Why gravity is an attractive force?     One may say that it is because of space time curvature but General Relativity is built on this law: $\displaystyle G \frac{m_1 \times m_2}{r^2}$ (To be more precise, it is  from it's potentiel form known as  that can be written like this: $\nabla \cdot g = - 4\pi Gp  $). So GR can't explain why gravity is attractive. General Relativity only explains how gravity occurs in terms of space time.    Another may stick with the Quantum theory stating that gravitons are responsible for the force of gravity, but why a massless particle with spin 2 will exchange positive momentum?
Why is the gravitational force always attractive? Is there another way to explain this without the curvature of space time?   PS: If the simple answer to this question is that mass makes space-time curve in a concave fashion, I can rephrase the question as why does mass make space-time always curve concavely?
What is the variance of the weighted mixture of two gaussians? Say I have two normal distributions A and B with means $\mu_A$ and $\mu_B$ and variances $\sigma_A$ and $\sigma_B$. I want to take a weighted mixture of these two distributions using weights $p$ and $q$ where $0\le p \le 1$ and $q = 1-p$. I know that the mean of this mixture would be $\mu_{AB} = (p\times\mu_A) + (q\times\mu_B)$.  What would the variance be?    A concrete example would be if I knew the parameters for the distribution of male and female height. If I had a room of people that was 60% male, I could produce the expected mean height for the whole room, but what about the variance? Why does a star beyond a certain mass limit (Chandrasekhar limit) only become a black hole? Why does a star beyond a certain mass limit () only become a black hole?   A star is first made of hydrogen, it undergoes nuclear fussion reaction combining into helium and releasing a large amount of energy. This process continues till star is made up of iron core as iron has largest value of binding energy per nucleon, after this if mass of the star is above the value of Chandrasekhar limit it becomes a black star, what is the reason for this and why is certain mass limit required? How do I undo the most recent local commits in Git? Best practice for Rails App to run a long task in the background? Recently, I have noticed that on most applications I have on Ubuntu 16.04, when I load the application, the window is displayed with a strange multi-coloured border (see the images below). If I maximise the window though, the border disappears and the window is displayed as expected.  This started happening for no apparent reason. If I reboot my machine, things return to normal at first, but after a while the problem comes back.  The issue occurs on most applications, including Nautilus, Software Centre, Terminal, System Settings, etc... I also get the same border appearing when I right click on the desktop, with the border surrounding the pop-up menu.  However, I have noticed that it does not happen on Chrome, but it does happen on other applications which did not come with Ubuntu by default.  Any ideas on what is causing the problem? Thanks! How to format an inline source code Meaning of U suffix Should I worry about an Amazon AWS doomsday scenario? Clever bounty reputation hack I say "hack" in the most favorable light. It's a clever idea and theoretically beneficial.  I noticed that an old question of mine suddenly started getting a lot of renewed attention. The question had been answered, with an answer accepted. But another user added a well reasoned and insightful answer to the list. He also opened a +100 bounty on that question.  The resulting increased attention quickly got his answer quite a lot of up-votes. Well more than the 100 points he had spent on the bounty. Therefore, he gets a net rep profit out of the transaction.  So here's the hack:   Find an interesting question Research and provide a very good answer Open up a bounty on that question to attract attention and votes to your new answer Profit!!!   2 and 3 may be out of order--I didn't see the timing of it. But either way, assuming he gets more than 10 votes, he still gets increased rep out of the deal.  I don't think this is necessarily bad for SO - it does generate some useful discussion and insightful answers. Plus you can increase your own rep very rapidly by making your answers highly visible, and therefore frequently voted upon.   However, it does slightly change the meaning and purpose of bounties away from starting a discussion and toward self-promotion. Still, interesting. How to filter IPv4 and IPv6 addresses? What is the difference of closing for duplicate and flagging for duplicate? When I encounter a duplicate, I have two choices: Vote closing because it is a duplicate, or flag it as a duplicate. What is the difference and should I do both? Backup and restore settings in Texstudio Does someone know, how to save all the settings of Texstudio and restore them in a simple way?  Thank you in advance! How to determine if string contains specific substring within the first X characters I want to copy a live production database into my local development database.  Is there a way to do this without locking the production database?  I'm currently using:  mysqldump -u root --password=xxx -h xxx my_db1 | mysql -u root --password=xxx -h localhost my_db1   But it's locking each table as it runs. How closely can we estimate $\sum_{i=0}^n \sqrt{i}$ By looking at an integral and bounding the error? I have a Lubuntu (now 14.04) installation. Recently, I logged in to find that the Wi-Fi icon had disappeared, and there was some sort of a keyboard icon in it's place. I have restarted multiple times, but it doesn't fix it. I can't find the same applet in the panel settings, and resetting the panel didn't help. When I try to manually start nm-applet, it starts, but prints a bunch of warnings to the console:  nm-applet-Message: using fallback from indicator to GtkStatusIcon   It then starts, using ugly icons for the Wi-Fi connectivity symbol.  What do I need to do to make it start correctly? Once it starts, why isn't it using the right icons? Are these gerund sentences grammatically correct? I bought this book titled 2 Hari Taklukan Grammar, written by Edward Rahardian in Bahasa (Indonesian language) and mostly talk about gerund and infinitive. And these are some examples of the gerund sentences that I found.        His mother suggested having lunch before we leave.     I will try studying harder.     The car needs washing.     Your hair needs washing.     My teacher disliked me coming late.        Somehow those words sound unnatural for me because I've never heard those in daily conversations. As a learner, I only get exposed with English by watching TV series and any other entertainment resources.  So in my thought, they sound more natural like this:        His mother suggested to have lunch before we leave.     I will try to study harder.     The car needs to be washed.     Your hair needs to be washed.     My teacher disliked me to come late.       Are those sentences in the first group grammatically correct? And, is it normal for one to say them in normal/daily conversations? How did nobody at Hogwarts (especially Dumbledore) figure out what killed Myrtle? $\mathbb Z[i]/ \langle 1+2i \rangle \cong \mathbb Z_5$ I am trying to prove that $\mathbb Z[i]/ \langle 1+2i \rangle$ is isomorphic to  $\mathbb  Z_5$.   The only thing that came to my mind was trying to apply the first isomorphism theorem using an appropiate function. If I consider the euclidean function $N: Z[i] \setminus \{0 \}  \to  \mathbb N$ defined as $N(a+bi)=a^2+b^2$, then I can express any element $z$ in $\mathbb Z[i]$ as $z=(1+2i)q+r$ with $N(r)=1,2,3,4$ or $r=0$.   If I define $f:\mathbb Z[i] \to \mathbb  Z_5$ as $f(x=(1+2i)q_x+r_x)=\overline{r_x}$, then it is clear that $f(x)=0$ if and only if $x \in  \langle 1+2i \rangle$. The problem with this function is that it doesn't satisfy $f(x+y)=f(x)+f(y)$ and it is not surjective for if $r_x=f(x)=3 (5)$, then if $r_x=a+bi$, we have $a^2+b^2=3$, which is absurd.  I don't know what else to do, any suggestions would be appreciated. I have a lot of svg images I want to include in a TeX-File.   So far I didn't have problems using the \usepackage{svg} with \includesvg.  However recently I've added a few more layers to the svg-files and now a lot of stuff is missing.   The resulting svg-tex.pdf files now have up to 61 pages and if I look into the svg-tex.pdf_tex files with texmaker I found the culprit: it only goes up to 50 pages:  \put(0,0){\includegraphics[width=\unitlength,page=50]{Sym_9999_svg-tex.pdf}}%   Putting the pages in manually like:   \put(0,0){\includegraphics[width=\unitlength,**page=51**]{Sym_9999_svg-tex.pdf}}%   does work, but would be very time inefficient (I have 100+ svg images) additionally the layers don't have the correct sequence and cover up text sometimes.   Does anyone have a solution for this problem?   If I open up the svg-image it shows up just fine.   One possibility would be to just export the svgs in one pdf file without the text as extra latex file, but this way I can't add formulas in Tex-Form.