This question is inspired by the following example given in Barnett's book on quantum information:        (PDF , starting at the bottom of page 5)  I am not a physicist, but I'll accept that the calculation of the increase in physical entropy associated with this procedure is correct. My confusion is about how the second law of thermodynamics can be saved by claiming that the process of measuring the position of the molecule produces an entropy of at least $k_B\ln2$.  My question is: Why can we just assume that "entropy" of information is comparable with physical entropy? The best explanation that I've been able to find is that they're defined in similar ways and satisfy the same basic properties. This seems no different from saying "decibels and earthquake intensity are both measured logarithmically and are therefore comparable", which of course makes no sense.  As I said above, my only physics background is a first-year course, so I'd appreciate if answers could try to be accessible to someone who hasn't done thermodynamics...
Context  In one of his most popular books , Terry Pratchett makes an entropy joke:     Knowledge equals Power, which equals Energy, which equals Mass   Pratchett is a fantasy comedian and every third phrase in his book is a joke, therefore there is no good reason to believe it.  Pratchett uses that madness to make up that a huge library has a tremendous gravitational push.  The question  I work with computers and mostly with encryption.  My work colleagues believe Terry Pratchett's statement because of entropy.  On the other hand, I believe, it is incorrect since entropy of information is a different entropy than the one used in thermodynamics.  Am I correct?  And if so, why do use the same name (entropy) to mean two different things?  Also, what would be a good way to explain that these two "entropies" are different things to non-scientists (i.e. people without a chemistry or physics background)?
Diamond moderator privileges vs. 10k rep privileges? As we are in election period, I don't get the difference between getting to 10k reputation point and the diamond. What additional controls do you earn with the diamond ? Design review - RGB LED color mixer using PWM How can a photon have no mass and still travel at the speed of light? When I receive a message on an SE post, I get a notification like this:    If I double tap this notification, the SE application opens, but my feed is empty approximately half the time. It looks like this:    If I refresh the feed (slide from the top), the feed does refresh and shows the new notification.   The notification, above, leads to  comment.  I haven't figured out the pattern yet, but this occurs roughly half the time I open a notification. It's occurred for chat messages, comments and answers - but not consistently. I have received notifications for the same post (for example, the two comments after the one linked above) that do not show an empty feed. But, a chat message barely 10 minutes later will show the empty feed again.  I am utilizing the beta app - version 1.0.72 on Android 5.0.1. Detecting an undefined object property bi-directional sync with rsync How do I set up new users with skel i have on my server a settings i use for all my users. every time i create a new user i have to copy all the settings over and over.  for example:   .vimrc. .profile .bashrc firefox homepage to our intranet evolution settings (server and username) etc...   i saw skel can do it, is there a easy way to setup a user with my settings when i adduser?  thanks Horizontal enumeration in multiple columns Consider the following minimal example:  \documentclass{article}  \setlength{\parindent}{0mm}  \usepackage{paralist} \usepackage{tabto}  \begin{document}  \NumTabs{3} \begin{inparaenum} \item text \tab\item text \tab\item text \tab\item text \tab\item text \tab\item text    \end{inparaenum}  \end{document}   Which results in:    It does exactly what I want, but I was wondering whether it was possible to create an environment, say tabbedEnum so that we can eliminate the use of the \tab, in particular, that the first case doesn't need a tab but all others do. Something of the form:   \begin{tabbedEnum}[3] \item text \item text \item text \item text \item text \item text \end{tabbedEnum} Recording iPad screen using QuickTime I need to record a demo on my iPad's screen where I narrate what's going on but I also want the sounds from the iPad to be in the video. It seems that choosing the Mac Built-in Mic option causes only my voice to be in the video while choosing the iPad Mic option cause only the sounds from the iPad to be in the video. What can I do to put both in the video? How do you do AppBar docking (to screen edge, like WinAmp) in WPF? Is there any complete guidance on doing AppBar docking (such as locking to the screen edge) in WPF? I understand there are InterOp calls that need to be made, but I'm looking for either a proof of concept based on a simple WPF form, or a componentized version that can be consumed.  Related resources: How to turn off notifications for individual apps? On my iphone, there is a "notifications" setting section, which basically just allows me to choose which apps has the power to notify me.  I was wondering if there's anything similar that is available on the Samsung Galaxy s2?  Basically, we have a new app called Scramble For Friends. And it keeps notifying us every time someone has finished their turn so that I can play. We play random people so this could be in the middle of the night or in a meeting etc.  It just vibrates but still - it's annoying and we want to turn it off. We also don't want to turn off other notifications like Email, Facebook etc. - we just want to turn off the notifications for Scramble For Friends.  I've been looking around in the Settings but there doesn't seem to be a universal page which deals just with notifications. Let$\ p_n$ be the$\ n$-th prime. Can you give me a proof for$\ \prod_{i=1}^\infty \frac{p_i-1}{p_i}=P\approx \frac{1}{11.0453}$? I found$\ \prod_{i=1}^\infty \frac{p_i}{p_i-1}\approx 11.0453$ on . Moreover, writing a paper, should one provide a proof or it is trivial? Thanks in advance. Find all the numbers $n$ such that $\frac{4n-5}{60-12n}$ can't be reduced. The popup when you click on your newest badge in your user profile has a &quot;Learn more&quot; button, but its alignment is suboptimal; it's too close to the top of its container:  It looks better with a 4px top margin: $\sin \frac{1}{x}$ is not uniformly continuous on $[1, \infty]$ The use of "exact same" Duplicate explanation should encourage improvement of original The new closed-as-duplicate banner says:     This question has been asked before and already has an answer. If those answers do not fully address your question, please .   I think it should instead say     This question has been asked before and already has an answer. If answers there do not fully address your question, please  or  to the pre-existing one.   &mdash; to discourage re-re-asking the same question. (I also changed "those answers", which has no plural , to "answers there", which doesn't need one.)    As of September 19, 2013, the original text quoted above has returned here. Hypothesis test for difference in medians among more than two samples Question  The test scores of three groups of people are saved as separate vectors in R.  set.seed(1) group1 &lt;- rnorm(100, mean = 75, sd = 10) group2 &lt;- rnorm(100, mean = 85, sd = 10) group3 &lt;- rnorm(100, mean = 95, sd = 10)   I want to know if there is a significant difference in the medians between these groups. I know that I could test group 1 versus group 2 using the Wilcoxon test, like so.  wilcox.test(group1, group2)   However, this compares only two groups at a time, and I would like to compare all three simultaneously. I would like a statistical test that yields a p value at the 0.05 significance level. Could someone please help?  Edit #1 - Mood's median test  Following user Hibernating's suggested answer, I tried Mood's median test.  median.test &lt;- function(x, y){     z &lt;- c(x, y)     g &lt;- rep(1:2, c(length(x), length(y)))     m &lt;- median(z)     fisher.test(z &lt; m, g)$p.value }  median.test(group1, group2)   However, this approach allows me to test for a significant difference between the medians of only two groups at a time. I am not sure of how to use it to compare the medians of all three simultaneously.  Edit #2 - Kruskal-Wallis test  User dmartin's suggested answer appears to be more or less what I need, and allows me to test all three groups simultaneously.  kruskal.test(list(group1, group2, group3))   Edit #3  User Greg Snow helpfully notes in his answer that the Kruskal-Wallis test is appropriate as long as it makes strict assumptions that make it also a test of means. Confused about complex numbers I am confused about something: \begin{eqnarray}     (e^{2 i \pi})^{0.5} = (e^{2 i \pi \cdot 0.5})= e^{i \pi}=-1 \end{eqnarray} but \begin{eqnarray}      e^{2 i \pi}=1~ and~ 1^{0.5}=1  \end{eqnarray} where is my mistake??  thanks How does the versioning work here? How does SO's (or other SE sites) versioning work of questions and answers? Do they use some standard piece of code or is it something homebrew?  With versioning I meant if for example a question is edited you'll see all the changes (a diff).