I was getting a certain error for a while. It took long reads and days to fix it. This error could have several causes, and I learned a few of them fixing mine.  So, I was thinking about asking and answering a question to group some causes and fixes in a single thread. However, doing that will cause me to ask a general question, "What are some causes and fixes for this error?", which could be downvoted/closed for being too broad.  Is it fine if I do that? I think that would be helpful for other people.  (Note that my meta question is somewhat similar to , except that that one is about changing a question, not asking a new one.)
As I understand it Q&amp;A style questions are  but a self answered question should be judged independently of the answer. Often after I've solved a problem I would like to share the question and answer on stack overflow (and have on a couple of occasions) but how to show &quot;minimal understanding of the problem&quot; is always challenging. For example I have been looking into the following question  How can I plot a straight line in the JMonkey Engine library I'm trying to plot straight lines between vertices that I specify using the JMonkey Engine 3D graphics library. So for example if I was to try to plot between: (2,0,0) (-1,0,1) (0,1,1) (1,1,1) (1,4,0) Then I would get:   This is something I do (and forget how to do) relatively often and the answer is harder to find than you'd imagine ( provides everything needed to figure it out but its spread out over several posts and isn't a complete solution on its own). Therefore I want to provide a Q&amp;A for it but at present this question feels like it would fail the minimal understanding test  Questions must demonstrate a minimal understanding of the problem being solved. Tell us what you've tried to do, why it didn't work, and how it should work  Should I make up some imaginary problem? (Probably the final source code messed up a bit) Or mention in the question that I’m self answering to assuage some of the normal &quot;This is not a do your work for you site&quot; comments.
How do I improve boot speed? I have seen many videos that make Ubuntu faster, but these methods only make desktop performance faster.  I am looking to make my computer boot faster. Is their anything I can do to make Ubuntu boot significantly faster? How to append something to an array? How do I append an object (such as a string or number) to an array in JavaScript? SO Blog icon has partial white background when tab is inactive When you open a tab on the , and switch to another tab, the icon has a partial white background: Firefox (Most obvious) - note the difference between that and the normal Stack Overflow logo  IE  Edge  Tested on Windows 10 with Firefox 41.0.2, Internet Explorer 11 and Microsoft Edge v20.10240.16384.0. (If someone could test this on chrome that would be great) The full prophecy by Trelawney, the part my question is about in bold:     "The one with the power to vanquish the Dark Lord approaches ... born to those who  have thrice defied him, born as the seventh month dies ... and the Dark Lord will mark him as his equal, but he will have power the Dark Lord knows not ... and either must die at the hand of the other for neither can live while the other survives ... the one with the power to vanquish the Dark Lord will be born as the seventh month dies ..."    – Sybill Trelawney (to Dumbledore)    I am interpreting      for neither can live while the other survives   as: Harry can't live while Voldemort survives and vice versa. But why? It clearly worked until the end of book 7. One could argue with Dumbledore's thery of the self-fulfilling prophecy. But clearly Voldemort was smart enough to see that there was no mechanism that would kill him just because Harry stayed alive.    and either must die at the hand of the other    Again: Why? If somebody else destroyed all Horcruxes and then killed Harry, Voldemort would be just as vulnerable and could be killed by anyone. On the other hand, Harry could have been killed by anyone - his mum's protection transferred to Voldemort by Harry's blood was only helping against Voldemort.  I guess that I am interpreting this part of the prophecy in the wrong way or maybe there is an alternate, less obvious and more tricky one. So my question is: What exactly does the highlighted part of Trelawney's prophecy state? What would be the easiest way to view classes, methods, properties, etc. inside a jar file? I'm looking for something equivalent to the very useful  Lutz Roeder .NET Reflector  - for Java Just beginning with photography.    Consider this image:     (This photo was taken by Harold "Doc" Edgerton in 1964 using his Rapatronic camera.)  I am looking for a  camera that can capture such an image. I am not looking for more fps. less fps is fine, but it must be able to capture such an instance.   What features should I look in such a camera?  How fast should be the shutter speed? What other things I should look for? Can I use a higher rank tensor field as the metric field? What a metric should necessarily do is it should give me a way to associate a frame invariant number with a given pair of spacetime events. Now, if I use a higher rank tensor field (say, for example, a tensor field of rank 3: $g_{\mu \nu \rho}$) then also I can certainly produce a frame invariant scalar out of a given displacement $\vec{A}$ in this trivial way: $ I := g_{\mu \nu \rho} A^{\mu}A^{\nu}A^{\rho}$. Since the components of the higher rank tensor and that of the displacement vector are going to transform in a covariant and a contravariant manner respectively, the cooked up quantity is certainly a scalar.   Another crucial property, which I think has more direct physical content than the previous one, is that between two inertial frames, at least one such transformation should exist that leaves at least one metric invariant. i.e., There should exist at least one combination of transformation matrix $\displaystyle\frac{\partial{x^{\alpha}}}{\partial{x^{\mu '}}}$ and metric $g_{\alpha \beta \gamma}$ that satisfies the following equation:      $\displaystyle\frac{\partial{x^{\alpha}}}{\partial{x^{\mu '}}}\displaystyle\frac{\partial{x^{\beta}}}{\partial{x^{\nu '}}}\displaystyle\frac{\partial{x^{\gamma}}}{\partial{x^{\rho '}}} g_{\alpha \beta \gamma} - \delta_{\mu '}^{\alpha}\delta_{\nu '}^{\beta}\delta_{\rho '}^{\gamma} g_{\alpha \beta \gamma} =0$    The last thing I can think of that can put a restriction on the choice of a tensor as a metric is the existence of a possibility of finding a metric compatible symmetric connection field. Following the usual procedure of finding the expression for a metric compatible symmetric connection field, I reached following condition (unlike the case of the usual two rank metric where we get a full-fledged expression) for the connection in the terms of the metric:      $g_{\nu \rho k_1} \Gamma^{k_1}_{\mu \lambda} - g_{\lambda \mu k_2} \Gamma^{k_2}_{\rho \nu} = \displaystyle\frac{1}{2} (\partial_{\nu}g_{\rho \lambda \mu} + \partial_{\rho}g_{\lambda \mu \nu}  - \partial_{\lambda}g_{\mu \nu \rho}  - \partial_{\mu}g_{\nu \rho \lambda}) $   My question is that if it is possible to satisfy the two highlighted conditions then can we use such a 3 rank (or even higher rank tensors with similarly produced conditions) tensor fields as metric fields?   PS: This is NOT a proposal for a new home-production theory of gravity (or that of anything for that matter) but rather it is just that I am trying to understand why a two rank tensor is used in General Relativity as the metric. Thank you. What's optimal hardness for a kitchen knife blade? Many knife manufacturers provide the hardness value for the knife blade in the specifications - like 53HRC or 57 HRC.  What's the optimal hardness for kitchen knives? Do I always prefer the ones with higher hardness all else being equal? I know that this question is a bit old or maybe overdone, but I'm running the latest edition of Blender and when I use the Cycles engine I get really fuzzy results and I can't find a simple, non-compromising solution to the quality.  I don't know exactly what I'm doing wrong here, but I'm sure others share my frustration.  Leaving everything in default settings, I started a new project and switched to the Cycles render.  I duplicated the cube and set colors for two Diffuse BSDF shaders, then went ahead and made walls and a floor all sharing the same diffuse shader.  I made two windows to emit blue light.  The screenshot has gaps between the walls because of the setup:  I'm aware that it's considered very incomplete and many have come to terms with some amount of noise, but is this normal?  Furthermore, with default settings or not, I can't change the amount of noise produced.  Supposedly, using "progressively refine" in the rendering tab should make it refine itself indefinitely, however Cycles only counts to 10 refines and then stops, creating a render which is a pixel-perfect match of the ordinary rendering method when it's completed.  I understand that there are tricks that can be used to reduce noise, but at the cost of extra processing time and usually small quality conflicts, like blurring.  My question essentially boils down to is this Cycles' current limit? Why is my total reputation less than my monthly reputation? When I went to the  to see my ranking in the reputation league, I saw this. Is this an error? My total reputation is less than my monthly reputation. How does a battery ( primary cell ) work? I'm having an hard time understanding primary cells. There are plenty of videos and explanations about the reactions that happen inside the battery, but you must have a strong background in chemistry to really understand them. Instead, I would love to have a description that abstracts from the chemicals details, and still manages to explain its basic working princeples! I would like it to address the following questions/doubts:     Electrons flow form higher potential to lower potential so, when you buy a  battery, is an electric field already there, before connecting it to a wire? (I presume yes) So,How is this field created? Are the electrons at the top and the protons at  the bottom, or just electrons at the top and the bottom is neutral? How are electrons kept together in the same place before connecting the battery  to the wire? What does prevent them to flow inside the battery? How does the battery pump up the electrons? and at which rate? What makes it burn out? and after many cycles does it burn out?       I know there are a lot of questions but my mind is exploding. I don't expect everything to be abstracted from the chemicals but as long as you can through analogies, or intuitive principles, i'd love that. Anyway the main intent of the answer must be addressing the doubts listed. What is DOCTYPE and why do I want to use it? What are the different DOCTYPEs I can use? What is the difference between standards and quirks mode, and what are some quirks I may run into with differently set DOCTYPEs?   Lastly, what is the proper DOCTYPE that I should be using? ${\rm Aut}(G)$ is cyclic $\implies G$ is abelian I would appreciate if you could please express your opinion about my proof. I'm not yet very good with automorphisms, so I'm trying to make sure my proofs are OK. Proof: Since ${\rm Aut}(G)$ is cyclic, ${\rm Aut}(G)$ is abelian. Thus for any elements $\phi, \psi \in{\rm Aut}(G)$ and some elements $g_i \in G$, $\phi\psi(g_1g_2)=\phi\psi(g_1)\phi\psi(g_2)=g_3g_4=\phi\psi(g_2)\phi\psi(g_1)=\phi\psi(g_2g_1)=g_4g_3$. Hence, $g_3g_4=g_4g_3\implies G$ is abelian. The proof seems to be quite straightforward, but I'd rather ask for advice. The question is raised from the viewpoint of a foreign language learner.  -ed is known to be added to a verb to mean past tense or past participle, but some phrases like four-legged animals, winged birds, are in the form of noun+-ed, why is it so? What is the logic behind such a structure? Meaning of "* */1 * * *" cron entry? Somehow, I am finding it difficult to understand tweaking around * parameters with cron.  I wanted a job to run every hour and I used the below setting:  * */1 * * *   But it does not seem to do the job. Could someone please explain the meaning of above and what is needed for the job? Can't deep learning models now be said to be interpretable? Are nodes features? For statistical and machine learning models, there are multiple levels of interpretability: 1) the algorithm as a whole, 2) parts of the algorithm in general 3) parts of the algorithm on particular inputs, and these three levels split into two parts each, one for training and one for function eval. The last two parts are much closer than to the first. I'm asking about #2, which usually leads to better understanding of #3). (if those are not what 'interpretability' means then what should I be thinking?)  As far as interpretability goes, logistic regression is one of the easiest to interpret. Why did this instance pass the threshold? Because that instance had this particular positive feature and it has a larger coefficient in the model. It's so obvious!  A neural network is  the classic example of a model that is difficult to interpret. What do all those coefficients mean? They all add up in such complicated crazy ways that it is hard to say what any particular coefficient is really doing.  But with all the deep neural nets coming out, it feels like things are becoming clearer. The DL models (for say vision) seem to capture things like edges or orientation in early layers, and in later layers it seems like some nodes are actually semantic (like the proverbial ). For example:    ()  This is a graphic () created by hand for presentation so I am very skeptical. But it is evidence that somebody thinks that is how it works.  Maybe in the past there just weren't enough layers for us to find recognizable features; the models were successful, just not easy to post-hoc analyze particular ones.  But maybe the graphic is just wishful thinking. Maybe NNs are truly inscrutable.  But the many graphics with their nodes labeled with pictures are also really compelling.    Do DL nodes really correspond to features? "To be subject to" vs. "to be subjected to" How to write permutations as product of disjoint cycles and transpositions $$\sigma=\begin{pmatrix} 1 &amp; 2 &amp;3 &amp; 4&amp; 5&amp; 6&amp;7 &amp;8 &amp;9 &amp;10 &amp; 11 \\ 4&amp;2&amp;9&amp;10&amp;6&amp;5&amp;11&amp;7&amp;8&amp;1&amp;3    \end{pmatrix}$$  (1) I am asked to write this permutation in $S_{11}$ as a product of disjoint cycles and also as a product of transpositions.   (2) Also find the order of the element. Is this permutation even or odd?  I think these are the disjoint cycles  $E_{1}=(1,4,10)$, $\;\operatorname{order}E_1 =3$  $E_{2}= (3,9,8,7,11),\;$ $\operatorname{order}E_{2} =5$  $E_{3}=(5,6),\;$ $\operatorname{order}E_{3} =2$  $S_{11}$=  $E_{1} \cdot E_{2}\cdot  E_{3}$  The order of $\operatorname{order}E_{3}$ is even so the order of the permutation is even. Why are they asking this? And what is the significance of it being even or odd?  Transpositions – I have read this a couple times but the one example in my textbook is rather unclear, I am not sure what this means?  I think the transposition for $E_{1}$ is $(1,4)(1,10)$ but I'm not sure what this means. Immediately, his insides started writhing as though he'd just swallowed live snakes -- doubled up, he wondered whether he was going to be sick -- then a burning sensation spread rapidly form his stomach to the very ends of his fingers and toes -- next, bringing him gasping to all fours, came to a horrible melting feeling, as the skin all over his body bubbled like hot wax -- and before their eyes, his hands began to grow, the fingers thickened, the knuckles were bulging like bolts -- his shoulders stretched painfully and a prickling on his forehead told him that his hair was creeping down toward his eyebrows -- his robes ripped as his chest expanded like a barrel bursting its hoops -- his feet were agony in shoes four sizes too small      Harry potter and the chamber of secrets   It is the description of the feeling of drinking Polyjuice Potion, which makes someone into a different person, from the point of view of Harry Potter turning into Gregory Goyle.  And I don't understand what 'bring him gasping to all fours' means, especially 'four'. Does four here mean number 4? How can I change the color of a part of a TextView?