Let’s assume I measure time t in my rest frame - thus in a moving frame I have t’ corrected according to the Lorentz factor.  I have a moving primed frame such that t’= 0.5t for example.  I measure 1 second in my rest frame, which is observed as 0.5 second in my primed frame.  If I now consider my primed frame to be the rest frame, and my previous rest frame to now be my “primed” frame, and measure 0.5 seconds in my now rest frame, I get 0.25 seconds in my now moving frame. How does that work out? Shouldn’t I get my whole 1 second back?  It is safe to assume I could consider any possible frame of reference, so what detail is it that I’m missing?  Edit*: I have 2 pairs of frames:  Rest1: Let time be t Motion1: moving observer relative to Rest1 such that t’=.5t  Rest2: chosen such that Rest2 is at same speed as Motion1. Let time be T Motion2: chosen such that Motion2 is at same speed as Rest1. T’ =  0.5T  If t = 1, then t’=0.5 Since Rest2 and Motion 1 are at the same speed, then T = t’ = 0.5 Therefore T’ = 0.5*0.5 = 0.25  Motion2 and Rest1 are at the same speed, thus T’ = t, 1=0.25!?
Suppose we have two twins travelling away from each other, each twin moving at some speed $v$:    Twin $A$ observes twin $B$’s time to be dilated so his clock runs faster than twin $B$’s clock. But twin $B$ observes twin $A$’s time to be dilated so his clock runs faster than twin $A$’s clock. Each twin thinks their clock is running faster. How can this be? Isn’t this a paradox?
Why Was It 'Essential' That Voldemort Kill Harry Potter? I am getting a Too many SOQL queries: 101 error on a trigger when I am trying to deploy another trigger.  I am posting the trigger which is causing the error.  trigger rollupAccountShowings on Account (before insert, before update) {    if (trigger.isinsert) {       for (Account a:Trigger.new){           a.No_of_Viewings__c = 0;        }    } else {      for (account a : [select                   id,                  (select id from pb__Showings__r)                  from account                   where id in:trigger.new LIMIT 1]) {           trigger.newMap.get(a.id).No_of_Viewings__c = a.pb__Showings__r.size();      } }   Can anyone correct me where I have gone wrong and suggest me the changes.  Thanks Why did Obi-Wan allow Leia to get adopted by such a high profile figure? When training a neural network using the back-propagation algorithm, the gradient descent method is used to determine the weight updates. My question is: Rather than using gradient descent method to slowly locate the minimum point with respect to a certain weight, why don't we just set the derivative $\frac{d(\text{Error})}{dw}=0$, and find the value of weight $w$ which minimizes the error? Also, why are we sure that the error function in back-propagation will be a minimum? Can't it turn out the error function is a maximum instead? Is there a specific property of the squashing functions that guarantees that a network with any number of hidden nodes with arbitrary weights and input vectors will always give an error function that has some minima? Unit Test - Creating Custom Metadata I have three questions that I'd like to be clarified.   Is their anyway we could create Custom Metadata in Test Classes? I tried to create on my Test Class but I got an error saying the fields of the metadata could not be writable.  If not, then does that mean we should declare real values in our Custom Metadata and use that instead in our test classes? If (2) is correct, then does this mean we have to create the Custom Metadata in the environment we'll be deploying our code before doing the actual deployment? Driver locked memory on a non-virtual machine "The ticket is printing" vs "...is being printed" You're standing in front of a ticket vending machine and it says "The ticket is printing". Is that correct or should it be "The ticket is being printed"?  EDIT:  If both are correct, which one should be preferred or is more common? I changed my username and now I cannot play online I don't understand this and I'm now worried as I have donated to a lot of servers and I don't want to lose this account. On the launcher it says my new username but when I log on it says "Account not Authenticated with minecraft.net" and "Non-Valid Username".  How can I regain the ability to use my account online? Missing whitespace in beta site statistics box CSS3's attr() doesn't work in major browsers "Who wants ice-cream?" — Should I say "(not) I" or "(not) me"? With the enthusiastic question of "Who wants ice-cream?", what is the more correct response?         (Not) I.   (Not) me.      Neither response is a sentence. The first response of "(not) I" sounds stuffy, like it should be followed with an indignant sniff. The second sounds like American idiom and acceptable for casual speech.    What do you say? Evaluate the integral $\int e^{-x}x^n dx$ Evaluating the integral $\int_{0}^{\infty}  e^{-x}x^n dx$ where n=0,1,2 ...   1st Integration by part: let $a=x^n$, $da= nx^{n-1} dx$, Also $db=e^{-x}$, $b=-e^{-x}$ We have $$ -x^n e^{-x} + n\int x^{n-1}e^{-x} dx$$  2nd: let $a=x^{n-1}, da= (n-1)x^{n-2}, db= e^{-x}, b= -e^{-x}$ We have $$-x^n e^{-x} + n\left[x^{n-1}(-e^{-x}) - \int(n-1)x^{n-2}\cdot -e^{-x}\right]$$  How would you find the general form? What would it be? The total number of locks exceeds the lock table size What is an efficient way to implement a singleton pattern in Java? What is an efficient way to implement a singleton pattern in Java? If $A^2 = I$, then $\operatorname{rank} (A+I) + \operatorname{rank} (A-I) =n$ If $A^2 = I$ where $A$ is an $n\times n$ matrix, then why is $\operatorname{rank} (A+I) + \operatorname{rank} (A-I) =n$.   I am not sure why this seems to be true. Plagiarism of Lecture Slides Original Post:  I recently attended a lecture with highly technical content.  One of the middle slides in the deck had a particular phrase that reminded me of something that I had read several years before.  It took me a few minutes, but I found the original source (another slide deck) and am shocked to find that the professor lifted 35 slides verbatim from the original source.  The University holds students accountable for plagiarism and strictly defines plagiarism such that this clearly fits.  The slides were used verbatim and no credit or reference was provided.  Further, logos were added and color schemes were changed to make make them look slightly more like original content.  What should I do?  This professor has a professional full time job and I can imagine this getting swept under the rug, but this is clearly plagiarism and is spelled out very clearly in the student conduct code.  Is this an overreaction or should I pursue this?  This is confounded by the fact that I am very disappointed by the rigor of the course and feel like the professor lacks adequate technical background to teach the course (I guess my suspicions came true).  I'm really busy at work so don't want to deal with a big todo, but believe this really discredits the academic integrity of the course.  Additional content in response to comments:  The University defines plagiarism as "Using another writer's words without proper citation."  There is no proper citation given here, and these are not educational materials.  This is 35 slides from someone else's tutorial presentation.  I do not believe that the professor and the author of the original content have a relationship.  I have emailed the author to enquire about any permissions or relationship.  Still, even with permission, this is still plagiarism as defined be most people and as defined by the University.  All original works in the US are implicitly copyright protected, so there is also a copyright issue, but this is not currently my concern, though it could be of interest to the original author.  I have emailed him, so this is up to him.  This is a US institution and is a top tier highly respected school.  I am also not a lay student, but a Ph.D. with a degree from a top tier university who has served as a faculty member at two top tier universities (including this one).  I have also taught undergraduate courses in the past.  I have never engaged in this type of plagiarism, have never known colleagues to do so, and am shocked that so many people suggest this is par for the course in teaching.  My doctorate is from a school that prides itself on its honor code and takes honor code violations very seriously and I have served on the honor council and deliberated on a case of plagiarism in the past.  I really am shocked by this incident.  Response from Original Author of the Slides:  I have received a response from the author of the slides and he states that the work is his original work, that there are no additional authors of the work, that no one has been given permission to present the work, and that he believes his copyright on the work has been infringed upon.  He has requested additional information to assert his claim on the copyright. The only place I am aware of is the . I'm using the  package to add citations and a bibliography to my LaTeX document. I've noticed that only the first author plus "et al." is displayed for works with more than three authors. That's fine with me for in-text-citations, but I'd rather have the complete author information in the bibliography. How can I do that? Empty intersection and empty union If $A_\alpha$ are subsets of a set $S$ then   $\bigcup_{\alpha \in I}A_\alpha$ = "all $x \in S$ so that $x$ is in at least one $A_\alpha$"  $\bigcap_{\alpha \in I} A_\alpha$ = "all $x \in S$ so that $x$ is in all $A_\alpha$"  It is the convention that $\bigcup_{\alpha \in \emptyset}A_\alpha = \emptyset$ and $\bigcap_{\alpha \in \emptyset} A_\alpha = S$.   But if $x$ is in $\bigcap_{\alpha \in \emptyset} A_\alpha = S$ then $x$ is in all $A_\alpha$ with $\alpha \in \emptyset$ and therefore $x$ is certainly in at least one $A_\alpha$ with $\alpha  \in \emptyset$. But then $x \in \bigcup_{\alpha \in I}A_\alpha$.  Can someone help me and tell me what is wrong with this? Thank you. Is there any elegant way to show that $\mathbb Q(\sqrt[3]{2}, w)=\mathbb Q(\sqrt[3]{2}+w)$, where $w=e^{i\frac{2\pi}{3}}$.  I was thinking to show that $ 9+9 x+3 x^3+6 x^4+3 x^5+x^6$ is the minimal polynomial of $\sqrt[3]{2}+w$, but checking irreducibility seems a bit tedious.