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Physically what does warping (of space-time) mean? So there's general relativity and Einstein's field equations that tell us "mass(or equivalently energy) warps space-time, and the warping tells mass how to move", but I'm still having trouble understanding how space (a thing I conceive to be 'empty' or nothingness) can be 'warped'.  After researching books, on-line articles, and this stack exchange itself I can't seem to find any descriptions or discussions that don't immediately resort to jumping into GR and its mathematics to provide a more physical intuitive understanding of what it means to for space to be warped.  Is it space, this empty thing, that's getting warped. Or rather is it some field (Higgs field?) that exists around matter that's getting warped?  Although this question appears similar to  , it's asking if it's empty space that's being warped by matter or rather a field in space that's being warped (the Higgs Field?). The other question and all 10 answers addressing it do not address fields vs. empty space - What's really getting warped? I want to have a script that takes the current working directory to a variable. The section that needs the directory is like this dir = pwd. It just prints pwd how do I get the current working directory into a variable? May I use a question mark in the middle of a sentence? Examples:  Would you like the drapes to be white? or perhaps something off-white? Would you like the logo to be centered? at the bottom? left off entirely? I am using extensively trigonometric functions when an angle is given in degrees. Some of these functions like sine or cosine have rational values, for example, the well   known example is that $\cos(\theta) =0.6 $ and $\sin(\theta) =0.8 $.       However besides the case of multiplicity of $90^\circ$ it seems there are no rational numbers $\theta$  with simultaneously rational  values of  sine and cosine.      Is it possible somehow to prove that for rational values of an angle given in degrees there are  no values simultaneously rational of sine and cosine functions, beside obvious case of multiplicities of $90^\circ$? How can you find out which process is listening on a TCP or UDP port on Windows? product distribution of two uniform distribution, what about 3 or more Why do some font commands behave differently? I've always been confused by the differences in behavior of font commands.  For example, we have \mathrm{} and \texttt{}, which can be used like this: \texttt{hello} world.  And then we have \it and \bf which must be used as {\it hello} world. If one uses \it{hello} world, both words are italicized.  Internally, what is the difference here? And was this difference a conscious design decision? If so, why? Disable password access through SSH? I'm setting up a server for backing up my desktop box remotely. I want to prevent remote password access to the server, permitting only users with private keys (AKA my desktop box) to access it. How can I block remote password access while allowing physical password access to the server? Tile Edge Challenge I've been having a problem with these problems for a week now so I thought I'd post it on MSE. Read the text below. . I've also typed it up:  Annabel made a shape by placing identical square tiles in a frame as shown in the diagram above. The tiles are arranged in columns. Each column touches the base but no columns touch the side or top. There are no empty gaps between columns. The frame can be enlarged as needed.  These are the questions. I've also typed them up.    A. Show that it is possible to arrange $7$ tiles so that the ant walks $8,9,10,11,12,13,14,15$ tile edges.   B. Show 6 ways of arranging 7 tiles so that the ant walks a total of 9 tile edges.  C. Show it is possible to arrange 49 tiles so that the ant walks a total of less than 21 tile edges.  D. Show four arrangements of 137 tiles, each arrangement with a different maximum height, so that the ant walks a total of 34 tile edges.  For question $a$, is there a formula relating the number of tile edges exposed to the number of tiles. These are my answers for $a$    For the above picture, it's the left hand side which has the $a$ answers.  However, I'm having a bit of trouble with $b$. I've already got four answers down but where are the other two. My four current answers are in the right hand side of the last image. Also, I'll also appreciate a formula to show the relationship.  I'm also having trouble with $c$. I found out that you get 21 tile edges exposes when you make a $7*7$ square but the answer is asking for less than 21. Can anyone help me. Also, as in the previous questions, a formula to show the relationships would be great.  And for $d$, I am totally lost. I have no idea where to start, and I certainly can't find out four arrangements. So can anyone help me? And as always, a formula is nice  P.S. Please explain this in an understandable formula, as I'm only a Year 7 with the ability to understand linear algebra and parts of quadratics and trigonometry. Also, sorry about the poor imaging. Mask and inherit the same systemd unit Suppose a package provides whatever.service file so certain events (including whatever.socket) cause a daemon to start with a certain configuration.  I want to disable this completely. In particular, I want the old socket and any other unit files that might refer to this service by name to be unable to start the daemon.  Instead, I want to create my own unit files for this daemon with a different .socket unit and different environment variables. I also want my override to automatically take account of possible upstream updates to the original unit file (which my current solution of copying whatever.service as whatever-modified.service and editing it unfortunately does not provide).  If I create the following symlinks and files: /etc/systemd/system/whatever.service → /dev/null /etc/systemd/system/whatever-modified.service → /usr/lib/systemd/system/whatever.service /etc/systemd/system/whatever-modified.service.d/fix.conf  systemd considers the new service to be masked as well and refuses to start it. How to avoid this? Is my MAC address public when browsing the Internet? Refused entry to UK, not sure what to do I'm a writer and theater/film director who has been traveling nearly all my life without incident. In February, I decided to pull up stakes in NYC and move to London. I am a freelancer and I'm working with three different organizations in NYC so I wasn't working illegally in the UK. I was, however, seeing if there might be some opportunities in London, ie. meeting with Artistic Directors of various theatre companies to see if they might be interested in producing my work.   In April, I was invited to a conference in San Diego and then a film festival in Switzerland. I didn't think it would be a problem if I went and then bummed around in France for a few days since I hadn't broken any laws and had left the UK well under my six month leave to stay. Well, when I tried to return to London, I was denied entry at Luton. The border control officer said I didn't have enough funds for a two month stay and put a black cross over a stamp in my passport. They put me in a detention room until the next flight back to Lyon, which was the following morning. I don't know anyone in Lyon so I ended up going to a friend's place in Paris.   After a few days of not knowing what to do, a friend suggested that perhaps I should try going back to London on the Eurostar since border control is in Paris. I wondered if I ought to go to the British Embassy but was deterred by something on their website that says that a visitors visa could take up to three weeks (I can't sit around here in Paris for three weeks) and anyway, the decision ultimately is with the border control, so I decided to take a chance on the Eurostar. I bought myself a return ticket in two weeks to Paris just so I had something to show.   Well, the UK border control denied me entry after giving me a third degree. They accused me of lying and seeking work in the UK. They also insisted that the amount of money I had was not enough to live on for two weeks. So I'm back at my friend's place in Paris, wondering what to do.   Is it possible for me to ever get back to the UK? I had to cancel one meeting and I'm wondering if I have to cancel going to the Sheffield DocFest. (Two of my projects were accepted to programs there.)   Should I apply for a visa from the British Embassy? Will this really take three weeks? When I started to say something about obtaining a visa, the border control officer cut me off and said, "Why are you going to the Embassy? This has nothing to do with the Embassy. We make the decisions." $$\lim_{n\to\infty} (1+\frac{2}{n})^{n^2} e^{-2n} = ? $$         $e$   $e^2$   $e^{-1}$   $e^{-2}$      My answer is 1. Since $$\lim_{n \to \infty} \left(1+\frac{2}{n}\right)^{n} =e^{+2}.$$  Therefore $$\lim_{n\to\infty} \left(1+\frac{2}{n}\right)^{n^2} =e^{2n}.$$  Where am I wrong? Was drafting an email and my senior wanted to type "Planting saplings is our way of saying we care for our Nature". I felt that's wrong English. Shouldn't it be "we care for Nature"? (it makes it a bit impersonal to remove the 'our', but if 'our nature' isn't right, can the cuteness factor of mentioning 'our nature' be preserved?. Which is correct?) The "I Get It" Reputation Problem What point (pt) font size are \Large etc.? In the preamble I have:  \documentclass[a4paper,11pt]{article} \usepackage{fontspec} \setmainfont{Arial}   What can be inferred about the real font pt size for the following?  \tiny, \scriptsize, \footnotesize, \small, \normalsize, \large, \Large, \LARGE, \huge, \Huge Bundling python library with addon I'm making an add-on that uses the websocket library from python. Is there a way to include it in the add-on .zip file? Or do I have to add it to the site packages folder in blenders included python folder? I want to show that if a real orthogonal matrix $A$ has determinant $-1$ then $\lambda=-1$ must be an eigenvalue of $A$.  I have proven this in a long-winded way and I was wondering if these is a quick way of seeing it. MacBook Pro crashes randomly after dropping it on the floor A few days ago my MacBook Pro slipped out of my hands and fell onto the tile floor. The outside got banged up quite a bit and the Touch Bar no longer lights up but still responds to touches sometimes but not all the time.   Anyway, since then it will randomly restart every once in a while with a kernel panic. I have the log posted below and wanted to know if anyone could tell me what is causing the panic? FileSystemWatcher Changed event is raised twice