In The Force Awakens, we see      Kylo Ren trying to get a map to use to kill Luke Skywalker. We also see Kylo Ren praying to Darth Vader and otherwise trying to emulate Darth Vader in many ways.    But I recall Darth Vader removing his mask as he was dying so that Luke could be close to his father. Annakin ended life reconciled with Luke. Why does Kylo Ren not seem to know this?
It seems Kylo has an obsession of Darth Vader and has an interest in the dark side because of it.   Does he not realize that Darth Vader turned good and helped destroy the Empire (Spoilers?)? I feel like Kylo would've seen how much better the Light Side was as it was able to turn Vader from the Dark Side if he had known this.
Generalized RBF Kernels There is the notion of Generalized RBF Kernels, for example in "Towards Optimal Bag-of-Features for Object Categorization and Semantic Video Retrieval" from Jiang (1) or in formula (2.72) in  (2).  They define: Gen. RBF Kernel: $e^{-pd(x,y)}$, where (1) says d can be any distance function and (2) requires it to be a metric.  I now have been wondering for a long time: Is a function defined by $e^{-pd(x,y)}$ where d is a metric always a Mercer's Kernel? I think in (2) it sounds like it, but if it were true, not many people know of it, since they are still looking to prove that $e^{-EMD(x,y)}$ is a kernel, where EMD = Earth Mover's Distance, which is a metric.  If its not a Mercer's Kernel - do you know of any counter example? P-adic expansion construction Proof for triangle inequality for vectors Generally,the length of the sum of two vectors is not equal to the sum of their lengths. To see this consider the vectors $u$ and $v$ as shown below.  By considering $u$ and $v$ as two sides of a triangle, we can see that the lengths of the third side is $\| u + v \|$ and we have $\| u + v \| \leq \|u\| + \|v\|$.  Under what circumstance equality occurs and how can one prove that? Can we prevent titles with an unnecessary tag in them? So we have lots of questions that are titled like this:  Specifically, questions that have one of their tags in front of their title. Thankfully, these silly users usually use a hyphen or a colon afterwards, which makes it really easy to . Can we clear up this clutter?  Perhaps with a filter that strips off the excess when posting? EDIT: As an added bonus, see  for another style of question title that bugs the heck out of me. How to perform Stream functions on an Iterable? On our minecraft server, I've built a Nether portal in my basement. Which connected two-way (tested) to a location in the Nether.    This nether portal took me to an area in the nether which was a small cave. I dug upwards and surfaced close to a Nether Fortress. After clearing the fortress of Blaze spawners, I decided to 'move in'. So I went back to the portal, dismantled it, and reactivated in in a location in the Fortress.    The fortress would be within the same 128m radius I would assume as it's really close to the original place. Literally some steps to the surface, then a ladder up the nearest Nether Fortress bridge support.  Now, taking this portal back to my original doesn't work, I spawn deep underground in an Abandoned Mine Shaft.  I read somewhere that my Nether portal has found a 'better match' and this could be remedied by disabling the 'wrong' portal in the mine shaft.  However, upon multiple attempts, a new nether portal is dynamically created in the same area. See screenie for example. You'll see two 'stacked' portals on the left (from my different attempts at disabling) and then the current active one on the right.    My question is, how can I make sure these portals go to the correct place. Is it a matter of returning the portal to it's original location or am I stuck for returning to the basement? Sass Interpolation of Mixin, Function, and Variable names Inverse metric in linearised gravity From what I've read, in the framework of linearised gravity, one perturbs the metric around a Minkowski background, $\eta_{\mu\nu}$, such that  $$g_{\mu\nu}(x)=\eta_{\mu\nu}+h_{\mu\nu}(x)\tag{1}$$  where $h_{\mu\nu}(x)$ is a small perturbation, i.e. $$\big\lvert h_{\mu\nu}\big\rvert&lt;&lt;1.\tag{2}$$  The inverse metric is then found by assuming the following ansatz:  $$g^{\mu\nu}(x)=\eta^{\mu\nu}+\tilde{h}^{\mu\nu}\tag{3}$$  where $\tilde{h}^{\mu\nu}$ is also small (i.e. $\big\lvert \tilde{h}_{\mu\nu}\big\rvert&lt;&lt;1$).   Using this, it is easy to find that  $$g^{\mu\nu}(x)=\eta^{\mu\nu}-h^{\mu\nu} \tag{4}$$  to first order.   My question is, what is the justification for this ansatz? Is it simply that one expects the inverse metric to have a similar form to the metric in order to satisfy $$g^{\mu\alpha}g_{\alpha\nu}=\delta^{\mu}_{\;\nu}~?\tag{5}$$ Proving a distance between molecules defines a metric space. A DNA molecule can be represented as a string of symbols $A$, $C$, $G$ and $T$, such as  $$GGATAATTCTAG. . .GACCGTACCC$$ For the purposes of this question, we will assume that all DNA molecules contain the same (large!) number $N$ of symbols. Thus, a DNA molecule is an $N$-tuple $x = (x_1, . . . , x_N)$ where $x_i  ∈ \{A,C,G,T\}$ for each $i$.  Define the distance between two DNA molecules $x$, $y$ as the number of elements $i ∈ {1, . . . ,N}$ such that $x_i \neq y_i$. Prove that this defines a metric on the set of DNA molecules. It would be nice if backticked code in question titles were rendered the same way they are in question bodies. Since there are so many questions with code in them I feel it would be a big plus. .  This would look a lot nicer in listings and on the page itself if the code strings were rendered as such.  Similar ideas discussed . To show that $2$ | $x^{2n} - x^n$, $n \in \mathbb{Z^+}$ is the following adequate? If $x+y+z=xyz$, prove $\frac{2x}{1-x^2}+\frac{2y}{1-y^2}+\frac{2z}{1-z^2}=\frac{2x}{1-x^2}\times\frac{2y}{1-y^2}\times\frac{2z}{1-z^2}$ given that $x^2~,~y^2~,~z^2\ne1$  I came across this question in an ancient ($19$th century) Trigonometry book, and this is the method they use to prove the result (please note: I understand this method fully): Let $x=\tan A$ ,$~y=\tan B$ and $z=\tan C$ which is acceptable without any loss of generality. This means that we are saying that $$\tan A+\tan B+\tan C=\tan A\tan B\tan C$$ Consider $\tan (A+B+C)$: $$\tan (A+B+C)=\frac{\tan A+\tan B+\tan C-\tan A\tan B\tan C}{1- \tan A \tan B- \tan C \tan A - \tan B \tan C}$$ So if $~\tan A+\tan B+\tan C=\tan A\tan B\tan C~~$ then $~~\tan (A+B+C)=0$. Hence, let $~A+B+C=\pi$. Now consider $\tan (2A+2B+2C)$: $$\tan (2A+2B+2C)=\frac{\tan 2A+\tan 2B+\tan 2C-\tan 2A\tan 2B\tan 2C}{1- \tan 2A \tan 2B- \tan 2C \tan 2A - \tan 2B \tan 2C}=0$$ $$\implies \tan 2A+\tan 2B+\tan 2C=\tan 2A\tan 2B\tan 2C$$ $$\implies \frac{2\tan A}{1-\tan^2 A}+\frac{2\tan B}{1-\tan^2 B}+\frac{2\tan C}{1-\tan^2 C}=\frac{2\tan A}{1-\tan^2 A}\times\frac{2\tan B}{1-\tan^2 B}\times\frac{2\tan C}{1-\tan^2 C}$$ $$\therefore\frac{2x}{1-x^2}+\frac{2y}{1-y^2}+\frac{2z}{1-z^2}=\frac{2x}{1-x^2}\times\frac{2y}{1-y^2}\times\frac{2z}{1-z^2}$$ as required.  My question is, is there any other way of proving this without this rather heavy use of trigonometry? I also would prefer not to work through heaps of algabraic manipulation and expansion to obtain the required result, although if that's necessary I will put up with it ;) Thank you for your help. Chain wire methods together in Lightning Web Components According to the documentation  in order to retrieve a list of picklist values for an object we need to pass in a Record Type Id which can be retrieved using the getObjectInfo method.   The issue is that these are both wire functions and I cannot figure out how to chain these methods.  If I try code like the following:  getObjectInfo({ objectApiName: ACCOUNT_OBJECT })             .then(result =&gt; {                 return getPicklistValues({recordTypeId: result.defaultRecordTypeId, fieldApiName: TYPE_FIELD});             })             .then(result =&gt; {                 this.picklistValues = result.data             })             .catch(error =&gt; {                 this.error = error;             });   I get an error      render threw an error in 'c:getpicklistexample' [Imperative use is not   supported. Use @wire(getObjectInfo).]   If I try something like   @track rtId;      @wire(getObjectInfo, { objectApiName: ACCOUNT_OBJECT })     handleResult({error, data}) {         if(data) {             this.rtId = data.defaultRecordTypeId;         }     }      @wire(getPicklistValues, {recordTypeId: this.rtId,fieldApiName: TYPE_FIELD})     picklistValues;   Then it throws an internal server error. Anybody have an idea as to how I could retrieve the record type Id and then call to get the pick list values like the documentation suggests?  FYI my imports are:  import { LightningElement, wire, track } from 'lwc'; import { getPicklistValues, getObjectInfo } from 'lightning/uiObjectInfoApi'; import TYPE_FIELD from '@salesforce/schema/Account.Type'; import ACCOUNT_OBJECT from '@salesforce/schema/Account'; Let   consider   a  square $10\times 10$   and  write  in  the   every   unit  square    the   numbers   from  $1$  to  $100$   such  that   every  two   consecutive  numbers  are  in   squares   which  has  a  common edge.  Then  there  are  two  perfect  squares   on  the  same line  or  column. Can  you   give  me  an  hint? How  to  start? Are split infinitives grammatically incorrect, or are they valid constructs? What is the difference between "source x", ". x" and "./x" in Bash? Does $ \int_0^{\infty}\frac{\sin x}{x}dx $ have an improper Riemann integral or a Lebesgue integral? In  wikipedia article for improper integrals,  $$ \int_0^{\infty}\frac{\sin x}{x}dx $$ is given as an example for the integrals that have an improper Riemann integral but do not have a (proper) Lebesgue integral. Here are my questions:   Why does this one have an improper Riemann integral? (I don't see why $\int_0^a\frac{\sin x}{x}dx$ and $\int_a^{\infty}\frac{\sin x}{x}dx$ converge.) Why doesn't this integral have a Lebesgue integral? Is it because that $\frac{\sin x}{x}$ is unbounded on $(0,\infty)$ and Lebesgue integral doesn't deal with unbounded functions? How do I clear Bash's cache of paths to executables? When I execute a program without specifying the full path to the executable, and Bash must search the directories in $PATH to find the binary, it seems that Bash remembers the path in some sort of cache. For example, I installed a build of Subversion from source to /usr/local, then typed svnsync help at the Bash prompt. Bash located the binary /usr/local/bin/svnsync for "svnsync" and executed it. Then when I deleted the installation of Subversion in /usr/local and re-ran svnsync help, Bash responds:  bash: /usr/local/bin/svnsync: No such file or directory   But, when I start a new instance of Bash, it finds and executes /usr/bin/svnsync.  How do I clear the cache of paths to executables? Do spell effects move if the object they are cast on moves? let's suppose that I cast a Silent image of a wall on an airship. Let's suppose that I don't move it with concentration.  Does the image of the wall move with the airship or it will progressively go far? I spotted a  (10k-only by now) and when I went to flag it, the flag dialog told me that I'd already flagged it as VLQ:    The thing is, I'd never seen this post before. And a look at the flag history in my user profile confirms that I haven't flagged a post since yesterday:    Certainly, well before the 2015-02-04 05:36:21Z time of Mr. Miracle's post.  I was able to reproduce this on SO from the VLQ review queue: when you're presented with an answer, click on link at the right side of the page, then click flag. You get the "you have already raised this type of flag" message on either the "it is not an answer" or "it is very low quality" options, I gather depending on the original flag that pushed the post into the VLQ queue.