have to be careful to chose $B$ so that $H^1(B)=0$.  But, as far as intuition goes, this works pretty well for me.
A demonstrative example of this, at least for me, is to think about the the complex variety $\mathbb{P}^1$, with $\mathcal{O}$ the structure sheaf and $\mathbb{C}_p$ the skyscraper sheaf at a point.  Then there is a surjective map (it is surjective because it is surjective on stalks):
$$ \mathcal{O}\rightarrow\mathbb{C}_p$$
which has kernel $\mathcal{O}(-1)$, the twisted structure sheaf.  This whole short exact sequence can be twisted by $(-1)$, noting that twisting a skyscraper sheaf $\mathbb{C}_p$ gives an isomorphic sheaf $\mathbb{C}_p(-1)$ (which I identify with the original sheaf):
$$0\rightarrow \mathcal{O}(-2)\rightarrow \mathcal{O}(-1)\rightarrow \mathbb{C}_p\rightarrow 0$$
On global sections, we then get
$$ 0\rightarrow \Gamma(\mathcal{O}(-2))\rightarrow \Gamma(\mathcal{O}(-1))\rightarrow \Gamma(\mathbb{C}_p)\rightarrow H^1(\mathcal{O}(-2))$$
We know that $\Gamma(\mathcal{O}(-1))=0$ and $\Gamma(\mathbb{C}_p)=\mathbb{C}$, so the middle arrow is no longer surjective.  Hence, $H^1(\mathcal{O}(-2))$ must contain at least $\mathbb{C}$ (in fact, it is exactly $\mathbb{C}$, since $H^1(\mathcal{O}(-1))=0$).
Higher cohomology may be also thought of this way: $H^{i+1}$ measures the failure of $H^i$ to preserve surjective maps.  However, I don't find this very useful for thinking about higher cohomology, since it would need that I somehow understand lower cohomology much better.
Answer: A sheaf $\mathcal{F}$ on a topological space $X$ is the same as a local homeomorphism into $X$: Starting with the sheaf you take the disjoint union of the stalks and put on it the topology generated by the sets $[U,f]:=$ {$f_x \in \mathcal{F}_x \mid x \in U$} where $U$ ranges over all open sets of $X$, $f \in \mathcal{F}(U)$ and $f_x$ denotes the image of $f$ in the stalk. This is called the "espace etalé" of the sheaf. The map which maps stalks to "their" point is a local homeomorphism.
On the other hand you can get back a sheaf from a local homeomorphism $E \rightarrow X$ by taking as the value on the open set $U$ the sections $U \rightarrow E$ of the given map. This defines an equivalence of categories.
So a way to see sheaf cohomology geometrically is to make the sheafs into geometric objects this way - then we have both schemes and sheaves living in the same environment and see that sheaf theory is about maps from schemes to sheaves.
Now an intuition about cohomology is that it measures how many more sections you gain when you go more local. To get into a framework where you can adequately treat this going local, you can pass to the category of simplicial sheaves over schemes and there introduce an adequate notion of when a map is an equivalence: A simplicial object is a sequence of objects connected by a bunch of maps; the example to care about at the moment is that of the nerve of a cover: Given a cover $\coprod U_i \rightarrow X$ you can produce such a sequence of objects by putting $\coprod U_i$ at level zero, the pairwise intersections of the $U_i$ at level 1, the triple intersections at level 2 and so on. Another example is to just put the same $X$ into each level -the notion of equivalence is such that these two simplicial objects are equivalent in our new category. Homming out of one is the same as homming out of the other one, up to equivalence, but there is a sense in which the intersection object is the right one to take ("it is cofibrant"), rather than $X$.
Now the different levels in the Cech complex arise from mapping out of each level of the nerve. Roughly, taking the $i$th cohomology then tells you how many of the compatible sections (compatible meaning if you pass to the next stage of intersection) at the $i$th stage already were there at the $i-1$st stage.
*Edit*I'll be a little more explicit about this: We have the sequence of intersections of the objects in a covering
$$\coprod U_i \Leftarrow \coprod U_i \cap U_j \Lleftarrow \coprod U_i \cap U_j \cap U_k \ldots$$
Here the two maps into the zeroth stage are those who include $U_i \cap U_j$ into $U_i$, $U_j$ respectively, the three maps into the first stage are those who leave away the $i$, resp. $j$, resp. $k$ part etc. Now map from this whole arrangement into a sheaf of abelian groups (i.e. apply the sheaf to all these objects and arrows). Mapping out of a disjoint union (coproduct) is the same as giving a bunch of maps, one from each constituent of the coproduct, so $\mathcal{F}(\coprod U_i)=\prod \mathcal{F}(U_i)$. Since the values of $\mathcal{F}$ are abelian groups we can take alternating sums of parallel arrows and thus get a diagram
$$\prod \mathcal{F}(U_i) \rightarrow \prod \mathcal{F}(U_i \cap U_j) \rightarrow \prod \mathcal{F}(U_i \cap U_j) \rightarrow \ldots$$
This is a complex and it's cohomology is what we are talking about. $(x_i) \in \prod \mathcal{F}(U_i)$ being in the kernel of the first morphism means that the difference of the two restriction maps is zero, i.e. the restrictions to the overlaps $x_i \mid _{U_i \cap U_j}$ and $x_i \mid _{U_i \cap U_j}$ are the same, i.e. since $\mathcal{F}$ is a sheaf they glue to something defined on all of $X$. This is why the zeroth cohomology of the complex (which is just the kernel, since there is no incoming map) are the gobal sections of the sheaf.
But when we took just the kernel out of $\prod \mathcal{F}(U_i)$, thus separating the compatible systems, how many *in*compatible systems did we throw away? Answering this would tell us how many more sections we get locally as opposed to globally (with respect to this chosen cover).
Any family of sections defined on the $U_i$, $(x_{i}) \in \prod \mathcal{F}(U_i)$, gives us a family in the double intersections $(x_{ij}:=x_i \mid _{U_i \cap U_j} - x_j \mid _{U_i \cap U_j}) \in \prod \mathcal{F}(U_i \cap U_j)$. Moreover, if our family was compatible, this is the zero family, by definition of compatible! So it is a good idea to study the families of sections on the $U_i$ via the families of sections on the $U_i \cap U_j$ that they induce - this way we get rid of the global sections and get exactly the difference we are interested in.
But how can we characterize the families $x_{ij} \in \prod \mathcal{F}(U_i \cap U_j)$ which come from families on the $U_i$ ? Well, these satisfy the "cocycle condition" $x_{ij} \mid_{ijk} - x_{ik} \mid_{ijk} + x_{jk} \mid_{ijk}$ - you see it by substituting $x_{ij}=x_i-x_j$ etc. - this is the same as being in the kernel of the second map in the complex. Let's call a family satisfying this a matching 2-family (2 because of the double intersections) and call the collection of them $m2Fam$ (likewise $2Fam$ for the collection of all 2-families). Being a matching 2-family is however not sufficient for coming from a 1-family; there are "exotic" matching 2-families not arising in this way - to see how many we can take the quotient of all matching 2-families by those coming from 1-families. This is $H^1$. It is an error term to our tentative calculation of the difference between global sections and sections on the covering in terms of matching 2-families.
Writing now very loosely equations for these collections (e.g. "$1Fam - 0Fam$" meaning the collection of 1-families without that 0-families, "=" meaning "is parametrized by" or whatever),
we have $1Fam - 0Fam = m2Fam - H^1$ because we more or less "defined" $H^1:=m2Fam - (1Fam - 0Fam)=m2Fam - (1Fam - m1Fam)$ (the latter because $m1Fam=0Fam$).
Likewise if we want to know how many 2-families are there which were not already there as 1-families (i.e. if we want to determine $2Fam - 1Fam$), it seems a good idea to display 2-families as matching 3-families because the 1-families will be killed in the translation process. However not all matching 3-families arise in this way; we get $H^2=m3Fam - (2Fam - 1Fam)$ and so on - $H^n=m(n+1)Fam - (nFam - (n-1)Fam)$.
It also is instructive to remember that before comparing $2Fam$ and "its subcollection" $1Fam$ we have to map $1Fam$ into $2Fam$ and in the process the subcollection $0Fam$ of $1Fam$ gets killed and $1Fam$ becomes $(1Fam - 0Fam)$. So actually we want are talking about $2Fam - (1Fam - 0Fam)$. Doing this small rectification recursively in the formula $H^n=m(n+1)Fam - (nFam - (n-1)Fam)$ gives you a bunch of differences in nested parentheses and makes the alternating sums appear which you know from the Euler characteristic... (end of edit)
I hope that was an intelligible first (edit: and second :-) approximation. The same picture is valid when you pass to cohomology over other sites - there you don't have the espace etalé but taking sections is still the same as mapping into the sheaf by the Yoneda lemma. You can read more about this and all the involved notions at the cohomology page of the nLab.
Comment: @bavajee There are quite a lot of discussions of this point about the nerve / Cech complex in notes here and there on the web. I wrote up some of this in the Menagerie (http://ncatlab.org/nlab/show/Menagerie), which works its way towards the description that Peter gives. Seeing the way that torsors interact with the Cech complex is something that is really beautiful, and then understanding that this gives a hint as to how go to higher dimensions provides insights into both the Abelian and non-Abelian situations.
Comment: This sounds really interesting. Could you elaborate slightly on the second to last paragraph? In particular what do you mean by "if you pass to the next stage" and "were there at the $i−1$  the stage"?

The nLab page is too sophisticated for me. Are there any introductions pitched at the level of someone who has taken an introductory class on algebraic geometry covering schemes and derived functors?
Comment: @Tim Porter: That Menagerie looks fantastic! I learned a lot from your Cubo paper and am looking forward to this one. Thanks for your pedagogical efforts! As you can see above your attitude is contagious:-)
Comment: @bavajee: Here you go
Comment: that was directed at Tim.

@Peter. Thanks a lot for the extensive edit. I'll look at it tomorrow.
Comment: @Peter: Thanks a lot. That was very enlightening.
Comment: Thanks, although it was not quite what I was looking for, I like this answer very much!
Comment: Haha wow Peter, I just found this, what a wonderful answer. :-)
Comment: I loved this answer. Seriously, I think this answer somehow made me see the light at the end of the sheaf cohomology tunnel.
Answer: I'm going to stick my neck out, rather than recycle some well-known phrases in sheaf theory. I suggest trying to answer this as two possibly simpler questions:
1) What is the intuitive meaning of a short exact sequence of sheaves of abelian groups? Is it seriously deeper than the exponential sheaf sequence (http://en.wikipedia.org/wiki/Exponential_sheaf_sequence) with its formulation of things about the complex logarithm that for some of us are intuitive?
2) Why did they invent cohomology all in a rush in the late 1930s, when homology theory took quite a while to come together as a theory? Wasn't it because the various different cocycle notions started to look more and more like aspects of a single type of "obstructiveness"?
From a rather reductionist but hands-on perspective, if cohomology of coherent sheaves allows one to recover so many key discrete invariants in geometry, as dimensions of some things that are not a priori dimensions of vector spaces of sections but seem like perfectly good extensions of the idea of Betti number into other interesting fields, I wonder quite where the problem is.
Of course it has certainly been said before on MO that learning sheaf theory is still not that easy, absent le Godement nouveau. It could be that trying to understand the general sheaf that we are talking about is not the right way. (I can't say that I have much intuition even about the general abelian group.) It is not that disrespectful of homological algebra to consider it a computational device, and the very general stuff as some guarantee that its concepts do at least have some sort of (denotational) meaning. In other fields that is considered worthy. I can quite see that geometers feel that "geometry qua intuition" is the way to understand techniques; but Weil wasn't so sure.
Answer: First you should ask what is the intuition behind sheaves and there it is possibly best to think of local sections of a map to a base space. So now you have local sections and thinking back to ideas from complex analysis, you start trying to patch the local sections of a bundle together. (Think of patching charts on a manifold or local trivialisations of a vector bundle for instance.) You need to get transitions on from one local description to another. On triply overlaping patches you need a compatibility condition (cocycle condition) in order to make things work. What about quadruple intersections? That way you get the Cech sheaf cohomology idea quite naturally.  (If you want to go up a level of abstraction you can now try using a Grothendieck topology on a category, and the process is very similar.) The higher cohomology groups (for Abelian sheaves) detect obstructions to patching like this. (This is related to an earlier answer about obstructions to global sections but does not need the exact sequence of coefficients.)
The nice thing about thinking about this as measuring obstructions to patching local descriptions of things is that, with care, you can even do if for sheaves of groups, or algebras or complexes of things, or ... whatever! (<-within reason.:-))
So intuitively they measure obstructions to patching local things together.
The question mentions homology, but in fact cohomology is possibly even more geometric than homology.
Comment: Thanks, you should have given the great Menagerie link here in your answer!
Comment: @ Jan.  Thanks.  If anyone wants it there is a version on the n-Lab.  Just search on Menagerie. (There are other sections that follow things up but they are a bit incomplete so I have not put a copy up there yet.)
Comment: @TimPorter could you please point out where in the Menagerie notes this is discussed?
Comment: @arrow:  Try about section 6.4.2, so page 193.  You will have to read back to see what terms mean if you do not know, but this handles some of the ideas.
Answer: This sounds like a cop-out, I know... what it is not very far from reality, at least in some contexts:
One is not really interested in the higher cohomology groups but only in the actual group of global sections, and higher cohomology groups' purpose in life is to allow us to do inductive proofs and other tricks like dimension shift.
Comment: Dimension shift is the fact that if $0\to M\to P\to N\to 0$ is is an exact sequence in which $P$ is projective, then $Ext^i(M,-)$ and $Ext^{i+1}(N,-)$ are isomorphic. You can find this put to good use in showing the uniquess of products in group cohomology already in the book by Cartan and Eilenberg, but it is a standard trick.
Comment: What do you mean by "dimension shift"? Also, do you happen to know of a good example that illustrates how sheaf cohomology is used to do "inductive proofs"? I'm somewhat new to sheaf cohomology.

What is sheaf cohomology intuitively?


When will Natty Narwhal 11.04 be stable to use?

Question: I have been wanting to try Natty Narwhal really bad. So about a week ago I tried it, and it was not at all stable. I know it's still in development but I desperately want Unity, I even reorganized my gnome panel with dockbarx and gnome window applets to try to emulate Unity. I tried Maverick early and it was great. :D (getting a little off topic here....) But anyways ;) When is Ubuntu Natty Narwhal 11.04 going to be ready for stable testing?
Answer: You can use stable release in April-2011
Answer: When it's released.
I don't mean to sound snide because I'm being serious. No pre-release version is recommended for production use. It may crash and break everything.
If you don't care about minor glitches, the beta releases and release candidates in late March through April should give a fairly robust experience.
Trying it at alpha stage is not recommended if you're not completely confident with all areas of an Ubuntu system.
Comment: It's the end of Aug 2011, and 11.04 STILL isn't stable. A USB 802.11n adapter caused my wife's box to crash 4 or 5 times a day. Seriously... when?
Answer: Ubuntu version numbers are the year and the month of any release, so 11.04 is 2011 April.  Anything before then is an unstable pre-release version and should only be used if you are okay with bugs and instability.
Closer to that date, there will be several beta releases followed by a few RC (release candidate) releases.  I've found that previous ubuntu versions are mostly good by the time the second beta comes out, which tends to be in the month or so before the official final release date. Even so, there may still be major bugs in the betas.
More about ubuntu's release process: https://wiki.ubuntu.com/UbuntuDevelopment/ReleaseProcess


Do floating bridge springs need changing ?

Question: I have a 9 year old Ibanez RG250 with floating bridge. When I use the tremolo my guitar goes slightly out of tune, goes flat if I push down, and sharp if I pull up (I'm talking of course after I stop using the tremolo). I can get it back on tune if I push/pull a bit in the opposite direction. I have a feeling this is normal even in new guitars, but I was wondering if it gets worse in time, and if that's related to the springs.
Answer: There are closely guarded methods to setting up a floating vintage tremolo (non Floyd Rose) so that it stays in tune. I've done quite a bit of research on it (hunted down interviews, videos, books, and asked techs) but I've not seen any solutions/explanations blaming the problem on old springs.
Often keeping a floating tremolo in tune has to do with how you setup the guitar. It can involve more obvious methods like lubricating the nut to reduce friction & stretching new strings, to less obvious ones like adjusting the bridge claw to a specific height.
Anyways, here are two great videos showing two different ways to keep a floating trem in tune:
http://www.youtube.com/watch?v=Iy-F7iSIopA
http://www.youtube.com/watch?v=O0Oyc6slYRc
Over time, I've learned to use a combination of all the above tips and I'm happy to say that I've been able to keep my Strat in tune after whammy use. Give some of these methods a try and see what works for you.. good luck!
Answer: With two of my old guitars (one with a Floyd Rose about 20 years old and one with a Kahler about 23 years old) they will go out of tune a bit the first few days I use them with a new set of strings, but after they settle down they'll then be in for months - and I do divebomb and pull up a fair bit:-)
They both have locking nuts, which definitely helps by reducing the amount of string slippage through the nut, and there isn't much behind the bridge either, about 3 mm before the string clamp blocks.
If you don't have a locking nut, you could try replpacing your nut with a graphite nut, or using lubricant.
Answer: Over time the knife edge of the trem unit where it rests against the pivot posts can wear down. This can mean that the trem is more likely to stick in certain positions just slightly out of tune. Floyd Rose patents cover a bunch of different things, one of which being the construction of the knife edge, and when they licence the design out this is one of the things that they keep back so that original Floyds have a leg up over copies. This may play a part in your problem.


How did we find out the shape of our own galaxy without going out of it?

Question: As far as I know, scientists have been able to see a lot of differently shaped galaxies in our visible universe through modern age telescopes. But I was wondering how it was possible to know how our own galaxy looks like without going out of it to see its shape?
Comment: You probably have images like this in mind http://commons.wikimedia.org/wiki/File:Milky_Way_2005.jpg
Comment: How do you know the shape of your room without going out of it? By looking at the things furthest away in a particular direction that you can see (i.e. walls) and measuring how far away they are. This will only give you certain parts of the room, but it is a start.
Answer: We obviously do not know the shape exactly, but by measuring the positions of visible stars in our neighborhood We can tell that it is a spiral arm galaxy. In fact to the naked eye, the fact that we see a band of diffuse light called the Milky Way shows that we are in a flat type of galaxy and not in a globular cluster or an elliptical galaxy. There is a lot of evidence that the supermassive black hole that is at the center of our galaxy is located in Sagittarius A and we know the distance to that black hole.  In addition we can measure the orbital velocity of stars rotating around the galaxy.
However, we can only see individual stars that are somewhat close to our position about 2/3 of the way out from the center of our galaxy - there is too much obscuring dust to see to the other side of the galaxy, for example.  So we will always be somewhat limited in our ability to map out our galaxy exactly. However we do know enough to confidently say that we are in a spiral armed type of galaxy.
Answer: We have utilized a huge number of tools to determine the shape of our galaxy over our existence on this planet...  the simplest of which is just looking up.  It is clear that the milky way (that grayish streak through the sky) is flat, and because we know this blotch is caused by millions of distant stars and all the dust between us and them, we can safely guess that our galaxy is flat at the very least.
Outside of this obvious fact, it is also possible to use the directions and distances to observable stars to create a 3-D model of the galaxy.
Clearly there are also more complicated and accurate ways of mapping our galaxy, however... if you wish to read about the basic idea of how we moved from "it's flat" to "it's a spiral galaxy", I recommend this article or a basic google search.


How can I Transfer mysql wkt directly into a postgis table?

Question: I have wkt geometry data in mysql stored in blob format.
I need to get this data into a postgis db and am looking for the quickest-easiest way to do it. I have managed to select the data "ASTEXT" but can then only copy it into QGIS -> export to shape -> import to postgis....but this is probably not the easiest way.
Is there a way to directly import a table from mysql into postgis?
thanks for any help,
Answer: I haven't tried this with mysql but I think ogr2ogr should be able to do it for you.


Fuji Thrill shimano gears

Question: I just bought my daughter a mountain bike (at a garage sale) a Fuji Thrill with Shimano gears.  Anyway we need to replace the right hand shift/brake combo lever(the little spring is shot and won't allow changing of gears).  It is a 3 x 7(with a little window to see the #'s 1-7 with a green indicator).  The guy at the bike store suggested a Shimano EF60 but I need to buy both and change all the wiring. I can do the work but would rather only replace the broken one.  Any ideas on where I can find a part online and what the part # would be?
Answer: In the UK you can buy OEM R/H only:
http://www.evanscycles.com/products/shimano/ef60-v-brake-8-speed-r-h-shifter-oe--ec028391?utm_source=froogle&utm_medium=froogle&utm_campaign=froogle
(That is the 8 speed that will work fine on 7).
Here is the tech.doc:
http://techdocs.shimano.com/media/techdocs/content/cycle/EV/bikecomponents/ST/EV-ST-EF60-2A-2744_v1_m56577569830630796.pdf
The part number is ST-EF60-7 - ask your LBS to order the part in for you, off the top of his/her head the sales staff may not know this can be ordered, but it almost certainly can, and definitely can in the UK.
Answer: If you don't want to order it through your LBS (local bike shop), eBay and Google shopping are often reasonably good places to start looking for parts.  The number your LBS gave you (EF60) is sufficient to find the right part in this case (you just want the right shifter, but they are sold in pairs, so look for something like "right EF60").
It's not directly related to the question you asked, but now might also be a good time to replace the shift cable as well (since you will need to remove at least the rear one anyway--that might be why the guy at the LBS suggested it).  Shift cables are fairly inexpensive--my LBS sells them to me for about $1 each.
Also, since the pair only costs about $20, I'm not sure you really come out ahead by buying just the right one.  First, buying just one of a bike part sold in pairs often costs much more than half the price of the pair.  Second, shipping just one will probably cost about 75% of shipping both (since this is a fairly small and light item).  If you ever need to replace the left shifter, you will be much better off if you had just bought the pair in the first place.
Finally, if you aren't already familiar with the procedure for installing a adjusting indexed shifters, pick up a copy of Zinn's book.  (Zinn and the Art of...)

Fuji Thrill shimano gears


What techniques should be used to ensure clear communication from the customer?

Question: Some customers use terms from the domain language interchangably and incorrectly. This has, on several occassions, lead to an implementation of a feature in a way that was not desired by the customer. Are there any techniques that can be used to enforce the correct use of terms? Are there any techniques that can be used to prevent someone from handing "back of a cigarette packet" requirements to a developer?
Comment: Added requirements and specifications tags.
Comment: This sounds like the domain language is not adequate for modelling your customers needs.
Answer: The best way to find out common ground/language with stakeholders is to write down requirements. This process should be iterative, so nothing wrong if something has been written incorrectly.
as one of the options - use Tom Gilb's requirements specification technic.
Comment: http://www.gilb.com/Requirements
Answer: I find that if I'm getting confused about what's actually desired, or if I suspect that we are not using the same words in the same way, that discussing specific examples together is the quickest and most effective way of discovering that you have different ideas. (I can't tell you how many times I've been sat in a meeting, and everybody's convinced they're in agreement - and then someone describes a specific example, and suddenly half the room is nodding yes, yes, that's it, and the other half is going "wait a minute, you want what?").
Of course, this is easiest if you're in the same room when the "back of a cigarette packet" requirements get handed over, and (to my mind) easier if you are working in an iterative fashion and clarifying small numbers of requirements at a time, but I've used this in a waterfall environment when reviewing requirements - my review comments just included examples.
As a tester, I do tend to immediately start thinking of concrete examples - both happy path and edge cases. If you're a programmer, it may be a good approach to pull a tester into the conversation with the customer too - you'll both think of different examples, and each one may reveal some misconception the customer has about what you're planning to implement, or what the system currently does. Everyone has a mental model of the system - the customer is likely to be less experienced than either a programmer or a tester at describing what their mental model is, so approaching that by discussing specific examples both gives you a set of acceptance tests, and helps to support them in explaining what they really want.
Another good approach is to ensure that you don't fall into the practice of using entirely different terms inside the tech team: in one company I worked in, this practice was endemic, and it drove me crazy - my monitor was peppered with little post its for each project with business to tech translations "business name: X, tech name: Y." It also frequently led to problems of the sort you describe as the meaning of each term would drift over time. As a tester, I always looked especially carefully for integration problems in areas I knew there were different terms for - because I knew it was likely that each development team would have come to a slightly (but critically) different interpretation.
These are things I've always tried to do informally as an individual on projects, but you should check out Gojko Adzic's work if you want to hear about how people implement this more formally as a part of the way they run projects. Check out the following blog link - I'd also recommend his two books, Bridging the Communication Gap, and Specification by Example:
http://gojko.net/2010/12/02/the-principle-of-symmetric-change/
Comment: +1 Especially for trying to always have concrete specific examples.
Answer: Don't try to "enforce" anything.  As a requirements analyst it's your job to make sense of what they're saying, not the other way around.
Definitely do take the time to explain your model to them, and if they use incorrect terminology in a meeting ("blah blah warehouse") then repeat it back to them - politely - as though they'd used the correct terminology ("blah blah inventory").  In most cases they will pick up on your language, as long as you yourself are consistent with its use.
But you absolutely must ultimately let the clients speak in their own language, otherwise you're just going to create an adversarial situation and slow the entire analysis process down.
Clarify terms as necessary during the live sessions, and send out final deliverables written in your language for review (usually with a glossary of some sort). Your objective isn't to shoehorn them into your way of thinking, it is simply to understand how they do business and implement/optimize where appropriate.
Just one other quick thing:

Are there any techniques that can be used to prevent someone from handing "back of a cigarette packet" requirements to a developer?

If you have clients sending any requirements directly to a developer then you have a problem in your team or organizational structure.  I'm not sure if you meant that literally, so please forgive me if I've misunderstood, but requirements should be going through a requirements analyst or business analyst, whose exclusive mandate is to translate between the business and system domains.
If you've got a tiny handful of developers that are all really good at this themselves, then, no problem - but as you're probably beginning to notice, that doesn't scale too well.