I am not from a country that regularly airs Doctor Who, and I wanted to know, what is doctor who's original name?  Does anybody knows this secret ?  Wikipedia said it was unrevealed, but I myself have seen doctor saying that he knows his name(obviously).   Also, I thought, Wikipedia is edited by the people, and it is not straight from the horse' mouth.
I recently decided to watch Doctor Who, and started viewing the 2005 version. I have the first two episodes from the first season, and I can't help but wonder what is the etymology of the name "Doctor Who"? And why does the protagonist call himself "the Doctor" (or is it "the doctor")?
Prove that $\phi(n) \geq \sqrt{n}/2$ So I'm trying to prove the following two inequalities: $$\frac{\sqrt{n}}{2} \leq \phi(n) \leq n.$$ The upper bound we get from simply noting that $\phi(n) = n \prod_{p | n}\left( 1 - \frac{1}{p}\right)$ and the fact that $(1 - \frac{1}{p}) \leq 1$. But how can we get the lower bound? I tried using the same expression for $\phi(n)$ but it seems to not really give me the inequality. Can you help? When using a new Windows 8 search bar:    What is the syntax of the search expression? Is it possible to use wildcards like "*", "?" or any other special symbol?  For example, when searching with Google i can use:   '-' (minus) for excluding certain words; "quoted phrase" for exact phrase matching. Do cell carries have access to FaceTime information? On the newest iPhone, do cell phone carriers have access to FaceTime call data (such as which caller initiated and ended a FaceTime call)? EDIT: Summary  I think I've found the best definition of what I want thanks to the discussion with @M. Tibbits:  When I open or refresh the SO, I get a notification of new activities that are of interest to me. Today these are (hard-coded): answers to my questions and comments addressed to me. I want a bit more control over it, that's all.     Yes, I've read  and , but I think I add new (good :) ) reasons for re-asking it:  The first question was answered before this so handy "inbox" notification feature was implemented. So now using favorites for "watching" a question is wrong, IMHO, for 2 reasons:   it splits essentially the same functionality (of getting notified when there is an activity you are interested in) between 2 very different user interfaces it's cumbersome - I need to: 1) add question to favorites; 2) click on my profile dropdown; 3) click on the "favorites" line; 4) see all my favorites with recent activity; 5) select the one I watch; 6) repeat this process occasionally to get updates; and 7) possibly remove the question from favorites at the end. All this as opposed to this little red button when there are news.   Favorites are different in nature that watching. I add a question to Favorites when I find the answers useful to me in my work, so I may want to have it handy in the future. By watching an interesting question I will be able to decide whether I want it in faviorites, after I see the answers.  EDIT: I see that I was not clear enough.  I want to add a question to Favorites when:   it has some good answers the question and answers are relevant in my work I want to keep them handy as my long-term (persistent) knowledge base   I want to watch a question for short while (matter of days/weeks) when:   it is interesting / relevant I want to follow it to see what are the answers. Then I can decide whether I want it in my favorites   As you see, the main differentiators are good answers and long/short term. For short-term, automatic notification is better.  Bottom line, all I ask is "watch this question" checkbox (which may expire after say a week if there is a need to free resources) Looking at the properties for a Windows file I get two attributes, “Size” and “Size on disk,”  and "Size on disk" is always larger.  What do these two metrics mean? What is the translation of what's written below?  I think it may be the poem of the One Ring, but I'm not sure. Area of a parallelogram, vertices $(-1,-1), (4,1), (5,3), (10,5)$. I need to find the area of a parallelogram with vertices $(-1,-1), (4,1), (5,3), (10,5)$.  If I denote $A=(-1,-1)$, $B=(4,1)$, $C=(5,3)$, $D=(10,5)$, then I see that $\overrightarrow{AB}=(5,2)=\overrightarrow{CD}$. Similarly $\overrightarrow{AC}=\overrightarrow{BD}$. So I see that these points indeed form a parallelogram.  It is assignment from linear algebra class. I wasn't sure if I had to like use a matrix or something. What is the fastest way to get from Courmayeur/Aosta to Milan? If $f: \Bbb{R}\rightarrow\Bbb{R}$ is continuous at $0$ and $f(x)=f(2x)$ for each $x\in\Bbb{R}$ then $f$ is constant. How do I prove that if $f: \Bbb{R}\rightarrow\Bbb{R}$  is continuous at $0$ and $$f(x)=f(2x)$$ for each $x\in\Bbb{R}$, then $f$ is constant? Martingale formulation of Bellman's Optimality Principle From David Williams' Probability with Martingales     Related question:   What I tried: For no 2, if $\ln Z_n - n \alpha$ is a supermartingale, then for $m &lt; n$, $$E[\ln Z_n - n \alpha | \mathscr F_m] \le \ln Z_m - m \alpha$$ $$ \to E[\ln Z_N - N \alpha | \mathscr F_0] \le \ln Z_0 - 0 \alpha$$ $$ \to E[\ln Z_N - N \alpha] \le \ln Z_0$$ $$ \to E[\ln \frac{Z_N}{Z_0}] \le N \alpha$$ Is that right?  For no 1, for $m &lt; n$, $$E[\ln Z_n - n \alpha | \mathscr F_m] = E[\ln Z_n | \mathscr F_m] - n \alpha$$ $$ = E[\ln \frac{Z_n}{Z_0} | \mathscr F_m] - n \alpha + \ln Z_0$$ $$ = E[\ln \frac{Z_n}{Z_{n-1}} | \mathscr F_m] + ... + E[\ln \frac{Z_{m+1}}{Z_{m}} | \mathscr F_m]$$ $$+ \ln \frac{Z_m}{Z_{m-1}} + ... + \ln \frac{Z_{1}}{Z_{0}} - n \alpha + \ln Z_0$$ Note that $$Z_n - Z_{n-1} \le |Z_n - Z_{n-1}| \le C_n |\epsilon_n - \epsilon_{n-1}| \le 2C_n \le 2Z_{n-1}$$ Also, I think $$\ln \frac{Z_n}{Z_{n-1}} \le |Z_n - Z_{n-1}|$$ Hence we have $$E[\ln \frac{Z_n}{Z_{n-1}} | \mathscr F_m] + ... + E[\ln \frac{Z_{m+1}}{Z_{m}} | \mathscr F_m]$$ $$+ \ln Z_m - n \alpha$$ $$\le E[2Z_{n-1} | \mathscr F_m] + ... + E[2Z_{m} | \mathscr F_m]$$ $$+ \ln Z_m - n \alpha$$ $$= 2(E[Z_{n-1} | \mathscr F_m] + ... + E[Z_{m} | \mathscr F_m])$$ $$+ \ln Z_m - n \alpha$$ One thing to do would be to show that $$2E[Z_{n-1} | \mathscr F_m] + ... + 2E[Z_{m} | \mathscr F_m] \le (n-m) \alpha$$ possibly by showing that $2E[Z_{\{\cdot\}} | \mathscr F_m] \le \alpha$ How would I do that? Something else: $$E[\ln \frac{Z_n}{Z_m} | \mathscr F_m] + \ln Z_m - n \alpha$$ $$ \le E[|Z_n - Z_m| | \mathscr F_m] + \ln Z_m - n \alpha$$ $$ \le E[2Z_m | \mathscr F_m] + \ln Z_m - n \alpha$$ $$ \le 2Z_m + \ln Z_m - n \alpha$$ Now $2Z_m \le (n-m) \alpha?$ We have $$2Z_m = 2\sum_{k=1}^{m} C_k(\epsilon_k - \epsilon_{k-1})$$ $$\le 2\sum_{k=1}^{m} Z_{k-1}$$ I'm not quite sure how to show that $$2\sum_{k=1}^{m} Z_{k-1} \le (n-m)\alpha$$ if that's even true. How can/else can I approach this problem?  For no 3, no idea. Any hints? I think it has something to do with a stopping time. Might we have to use the ff lemma (red box):    ? Laptop w/o battery US bound flight? According to some reports, your electronic devices are checked whether they turn on before you can get on a US bound flight. What if I carry around a laptop without a battery? Keeping tables/figures close to where they are mentioned Is there any package or a method to force LaTeX to keep floating environments like table and figure closer to where they are declared? Sign of determinant when using $det A^\top A$ We have been given matrix: $$A =          \begin{pmatrix}         a&amp; b&amp; c &amp;d \\         b &amp;−a&amp; d&amp; −c\\         c&amp; −d &amp;−a&amp; b \\         d &amp;c&amp; −b&amp; −a\\         \end{pmatrix}     $$ ...and have been asked to calculate $\det(A)$ using $AA^T$.  We see that:  $$AA^T=\begin{pmatrix}         a^2+ b^2+ c^2+ d^2&amp; 0&amp; 0&amp;0\\         0 &amp;a^2+ b^2+ c^2+ d^2&amp; 0&amp; 0\\         0&amp; 0 &amp;a^2+ b^2+ c^2+ d^2&amp; b \\        0 &amp;0&amp; 0&amp; a^2+ b^2+ c^2+ d^2\\         \end{pmatrix}     $$   So, $\det(AA^T)= (a^2+ b^2+ c^2+ d^2)^4$  Now which should I choose: $(a^2+ b^2+ c^2+ d^2)^2 $ or $ -(a^2+ b^2+ c^2+ d^2)^2$ ?  Please explain me which one and why. glob() - sort array of files by last modified datetime stamp I'm trying to display an array of files in order of date (last modified).  I have done this buy looping through the array and sorting it into another array, but is there an easier (more efficient) way to do this? A very recent post asking people to go "on strike" was just deleted I've often heard that Einstein shattered the notion of absolute motion (i.e. all things move relative to one another) and that he established the speed of light as being absolute. That sounds paradoxical to me; I cannot understand how the two concepts can be reconciled.  Before going further, I'd like to say: 1) Over the years, I've seen many layman's explanations on these topics (including the nice YouTube video by Vsauce, ). I understand everything that's said (or, at least, I think I do). Just nothing I've found seems to address this apparent contradiction. 2) More recently, I've tried to find the answer on my own. That includes searching the posts on this site. Some come close (), but nothing I've been able to find seems address specifically what I'm asking.  Back to the question: Relativity shows us that there is no universal frame of reference by which to judge motion, so object A might be reckoned as moving at 10&nbsp;m/s relative to object B or as stationary relative to object C. This is fine for me. I can grasp that the universe has no intrinsic coordinate system, that we only think that way on Earth because we have the ground to move over.  Then there's the speed of light (in a vacuum). The speed of light is the ultimate "speed limit," it's often said. But if there is no universal frame of reference, how can there be any such speed? The very idea only make sense if there is a universal frame.   If one object is moving (uniformly) at 60%&nbsp;c and another object is also moving at 60%&nbsp;c, but in the exact opposite direct, then from the perspective of either one (if they could still see each other) the other would appear to violate that speed limit. All these spacetime bending consequences used to explain why nothing can move past this speed only seems to enshrine the concept that there is some ultimate speed standard. If there is only relative speed, then the concept of light having a specific speed in the vacuum should be a nonsensical one since it having speed (x m/s) would only make sense when measured against some other body.   Since I was very young, it has always sounded to me like motion is only mostly relative, that until you get close to the speed of light, the effects of an absolute frame of reference are negligible. Perhaps that there is an actual fabric of space which everything moves relative to, which is why there is something to expand between galaxies (faster than light can propagate) in the metric expansion of space. Growing up, I always thought this would just start makes sense with time. Now I'm up to a first year (college) level in physics, I even know basic calculus, yet I'm still hopelessly confused.  EDIT:  Thank you to whoever suggested this may be a duplicate of . It and others are very much related and at least partially answer my question. Unfortunately, explaining that distances become shorter and time becomes slower as a way to stop you from exceeding the speed of light does not explain how that speed is not an absolute.  By my reckoning, if all speed is relative, then no matter how fast you go light should always race away from you at the same apparent speed. I.e. there should be no speed limit. For there to be a speed which you cannot exceed or you would catch up (and make time irrelevant) requires the very concept of some external speed by which light can travel and nothing else can reach - thus my logical paradox continues unabated. Invariance, covariance and symmetry Though often heard, often read, often felt being overused, I wonder what are the precise definitions of invariance and covariance. Could you please give me an example from field theory? I updated to Ubuntu 20.04. When I use the default terminal, everything is fine. But if try to use terminator, I cannot use sudo. I get permission denied. Again, only when using terminator.  How can I sudo from the terminator? I really would like to continue to use a terminator.  Edit: I just also noted that it cannot find make either. I guess it's all messed up. I'll try to uninstall it and install again I guess. I've installed a version of Ubuntu Server and although I'm fairly still fresh with Ubuntu, I'm trying to create a bash file to run a program in the background. More importantly, I'm trying to get a file nameto display correct and create it before I start running the program (I like my debug stuff).  However, here is my bash script:    #!/bin/bash  PATH="/var/log/servers/Game/"  FILENAME="startup"  EXT=".log"  DATE=$(date +%d-%m-%Y)  NEWFILE=${PATH}${FILENAME}_${DATE}${EXT}   I have verified that the file does exist in the PATH directory. However, the issue is with the date command. When I run the script bash -x game.sh this is what is displays.   + PATH=/var/log/servers/Game/  + FILENAME=startup  + EXT=.log  ++ date +%d-%m-%Y  game.sh: line 5: date: command not found  + DATE=  + NEWFILE=/var/log/servers/Game/startup_.log  + echo /var/log/servers/Game/startup_.log   I don't understand why it would say the command doesn't work, when I can go to the main console and run date and get a valid response.  Any help is greatly appreciated! Differences between pure/mixed/entangled/separable/superposed states