How to see that this is uniformly distributed on the unit sphere?
Uniform distribution on the surface of unit sphere
Bug with Excavator Badge I edited this post today  on stack overflow. I was approved of the edit, so I waited a few minutes to get my  badge because this answer was posted on Jan 28 '10 at 1:06, but it never came. I have read multiple articles on meta that there have been bugs with this badge, but they have been about winning it multiple times (), or earning it then losing it (). Am I missing something here? Years ago I read short story about a man sitting in his room. Suddenly appears the same man but from the future and gives him an advice about the future. Original man seems to agree to follow that advice. Man from the future goes away. Then another version of that man from another future comes and gives a completely opposite advice and begs original man to follow it. Then this second version of this man from future also left. Original man stays alone not knowing which advice from future he must follow. Why does Google not consider dot in usernames of Gmail addresses? E.g.: If your Gmail ID is abc.xyz@gmail.com, it considers this the same as abcxyz@gmail.com.  Why is this so? Are there any references to Eru or the Valar in the Lord of the Rings movies? The closest references to Eru or the Valar in Peter Jackson's Lord of the Rings and The Hobbit movies I can think of are Gandalf's vague description of his resurrection ("I've been sent back... until my task is done.") and his later description of Aman to Pippin ("White shores and beyond, a far green country under a swift sunrise." -- as an aside, he's taunting Pippin here, since Hobbits suffer from the Gift Of Men) and the equally vague information viewers are given about where the elves are going when they leave Middle Earth.  Are there any more direct references I'm missing? Maybe a mention of Aule by a dwarf? I would like site specific magic links. Currently you can write [so] in a comment, and it links like this: . I would like to be able to have site specific ones, so for example: English Language &amp; Usage  [dictionary] would go to http://dictionary.com and shows as   Ubuntu  [launchpad] would go to https://launchpad.net/ubuntu and shows as   [launchpad#bugnum] would go to https://bugs.launchpad.net/bugs/bugnum and shows as   [forums] would go to http://ubuntuforums.org/ and sows as   [discourse] would go to http://discourse.ubuntu.com and shows as   [paste] or [pastebinit] would go to http://paste.ubuntu.com and shows as   [install-d] would go to http://ubuntu.com/download/desktop/install-ubuntu-desktop and shows as   [install-s] would go to http://ubuntu.com/download/server/install-ubuntu-server and shows as   ppa:peterlevi/ppa would go to https://launchpad.net/~peterlevi and shows as   There is    Ask Different  [applesup] would go to http://www.apple.com/support and shows as   Christianity  [bible] would go to http://biblegateway.com and shows as   Currently, they are all the same, for all sites. I would like devs (mods maybe) to be able to add them on a per site basis. This is just a selection of examples. People can comment or answer with ones they would like and I'll edit them into this question. I asked this because  on Ask Ubuntu Meta wasn't possible right now - because it wasn't a feature.  [The devs] said right now it isn't possible because magic links are network wide, and they weren't sure it was high enough priority to really get done anytime soon, but if you want you can post a feature-request on Meta Stack Exchange requesting site specific magic links and see if you can garner more support for the feature and maybe get a dev to champion it.  So that's what I've done! Say that we have a secure random number generation that outputs 32 bit random numbers, so it's output is a true random number between 0 and a MAX.  What is the best way to map this random number to a defined range (say I want something random between X and Y) without loosing too much entropy? Logistic regression is predicting all 1, and no 0 I am running an analysis on the probability of loan default using logistic regression and random forests.    When I use logistic regression, the prediction is always all '1' (which means good loan).  I have never seen this before, and do not know where to start in terms of trying to sort out the issue.  There are 22 columns with 600K rows.  When I decrease the # of columns I get the same result with logistic regression.   Why could the logistic regression be so wrong?  **Actual from the data**  0 :   41932  1 :   573426  **Logistic regression output**   prediction for 1 when actually 0: 41932 prediction for 1 when actually 1:573426  A**s you can see, it always predicts a 1**   **Random forests does better:**  actual 0, pred 0 : 38800  actual 1, pred 0 : 27  actual 0, pred 1 : 3132 actual 1, pred 1 : 573399 Move Lifejacket and Lifeboat to Answer Badges section in Help Center The new blog post  mentions the new badges  and  are answer badges, but they are listed on the  under Question Badges:    Since you earn these primarily by posting an answer (you're not required to do anything about the question, though editing it will probably help), they definitely belong to the Answer Badges. Is it true that $\mathbb{R}$ and $\mathbb{R}^2$ are isomorphic as abelian groups? Use of "would" for subjunctive phrases This has been bugging me for some time; I tried to look for previous questions here but my language tools may not be sharp enough to phrase my query correctly so please forgive me if this has already been posted here.  Speakers of English as a foreign language tend to incorrectly use the word "would" when using some particular subjunctive constructs. Here is  (this time presumably by a native English speaker):     If that would happen, you won’t be alone.     (One correct version being "If that happens, you won't be alone".) I have detected this in speakers of a number of languages so I feel this is more likely to be a feature of the English language itself than a carry-over from their native language.  I have a faint intuition that this is because , and it certainly doesn't help that , but I can neither make that precise nor even really phrase a concrete question. Can someone shed some light on this?    Edit: just to provide some real-world examples of what I mean, here is one example taken from :     Publish or Perish is designed to empower individual academics to present their case for research impact to its best advantage. We would be concerned if it would be used for academic staff evaluation purposes in a mechanistic way.   This is obviously ungrammatical (to me), but I'm not sure how to characterize the mistake, or what the likely causes are (e.g. whether it follows from analogous constructions in other languages). Construction of "it's too hard a task" When are Opportunity Attacks provoked while holding a reach and a non-reach weapon? Assume I wield a Whip in one hand and a dagger in the other.  If a creature moves from 5ft to 10ft it has technically moved out of my reach (dagger), but at the same time it is still inside my reach (whip). When does it provoke opportunity attacks from me?  I am fully aware that this would not enable me to make off-hand attacks since the whip is not a light weapon, just to cut that issue out of the question. Pull Down Resistors In my quest to understand electrical engineering, I have stumbled across this tutorial:    I have understood the diagrams until I got to switches. I am not sure how switches work on the breadboard or the diagrams. This is the specific one I am thinking of (this is of a pull down resistor):    The implementation is:    Based on the diagram, what I think is happening is: Power goes to the switch, if the button is up then the circuit is not completed. If the button is pressed then the current takes the path of least resistance to pin2 because it has more pull (100ohm &lt; 10kohm).  The way it is described in the tutorial sounds like when the button is up, the circuit is still complete, but the 10k ohm resistor pulls the power to the ground. I am not positive how or why if both the 10k ohm and 100ohm are receiving equal current, the current would get pulled to the ground through a higher resistance than is open to pin 2. So the first picture is right after I selected where I will cut, and the second picture is after pressing Enter/Space Bar which should apply my previous result to the world. But it is not what I asked blender for, and it tries to snap at vertices. In the tutorial video, it seems that I can cut edges without already existing vertices but it is not the case for me. How do I change this? We are using .Net to make web service calls the Salesforce API. Is there a way to know for sure that the calls are using TLS 1.2? Are there any API logs or records of the protocol is use in Salesforce we can review to be confident the change is working? Rsync filter: copying one pattern only How to not count blank pages in frontmatter of two-sided document Only charge capacitor when button pushed then turn on LED momentarily with capacitor when button released I am trying to make circuit to turn on an LED momentarily. I would like to charge the capacitor when the button is pushed, then when released turn on the LED momentarily with the capacitor. Problem putting matrix operations in an equation Possible Duplicate:          I'm trying to use official equation container for the first time, and it's giving me some trouble.  I have this equation of a simple matrix operation, and LaTeX isn't liking it.  What's wrong with this statement?  \begin{equation}      y = \begin{bmatrix}         T &amp; I      \end{bmatrix}     \begin{bmatrix}         a \\         e     \end{bmatrix}  \end{equation} Finding the limit of $\frac{Q(n)}{P(n)}$ where $Q,P$ are polynomials Suppose that $$Q(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots+a_{1}x+a_{0} $$and $$P(x)=b_{m}x^{m}+b_{m-1}x^{m-1}+\cdots+b_{1}x+b_{0}.$$ How do I find $$\lim_{x\rightarrow\infty}\frac{Q(x)}{P(x)}$$ and what does the sequence $$\frac{Q(k)}{P(k)}$$ converge to?  For example, how would I find what the sequence $$\frac{8k^2+2k-100}{3k^2+2k+1}$$ converges to?  Or what is $$\lim_{x\rightarrow\infty}\frac{3x+5}{-2x+9}?$$   This is being asked in an effort to cut down on duplicates, see here: Coping with  duplicate questions.  and here: .