Shutdown Cause -20 after dropping my MacBook
MacBook Pro 2018 Random Restart > Previous shutdown cause: -20
Trying to remember a short story (most likely from the sixties).  It starts with a soldier at the front line fighting an unknown enemy on the other side of the front line.  He then gets withdrawn and you realise that time is passing slower the further he moves from the front. He then spends years in peace away from the front, before being sent back to the front where only a short time (hours or days perhaps) have passed.      I seem to remember their was an inference that they were actually fighting against themselves, with their attacks coming back at themselves, which was perhaps the entire cause of the war, and an interesting critique on war.  I can't remember if this all this was stated explicitly, or just left for the reader to infer. Solve $x^2+5x+6 \equiv 187 \mod 187$ Solution $$x^2+5x+6 \equiv 187 \mod 187$$ $$ (x+\frac{5}{2})^2 \equiv \frac{1}{4}$$ $$ 4(x+\frac{5}{2})^2 \equiv 1$$ $$ y:= x+\frac{5}{2} $$ $$ 4y^2 \equiv 1 \mod 11 \wedge 4y^2 \equiv 1 \mod 17  $$ $$ ( 2y \equiv 1 \mod 11 \vee 2y \equiv 10 \mod 11 ) \wedge ( 2y \equiv 1 \mod 17  \vee 2y \equiv 13 \mod 17)  $$ $$ ( y \equiv 6 \mod 11 \vee y \equiv 5 \mod 11 ) \wedge ( y \equiv 9 \mod 17  \vee y \equiv 15 \mod 17)  $$ Combining that from CRT I got: $$ y \in \left\{49, 60,83,94 \right\} $$ and for example: $$ x+\frac{5}{2}  \equiv 94 \mod 187$$ $$ 2x  \equiv 183 \mod 187$$ some calculus and get... $$x \equiv 185 $$ And the same thing for each other case. Question Is there any faster (or smarter) way to solve equations like that? How many possible electromagnetic wavelengths are possible? Disclaimer: Please keep in mind that I am a young highschool student with no background in physics, this research was done in the course of an hour, and my reasoning could very well be wrong.  After a short conversation about color, I did some thinking, and read  The answer claims that there are $\infty^{\infty}$ colors   My first problem is the definition of colors, I'm going to simplify this (although it's not the same thing) as electromagnetic frequencies. This is what I mean when I refer to color in the rest of this question  The problem with $\infty^{\infty}$ colors is that the plank length exists. This causes two problems to arise with $\infty^{\infty}$. If $l_p$ is assumed to exist (as it is), this means the smallest distance in the universe is $l_p$. So, all wavelengths of light can be divided into a set, of the wavelengths produced by objects at $0^{\circ}$ Kelvin to $\infty^{\circ}$ Kelvin. According to this logic, there are simply $\infty$ colors.  Things are complicated further, when you introduce the Plank Temperature ($P_t$). $P_t$ is the theoretical limit temperature of the universe (at least for the purposes of light and color) Because an object hotter than $P_t$ will produce light with wavelengths shorter than $l_p$. This would introduce an upper limit on colors too.  Wouldn't this mean that the total number of possible colors is equal to however many plank lengths difference there is between an electromagnetic wave produced by a 0 degree object and a $l_p$ object? And therefor far less than $\infty$? Does this reasoning make sense at all? What is the difference between user and service account? I would like to know difference between user and service account.  I know that e.g. Jenkins installed to ubuntu is not a user, .    What is use of service account? When we need them? How can I create service account? Suppose $f$ is entire and    $$\iint_\mathbb{C}|f(z)|^2dxdy &lt; \infty$$Prove that $f\equiv 0.$   So far I have:  Suppose $f$ is bounded.  Then $f$ is constant by virtue of Liouville and so the conclusion is obvious.  Thus, assume $f$ non-bounded.  Then  $$\Big|\iint_\mathbb{C}f^2(z)dA\Big| \leq \iint_\mathbb{C}|f(z)|^2dxdy &lt; \infty$$ We can parameterize \begin{align*} \iint_\mathbb{C}f^2(z)dA &amp;= \int_0^{\infty}\int_0^{2\pi}f^2(re^{i\theta})\;d\theta\;rdr \\ &amp;= \int_0^{\infty}\int_0^{2\pi}f^2(re^{i\theta})\;ire^{i\theta}[-i\frac{1}{r}e^{-i\theta}]d\theta\;rdr \\ &amp;= \int_0^{\infty}\oint_{C_R}f^2(z)\;[-i\frac{1}{z}]dz\;rdr \\ &amp;= \int_0^{\infty}2\pi r dr\frac{1}{2\pi i}\oint_{C_R}\frac{f^2(z)}{z}dz \\ \\ &amp;= 2\pi f^2(0)\int_0^\infty rdr  \end{align*}  Whence f(0) = 0.  And I have no idea where to go from there.  The "entire" bit seems to suggest Liouville but I have already dealt with the bounded case.  Please advise ... How to register my unregistered account Possible Duplicate:          I've been using my SO account for couple of days, but I am not registered and I do not want to lose all my questions. How can I register and keep my questions from my unregistered account? Are there any drawbacks to legacy BIOS as opposed to UEFI? Are there any drawbacks to installing Ubuntu 13.10 (and soon 14.04) in Legacy BIOS instead of UEFI?  I have installed 13.10 64bit in Legacy by mistake and was just wondering if it would hurt anything to simply leave it there as is?  EDIT  Everything seems to be running just fine in Legacy and all my drivers work. Calculate the limit including binomial coefficients Which pronoun to refer to "person"? It? He or She? They? "When he found his seat on the plane, Sam recognized the person who was sitting in the seat next to his. It? She? was a woman he knew."  Which is more common/natural? Isn't 'it' more correct – grammatically speaking – than 'she', since 'a person' can be a 'he' or a 'she', and obviously you cannot use the singular 'they' here? Display Database Instance Relationship with TikZ I'm trying to display all of my corporate database instances and their relationship to each other, so to speak the database links. I found the geometry shape cylinder using TikZ \usetikzlibrary{shapes.geometric}, but I'm new to the whole TikZ stuff and it doesn't worked out that well so I thought maybe you could help me getting something like the following figure:    There will be a ton of instances and arrows, but I hope that you guys could give me a start so that I could do the rest on my own. How to get the date in a batch file in a predictable format? In a batch file I need to extract a month, day, year from the date command.  So I used the following, which essentially parses the Date command to extract its sub strings into a variable:  set Day=%Date:~3,2% set Mth=%Date:~0,2% set Yr=%Date:~6,4%   This is all great, but if I deploy this batch file to a machine with a different regional/country settings, it fails because month, day and year are in different locations.   How can I extract month, day and year regardless of the date format? I have little experience with testing and I'm being hired to work on a team where I am the only tester. I'm struggling to find the best approach for the process. Being alone should I write down a test script or not? Wouldn't it take too much time? I have no experience in writing test scripts, could anyone help with a good reference (book, video or whatever), please? How to draw simple table Good reading on the Keldysh formalism I'd like some suggestions for good reading materials on the Keldysh formalism in the condensed matter physics community. I'm familiar with the imaginary time, coherent state, and path integral formalisms, but lately, I've been seeing Keldysh more and more in papers. My understanding is that it is superior to the imaginary time formalism at least in that one can evaluate non-equilibrium expectations. How do I change a switched outlet to a half-hot outlet? I am trying to change a switched outlet to a half-hot outlet. If you can see the picture, the outlet currently only has a white, black, and ground wire coming to it.   The switch is on the other side of the wall and it would be eextremely difficult and ugly to run another wire to it. (no crawl or attic space). So my question is, can I change the current outlet/wiring within the outlet to make it a half-hot? My understanding is that removing the brass connector will just make half of it dead. Why is $\frac{1}{\infty } \approx 0 $ and $ \frac{1}{0} = {\infty}$? First I have checked the search option but found nothing relevant to my problem and also level of math. I just started learning the language of mathematics, on my own and I have trouble understanding why  $  \frac{1}{\infty } \approx 0 $ and  why $\frac{1}{0} = {\infty}$?  I want to know how exactly do I get to these answers. It might sound strange but it's hard for me as a beginner to picture things like this on my own. Tips for getting really good answers on SO The way the askers write questions is a factor in determining how good the answers we get are. Obviously, if you ask a clear, direct question it is easier for a someone to answer you.  But, sometimes I've done that and my questions have still been overlooked.  I've noticed some question-posting methods that aren't exactly obvious, but do help me get better answers.    Some tricks I've learned...   Even if my question is very complicated, I try to write a short question.  People get turned off by longer questions, probably because they think its not worth their time (relative to other questions with equal reputation potential).  After I get some traffic and votes on my question, and maybe some comments like "Can you post the code?" or "Clarify this..." I might post more, but by then I am already getting attention to my question.  So, in summary, even if I know the answer requires a long question, I don't make it long until I've already gotten people to look at it. I use more generic tags when possible.  People are more likely to have c# and linq as a favorite tag, than MethodCallExpression, and I tend to get more views if I use at least one or two general purpose tags along with my more specific tags. I've noticed that if I give my question the performance tag, then SO heavy-weights like Marc Gravell, Jon Skeet and Eric Lippert are more likely to answer my question (especially if I use it in conjunction with a C# tag).  Since having this realization, if I can think of a way to rephrase my question to sound like it is related to C# performance, I will word it as such and tag it accordingly.   "Be polite. SO Users HATE when people be impatient, rude or impolite." - Benny   So,  Does anyone else have any tips for getting better answers and question-recognition on SO?  I think it would be really helpful if everyone contributed their own observations and techniques here.  P.S. This question is probably too long. During the end credit scene of Spider-Man: Far from Home, we see that,      Nick Fury and Maria Hill are two Skrulls, Talos and (presumably) his wife.   And we also see that,      Nick Fury is in a spaceship like structure, presumably away from Earth.   So that begs the question,      How long has Talos been impersonating Nick Fury? Is it since the events of Captain Marvel or since Avengers: Endgame or sometime in between? What's the meaning of the term "gib"? Especially while talking about FPS, the term "gib" is quite common. While I get it's related to a sudden and gruesome death, I'd like to know its actual meaning and where it comes from. I was able to read and write NTFS filesystems normally in Mountain Lion, but after the upgrade this stopped to work.  I installed ntfs-3g and fuse4x using homebrew in Mountain Lion and followed the instructions displayed by homebrew to finish the installation of fuse4x kernel extension.  To try to solve this problem I removed ntfs-3g, fuse4x and fuse4x-kext and reinstalled them. But this didn't solve my problem.  Does anyone know how to solve this? Thanks.