I have read that light is an electromagnetic wave. Every ray of light has a specific wavelength. The colour perceived by any observer is dependent upon the wavelength of the incident light.  What I don't understand is that how do electromagnetic waves of different wavelengths combine to form a single wave of another wavelength? Simply put, I have the following two related questions to ask:    When we look upon a, say, completely white object, what is the composition of the individual rays that strike our eyes? Are those rays waves formed by the addition of waves corresponding to individual wavelengths that constitute white colour? I get that white light is composed of all wavelengths of visible light, but how are those wavelengths combined into a single unit which we call white light? If it is so, then how are prisms able to disperse light into its constituent colours?   Also, as a side question, how does all of this relate to light being composed of photons?
Does a photon having superimposed frequencies exist?  (wrt frequency detected by prism or other detectors, not wrt human eye as only rod-cells can detect one photon falling in the detectable (visible) frequency band and the single photon is perceived by eye+brain as grey irrespective of frequency).  Also, with white here, I do not wish to restrict the question implying all VIBGYOR frequencies or only RGB as each color is also a range of frequencies and white to trichromatic-sensor human eye is just output from three frequencies RGB.  Or can it be that materials which slow light down cause a photon of some single frequency and higher energy to split into VIBGYOR? || and the entire spectrum of human eye's detection range is VIBGYOR+W (as monochromatic light of high intensity can also be perceived white by human eye and it is not related to individual color sensors of human eye at all but that above a certain energy per unit volume (referring to detector area of eye cells), we perceive it white, (somewhat but not exactly) similar to combination of red and green which human eye+brain calls yellow.  I have added the additional description to make the question more precise. If my description causes confusion, please stay with the original question and use description just to get an idea of the intent of the question.
No sound ALC294 Asus ROG Strix 512 Ubuntu 20.04.01 How to install pygments on windows 7 When I run LaTeX file its gives error as  "! Package minted Error: You must have pygmentize installed to use this package", you must have pygments installed. when I go through minted documentation minted itself required pygments, so Tex friend How do I install this pygment, I don't know the procedure to install. Please guid me or any link pygement.exe file Messages on Macs don't work I've tried every suggestion I could find on Apple forums. Deleted .plist files, removed message caches, reset passwords, coordinated sign on/offs between my iPhone and my Macs, reset iPhone and reinstalled Mavericks on my Macbook Air. All pointless exercises.   I suspect it all started because I jailbroke my iPhone using Pangu. It may or may not have been the culprit, but my problems started a couple of days after I did it. All my phone conversations went green and stopped synchronizing with Messages apps on my Macs. Trying to send a new message from Macs would result in either "Your message could not be sent" error with a warning icon next to it, or:     XXX is not registered with iMessage.   So I restored my iPhone to factory defaults using iTunes. That didn't help immediately, but in a day or two, my conversations with other iPhone users went blue. So I am happy that works.  So now I sacrificed my Macbook Air to try and make messages work on it. I reinstalled Mavericks several times, each time trying different approaches: not immediately signing into iCloud, not associating an iCloud profile with login profile, etc. Nothing helps. I launch Messages app, it asks me to sign in (and I do, successfully), and then nothing goes through.   Sending messages to myself also works inconsistently. Yesterday, whatever I sent to myself (using phone number) would appear delivered to the same window, but not on my phone. Today I get "... not registered with iMessage" error. Determining statistical probability related to a string event of dates How to enable virtualization without using bios? I am using android studio.I want to run my app on simulator but it is asking me to install intel haxm,.When i install intel haxm it says that vitualization is not enabled/.To enable virtualization i need to goto bios but issue my bios is password protected &amp; i don't know password.So please tell me is there any other way by which i can enable the virtualization without going into bios? Better extensible arrows Periodically, my MacBook Pro 17" stops recognizing my headphones. No amount of unplugging and replugging seems to help. The sound settings never show headphones as an output device. How can I fix this? The only thing I can find elsewhere on the Internet are people saying, "Reboot!" This works, but is impractical and annoying. I am studying homology groups and I am looking to try and develop, if possible, a little more intuition about what they actually mean. I've only been studying homology for a short while, so if possible I would prefer it if this could be kept relatively simple, but I imagine it is entirely possible there is no real answer to my query anyway.   As I said above, I want to gain a little deeper understanding of what the n-th homology group actually means: I can happily calculate away using Mayer-Vietoris but it doesn't really give me a great deal of intuition about what the n-th homology group actually means. For example, with homotopy groups, the fundamental group is in some sense a description of how loops behave on the object in question, and it is obvious to me why that is what it is for say, the torus or the circle. However, I have no idea what, if anything, I am actually saying about a triangulable object when I talk about it having 0-th homology group this or 1st homology group that.  The best I have been able to find online or in my limited book selection is the brief description "intuitively, the zeroth homology group counts how many disjoint pieces make up the shape and gives that many copies of $\Bbb Z$, while the other homology groups count different types of holes". What 'different types of holes' are there, roughly speaking? I appreciate that it may often be completely non-obvious what the low-order homology groups are for some complicated construction, but perhaps in simpler examples it might be more explicable. Are there (simple) cases where I could say, just from looking something like e.g. the torus, what its zero-th or first or second etc. homology group was based on the nature of the object? I guess in the zero-th case it is, as my source () above says, related to the number of disjoint pieces. Can we delve deeper than this for the other homology groups?   Any book/website suggestions would be welcomed (preferably websites as I am nowhere near a library!) - I have Hatcher but not a great deal else, and I haven't gleaned as much as I wish to from that alone. Of course I know that there is a great deal we don't know about homology groups even today, so I don't expect some magical all-encompassing answer, but any thoughts you could provide would be appreciated. I hope this question is appropriate for SE Mathematics, apologies if not! -M Joining two rigged models I currently trying to join two rigged (and animated) models, which both has separate meshes, separate bones and separate animations. The first mesh is the horse while the second mesh is human:   So I am interested to join human model onto horse model to make a rider:   I think the best way would be to make horse as a parent and human as a child during the join process. In that case I would like that all horse animations (there are 3 of them - idle, walk and run) would remain as they are, while I can lose human animations, as I will need different ones for it. I was also thinking to make human root bone as a child of one horse back bones, that when horse moves up and down it would move entire human mesh together. It would be also good to keep the same weights that human bones would not start deforming horse mesh and vice versa.  I tried to use Ctrl+J by selecting various combinations between bones and meshes in object mode, however, I noticed that it messes up scaling and rotation of the child object. So I was wondering how it would be possible to properly join these models to create a rider? Getting error message when trying to start a virtual machine I have been using VMWare on Windows for a long time. But after a long wait, I moved to VirtualBox on Ubuntu 11.10. I installed Ubuntu, 32 Bit, installed all available updates and installed Virtual Box. When I try to create a new Windows installation inside VirtualBox, I got the following error messages.  VirtualBox - Error  Failed to open a session for the virtual machine Windows XP. The virtual machine '**Windows XP**' has terminated unexpectedly during startup with exit code 1. Details  Result Code: NS_ERROR_FAILURE (0x80004005) Component: Machine Interface: IMachine {5eaa9319-62fc-4b0a-843c-0cb1940f8a91}   2nd error dialogue  Virtualbox - Error in suplibOsinit Kernal driver not installed (rc--1908) Please install the virtualbox-dkmbs package and execute 'modprobe vboxdrv' as root.    I have already tried reinstalling VirtualBox. Google result seem to indicate the the problem happens due to Kernel updates.   Is there anyway I can get this working? I need this for malware analysis and if VirtualBox is going to crash on me all the time, then I won't be able to use Ubuntu for work.  Output to dpkg -l | grep virtual   server rc  virtualbox                             4.1.2-dfsg-1ubuntu1                     x86 virtualization solution - base binaries rc  virtualbox-qt                          4.1.2-dfsg-1ubuntu1                     x86 virtualization solution - Qt based user interface  cute 'modprobe vboxdrv' as root.&lt;p&gt; Minecraft jar not marked as executable How to zero out a drive? Some sites are . What additional sites should the chat support?  One suggestion per answer. Types of things vs. types of thing Evaluating $\int\limits_0^{\pi} \frac{dx}{1+2\sin^2x}$ After making u substitution two times, I am getting indefinite integral as $$\int\limits\dfrac{dx}{1+2\sin^2x} = \dfrac{\arctan(\sqrt{3}\tan(x))}{\sqrt{3}}+ C$$  I am stuck at working the bounds because I am getting $0$ but the answer needs to be $\pi/\sqrt{3}$.  I think $\arctan(x)$ is defined in $-\pi/2 \lt x\lt\pi/2$ while making u substitution. However I don't see how to use this observation to my advantage. Can anybody help in getting the answer and understanding whats going on. Thanks ! Can I nohup/screen an already-started process? How to upload LaTeX-generated pdf paper to arXiv without LaTeX sources arXiv is smart enough to detect whether your PDF is generated by LaTeX. If it is, arXiv asks for the sources of the PDF instead of the PDF file itself. This is really annoying and inconvenient.  I ask a way to fool the arXiv and avoid PDFs being detected as generated by LaTeX (even if they were indeed).  I have tried this: : "create a pdf from word and then simply insert pages from your article, and delete the word's page".  And it did not work. I'm trying to write a simple bash function that takes, as its arguments, a number of files and/or directories. It should:   Fully qualify the filenames. Sort them. Remove duplicates. Print all that actually exist. Return the number of non-existent files.   I have a script that almost does what I want, but falls down on the sorting. The return value of the script as it stands is correct, but the output is not (unsorted and duplicates). If I uncomment the | sort -u statement as indicated, the output is correct but the return value is always 0.  N.B. Simpler solutions to solve the problem are welcome but the question is really about why is this occurring in the code I have. That is, why does adding the pipe seemingly stop the script incrementing the variable r?  Here's the script:  function uniqfile {     local r=0       for arg in "$@"     do           readlink -e "$arg" || (( ++r ))      done #| sort -u    ## remove that comment      return $r } martingale and stochastic Integral Loopback to forwarded Public IP address from local network - Hairpin NAT This is a  about Hairpin NAT (Loopback NAT).   The generic form of this question is:  We have a network with clients, a server, and a NAT Router. There is port forwarding on the router to the server so some of it's services are available externally. We have DNS pointing to the external IP. Local network clients fail to connect, but external work.   Why does this fail? How can I create a unified naming scheme (DNS names which work both locally and externally)?   This question has answeres merged from multiple other questions. They originally referenced FreeBSD, D-Link, Microtik, and other equipment. They're all trying to solve the same problem however.