This is a question thats been bothering me a while. I don't even know if it makes sense or not (like if it is a physics question or becoming a philosophical one). But here it goes. The crux of my question basically is that we all know that we can't see light (like in its photon or electromagnetic wave form) directly when it is traveling past us. However, we also know that the way we see objects is by light reflecting off them. This then means that we are "seeing" the light reflecting from the object which then sends the signal to our brain saying that we are seeing a particular object. We know that both light traveling past us and light reflected from objects are made of photons (so they are the same kind)? So then my question is that what is happening to the photon of a light after it is reflected from the objects, that causes us to see it or the object, but on the other hand we can't see light as it is directly traveling past us.
Let's say we have a cloud of dust which is a lightyear across and someone shoots a beam of light from point A to B , why it is not possible for an observer far far away to see the light while it travels through the cloud at the speed of light?
No \xrightrightarrow[a]{b}? I want my Qt application to be able to save simple vector graphics to clipboard in a compatible way. On windows I want to be able to paste the graphics into Microsoft Word or Powerpoint. On Linux I want to be compatible with the Open Office.   Which format would you recommend? Can Qt generate EMF in an easy way? Is SVG an option?  Update:  My current plan is to add a piece of native win32 code to render the graphics to emf on windows. This code will not be available on linux. How to make a vf page with the same look &amp; feel as salesforce1, any ideas? I want to compile my program with the latest version of gcc.  Ubuntu 14.04 comes with gcc 4.8.2, however there's 4.9.0 available, moreover, I see that it is available as a package: . I tried to install it  sudo apt-get install gcc-4.9   but it says  Reading package lists... Done Building dependency tree        Reading state information... Done Note, selecting 'gcc-4.9-base' for regex 'gcc-4.9' gcc-4.9-base is already the newest version. 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.   Looks like it is already installed, just not as the default one? How do I utilize it to build my program? Let $\{a_n\}$ be an unbounded, strictly increasing sequence of positive real numbers and let $x_k=\frac{a_{k+1}-a_{k}}{a_{k+1}}$. Which of the following statements is/are correct? (CSIR NET December 2014)         For all $n\geq m, \sum\limits^{n}_{k=m}x_k&gt;1-\bf{\frac{a_m}{a_n}}$   There exist $n\geq m, \sum\limits^{n}_{k=m}x_k&gt;\frac{1}{2}$      My attempt:  Analysing question in light of $a_k=k\implies x_k=\frac{k+1-k}{k+1}=\frac1{k+1}$, I feel both are correct, I doubt if  I can generalise the result in light of this one example.   Any way to prove that this true for general case?    Note: Please do not confuse  with my question. The first two options are different, I've marked the difference in bold. On the hardness of data to learn Almost in all texts which are discussing theorems of statistical learning, they assume analyzing arbitrary unknown distribution (the worst case). But in practice different problems (different data) have different levels of hardness, for example linear separable data is easier to learn than the data that are less (or not) separable by hyperplanes.  Are there any works on formalizing the hardness of data (similar to the stuff done in complexity theory)  Note: I am not sure if the same as analyzing VC-dimension or not, but I think it is not. When does $(e^a)^b = e^{ab}$ hold? For a complex number $A$ and a real number $B$, when does the well-known formula $(e^A)^B = e^{AB}$ fail? Or does it hold at all for complex A?     Since $e^{2\pi i} = 1$, if this formula holds for all complex numbers $A$ and real numbers $B$, then it would imply that $e^{2\pi ti}=( e^{2\pi i} )^t = 1^t=1$ for all $t$, which is obviously false. I have a script that reads a text stream and generates a file of sed commands that is later run with sed -f. The generated sed commands are like:  s/cid:image002\.gif@01CC3D46\.926E77E0/https:\/\/mysite.com\/files\/1922/g s/cid:image003\.gif@01CC3D46\.926E77E0/https:\/\/mysite.com\/files\/1923/g s/cid:image004\.jpg@01CC3D46\.926E77E0/https:\/\/mysite.com\/files\/1924/g   Assume the script which generates the sed commands is something like:  while read cid fileid do     cidpat="$(echo $cid | sed -e s/\\./\\\\./g)"     echo 's/'"$cidpat"'/https:\/\/mysite.com\/files\/'"$fileid"'/g' &gt;&gt; sedscr done   How can I improve the script to ensure all regex metacharacters in the cid string are escaped and interpolated properly? As we all know, going near a black hole (Gargantua in this case) slows down time, according to the theory of relativity.  So when Cooper comes out of the black hole, after spending a fair bit of time there, shouldn't he be much older than Brand who hasn't gone inside Gargantua? Interpreting plot.lm() How to evaluate the integral $\int_0^{\pi}\frac{a^n\sin^2x+b^n\cos^2x}{a^{2n}\sin^2x+b^{2n}\cos^2x}dx$? Evaluate the integral $$\int_0^{\pi}\frac{a^n\sin^2x+b^n\cos^2x}{a^{2n}\sin^2x+b^{2n}\cos^2x}dx.$$   I have no idea.   $$\int_0^{\pi}\dfrac{a^n\sin^2x+b^n\cos^2x}{a^{2n}\sin^2x+b^{2n}\cos^2x}dx=\int_0^{\pi/2}\dfrac{a^n\sin^2x+b^n\cos^2x}{a^{2n}\sin^2x+b^{2n}\cos^2x}dx=\int_0^{\pi/2}\dfrac{a^n\tan^2x+b^n}{a^{2n}\tan^2x+b^{2n}}dx$$  I try the substitution $\tan{x}=t$, but it doesn’t work. How to differentiate read and unread messages in android ListView? Should the eigenkets be weighted in $|P\rangle = \sum\limits_{r}|\xi^r\rangle$? Page 37 of Dirac's book The Principles of Quantum Mechanics, states  The condition for the eigenstates of $\xi$ to form a complete set must thus be formulated, that any ket $|P\rangle$ can be expressed as an integral plus a sum of eigenkets of $\xi$, i.e. $$|P\rangle = \int |\xi'c\rangle\; d\xi' + \sum\limits_{r}|\xi^rd\rangle$$ where the $|\xi'c\rangle$, $|\xi^rd\rangle$ are all eigenkets of $\xi$, the labels c and d being inserted to distinguish them when the eigenvalues $\xi'$ and $\xi^r$ are equal, and where the integral is taken over the whole range of eigenvalues and the sum is taken over any selection of them.  I find it inconsistent that the eigenkets under the integral are weighted by what appears to be a differential eigenvalue $d\xi'$, yet all the eigenkets under the summation are weighted by the value 1. Is this correct? I'm writing code to do Xml serialization. With below function.  public static string SerializeToXml(object obj) {     XmlSerializer serializer = new XmlSerializer(obj.GetType());     using (StringWriter writer = new StringWriter())     {         serializer.Serialize(writer, obj);         return writer.ToString();     } }   If the argument is a instance of class without parameterless constructor, it will throw a exception.     Unhandled Exception:   System.InvalidOperationException:   CSharpConsole.Foo cannot be serialized   because it does not have a   parameterless constructor.    at   System.Xml.Serialization.TypeDesc.CheckSupported()   at   System.Xml.Serialization.TypeScope.GetTypeDesc(Type   type, MemberInfo sourc e, Boolean   directReference, Boolean throwOnError)   at   System.Xml.Serialization.ModelScope.GetTypeModel(Type   type, Boolean direct Reference)    at   System.Xml.Serialization.XmlReflectionImporter.ImportTypeMapping(Type   type , XmlRootAttribute root, String   defaultNamespace)    at   System.Xml.Serialization.XmlSerializer..ctor(Type   type, String defaultName space)    at   System.Xml.Serialization.XmlSerializer..ctor(Type   type)   Why must there be a parameterless constructor in order to allow xml serialization to succeed?  EDIT: thanks for cfeduke's answer. The parameterless constructor can be private or internal. I'm trying to watch for any new output of a log file. Another script (not under my control) is deleting the file then creating a new one with the same name. Using tail -f doesn't work because the file is being deleted. How can I send single file to multiple remote sites at the same time? Can scp be used to send a single file to multiple remote servers at the same time? If so, how? If not, what's the alternative? How to evaluate this infinite sum?  $$\sum_{n=1}^{\infty}\frac{1}{2^n-1}$$ How do I take the limit as $n$ goes to $\infty$ of $\frac{\sqrt{n}}{\log(n)}$? How do take this limit:  $$ \lim_{n\to\infty} \frac{\sqrt{n}}{\log(n)}$$  I have a feeling that it is infinity, but I'm not sure how to prove it. Should I use L'Hopitals Rule? This is a  about  Related:      I have a question regarding capacity planning. Can the Server Fault community please help with the following:   What kind of server do I need to handle some number of users? How many users can a server with some specifications handle? Will some server configuration be fast enough for my use case? I'm building a social networking site: what kind of hardware do I need? How much bandwidth do I need for some project? How much bandwidth will some number of users use in some application? LaTeX multi-character subscript