In the movie Interstellar, there's a lot of things that I don't get.   Humans, most significantly Dr Brand, were hard at work for years solving the gravity equation. Brand wanted to do something to help humans leave the Earth, he'd known for a while we were dying a slow death, and he wanted to save the species by its relocation, either with Plan A or Plan B.  The station that housed NORAD seemed to be designed to be able to take off, but why would we need the equation solved for that? Supposedly, if we never needed to come back to the Earth, we'd have a lot of fuel to burn to propel the facility out, right?  Also, how does Cooper Station tell us that we did solve gravity? It's just a huge station orbiting Saturn, so we didn't even go beyond the Solar System. So it's less than believable if we were trying to 'use' gravity to travel faster than light (I just can't see how that comes to be).  What is it, then? Were we trying to conquer time? Travel faster than light? Evolve to the beings that were shown in the movie?  The part that intrigued me the most is this dialogue:     Murph: His solution was correct. He'd had it for years.      Getty: It's worthless?      Murph: It's half the answer.      Getty: Okay, how'd you find the other half?      Murph: Out there? A black hole. But stuck here on Earth, I'm not sure you can.
In Interstellar, what do Murph and NASA do to save humanity after solving Brand's equation? Do they get the entire human race on giant space ships and transport them to a habitable planet? (How exactly do they do  this?)  If yes, is this habitable planet Edmunds' (the one that Amelia lands on)?
Bayes rule logic. Why we do use this? I tend to use the terminal a lot,  So I wondering if there is a way I can make Ctrl+Alt+T focus the existing terminal if there is one, otherwise create a new terminal? Stealing and reattaching a running process It's sunday and I left an instance of R running in the office. The script finished running, and I would like to save my workspace without going to the office. I can ssh to the computer, but I have not run the program into screen.  Is there a way, over ssh, to disown the process (I don't have access to jobsid of the terminal the program is running on!) and reattach it with say, reptyr? Reptyr and reptyr -T don't work without previously disowning the process  28845 3diag       20   0  139.3m  10.4m   0.0  0.1   0:12.06 S  `- urxvtd                                                                                        5327 3diag       20   0   16.4m   4.6m   0.0  0.1   0:00.02 S      `- bash                                                                                      5335 3diag       20   0 3499.3m 3.244g   0.0 43.3 171:57.89 S          `- R    The unique part of my question is that I explicitly require to detach a program without having access to the terminal in which it was created. How to make a circular array using offset object as center? Please help solve 'oracle-java7-installer' missing. Error below  dpkg: warning: files list file for package !['oracle-java7-installer' missing;][1]  assuming package has no files currently installed (Reading database ... 302933 files and directories currently installed.) Removing linux-image-extra-3.8.0-19-generic ... /var/lib/dpkg/info/linux-image-extra-3.8.0-19-generic.postrm: 6: /var/lib/dpkg/info/linux-image-extra-3.8.0-19-generic.postrm: Syntax error: ")"  unexpected dpkg: error processing linux-image-extra-3.8.0-19-generic (--remove):  subprocess installed post-removal script returned error exit status 2  Errors were encountered while processing:  linux-image-extra-3.8.0-19-generic  E: Sub-process /usr/bin/dpkg returned an error code (1) A package failed to install.  Trying to recover: If a topology contains all infinite subsets, then it is the discrete topology I am solving question $8$ of exercises in section 1.1. of chapter 1 in "Topology without tears". The question reads as follows.     Let $X$ be an infinite set and $\tau$ be a topology on $X$. If every infinite subset of $X$ is in $\tau$, prove that $\tau$ is the discrete topology   My idea was to show that every singleton set is in the topology and thereby the topology is discrete.  Choose an infinite set $A$ from $X$ such that $A^c$ is also infinite. $A$ and $A^c$ belong to $\tau$ since they are infinite sets. Now consider any $x \in X$. Note that $A \cup \{x\}$ and $A^c \cup \{x\}$ belong to $\tau$ since they are infinite sets. Hence, their intersection which is nothing but $\{x\} \in \tau$ for every $x \in X$.  The problem I have is I don't know how to prove the first sentence in the previous paragraph. These are my line of thoughts to prove them.   If $X$ is a countably infinite set, then I can list the elements are let the odd numbered elements fall into $A$. This guarantees $A$ and $A^c$ are both infinite. If $X$ is uncountable, then I can choose a countably infinite subset and call it $A$.   Are the above arguments rigorous? I am not especially happy with my second argument of choosing a countably infinite subset from an uncountable set since I do not give an explicit procedure of constructing the set $A$.  Also, is there any other simpler way of answering the original question? In some books the word "if" is used in definitions and it is not clear if they actually mean "iff" (i.e "if and only if"). I'd like to know if in mathematical literature in general "if" in definitions means "iff".  For example I am reading "Essential topology" and the following definition is written:     In a topological space $T$, a collection $B$ of open subsets of $T$ is said   to form a basis for the topology on $T$ if every open subset of $T$ can be written as a union of sets in $B$.   Should I assume the converse in such a case? Should I assume that given a basis $B$ for a topological space, every open set can be written as a union of sets in $B$?  This is just an example, I am not asking specifically about this sentence. A Terms of Service update restricting companies that scrape your profile information without your permission @class vs. #import It is to my understanding that one should use a forward-class declaration in the event ClassA needs to include a ClassB header, and ClassB needs to include a ClassA header to avoid any circular inclusions. I also understand that an #import is a simple ifndef so that an include only happens once.  My inquiry is this: When does one use #import and when does one use @class? Sometimes if I use a @class declaration, I see a common compiler warning such as the following:     warning: receiver 'FooController' is a forward class and corresponding @interface may not exist.   Would really love to understand this, versus just removing the @class forward-declaration and throwing an #import in to silence the warnings the compiler is giving me. Is it possible to tell a Valyrian steel sword from a very well crafted steel sword, by sight alone I'm sure in Westeros there are some incredibly well crafted steel swords, but could someone instantly spot a Valyrian steel sword over one of these?  Does Valyrian steel have any visual indications that it is Valyrian steel and not just a very well crafted steel sword?  I'm wondering, in canon, has anyone seen a sword and instantly recognised it as Valyrian steel.  For the purpose of this question, no one is allowed pick up or use the sword, so they cant feel it's weight, balance, sharpness, etc... Performance differences between visibility:hidden and display:none How can I simplify the use of flags with Views Bulk Operations? I have an administrative display (made with views) that lists content that is pending approval.  In the case of my site, approval means flagging with the approval_for_pub flag (which triggers a custom rule).   allows nodes to be flagged/unflagged all at once by clicking a handy button:    However, upon clicking this button, by default it shows all possible flags and the flag/unflag option:    This is a problem on my site because some of the people responsible for approval get confused by the names of the flags and select the wrong option.  So, what I would like to do is create a VBO option that, when the button is pressed, automatically flags all applicable content with the approval_for_pub flag.  How can I approach this?  It seems like a small detail, but this step happens several times a day, so the chance of making a mistake is quite high. What is the correct pronunciation of TeX and LaTeX? Is it tex(tech)? Or Is it tex(like touch)?  Lay-TeX? or La-TeX?  Should I use TeX pronunciation in LaTeX? Quantum systems without a classical analogue? I am now reading the quantum mechanics textbook by Dirac (chap. 4, $\S21$, p. 88).   He says that his quantization procedure does not include all possible systems in quantum mechanics and there are systems without a classical analogue.  How is this possible? Convergence in measure and almost everywhere In a finite measure space, let $\{f_{n}\}$ be a sequence of measurable functions. Show that $f_{n}  \rightarrow f$ in measure if and only if every subsequence $\{f_{n_{k}}\}$ contains a subsequence $\{f_{n_{k_{j}}}\}$, that converges almost everywhere to f.   I can prove from converge in measure to converge almost everywhere, but I don't know how to write it down for the other direction. How to recover data from a USB-connected hard disk that shows no partition? Using Regex to generate Strings rather than match them How to determine function name from inside a function Reading Excel files from C# Why are two different concepts both called "heap"?