I am just 16 and curious to learn about Theory of Relativity. Can any one explain it simple enough for me to understand? I read that it is bending of time-space or space-time that causes gravity. How can bending of time takes place?
I understand that people explain (in layman's terms at least) that the presence of mass "warps" space-time geometry, and this causes gravity. I have also of course heard the analogy of a blanket or trampoline bending under an object, which causes other objects to come together, but I always thought this was a hopelessly circular explanation because the blanket only bends because of "real" gravity pulling the object down and then pulling the other objects down the sloped blanket. In other words, to me, it seems that curved space wouldn't have any actual effect on objects unless there's already another force present.   So how is curved space-time itself actually capable of exerting a force (without some source of a fourth-dimensional force)?  I apologize for my ignorance in advance, and a purely mathematical explanation will probably go over my head, but if it's required I'll do my best to understand.
I ask a lot of question on SO, so this recommendation/idea comes from that experience. I'm not really sure how this would fit in with the current structure of SE.   Oftentimes after asking a question, maybe after an hour or so, I end up finding the answer I needed somewhere. And it comes time for me to answer the most difficult question of all: do I delete this question, or do I keep it in case someone answers and others may benefit from it. The problem is, if I don't delete it and no one answers, my acceptance rate goes down. So usually I'll just delete it.  However, sometimes I fear that someone is typing a really really long answer to my question since itäs only been an hour, and so I imagine the nightmare that person experiences when they find out their essay will be gone to waste. Overall, this never-to-be-seen-again answer could have benefitted many people had the question remained.  Since SE has gone "live-happy" lately, where answers and comments refresh live, I thought it might be interesting if the original asker of the question (or anyone else for that matter) could see how many people are currently responding to the question (just count, not necessary to display their names). This way, if I know someone is replying, I won't delete the question, and others can benefit from it. double perpendicular symbol (for independence) I found from  that I could use the independence symbol:     \newcommand\independent{\protect\mathpalette{\protect\independenT}{\perp}} \def\independenT#1#2{\mathrel{\rlap{$#1#2$}\mkern2mu{#1#2}}}    I was wondering how this works. Can anybody explain? I don't know the commands mathpalette, rlap, and mkern2mu. $e^{mx}$ in solving second order differential equations In a book I am reading on differential equations, the author writes about the solution to a homogenous, linear, second order differential equation with constant coefficients. The author says something like, "Let us suppose that the solution is of the form $y=e^{mx}$ " . After this the author introduces the characteristic equation of a differential equation of the form mentioned above, and proceeds to describe how to solve it w/ undetermined coefficients, variation of parameters, etc.   How did mathematicians first come up with this "assumption" that the solution was of the form $y=e^{mx}$? And, are there any other forms of solutions for these types of equations? Possible Duplicate:          I would like to know if when I'm writing about a "user" (in the broad sense), what do I use? Example: "from the user’s perspective, saving a file is very easy; ? only needs..."  What is correct: she, he, she or he, or they. Removing blocks from configuration files? Why don't the Google Docs CTRL + ALT shortcuts work? I'm currently using Google Docs, but when I try to use the keyboard shortcuts like Ctrl+Alt+M it gives µ instead.    Is Chrome (9) overruling Google Docs in some way?  How can I get these shortcuts working?  I'm using Chrome dev 9 on a Dutch Windows 7 with a US-layout keyboard If "I'm thinking" is correct, why isn't "I'm knowing" correct in formal English?  think+ing = thinking is correct know+ing  = knowing isn't correct   Why? Mining cryptocurrencies with Ubuntu and sgminer What are the steps for setting up a Ubuntu machine for mining of crypto-currencies?  I am looking for a full guide to follow - from installing Ubuntu to how to config and start the miner itself. Deploy a project using Git push Is it possible to deploy a website using git push? I have a hunch it has something to do with using  to perform a git reset --hard on the server side, but how would I go about accomplishing this? Writing comments in QGIS Graphical Modeler I want to explain my model step by step so anyone can easely understand what's going on. So, is it possible to write comments in the QGIS's Graphical Modeler? Wielding two weapons without "Two-Weapon Fighting" or "Dual Wielder"? We have a Barbarian on our team that very much likes to switch up his weapons; he goes from a Dwarven Hammer, to a pair of Hand-Axes, to occasionally just going bare-fisted. No issues there, he's fairly adept with all 3.  However, I have only just recently picked up on the way that he rolls his attacks for the two Hand-Axes: He rolls the first attack, adds his modifiers etc. Then he rolls the second attack, this time without modifiers, which is all well and good. But I'm not sure if this action uses his bonus action or not, or is considered a separate action (though, being a level 4 Barbarian, he only has one action per turn), or is merely part of the same action.  If we have a look at the Two-Weapon Fighting feature from the Fighter's fighting styles:     Two-Weapon Fighting   When you engage in two-weapon fighting, you can add your ability modifier to the damage of the second attack. (PHB5e p.72)   Similarly, the Dual Wielder feat also uses the Two-Weapon Fighting feat:     Dual Wielder   You master fighting with two weapons, gaining the following benefits:      ...         You can use two-weapon fighting even when the one-handed melee weapons you are wielding aren’t light. (PHB5e p.164, emphasis mine)      So; yes, this gives a bonus to the second weapon attack, but having asked a  to clarify which action this secondary weapon attack belongs to, it was determined that this uses your bonus action;     [...] the second attack requires a bonus action   So after that long winded explanation, here is the question: Without any additional feats, can you wield and use two weapons at once, and if so, how many actions does it require to make a full attack with both weapons in a turn? I'd like to know how I can recursively (edit: iteratively) compute variance, so that I may calculate the standard deviation of a very large dataset in javascript. The input is a sorted array of positive integers. Is abstract algebra (mostly?) restricted to $2$-ary operators? This may be due to my own pure ignorance but it's my experience that all abstract algebra I've been introduced to, both in actual courses and in self-studies only exclusively deals with algebraic objects consisting of a set together with one or more binary operators defined on that set, perhaps over some other algebraic structure. Not counting categories here, just "low-level"-ish stuff.  I'm an undergraduate so my knowledge is of course very limited but I can't help to wonder why I never stumble upon algebraic structures with $n$-ary operators? Is there a good reason for this, something along the lines of $n$-ary operators behave "badly" when $n&gt;2$ or is it just my ignorance because I'm a beginner in the field? What's the purpose of the CIL nop opcode? I'm going through MSIL and noticing there are a lot of  instructions in the MSIL.  The MSDN article says they take no action and are used to fill space if the opcode is patched. They're used a lot more in debug builds than release builds.  I know that these kinds of statements are used in assembly languages to align later instructions, but why are MSIL nops needed in MSIL?  (Editor's note: the accepted answer is about machine-code NOPs, not MSIL/CIL NOPs which the question originally asked about.) Any good relational database tutorials? Spacing before and after section titles I know this subject has been mentioned before, but I'm still having a problem in creating a space under a section title. I used the titlesec package and then tried using the command \titlespacing{\section}...  This is my code. Can anybody help?  \documentclass[10pt]{book} \usepackage[utf8]{inputenc} \usepackage{fullpage} \usepackage[compact]{titlesec} \usepackage{setspace} \usepackage{sectsty} \chapterfont{\huge} \sectionfont{\Huge} \begin{document} \chapter*{Kapitel 1} \section*{Einleitung} \begin{large} \subsection*{1.1 Motivation} What is the best way to call a script from another script? How to render a 30K image with cycles? I have to render an image of 27000 x 7000 for a 150dpi print. The scene is quite big, but cycles preview and a render in 2700x7000 works as expected.  If I hit render my memory raises up to 20gb, but my cpu usage is at 5%. Why cycles does not using the full cpu power during the render process?  Here are my rendersettings:  Pathtracing Samples:3000 Tilesize: 64x64 Bounces: Max 12 | Min 3 Diffuse: 4 Glossy: 4 Transmission: 12 Volume: 1   Is there a way to optimize things? If $k=1$, we have \begin{align} \sum_{n\ge1}\frac{1}{\binom{2n}{n}}&amp;=\frac12\sum_{n\ge1}n\mathrm{B}(n,n)\\ &amp;=\frac12\int _{0}^{1}\sum_{n\ge1}n(t-t^2)^{{n-1}}{\mathrm  d}t\\ &amp;=\frac12\int _{0}^{1}\frac{1}{(t-t^2-1)^2}{\mathrm  d}t\\ &amp;=\frac13+\frac{2\sqrt3\pi}{27} \end{align} I wonder if there exists a general formula of $\sum_{n\ge1}{\binom{2n}{n}^{-k}}$ with $k\in\Bbb N^*$. This may involve some ${}_pF_q$ functions. What is the ideal way to handle data pins D+ and D- on a USB power adapter to be compatible with fast charging on devices?