We know that an object that feels no force should travel at a constant speed. But a body accelerating because of gravity feels no force. This seems to be a paradox. Could we possibly find the origins of gravity if we solve this paradox?
So I understand the concept of gravity, in that it's not actually a force, but more of a displacement in the spacetime grid. An object with a big enough mass will bend the spacetime, causing smaller objects to "attract" to it (not really, but good enough for what I am trying to figure out)   Ok so that makes sense, but what I am not understanding is, how come planets don't just get engulfed by the Sun? There must be something acting against the gravity for the planet to be a certain distance away from the sun. Am I not understanding this concept correctly?
How do you repair an "input/output error" in an NTFS partition? So I'm getting my listItems with a Camlquery, but i want to calculate the avg of the "price" rows  This is the code I've used so far:  function VisaLista() {     namn = document.getElementById("txtNamn");     var camlQuery = new SP.CamlQuery();     camlQuery.set_viewXml(     "&lt;Where&gt;" +     "&lt;And&gt;" +     "&lt;Eq&gt;&lt;FieldRef Name='Title'/&gt;&lt;Value Type='Text'&gt;" + namn + "&lt;/Value&gt;&lt;/Eq&gt;" +     "&lt;Or&gt;" +     "&lt;Eq&gt;&lt;FieldRef Name='Prioritet'/&gt;&lt;Value Type='Text'&gt;Hög&lt;/Value&gt;&lt;/Eq&gt;" +     "&lt;Eq&gt;&lt;FieldRef Name='Status'/&gt;&lt;Value Type='Text'&gt;Startad&lt;/Value&gt;&lt;/Eq&gt;" +     "&lt;/Or&gt;" +     "&lt;/And&gt;" +     "&lt;/Where&gt;");     listItems1 = list.getItems(camlQuery);     clientContext.load(listItems1);     clientContext.executeQueryAsync(OnSuccessVisa, OnFail); } function OnSuccessVisa() {     var listEnumerator = listItems1.getEnumerator();     var elmt = 0;     while (listEnumerator.moveNext()) {         var currentItem = listEnumerator.get_current();         elmt = (currentItem.get_item('_x0072_zb6'));          var sum = 0;         for (var i = 0; i &lt; elmt.length; i++) {             sum += parseInt(elmt[i], 10);         }          var avg = sum / elmt.length;          document.write("The sum of all the elements is: " + sum + " The average is: " + avg);     }     $("#Kategori1").text = "Medelvärdet för dessa ordrar: " + avg }   I am getting following error     "Cannot get the value length of null - at elmt, line 43 Solve the recurrent relation Is the claim that functions of independent random variables are themselves independent, true?   I have seen that result often used implicitly in some proofs, for example in the proof of independence between the sample mean and the sample variance of a normal distribution, but I have not been able to find justification for it. It seems that some authors take it as given but I am not certain that this is always the case. Is it safe to delete from C:\Windows\Installer? I've been looking on an XP machine what is using all that diskspace, and it turns out C:\Windows\Installer is high up there on the list of directories that use the most diskspace.  It seems to contain a cache of msi and msp files.  Is it safe to delete those? To save diskspace, I've been deleting the "$KB...$" directories for ages without any problems. I want my Windows Updates in my system, why you would want to uninstall them is something that I have never understood. (Except when you're on an update revision board professionally or something of that order.) Does math have an incorrect notation / syntax? I don't mean writing misaligned notation (google), but when you take something like a number to powers to powers to powers, $${{2^2}^2}^3$$ (I was told this is incorrect notation by a teacher). Is it really incorrect, or does it just need to be simplified with parentheses? Do people write maths like this?  a radical expression with the root being a radical expression? $$\sqrt[\sqrt{2^3}]{2}$$ Isomorphisms preserving integral domains and fields Let $R \simeq S$ be isomorphic commutative rings with unity. Prove the following:  a). If $R$ is an integral domain then $S$ is an integral domain.  For this, I said that If I let $f: R \to S$ be an isomorphism and $(R, + , \circ), (S, \oplus, \ast)$, then let $x, y\in R$,  such that $x \circ y = 0_R$, because $f$ is an isomorphism, $f(x \circ y) = f(x) \ast f(y) = f(0_R)$. If I let $R$ be an integral domain then, as per the definition $R$ is commutative, has unity, and no zero divisors.   So $f(x \circ y) = f(x) \ast f(y) = f(0_R)$ where we have either $f(x \circ y) = f(0_R) \ast f(y) = f(0_R)$ or $f(x \circ y) = f(x) \ast f(0_R) = f(0_R)$.   Since $f$ is an isomomorphism, let $s = f(x), t = f(y)| s,t \in S$. Then $s \ast t = f(0_R)$. By definition, $S$ also has unity so $0_S$ exists. If we map $0_R \to 0_S$. Then either $s = 0_S$ or $t = 0_S$.   So then, since $S$ has unity, is commutative, and has a no zero divisors as we showed above, it is also an Integral domain.  I'm not sure I have this correctly.  b). If $R$ is a field then $S$ is a field. I don't really understand how to do this one. Since $S$ is an integral domain, it has a $0_S$. So I need to show that $S$ distributes $\ast$ over $\oplus$.  Any help with these is appreciated I want to search for what += means, but Google won't return any documents.  Also when I come across some PHP code I don't understand I can't search for the keywords as written.  How can I search for these special characters or include these special characters in a search. Why is there so much fear surrounding LiPo batteries? I've been trying to design a charging system for a small robot powered by a 2S 20C  (LiPo) battery. Were I to trust everything I read online, I would believe that the LiPo will kill me in my sleep and steal my life savings. The common advice I read, if you are brave enough to use LiPo batteries, is "never leave unattended", "never charge on top of a flammable or conductive surface", and "never charge at a rate faster than 1&nbsp;".  I understand why this is prudent, but what is the actual risk with LiPo batteries?  Nearly every cell phone, both Android and iPhone alike, contains a LiPo battery, which most people, including myself, charge while unattended&mdash;often-times while left on a flammable or conductive surface. Yet you never hear about someone bursting into flames because their cell phone exploded. Yes, I know there are freak accidents, but how dangerous are modern LiPo batteries? Why do so many online commenters treat stand-alone LiPo batteries like bombs waiting to go off, but don't even think twice about the LiPo sitting in their pocket? Can one introduce magnetic monopoles without Dirac strings? To introduce magnetic monopoles in Maxwell equations, Dirac uses special strings, that are singularities in space, allowing potentials to be gauge potentials. A consequence of this is the quantization of charge.  Okay, it looks great. But is this the only way to introduce magnetic monopoles? What is the noun for someone who receives a referral? When a referrer (noun) gives a referral (noun) to another person, what is the term (noun) used for the recipient of the referral? "The referred" may work, but am I missing another term? "Referred" indicates past-tense, but I intend to use the term in future and present tense as well. How do I troubleshoot high 'svchost.exe' usage in Windows 7? I'm having a problem with Windows 7 64-bit. I thought it was slow and all, but then I saw that the CPU usage was always around 80% and started searching for a solution.  There are two svchost.exe's consuming around 30% each and in the resources monitor there's a system interrupts consuming 45% all the time. I tried closing the applications, but it makes no difference.  I tried some other things that I've found on Google, like disable system updates, but it didn't work.  I don't know if it will help but here's my specifications:  Core 2 Duo 4400 ATI Radeon 4850 4 GB DDR2 RAM     EDIT  I ran the suggested program and got this information; did I get it right?      EDIT  As you asked here it is, did I get it right now? The other TCP/IP there's nothing.    EDIT  I ran msconfig and took the services that one of the svchost.exe processes was using out of the startup and now my CPU is around 50%, but I still would like to improve it further. I can't lose that much CPU power just because of Windows...    EDIT  Yeah, there's nothing I can do here. I am going to reinstall Windows&nbsp;XP soon, it's really weird... How to change the "User License" type for customer portal users using a script? In the special relativistic action for a massive point particle, $$S=\int_{t_i}^{t_f}\mathcal {L}dt,$$ why is the Lagrangian $$\mathcal {L}=-E_o\gamma^{-1}$$ a negative number? I've just installed Ubuntu 16.04 LTS on dual boot. I've looked for many solutions and tried them all but Chrome never starts; the logo appears on the left but no window opens.  I downloaded the deb file on google chrome website and installed it through Ubuntu Software, but it doesn't start.   I have tried installing it through the command line with   sudo dpkg -i --force-depends google-chrome-stable_current_amd64.deb sudo apt-get install -f   I have checked with uname -a and my system is 64 bit. I have also tried gdebi with the same result.   My repository universe is up to date.  I only have one display in settings>displays> so I can't turn off built-in display nor check the mirror display (I read it could be the problem as I also have a graphic card but it seems it is not in my case).  Here is what I get in the command line when I try to run Chrome from it ( the message is the same, whatever the method I used to install Chrome):  ~$ google-chrome [11831:11831:1122/114854.195473:ERROR:process_singleton_posix.cc(433)] readlink failed: Permission denied (13) [11831:11831:1122/114854.195493:ERROR:process_singleton_posix.cc(256)] readlink(/home/basil/.config/google-chrome/SingletonLock) failed: Permission denied (13) [11831:11831:1122/114854.195508:ERROR:process_singleton_posix.cc(256)] readlink(/home/basil/.config/google-chrome/SingletonLock) failed: Permission denied (13) [11831:11831:1122/114854.195515:ERROR:process_singleton_posix.cc(280)] Failed to create /home/basil/.config/google-chrome/SingletonLock: Permission denied (13) [11831:11831:1122/114854.195538:ERROR:process_singleton_posix.cc(433)] readlink failed: Permission denied (13) [11831:11831:1122/114854.195564:ERROR:process_singleton_posix.cc(256)] readlink(/home/basil/.config/google-chrome/SingletonLock) failed: Permission denied (13) [11831:11831:1122/114854.195622:ERROR:chrome_browser_main.cc(1498)] Failed to create a ProcessSingleton for your profile directory. This means that running multiple instances would start multiple browser processes rather than opening a new window in the existing process. Aborting now to avoid profile corruption. [11831:11868:1122/114854.209297:ERROR:browser_gpu_channel_host_factory.cc(108)] Failed to launch GPU process.   Any new approach will be much appreciated "State-of-the-art" and "technology" Beamer: how to justify the whole text? How can I justify the text in the whole document in beamer without using \usepackage{ragged2e} and \justifying at the beginning of each frame?  \documentclass[8pt,handout,t]{beamer} \usepackage{pifont} %used inside itemize environment \item[\ding{226}] \usepackage{lipsum} \begin{document}  \begin{frame} \begin{columns}[T]  \begin{column}{0.3\textwidth} \includegraphics[width=\columnwidth]{example-image-1x1} \end{column} \begin{column}{0.65\textwidth} \begin{itemize} \item[\ding{226}] \lipsum[2] \item[\ding{226}] \lipsum[3] \end{itemize} \end{column}  \end{columns} \end{frame}  \begin{frame}  \lipsum[3]  \begin{itemize}    \item[\ding{226}] \lipsum[4]  \end{itemize} \end{frame} \begin{frame}   \begin{columns}[t] \begin{column}{0.4\textwidth} \lipsum[3] \end{column} \begin{column}{0.4\textwidth} \lipsum[5] \end{column} \end{columns} \end{frame} \end{document}     Edit: I had already checked  out but it does not work for both the columns and the itemize environment. Why Faddeev-Popov ghost cannot exist in external line? Stringification of a macro value Could the Horcruxes be destroyed with Avada Kedavra? In The Deathly Hallows Hermione says this about destroying Horcruxes:     “It doesn’t have to be a basilisk fang,” said Hermione patiently.   “It has to be something so destructive that the Horcrux can’t repair   itself. Basilisk venom only has one antidote, and it’s incredibly   rare—"      "That’s a problem we’re going to have to solve though, because ripping, smashing, or  crushing a Horcrux won’t do the trick. You’ve got to put it beyond magical repair.”   Mad-Eye Moody from The Goblet of Fire tells us this about Avada Kedavra,     ...there's no countercurse. There's no blocking it.   but also that,      Avada Kedavra's a curse that needs a powerful bit of magic behind it - you could   all get your wands out now and point them at me and say the words, and I doubt   I'd get so much as a nosebleed.    Harry is also seen once attempting to use Crucio on Bellatrix Lestrange in The Order of the Phoenix out of anger at the death of Sirius, but he fails. She tells him,     "You need to mean [Unforgivable Curses], Potter! You need to really want to cause pain - to enjoy it - righteous anger won't hurt me for long - I'll show you how it is done, shall I? I'll give you a lesson -"   Even if Harry and company are not powerful enough to perform the curse themselves, they know several powerful wizards (Kingsley, Lupin, et al.) who could likely perform the curse.  Lastly we know that Voldemort himself destroyed the last bit of his soul that was inside Harry with Avada Kedavra.  Could the Horcruxes be destroyed with Avada Kedavra as well?