This question seems to be a close parallel of , but it's about a different design by a different author.  I read a  about a "helical engine" design by NASA engineer David Burns. The design allegedly exploits relativistic effects to seemingly violate conservation of momentum (as in the earlier question). It involves an oscillating mass which travels faster in one direction than the other, thus having higher relativistic mass on one side and imparting unbalanced momentum to its container.     But, Burns asks, what if the ring’s mass is much greater when it slides in one direction than the other? Then it would give the box a greater kick at one end than the other. Action would exceed reaction and the box would accelerate forwards (see video below).   Read more:   Now, I'm not a physicist, but I'm just smart enough to have gotten the sense that this is almost certainly nonsense. As soon as I read "may violate the laws of physics" in the headline, in fact. Is it nonsense, and if so, what is unaccounted for in this model that would balance the momentum transfer at each side of each oscillation? How does the math play out?
The  is a proposed propulsion mechanism for spacecraft in which some form of microwave device provides the propulsion. The consensus from the physics community, including many voices on this site, is that the proposed device would violate conservation of momentum.   Several experiments have been conducted, by three main groups: (i) , from Satellite Propulsion Research Ltd, (ii) a research group at the Northwestern Polytechnical University in Xi'an, China, and (iii) Eagleworks Laboratories at NASA's Lyndon B. Johnson Space Center in Houston, Texas. However, few of these experiments have been performed in vacuum (and none of the vacuum tests has been published in a peer-reviewed journal), which means the effect of air currents around the device cannot be ruled out.  This device has been the subject of many questions on this site, including          and their many closed duplicates.  Many of these questions ask what the proposed explanations are, but then veer off into territory of the form "assuming it is true, how does it work?", so they have been (rightfully) closed as counterfactual physics. I feel this sort of bundling does a lot of harm to the discussion, and there is some scope to ask what exactly is being proposed as an explanation. So:     What do the proponents of EmDrive claim is the theoretical justification of the device's function?   Please limit answers exclusively to references, and indicate whether they are peer-reviewed or not. Please limit answers to serious attempts at explanations, as opposed to vague claims about the 'quantum vacuum' - or indicate if an experimental paper does not have any such theoretical explanation or reference.  To be clear, this is not the place to discuss whether the explanations are correct or not. If you have specific questions about any of these sources, ask it separately. (However, if your question starts with "assuming that this works", be prepared for it to be closed.) If you feel there are not enough resources on this thread, you can  but please do not post another question asking people to look for more references.
What exactly is "base ISO" and how do I find what is base ISO on my camera? If I understood correctly, base ISO is in full stop steps from the lowest possible ISO setting on my camera. For example if the lowest setting on my camera is ISO 100, than the following table would be base ISO:    100, 200, 400, 800, 1600, 3200, 6400   While steps in between like   125, 160, 250, 320, 500, 640, 1000, 1300, 2000, 2500, 4000, 5000   would be third-stop "pulled" values, which result more noise than perhaps higher base ISO values (for example 2500 is worse than 3200).   Did I get this right or missed by a mile, what did I miss? Do non-base ISO values generate more noise than next higher base-value ISO stop? How do I find what are my base-value ISO stops (is it the lowest ISO value multiplied by 2n)? I'm struggling a bit with functions(limits, squeeze theorem, etc).  I have done some research and found a list of books on calculus but I'm not sure which one would be better suited for me, so I would appreciate if some experienced people here could advise me which books would be better to master the basics so I can move on with derivatives, etc. Limits is my main problem, so I need a book which explain this in depth so I can master it. Then I'll keep going on with the same book for other chapters.  Below is the list which I found :   Apostol T.M. Calculus Vol. 1 Burn R.P. Numbers and Functions: Steps into Analysis  Courant R. and John F. Introduction to Calculus and Analysis I - One of the better calculus text in print.  Crowell B. Calculus  Dawkins, P Calculus I and Calculus II  Garrett P. Calculus  Ghorpade S.R. and Limaye B.V. A Course in Calculus and Real Analysis  Gill G.S. Calculus Bible  Guichard D. Whitman Calculu.  Hardy G.H. A Course of Pure Mathematics  Hwang A.D. Calculus for Mathematicians, Computer Scientists, and Physicists: An Introduction to Abstract Mathematics  Santos D. Differential Calculus  Shapiro B.E. Calculus and Analysis  Spivak M. Calculus  Strang G. Calculus  Thomas G.B. and Finney R.L. Calculus and Analytic Geometry  Tranter C.J. Advanced Level Pure Mathematics  Tranter C.J. Techniques of Mathematical Analysis  Veeh J.A. Lectures Notes on Calculus  So far I narrowed my list down to Hardy, Spivak and Apostol based on further research, but I haven't got my hands on these books yet to compare them and I'm not sure if these books will be good for me.  Thanks. Where should I copy-paste-install software to? I'm installing IntelliJ, and the readme tells me to choose an installation folder. Where is a good, standard place to put installed programs? Neural network references (textbooks, online courses) for beginners I want to learn Neural Networks.  I am a Computational Linguist. I know statistical machine learning approaches and can code in Python.   I am looking to start with its concepts, and know one or two popular models which may be useful from a Computational Linguistics perspective.  I browsed the web for reference and found a few books and materials.   Ripley, Brian D. (1996) Pattern Recognition and Neural Networks, Cambridge Bishop, C.M. (1995) Neural Networks for Pattern Recognition, Oxford: Oxford University Press. some links, like ,  (University of Toronto Psychology Department),  (University of Wisconsin Computer Science) and  (Facebook Research).   Coursera courses are generally nice, if anyone knows anything relevant from them. I prefer materials with lucid language and ample examples. Is there a symmetry associated to the conservation of information? Conservation of information seems to be a deep physical principle. For instance, Unitarity is a key concept in Quantum Mechanics and Quantum Field Theory.  We may wonder if there is an underlying symmetry, in some space, which may explain this conservation of information. How do I control how Emacs makes backup files? Emacs puts backup files named foo~ everywhere and I don't like having to remember to delete them.  Also, if I edit a file that has a hard link somewhere else in the file system, the hard link points to the backup when I'm done editing, and that's confusing and awful.  How can I either eliminate these backup files, or have them go somewhere other than the same directory? Why are empty and non empty TikZ matrix cells not equally placed? I wanted to draw an almost empty matrix of nodes with TikZ similar to the left most one below. All nodes would have same size (through minimum width and minimum height) and no separation between columns and rows. But when I include a text which needs two lines I obtain the central matrix and, if the text just needs one line the right most one. I don't know what's wrong. Do you? I'm using CVS version of TikZ.  \documentclass[tikz,border=2mm]{standalone} \usetikzlibrary{matrix}  \tikzset{ proces/.style={draw, minimum height=15mm, minimum width=2cm, outer sep=0pt, text width=1.5cm, align=center} }  \begin{document} \begin{tikzpicture}  \matrix (A) [matrix of nodes,nodes=proces,nodes in empty cells] {  &amp; \\  &amp; \\ };  \begin{scope}[xshift=4.5cm] \matrix (A) [matrix of nodes,nodes=proces,nodes in empty cells] {  &amp; OOO OOO \\  &amp; \\ }; \end{scope}  \begin{scope}[xshift=9cm] \matrix (B) [matrix of nodes,nodes=proces,nodes in empty cells] {  &amp; A \\  &amp; \\ }; \end{scope}  \end{tikzpicture} \end{document} It seems that we are . This is the speed of our galaxy relative to the cosmic microwave background. Where does this rest frame come from? Is this special in any way (i.e., an absolute frame)? EDIT: I think the more important question is &quot;where does the CMB rest frame come from?&quot;. How to break the Y axis in an Excel sheet I want to break the Y-axis in an Excel sheet. How can I do that?  For example, suppose I have the data in a range from 0-7000 and then range from 22000-28000. I want a break in the Y axis from 8000-20000. Why is Euclid's proof on the infinitude of primes considered a proof? I've expressed Euclid's proof on the infinitude of primes on Mathematica:  f[x_] := Product[Prime[n], {n, 1, x}] + 1 TableForm[Table[{f[x], PrimeQ[f[x]]}, {x, 1, 20}]]   Which results in:  $\begin{array}{ll}  3 &amp; \text{True} \\  7 &amp; \text{True} \\  31 &amp; \text{True} \\  211 &amp; \text{True} \\  2311 &amp; \text{True} \\  30031 &amp; \text{False} \\  510511 &amp; \text{False} \\  9699691 &amp; \text{False} \\  223092871 &amp; \text{False} \\  6469693231 &amp; \text{False} \\  200560490131 &amp; \text{True} \\  7420738134811 &amp; \text{False} \\  304250263527211 &amp; \text{False} \\  13082761331670031 &amp; \text{False} \\  614889782588491411 &amp; \text{False} \\  32589158477190044731 &amp; \text{False} \\  1922760350154212639071 &amp; \text{False} \\  117288381359406970983271 &amp; \text{False} \\  7858321551080267055879091 &amp; \text{False} \\  557940830126698960967415391 &amp; \text{False} \\ \end{array}$  The proof flaws for all those values, how is it considered a proof then? I guess that there might be infinite prime numbers according to the proof, but what is the guarantee that at some point it won't fail indefinitely? I am doing some challenges. This is one them. I am trying to brute-force 4 digit pin with the password to get my desired answer. After connecting to the port It prompts me to enter the password then space then 4 digit pin. I tried to brute-force the pin using the script:  #!/bin/bash   nc localhost 30002   sleep 2    for i in {0000..9999};       if [[ $(echo 'UoMYTrfrBFHyQXmg6gzctqAwOmw1IohZ $i' &lt;/dev/stdin) = ^Wrong*]];                         then          continue       echo '[+] Pincode Cracked! Pincode = $i'       fi   done  but it seems that this doesn't input the pass and pin to stdin, before i tried doing something like this -&gt; if [[ $(echo 'UoMYTrfrBFHyQXmg6gzctqAwOmw1IohZ $i') = ^Wrong* ]]; What am I doing wrong here? UPDATE: Okay, so after researching around. I wrote this: for i in {0000..9999} do     if [ (echo &quot;UoMYTrfrBFHyQXmg6gzctqAwOmw1IohZ $i&quot; | nc localhost 30002 | grep -o Wrong) == &quot;Wrong&quot; ]    then       sleep 0.1       continue    fi    echo &quot;- - - - - - - - - - - - - - - - - - - - - - - - [$i]&quot; done  This might even work but as you can see it opens new connections in the loop which makes it really slow and exhaust the system. Why sets of nonzero measure contain almost all the point from Borel-cantelli Leems? How do suggested edits work? There should be a notification when a moderator reviews or looks at a post which you've flagged.  The notification could show the status (helpful, declined, disputed, or something else) of your flag.  Edit  The reason for doing this is so that you would be able to see when a post which you have flagged has received moderator attention, at which point you could go back to the post. This would be good, for instance, if:   you flagged a post for migration to another site; after migration occurs, you could answer the question, since  that only unanswered questions should get migrated you flagged a post for removal of spam or otherwise nonconstructive content, and the content removal has to be carried out in batches is it possible to raise the tip while raising the back and lowering the center of the tongue when making /R/ sound? Following , this is how we correctly make the r sound:   Let the throat vibrate since it is voiced. Round the lip a little. Raise the tip of the tongue towards the hard bump behind the upper front teeth,  but do not let the tip of tongue touch the bump. This also makes the center of the tongue go down. The back part of the tongue is raised because you pull it into a tight ball Fold and raise the sides of the tongue so they touch the upper side-teeth.   If we follow the above requirement, our tongue should have an s shape when we pronounce the r sound as depicted in the following sketch:    Is it possible to raise the tip while raising the back and lowering the center of the tongue when making an r sound?   How do native speakers make an r?  P.S. My tongue is very short anyway! Let $R$ be a commutative ring with 1 then why does $a\in N(R) \Rightarrow 1+a\in U(R)$? Let $R$ be a commutative ring with 1, we define  $$N(R):=\{ a\in R \mid  \exists k\in \mathbb{N}:a^k=0\}$$  and  $$U(R):=\{ a\in R \mid a\mbox{ is invertible} \}.$$  Could anyone help me prove that if $a\in N(R) \Rightarrow 1+a\in U(R)$?  I've been trying to construst a $b$ such that $ab=1$ rather than doing it by contradiction, as I don't see how you could go about doing that. Proving the measure of an increasing sequence of measurable sets is the limit of the measures Show that if $A_1\subseteq A_2\subseteq A_3\subseteq\cdots$ is an increasing sequence of measurable sets (so $A_j\subseteq A_{j+1}$ for every positive integer $j$), then we have $$m\left(\bigcup_{j=1}^\infty A_j\right)=\lim_{j\to\infty}m(A_j)$$  Here is my proof: According to the $\sigma$-algebra property, $\bigcup_{j=1}^{\infty}A_j$ is a measurable set, so it makes sense to talk about $m(\bigcup_{j=1}^{\infty}A_j)$. Firstly, I prove that $\lim_{j\to\infty}m(A_j)\leq m(\bigcup_{j=1}^{\infty}A_j)$. This is because for any given positive integer $N$, $A_N\subseteq \bigcup_{j=1}^{\infty}A_i$, according to monotonicity, we have $m(A_N)\leq m(\bigcup_{j=1}^{\infty}A_i)$. Take the limit,we will have $\lim_{j\to\infty}m(A_j)\leq m(\bigcup_{j=1}^{\infty}A_j)$. Secondly, I prove that $m(\bigcup_{j=1}^{\infty}A_j)\leq \lim_{j\to\infty}m(A_j)$. For any given positive integer $N$, $\bigcup_{j=1}^N A_j = A_N$. According to monotonicity,we have $m\left(\bigcup_{j=1}^N A_j\right)=m(A_N)\leq \lim_{j\to\infty}m(A_j)$. Take the limit, we will have $m\left(\bigcup_{j=1}^\infty A_j\right) \leq \lim_{j\to\infty} m(A_j)$. Combine the above two arguments, we will see that $$m\left(\bigcup_{j=1}^\infty A_j\right)=\lim_{j\to\infty} m(A_j)$$$\Box$  The above is my proof, unlike many books, my proof does not use the property of countable additivity. So I doubt my proof is correct. Who can point out where are my mistakes? Story about lost colonized planet sent into orbit around "free" star find exec '{}' not available after > Exec allows us to either pass all arguments at once with {} + or to pass them one by one with {} \;  Now let's say I want to rename all jpeg, no problem doing this:  find . \( -name '*.jpg' -o -name '*.jpeg' \) -exec mv '{}' '{}'.new \;   But if I need to redirect output, '{}' isn't accessible after redirection.  find . \( -name '*.jpg' -o -name '*.jpeg' \) -exec cjpeg -quality 80 '{}' &gt; optimized_'{}' \;   This wouldn't work. I'd have to use a for loop, storing find's output into a variable before using it. Let's admit it, it's cumbersome.  for f in `find . \( -name '*.jpg' -o -name '*.jpeg' \)`; do cjpeg -quality 80 $f &gt; optimized_$f; done;   So is there a better way? Should I use #define, enum or const?