As an engineer, we are taught that the root cause of any problem can be solved if we ask why 5 times.  Sometimes you can figure it out at 4 and sometimes at 6, but it always averages to 5 times. - You can occasionally add a "how" into that root cause analysis, but generally, it is "why".  So I was reading an article on the internet about how black holes form and I started asking why.   Unfortunately, my analysis broke down on the first why.   So why a singularity? -  If the sum of a massive star's core is crushed to become a black hole, why and how does it become a singularity?  How do you crush point-like particles (quarks, electrons, etc) beyond their current size?  Logic dictates that there has to be a size where you cannot make an object anymore dense.     How do you get around Heisenberg's uncertainty principle?  We now know the exact location for all of the matter in the black hole.  We also should know the state of all of the matter in the black hole.  How do you get around Pauli's Exclusion Principle? - Do electrons cease being electrons when you squeeze them hard enough?  If so, at what point is it no longer an electron?  If a BH is a point-like object smaller than an electron, how does matter falling onto it smear over the surface?  Can an object be Planck size and still be a singularity? If so this would solve some of these questions....  Does matter falling onto the surface of a BH cause it to shrink further or does it grow with all of the matter smearing onto it?   If it grows in size, does this mean its gravity gets weaker?  After all, its gravity is inversely proportional to its size isn't it?
A star's collapse can be halted by the  due to the Pauli exclusion principle. In extreme relativistic conditions, a star will continue to collapse regardless of the degeneracy pressure to form a black hole. Does this violate the Pauli exclusion principle? If so, are theorists ok with that? And if it doesn't violate the Pauli exclusion principle, why not?
Merging banking and casual style in moderncv (2) I really like the solution given in  but what to do if I want to keep the footer information of the casual style from page 2 on? That is, with this solution, I can put the header as I want in the first page, but the footer disappears from the rest of the pages and I do not want that.  I want the header of the first page to look like this (with an empty footer):   And the footer from the second page on to look like this: Short connection at IAD (Dulles international airport) I am flying from New Orleans to Dulles (IAD) on United Express, and from IAD to Frankfurt on United. I have a short connection (45 minutes) in IAD.   I'm trying to figure out how can I make it:  Will I need to go throughout security and border check since I'm leaving the US? How big is IAD airport? and are there different terminals for domestic and international flights? If so, how long would it take to walk between them? How do you assert that a certain exception is thrown in JUnit 4 tests? How can I use JUnit4 idiomatically to test that some code throws an exception?  While I can certainly do something like this:  @Test public void testFooThrowsIndexOutOfBoundsException() {   boolean thrown = false;    try {     foo.doStuff();   } catch (IndexOutOfBoundsException e) {     thrown = true;   }    assertTrue(thrown); }   I recall that there is an annotation or an Assert.xyz or something that is far less kludgy and far more in-the-spirit of JUnit for these sorts of situations. From the man page on git-merge, there are a number of merge strategies you can use.     resolve -  This can only resolve two heads (i.e. the current branch and another branch you pulled from) using 3-way merge algorithm. It tries to carefully detect criss-cross merge ambiguities and is considered generally safe and fast. recursive -  This can only resolve two heads using 3-way merge algorithm. When there are more than one common ancestors that can be used for 3-way merge, it creates a merged tree of the common ancestors and uses that as the reference tree for the 3-way merge. This has been reported to result in fewer merge conflicts without causing mis-merges by tests done on actual merge commits taken from Linux 2.6 kernel development history. Additionally this can detect and handle merges involving renames. This is the default merge strategy when pulling or merging one branch. octopus -  This resolves more than two-head case, but refuses to do complex merge that needs manual resolution. It is primarily meant to be used for bundling topic branch heads together. This is the default merge strategy when pulling or merging more than one branches. ours -  This resolves any number of heads, but the result of the merge is always the current branch head. It is meant to be used to supersede old development history of side branches. subtree -  This is a modified recursive strategy. When merging trees A and B, if B corresponds to a subtree of A, B is first adjusted to match the tree structure of A, instead of reading the trees at the same level. This adjustment is also done to the common ancestor tree.   When should I specify something different than the default?  What scenarios are each best for? I have lost my passport here in Beograd. Can I travel just with my Czech ID card from Belgrade to Budapest? Optional argument to \item Why do adult insects have 6 legs? Apparently, there is an advantage to having 6 legs in the insect world. What is that advantage, if anything? Why would such an advantage exist for insects, but not for other, larger land animals?  What do those middle legs do that the front and hind legs cannot, if anything? Are they really essential, or do they just generate more muscle power? Is $$d_1\mid n,d_2\mid n\iff [d_1,d_2]\mid n$$ true ? And if yes, how can I prove it ? I recall that $[d_1,d_2]$ is the least common multiple.  My tries  For the implication : Let $d_1\mid n$ and $d_2\mid n$. Then, $d_1d_2\mid n^2$. By the way, since $d_1,d_2\mid n$, we have that $(d_1,d_2)\mid n$ where $(d_1,d_2)=:\gcd(d_1,d_2)$  and thus $$[d_1,d_2](d_1,d_2)\mid n^2.$$  Question: How can I get $[d_1,d_2]\mid n$ from this?  For the converse, since $d_1,d_2\mid [d_1,d_2]\mid n$, the claim follow. What does "Change" represent in the User Leagues? What does the Change field represent on the  for SO? Refer to the highlighted areas in the image below:   Rank: the user's ranking for the selected time period (week, month, quarter, year) Change: +/- change representing... ??? Total Reputation: the user's total reputation [Time Period] Reputation: the user's reputation for the selected time period (week, month, quarter, year)  So what is the Change field measuring? After upgrading to macOS Sierra, I'm getting the notification that "Your disk is almost full. Save space by optimizing storage.":    The options appear to be to store my files in iCloud, automatically delete files, or manually delete files:    My problem/irritation is that I have 80GB free of my 440GB volume.  The question: is there a way to silence this notification in a (semi-)permanent fashion, or to change the threshold it uses for the notification? Setting environment variables for latex and bibtex in .bashrc Possible Duplicate:          I recently started using TeX to write journal articles. I use TeX Live version 2009-10 on a laptop running Ubuntu 10.10 (64-bit). I edit and compile the tex files using vim and vim-latexsuite.   Currently for each journal article I have all associated tex, bib, eps, etc. files in individual folders. I would like to simplify my life a bit and have a dedicated folder containing a "master" bib file - And maybe another folder for my custom style files.   My problem is that can't figure out how I should define the PATH, and other environment variables in my .bashrc file to find the necessary support files (e.g., the .bib file). Which variables do I need to set? PATH? MANPATH? TEXINPUTS? BIBINPUTS? Suppose I have a directory structure as follows  test test/a test/b   Now I want to execute a command, such that in the . folder I can execute a command on the basename of the files a and b.  So basically, I want something like this, which I naively tried  find test -type f -exec touch `basename {}` \;   Only, this does not result in empty files a and b in the parent directory. Suppose that my touch command can only take a single argument.  This will result in a directory structure like this  a b test test/a test/b   I know how to do this in a bash script, but I am interested in single command solution. I have read in a book that the limit of the ratio of consequent Fibonacci numbers is the golden ratio. However, it was just mentioned thus not justified. So, my question is how would you derive the following limit: $$\lim_{x\to\infty}{\frac{F_n}{F_{n+1}}}=?$$ Where $F_n$ is the nth Fibonacci number? On Linux can I keep a program running in background even after I disconnect? If I'm logged into a remote Linux machine, I know I can suspend a process (cntr-z) and move it to the background (bg 1) but if I disconnect from the machine, the process stops.  Is there a way I can leave it in the background and have it there when I log back in? This is a very long running process.  On Ubuntu, logged in via SSH. Where can I obtain an English dictionary with structured data? Using a variable in a SELECT statement? public static void handleCaseComment(CaseComment caseComment) {    User[] users = [SELECT LastName FROM User WHERE Id = caseComment.CreatedById LIMIT 1]; }   This gives me the following error:  unexpected token: 'caseComment.CreatedById'   How do I use the value of the variable caseComment.CreatedById in a SELECT statement? Why was Count Dooku not given the title "Darth"? I don't know the exact significance of the word "Darth" in the Sith world, but I think it was a word of honor for powerful Sith. That's why Anakin was given this word in his new name.  All powerful Sith in canon had this word in their names: Darth Plagueis, Darth Bane, Darth Sidious, Darth Vader, Darth Maul, etc. As such name similarity can't be names given by their parents, I can assume they were given such words in names as a honor.   Now, look at Count Dooku... he was a powerful Sith too. So, why wasn't he given this title?    Darth word to address Dooku hasn't been used in the movies, as far as I know. If you are claiming that Darth and Lord words are same, give citations because my vocabulary rejects it. Find all integral solutions of $y^2=x^3+7$ Find all integral solutions of $y^2 = x^3+7$.  I tried to use many different moduli, but it never works. With modulo $9$, you can get $x$ is divisible by $3$. Python metaheuristic packages How can I know if my macbook is hacked?