How old were the War Doctor, Nine and Ten when they regenerated, and how certain are we of these ages?
How old were each of the Doctor's incarnations?
How fast does gravity propagate? A thought experiment: Imagine the Sun is suddenly removed. We wouldn't notice a difference for 8 minutes, because that's how long light takes to get from the Sun's surface to Earth.   However, what about the Sun's gravitational effect? If gravity propagates at the speed of light, for 8 minutes the Earth will continue to follow an orbit around nothing. If however, gravity is due to a distortion of spacetime, this distortion will cease to exist as soon as the mass is removed, thus the Earth will leave through the orbit tangent, so we could observe the Sun's disappearance more quickly.  What is the state of the research around such a thought experiment? Can this be inferred from observation? Suppose we have a natural number $N$ with decimal representation $A_kA_{k-1}\ldots A_0$. How do I prove that if the $\sum\limits_{i=0}^kA_i$ is divisible by $9$ then $N$ is divisible by $9$ too? I know how to define a package or a class, but how do I make it available (to myself) at all times?  Say I have the package file commonstuff.sty (or myprettyclass.cls), that I want to be able to include in any .tex file I create on my computer. Where do I put it? Do I need to run some installer on it, or is it enough to keep it in a certain folder?  Note: I know I can just place it in the same folder as the .tex file, but that's not what I'm after here. I'm looking for a way to "install" the package centrally on my computer. Intuition on the Kullback–Leibler (KL) Divergence I have learned about the intuition behind the KL Divergence as how much a model distribution function differs from the theoretical/true distribution of the data. The source I am reading goes on to say that the intuitive understanding of 'distance' between these two distributions is helpful, but should not be taken literally because for two distributions $P$ and $Q$, the KL Divergence is not symmetric in $P$ and $Q$.   I am not sure how to understand the last statement, or is this where the intuition of 'distance' breaks down?   I would appreciate a simple, but insightful example. Example to show the distance between two closed sets can be 0 even if the two sets are disjoint Let $A$ and $B$ be two sets of real numbers. Define the distance from $A$ to $B$ by $$\rho (A,B) = \inf \{ |a-b| : a \in A, b \in B\} \;.$$ Give an example to show that the distance between two closed sets can be $0$ even if the two sets are disjoint. Background on color perception:  Due to the nature of the human eye and visual processing by the brain, there's an optical illusion that the same color will look different depending on the background.   It is known as the , illustrated below — center rectangles are identical:   Source:   An illustration  makes the effect of the background's color even more obvious:     Source:   (Note how the two upper-most colors in the second image appear the same, but are actually completely different.)    What about web design?  My question pertains to web design, specifically in this case, the color of link text on different backgrounds.  For a given color of text, how can one find the complementary color to make it appear the same on a certain background?    Let's take a look at an example for this question:  Consider my example below, with yellow text #FFF000 on the following backgrounds:    white #FFFFFF, black #000000, and grey #555555.          As expected, doesn't look the same at all. ()  How can we make it look the same on all three? Clearly, the text on the white background needs to be a darker yellow, and the one on the grey needs hue/tone adjustments. (The surrounding text will also affect it — but that's likely harder to account for.)  Can this perfect color somehow be calculated, based on the Hex, RGB or another system? That's where the crux of this question lies, as it would be much more efficient than manually approximating. Make display of reputation in revisions list consistent with the user card display VS Code Salesforce plugin deploy does not provide an error message VS Code plugin for salesforce seems to be broken yesterday, It does not provide proper error message in case of failure.  Tried this in a developer org as well as scratch org. Neither deploy code or push gives an error message, and every time we need to go to Salesforce setup -> Deployment Status to view the details.  Is anyone aware of any workaround? Normal subgroups of $S_4$ Can anyone tell me how to find all normal subgroups of the symmetric group $S_4$?  In particular are $H=\{e,(1 2)(3 4)\}$ and $K=\{e,(1 2)(3 4), (1 3)(2 4),(1 4)(2 3)\}$ normal subgroups? Why did the descriptive "Orientals" shift into a pejorative? Using expect for inputting commands Heres the thread I'm bouncing off of:   So I'm trying to run this command: cd /etc/openvpn/easy-rsa; . ./vars; ./build-key username  However, after running that command, I need to input nothing [just press enter] 10 times, and press y twice. The user on the last thread suggested I use except, but I couldn't get it working. Here are the questions it asks:  root@suffice-vpn:/etc/openvpn/easy-rsa# ./build-key usernamtest Generating a 2048 bit RSA private key ..................+++ ........+++ writing new private key to 'usernamtest.key' ----- You are about to be asked to enter information that will be incorporated into your certificate request. What you are about to enter is what is called a Distinguished Name or a DN. There are quite a few fields but you can leave some blank For some fields there will be a default value, If you enter '.', the field will be left blank. ----- Country Name (2 letter code) [US]: State or Province Name (full name) [NY]: Locality Name (eg, city) [Merrick]: Organization Name (eg, company) [IceWare]: Organizational Unit Name (eg, section) [IceWare]: Common Name (eg, your name or your server's hostname) [usernamtest]: Name [server]: Email Address [iceware@programmer.net]:  Please enter the following 'extra' attributes to be sent with your certificate request A challenge password []: An optional company name []: Using configuration from /etc/openvpn/easy-rsa/openssl-1.0.0.cnf Check that the request matches the signature Signature ok The Subject's Distinguished Name is as follows countryName           :PRINTABLE:'US' stateOrProvinceName   :PRINTABLE:'NY' localityName          :PRINTABLE:'Merrick' organizationName      :PRINTABLE:'IceWare' organizationalUnitName:PRINTABLE:'IceWare' commonName            :PRINTABLE:'usernamtest' name                  :PRINTABLE:'server' emailAddress          :IA5STRING:'iceware@programmer.net' Certificate is to be certified until Jan 14 18:27:48 2026 GMT (3650 days) Sign the certificate? [y/n]:y   1 out of 1 certificate requests certified, commit? [y/n]y   As you can see, I press enter 8 times initially [to keep the default input] and then press enter another 2 times to skip the optional commands. Then, I need to press y twice. How can I automate this? I need to have this all happen in one command. Any suggestions? Thanks in advance. When can a noun be used attributively? Nouns can modify nouns: cat food, coffee cup, gold ring, laser surgery, flood insurance. It seems to me there are even cases where a noun sounds better than the corresponding adjective: sociology papers sounds a bit better than sociological papers.  Some noun-noun combinations don&rsquo;t work. You wouldn't say America gangsters or measurement spoons or greed crimes. If you spilled water on your keyboard you probably wouldn't call it a keyboard spill or even a water spill.  Are there rules that tell which combinations are acceptable? I have a long running BASH script that I am running under CYGWIN on Windows.  I would like to limit the script to run for 30 seconds, and automatically terminate if it exceeds this limit. Ideally, I'd like to be able to do this to any command.  For example:  sh-3.2$ limittime -t 30 'myscript.sh'   or   sh-3.2$ limittime -t 30 'grep func *.c'   Under cygwin the ulimit command doesn't seem to work.   I am open to any ideas. Product of quotient maps and quotient space that is not Hausdorff I am looking for easy(!) counterexamples that the product of two quotient maps is not necessarily a quotient map and that the quotient space of a Hausdorff space is not necessarily Hausdorff. Ubuntu 17.10 and later: can't change the input switching shortcut to alt+shift Where is the icon used in this dialogue box? Where on my disk can I find the icon used in this dialogue box in OS X？    It may be Security.icns in OS X 10.7.3    I cannot find it in:   /System/Library/CoreServices/CoreTypes/Contents/Resources There are only LockedIcon.icns and UnlockedIcon.icns in this folder who looks like the icon in the dialogue box,the size of the icon in the dialogue box is 128x128px, but LockedIcon.icns and UnlockedIcon.icns is 32x32px.   lockedIcon.icns    So they are not the same icon.   /System/Library/CoreServices/Finder.app/Contents/Resources/ /System/Library/CoreServices/Problem Reporter.app/Contents/Resources /Applications/System Preferences.app/Contents/Resources /Applications/Utilities/Keychain Access.app/Contents/Resources /System/Library/CoreServices/Certificate Assistant.app/Contents/Resources/ When do we double the consonant before '-ing' affix? My son is learning how to spell. He is doing a good job listening to sounds and working out spelling that way (which doesn't work for many words, but at least a lot of common ones), but although he's gotten the -ing chunk, he frequently misses doubling letters in these words.  Is there a guideline for when the end consonant is doubled? He's working on these sorts of words:        riding   sitting   skating   writing   getting `sudo echo "bla" >> /etc/sysctl.conf` permission denied Disclaimer: I'm pretty novice at sysadmin stuff.  I'm trying to set up port forwarding in an AWS EC2 instance, this has to be done in the command-line because I don't want to go in and edit anything, it has to be automatic (it's part of a build process).   sudo echo "net.ipv4.ip_forward = 1" &gt;&gt; /etc/sysctl.conf      Permission denied   The weird thing is I've been (successfully) using sudo for pretty much every command that required su privileges. If I do sudo su before the command (trying it out by hand in an ssh session), then it works.  Reasons behind this? Possible solutions that don't involve sudo su or manual edits? Why are these black dots / spots appearing in my pictures? Prove Equivalence Relation in G Hei, guys!  I'm having some trouble with the next problem:  Let $A$ and $B$ be subgroups of $G$. Show that $\sim$ is an equivalence relation when it is defined as follows: $g\sim g'\Leftrightarrow g' = agb$ for some $a$ from $A$, $b$ from $B$.  Should I prove this is valid for any a and b? It says for some elements a and b. But I might as well take the unit element.   Could you give me a clue on how to solve it?  Cheers!