Some time ago I encouraged by 11 year old son to watch Cosmos: A Spacetime Odyssey with Neil DeGrasse Tyson, and subsequently Cosmos: A personal Voyage with Carl Sagan, as well as other astronomy shows including History Channel's The Universe. One of these such shows inspired a question about black holes and gravity.  Can a black hole be so large that not even the effects of its own gravity can escape?  Perhaps the question rephrased might be: Why are gravitational waves immune to the effects of gravity?
My understanding is that light can not escape from within a black hole (within the event horizon).  I've also heard that information cannot propagate faster than the speed of light.  It would seem to me that the gravitational attraction caused by a black hole carries information about the amount of mass within the black hole.  So, how does this information escape?  Looking at it from a particle point of view: do the gravitons (should they exist) travel faster than the photons?
How to share variable between two c# projects Given  $$ y_n=\left(1+\frac{1}{n}\right)^{n+1}\hspace{-6mm},\qquad n \in \mathbb{N}, \quad n \geq 1. $$ Show that $\lbrace y_n \rbrace$ is a decreasing sequence. Anyone can help ?  I consider the ratio $\frac{y_{n+1}}{y_n}$ but I got stuck. How do you get git to always pull from a specific branch? Cannot log in with Apple ID after performing password reset My wife forgot the password to her Apple ID account. Her Macbook Air (OS X Yosemite) restarted to install some updates. She has her user account set up through her Apple ID account.  Since she forgot the password she reset it from my laptop.  She can log in to iCloud and Apple ID with the new password, but cannot log in with the new password on the Air.  When she tries to log in she is greeted with this message:     "This account uses an iCloud password to log in. If you need to change   the password, use another device to change it at appleid.apple.com." Is there a human home planet? Did all the humans in the Star Wars universe originate on a single planet some time in the distant past, or did they originate on different worlds and intermix into one species over millenia?  This is specifically about only humans, not humanoid aliens. I would prefer answers from the main canon or EU canon. What are the scars on the face of Dryden Voss? Dryden Voss, the iconic villain in Solo: A Star Wars Story, has some pretty radical facial scarring.    I'm wondering if there is any evidence how he got these scars?  In particular is it possible he got the scars in battle, or from exposure to a particular substance or drug.  It also seems he is under the service of a Sith Lord (if not an apprentice himself) and if so, could this have come as part of an initiation into, or training with, the dark arts. Since I first learned English, I have been holding this understanding that "and", as a conj. but unlike "but",  can only connect two clauses, not two sentences ended with periods.  But recently, I have seen so many prints, either in entertainment or in academia, where "And" is popularly used in the beginning of a sentence. It seems like the author is trying to connect the sentence just right before and the sentence following "And" in some intended meaning which I don't quite get.  I was wondering if I have been wrong all the time, or if there is a new trend that I fail to understand and accept? How to understand such usage of "and" in rigorous English grammar? If I am right, why it is used differently from "but" in terms of what I mentioned at the beginning of this post? After hitting 80% LTV, my mortgage lender refuses to remove PMI. Any recourse? I recently refinanced my home. At the time based on the appraisal vs. amortization I found I would be stuck with PMI (private mortgage insurance) for about 9 months.  I've paid extra on the mortgage each month and after 7 months I got my LTV (loan-to-value ratio) to be 79%. Yay! So I called Pacific Union and asked for PMI to be removed.  The woman said I'd need to fax in a written request. Then she added that my written request would likely be denied because my account had not been in good standing the last 12 months. I pointed out that I'd only had the loan for 7 months and had never been late, but that didn't seem to matter to her.  So I faxed in my written request. Then I read through all my documentation on my loan. Nowhere did it say that I needed to have the loan for 12 months.  After a week I called them back and they said it would be another week for a decision.  So, I waited another week and called. They now just had a recording saying they were too busy to take a call and I could leave a callback number. I did this and never heard back. I've now tried twice more to call them. Each time I leave a number and each time I don't hear back. So I've fired off a written request again.  At this point we've gone around the horn to the next month and in two short days I'll be paying PMI on March's payment.  Do they have any grounds to not remove PMI? Isn't it federally mandated that PMI must be removed at 80%? Any recourse anyone can think of?  [EDIT] - I heard back from Pacific Union. They state that I did not sign anything agreeing to these terms which is what I was certain of. They state these terms are simply automatic with Fannie Mai backed loans and it doesn't matter if I was informed or not about these terms. They also chose not to hide behind the "no late payments" clause and instead said they were requiring an appraisal to remove PMI. Of course an appraisal is $400 and I'll hit 78% LTV before I would pay that much extra in PMI. I have now contacted a lawyer. I'll update again with whatever opinion the lawyer has and whether I proceed or not.  [EDIT] - I filed a BBB complaint. They waited 30+ days to respond. In their response they indicate that the first woman (and some SE users below) are wrong. The loan does NOT have to be in good standing for 12 months. The loan simply needs no late payments within 12 months. They then hide behind the request for another appraisal as the sole reason to not remove it. I checked with Fannie Mae who backs the loan and was told this is optional per the lender, however the lender can force it and I have no recourse. Additionally, they could have asked for a Broker's Price Option (BPO) or a certificate of value which would cost me hundreds less.   At this point I cannot continue to fight them because the amount of PMI I'll pay until 78% LTV is equal to or less than the appraisal cost of $400.  [EDIT] As of August 2015 I've hit 78% LTV. I called Pacific Union to ensure that the automatic cancellation of PMI had happened. They said no, I'd need to request that in writing. This is a violation of federal law as it's supposed to be automatic. They also said they would still deny it because now they want 24 months of good history. I've sent a threatening letter off and am waiting for a reply. If any lawyers come along and read this I'd sure like to hire you.  [EDIT] After my letter they said they would remove PMI. They did not and I was charged again in September. I called them yet again and complained. They said PMI was going to be removed. They then charged my again in October! I called again. I called again and went berserk on the phone. PMI was finally removed for November 2015. First month without it. I am trying to create Thiessen (Voronoi) polygons, based on points within a defined shapefile extent. The output should be inclusive to the feature.  The output I receive now is the rectangular area around the selected points.    Steps I am using: 1. select points of interest (inside and outside spatial extent) 2. set primary display field to FID (aka:ObjectID) 3. Environment… > Set 'Analysis Mask' to shapefile with feature (in this case, a watershed)  Now here is where the problem starts. I have a set of instructions for arc 9.3, but I am now operating on ArcGIS 10 (Spatial Analyst installed &amp; activated). Also, just to clarify, I did scour the inter-webs for some number of hours- Esri support, gis.SE, Professor Google...  ########  9.3.1 version: Spatial Analyst >> Distance >> Allocation - set 'Assign To' as point shapefile of selected data - set cell size  10.0 methods tried: Analysis >> Create Thiessen Polygons -- Many variations of selected features -- File locations, both inside and out of file geodatabase  I am open to any solution, using Arc 10.0 and/or python would be ideal.  The first image is an example.  The output does not need to be exact.  wiki: USB composite device driver I am wondering if it possible to create a USB device (in following the device) composed from   a custom circuit (eg arduino) and  a flash storage   in such a manner that the device is recognized as a standard usb flash storage (and as such is operable with standart OS drivers), while said storage holds the utilities to operate with the custom circuit (dispalying the data colled by the circuit); and if so, how?  My first thought was to smack a cheap usb-hub and usb-pen before my circuit but that solution, is not pleasing to me.  My goal is to eliminate the need to carry an extra flash-drive just for the operating software, and use default os drivers, make it plug-and-just-work:   i plug the device in the os (windows) mounts a new flash-drive without needing a special driver is start (manually or via autorun) my custom.exe from that flash-drive i recive data measured by the circuit Find all natural numbers $n$ and $m$ for which $n^m=(n-1)!+1$ Can you flank with a reach weapon? The Variant: Flanking rules in the DMG (page 251) require adjacency, but is the intent that the Enemy has combatants on opposite sides and thus someone with Reach (and using the reach) could still flank even if not directly adjacent?  Looking for both RAW as well as Intent of the flanking rule. We know that you can't transfigure food, so you have to grow it or buy it. Ditto money.  I'm sure that aside from some medicinal plants Herbology Professor had there were no farmlands at Hogwarts. So they must have bought food (as well as potions ingredients for Snape etc...). And they needed to pay the teacher salaries.  Where did all that money come from according to canon?  Ministry funding?  Tuition?  Patent money on Dumbledore's inventions?  Philanthropic donations by Malfoys and co?  Other? What happens to the view.frame.size attribute after a CGAffineTransform (Rotate)? Can someone tell me what's wrong with this? because i can't figure out where the missing \right( is.  \begin{equation}  \begin{split} Μ=&amp;-\pi \rho \frac{c^{2}}{4}    \left[c\left(\frac{α}{c}-\frac{1}{2}\right)\ddot{h}+Uc\left(\frac{3}{4}-     \frac{α}{c}\right)\dot{\alpha} +\frac{c^{2}}{4}\left(\frac{9}{8}+      \frac{4α^{2}}{c^{2}}-\frac{4α}{c}\right)\ddot{\alpha} \\  &amp;-\left(\frac{4α}{c}-1\right)U C(k) \left(-\dot{h} +U\alpha + c \left(\frac{3}{4}-\frac{α}{c}\right)\dot{\alpha}\right)\right]  \end{split} \end{equation} What are "Community Wiki" posts? Some questions and answers are marked Community Wiki and are owned by a community wiki user:  (In fact, this very question is one of them)  Why have Community Wiki posts? How do Community Wiki posts work? How does a post become a Community Wiki post? How can the Community Wiki status be removed from a post? How can I find Community Wiki posts? Name tikz pic as if it was a node I'm confused about tikz pics. I can freely define them without issue, and even add coordinates inside that will be available by name inheritance like (-A) as for example in \pic (S) at (0,0) {myPic}; \draw (S-A) -- ++(0,0);. This is all documented around p. 255 of the pgf manual.  However I don' understand why it is not possible to give a name to a pic like the one above if no coordinate is defined inside it. By default it would be great if it could behave like a normal node.  MWE:  \documentclass{minimal} \usepackage{tikz}  \tikzset{     myBlock/.pic = {         \node[draw,minimum width=1cm,minimum height=0.5cm] at (0,0) {};     },     myBlockNamed/.pic = {         \node[draw,minimum height=1cm,minimum width=0.5cm] (-m) at (0,0) {};     }, }  \begin{document} \begin{tikzpicture}     \pic () at (0,0) {myBock}; % can't give it a name     \pic (S) at (3,0) {myBlockNamed}; % can give it a name     \draw (S-A) -- ++(2,0); \end{tikzpicture} \end{document}   The underlying point is I'm working on a control blocs library (so that we can stop the chat below with @Alenanno). For example here is the definition of a math operator  \tikzset{     mySum background/.style = {         circle, minimum size=1.5em, fill=white,     },     mySum edge/.style = {         draw=black, circle, minimum size=1.5em, line width=.5pt,     },     pics/bOp/.style = {     code = {       \node [mySum background] {};       \foreach \t [count=\i] in {#1}{         \pgfmathsetmacro{\angle}{\i*90}         \node[anchor=center, font=\tiny] at (\angle:0.45em) {$\t$};       }       \node [mySum edge] {};     },   }, } Is it possible to access a 64-bit dll from a 32-bit application? Did the Nazgûl retain their Rings of Power? In The Fellowship of the Rings, Frodo sees the true appearance of the Nazgûl:      He was able to see beneath their black wrappings. There were five tall figures: two standing on the lip of the dell, three advancing. In their white faces burned keen and merciless eyes; under their mantles were long grey robes; upon their grey hairs were helms of silver; in their haggard hands were swords of steel. Their eyes fell on him and pierced him, as they rushed towards him.   The Fellowship of the Ring - J.R.R. Tolkien - chapter 11, A Knife In the Dark   There's no mention of the Nazgûl wearing the rings of power that Sauron gave them, although their hands are referenced. Did the Nazgûl retain their rings of power once they became wraiths? Or did something else happen to the rings once the Nazgûl emerged?&#185;  &#185; As an FYI, I am currently re-reading The Lord of the Rings trilogy and am just pages from being done with The Fellowship of the Ring. I'm very familiar with the Peter Jackson movies. So that's where I'm coming from as far as canon knowledge goes. Unicode identifiers in Python?