Why do we perceive a mixture of blue and yellow paint as green?
Why does adding red light with blue light give purple light?
Why does the One Ring make the wearer's clothes invisible? The One Ring turns invisible the person wearing it.  Is there an explanation for how it does this? It seems that direct contact with the skin activates the Ring's invisibility effects;  why would it also affect the person's clothing, weapons, etc, as well? The Invisible Man's clothing is visible, so why aren't Frodo's clothes visible?  The Hobbit makes it clear that Bilbo's clothing is invisible, since Smaug doesn't see it.  Is there any possiblity that this varies from character to character? Review filter appears to be broken When browsing questions for a given tag, a review indicator has recently started showing up that links to the open review tasks for that tag.  For example, this is what I see when viewing :    The number 187 in the screenshot above would link to    However, clicking on that often opens review tasks that do not have the tag in question.  For example, it opened the following on successive attempts:   (c)   (java)  It seems that the filters are broken.  A sample screenshot (note the mention of the filter on the review page): Character Limit in HTML Does RSA work for any message M? Outlook from time to time makes an operation 'Send and Receive.' This can sometimes be quite slow and Outlook hangs while this is done.    Is is possible to set different intervals for different mail accounts (if user has multiple accounts configured within Outlook, e.g., main Exchange account and one or more IMAP accounts) If yes (or even if only for some [e.g., IMAP accounts], where in the settings it can be configured?  (e.g., Outlook 2007) How do I copy a file in Python?  I couldn't find anything under . What are the mechanics of time dilation and length contraction? Going beyond the mathematical equations involving light and the "speed limit of the universe", what is observed is merely a phenomenon and not a true explanation of why time dilates or length contracts.  It has been proven to work out, but do we know why?  Is it something that happens at a subatomic level? Equals(=) vs. LIKE When using SQL, are there any benefits of using = in a WHERE clause instead of LIKE?  Without any special operators, LIKE and = are the same, right? Why does reputation start at 1, and have a lower bound of 1? If a user is the type of person to consecutively get downvoted to potential negative reputation, so be it. What's the reasoning to maintain a minimum of one?  One reason that may justify this is of trying to not deter new users from the site who haven't read the FAQ and unknowingly and wrongly ask or answer a question. But most of us acknowledge this and not downvote in such a scenario.  So what's the reasoning behind this lower bound of 1? can't find using System.Web.UI.HtmlControls namespace Does this email mean that I have been granted the visa? I received the following email this morning. Does it mean that my visa has been granted?  UK Visas &amp; Immigration has now assessed your UK visa application and made a decision. Your documents and the decision will be sent back to either the UK Visa Application Centre where you applied, where we will contact you by email over the next few days to collect them, or if you are using the courier return service, will be sent directly back to the address provided. Please note that TLScontact does not know the outcome of the assessment and has played no role in the decision-making process. Kind regards, TLScontact UK VIsas &amp; Immigration You should choose your Display Name when signing up When a user signs up , their username is something along the lines of "user########"  Granted, in the welcome email it does say something along the lines of "Head over to your user account page to chose a display name!", however only a few people actually read that email.  I'm not saying we should restrict people from changing their display name again in the future - Everyone would still be able to do so. It's just that when you sign up you choose an initial display name that will be what your first display name is instead of "user########". On this  there are more than 50 links to Stack Overflow questions. However, the last 6 links aren't converted to titles (http://facebook.stackoverflow.com/questions/6530420/control-the-image-that-facebook-shows-when-i-like-a-url should be converted to ).   However:  all http://facebook.stackoverflow.com/... into http://stackoverflow.com/... fixes this, both in the preview and the final result. Also, the preview won't show any title for http://facebook.stackoverflow.com/... links.  My question is, what limitations does this converting have? How are these question titles retreived? Via API? Through database?  I'm not sure about title, feel free to edit that I am trying to solve the following exercise:     Prove that complex multiplication does not extend to a multiplication   on $\mathbb R^3$ so as to make $\mathbb R^3$ into a real division   algebra.   I am aware of Frobenius' theorem that there are only three finite dimensional real associative division algebras. But the exercise would be pointless if the theorem was assumed.   Let $x,y \in \mathbb R^3$. Since $x y$ has to extend the complex multiplication:  $$xy = (x_1y_1-x_2y_2, x_1y_2 + x_2 y_1, ?)$$  I have no idea how I can proceed from here. Could someone tell me how to do this? It should be easy as the other exercises I did so far were also easy. filling an occluded plane with the smallest number of rectangles I've got a specific problem which I'll try to describe as clearly as possible.   I have a defined rectangular region on a cartesian plane, and within that region there are other given rectangular sub-regions that are described in terms of their 4 vertices, ie {(x1, y1), (x1, y2), (x2, y1), (x2, y2)}, so that these regions form 'occlusions' on the plane. These regions don't overlap, but they can form more complex polygons when different-sized rectangles adjacent to each other appear joined.  here's an illustration:   I am interested in the space between these shapes, and how to define the space in the same way the occlusions are defined, that is as a set of rectangles. In particular I want the definition optimised so that the space is described using the smallest possible number of rectangles. For example, an incomplete rendering might look like this:   Can anyone suggest a way forward with this? How can I have the original set of vertices (describing the black rectangles) generate the 'complementary' set of vertices (red rectangles) such that the number of red rectangles is minimal?  I suspect it's a variation of a 'packing problem', but I have a feeling it might be fairly simple... What is the difference between an Intel i7 and a Xeon quad core processor? I know the  processors have been around for a long time and are mostly used in servers, but I am curious, why do people not use the Xeons in a high performance desktop?    As far as I know about the best desktop processor out there now is the  line. The i7's and Xeons are both quad-core processors, what is the main difference in these? I just saw that the MacBook Pro's are using the quad core Xeons instead of the i7's. How can I have `date` output the time from a different timezone? I have a server running with the timezone set to UTC. It seemed like that was generally a good practice (please correct me if I'm wrong).  Anyhow, one of the servers I connect to, in order to scp files, is running on EDT and stores files that I need to copy in the format /path/to/filename/data20120913  I looked at trying to rsync files using something like find's -mtime -1 flag for files modified in the last day, but I didn't have any luck.  I don't mind just using scp to copy the current day's file, but as of right now there is a 4-hour window where running date +%Y%m%d will give a different day on each server and that bugs me a little.  Looking through man date I see that I can have the time output as UTC, but I don't see a way to have it output as another timezone like EDT  I suppose I could also use something like the GNU date extension date -d 20100909 +%s to get the date in seconds from the epoch, apply a manual 4 * 60 * 60 second calculation, and see about rendering that as a date - but then when daylight time kicks in it will still be an hour off.  Is there a simpler way to output the date in a YYYYMMDD format for EDT on a server that is set to UTC ? How to acknowledge a deceased advisor’s contributions to a paper? Homotopy equivalence of universal cover As part of am exam question (Q21F ), I'm trying to prove that if $X$ and $Y$ are path-connected, locally path-connected spaces with universal covers $\widetilde{X}$ and $\widetilde{Y}$, respectively, then if $X \simeq Y$ then $\widetilde{X} \simeq \widetilde{Y}$.  My attempt might be correct, but it seems too complicated and amongst the jumble I may have made some incorrect assumptions. So what I'm looking for is (a) verification or correction; and (b) ideas as to how I could simplify my argument.    My argument:  Let $p:\widetilde{X} \to X$ and $q:\widetilde{Y} \to Y$ be the covering maps, and let $X \overset{f}{\underset{g}{\leftrightarrows}} Y$ be a homotopy equivalence.  Fix a point $\widetilde{x} \in \widetilde{X}$, let $x=p(x) \in X$ and $y=f(x) \in Y$, and fix $\widetilde{y} \in q^{-1}(\{y\}) \subseteq \widetilde{Y}$. Also let $x' = g(y) \in X$ and fix $\widetilde{x'} \in p^{-1}(\{x'\}) \subseteq \widetilde{X}$.  Define a map $\widetilde{f} : \widetilde{X} \to \widetilde{Y}$ as follows. For $\widetilde{z} \in \widetilde{X}$ let $\widetilde{u}:[0,1] \to \widetilde{X}$ be a path from $\widetilde{x}$ to $\widetilde{z}$. Let $z=p(z)$ so that $u=p\widetilde{u}$ is a path in $X$ from $x$ to $z$. Let $v=fu$, so that $v$ is a path in $Y$ from $y$ to $f(z)$. Lift $v$ to a path $\widetilde{v}$ in $\widetilde{Y}$ with $\widetilde{v}(0) = \widetilde{y}$. Define $\widetilde{f}(\widetilde{z}) = \widetilde{v}(1)$.  Notice that $q\widetilde{v}=v$ so that $q\widetilde{f} = fp$.  Define $\widetilde{g}:Y \to X$ analogously: For $\widetilde{z} \in \widetilde{Y}$ let $\widetilde{a}:[0,1] \to \widetilde{Y}$ be a path from $\widetilde{y}$ to $\widetilde{z}$. Let $z=q(z)$ so that $a=q\widetilde{a}$ is a path in $Y$ from $y$ to $z$. Let $b=fa$, so that $b$ is a path in $X$ from $x'$ to $g(z)$. Lift $b$ to a path $\widetilde{b}$ in $\widetilde{X}$ with $\widetilde{b}(0) = \widetilde{x'}$. Define $\widetilde{g}(\widetilde{z}) = \widetilde{b}(1)$.  Likewise, notice that $p\widetilde{g}=gq$.  Claim: $\widetilde{X} \overset{\widetilde{f}}{\underset{\widetilde{g}}{\leftrightarrows}} \widetilde{Y}$ is a homotopy equivalence.  We have $p\widetilde{g}\widetilde{f} = gq\widetilde{f}=gfp \simeq p$ and $q\widetilde{f}\widetilde{g} = fp\widetilde{g} = fgq \simeq q$.  This shows that $\widetilde{g}\widetilde{f}$ and $\widetilde{f}\widetilde{g}$ are covering translations (deck transformations) and are therefore homotopic to the respective identity maps. So we have a homotopy equivalence.    Any comments would be appreciated. We've upgraded some machines to Windows 10 and realized there were some updates which updated as required. However, I realized there was no option available to stop the download similar to that on Windows 7 and 8.1. The only way I could stop the download was to stop the Windows Update service.  My question is does anyone know of a way to stop auto updates or is stopping the service is the only solution?