The velocity of light changes between mediums, but does light specifically decelerate when it enters a denser medium, or is the change is speed instantaneous?
Photons travel at the fastest speed in our universe, the speed of light.  Do photons have acceleration?
Well, I already searched meta as well as cleared my browser cache.  I realize this may be a SO cache problem, but it still seems kind of strange to me.    The deleted question is (assuming it still exists).  Shouldn't deleted questions only be visible to 10k users?  I'm only at 2k. Installing IE8 in wine - error rename/sha1sum mismatch winetest.cat Please note, this is an informative QA post rather than a question specific, due to this issue popping up many a time.  QUESTION / ISSUE  How to solve the issue of installing IE8 (Internet Explorer) in wine (any version - to my knowledge).  Related Wine Errors:  Terminal install method  Installing IE8:  winetricks -q ie8   should give you a similar error:  Executing w_do_call ie8 Executing load_ie8 Executing wine iexplore -unregserver Executing w_do_call msls31 msls31 already installed, skipping Using native,builtin override for following DLLs: iexplore.exe itircl itss jscript msctf mshtml shdoclc shdocvw shlwapi urlmon wininet xmllite Executing winetricks_early_wine regedit /S C:\windows\Temp\_ie8\override-dll.reg Using builtin override for following DLLs: updspapi Executing winetricks_early_wine regedit /S C:\windows\Temp\_ie8\override-dll.reg Downloading http://winezeug.googlecode.com/svn/trunk/winetricks_files/winetest.cat to /home/user/.cache/winetricks/ie8 --2016-09-08 23:03:12--  http://winezeug.googlecode.com/svn/trunk/winetricks_files/winetest.cat Resolving winezeug.googlecode.com (winezeug.googlecode.com)... 66.102.1.82, 2a00:1450:400c:c06::52 Connecting to winezeug.googlecode.com (winezeug.googlecode.com)|66.102.1.82|:80... connected. HTTP request sent, awaiting response... 404 Not Found 2016-09-08 23:03:13 ERROR 404: Not Found.  ------------------------------------------------------ Downloading http://winezeug.googlecode.com/svn/trunk/winetricks_files/winetest.cat failed ------------------------------------------------------   GUI Install via Winetricks GUI method  or using the GUI method, you should see a error dialog similar to this: I can't destroy blocks in Minecraft Creative Mode (singleplayer) Firstly, how do I read it? Is below right? With braces   $$p \vdash (q \Rightarrow p)$$  The given proof is:    ${p}$, premise ${q}$, assumption  $p$ by (1) // what???  ${q} \Rightarrow p$ by implication introduction with 2 and 2.1 QED...    I can't really get the link between $p$ and $q$ in 2.1 ... How can one prove that numbers of the form $4x^2+1$ can only be divided by primes of the form $4y+1$ (e.g. there is no $x$ for which $7$ divides $4x^2+1$)?   On a quick lookup, the statement is given as the first comment in  and of course, manual testing concurs with this I'm trying to display models that have shading drawn or baked directly on the textures, but I can't figure out how to disable Blender's default scene lighting. If there are no lights in the scene, everything is black, but I want to see the textured objects fully bright. How do I disable the lighting?  NOTE: Just before posting this, I found the "Shadeless" material property, which does more or less what I want. However, is there a way to globally toggle the default lighting? Getting the location from an IP address I want to retrieve information like the city, state, and country of a visitor from their IP address, so that I can customize my web page according to their location. Is there a good and reliable way to do this in PHP? I am using JavaScript for client-side scripting, PHP for server-side scripting, and MySQL for the database. How to type the Indian Rupee Symbol? I want to type the Indian Rupee Symbol. So I went to System Settings >> Keyboard Layout and clicked on the Options button. Under the Adding Currency signs to keys sections, I checked the Rupee on 4 option.    Later when I opened the Layout Chart of the Keyboard there was Rupee sign in the 4 key but I do not know how to type the symbol. What combination of the keys will type the Rupee symbol on the screen? Is there a way to output for Print. I want to save in a higher DPI than the default 72dpi say 300dpi that's a good quality for printed pieces. I tried downloading an add-on but don't know if I am installing it correctly it isn't showing up but the bar in python is green. I'm using the 2.69 version of Blender. If no such feature exists what size have any of you found best for print quality. Thank you Why can `root` run any command as any user without providing password? My /etc/sudoershas content:  Defaults        env_reset Defaults        mail_badpass Defaults        secure_path="/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/snap/bin"  # Host alias specification  # User alias specification  # Cmnd alias specification  # User privilege specification root    ALL=(ALL:ALL) ALL  # Members of the admin group may gain root privileges %admin ALL=(ALL) ALL  # Allow members of group sudo to execute any command %sudo   ALL=(ALL:ALL) ALL  # See sudoers(5) for more information on "#include" directives:  #includedir /etc/sudoers.d   There is no rule above specifying NOPASSWD. I was wondering  why user root seem to be able to execute any command as any user without providing password?  Thanks. How to prove that the set of rational numbers are countable? How small does a land-mass have to be before you live "on" it, rather than "in" it? I'm sure virtually everyone agrees that people live on the Isle of Wight, but in Ireland.  Apparently the usage depends somewhat on physical size, but that can't be the whole story. How exactly do we decide which form to use? And are there any really glaring 'outliers' that don't fit the normal pattern?  LATER - I must just add that the most uncertain case I've found so far is The Falklands. Most people go for in there, but a substantial minority (about 1 in 3) opt for on. Can a 64-bit OS run as a guest on a 64-bit VirtualBox host? Is it possible to run a 64-bit OS as a guest on a 64-bit machine with VirtualBox? I'm guessing it should be, but I'd like to make sure.  Do some virtualization technologies allow a single guest machine to use multiple cores? I guess it should be possible, but my VirtualBox open-source edition doesn't seem to do it. Text won't appear in interface? There is one problem, it seems that text won't appear on my program. The three images show the errors and also my laptop specs (I believe I just have very small amount of laptop power that makes Blender glitch).  Everything else works fine (zooming, panning, rotating, etc.) and the buttons are still there and do what they're supposed to do, but the text just won't appear.  Might anybody know how to fix this?        The drive update didn't help either. I know a way around it though, does anybody know a page which shows screenshots of more or less the buttons on blender Connect iPhone to Mac Without Charging I am developing iOS apps and I hate, that always when I connect my iPhone to my Mac to install and test an app, the iPhone gets charged. Is there any possibility to connect my iPhone to my Mac without charging the phone?    My Environment: -  iPhone 4S (No Jailbreak) -  MacBook Air3,2 (Late 2010) Fubini's theorem for series with dependent indices As a part of a proposition about power series that I am trying to prove I have to show that  $$ \sum_{m=0}^{\infty} \left(\sum_{n=m}^{\infty} \frac{n!}{m!(n-m)!}(b-a)^{n-m}c_n\right)(x-b)^m = \sum_{n=0}^{\infty}c_n(x-a)^n$$  Proof: What I have done so far is to show that  $$\sum_{m=0}^{n} \frac{n!}{m!(n-m)!}(b-a)^{n-m}(x-b)^m = (x-a)^n $$  So the next idea is to use Fubini's rearrangement theorem for infinite series (I have also shown that the series are absolutely convergent). However, the theorem does not accomodate for dependent indices. Intuitively (using triangular summation), I think that the proper way to interchange series would be \begin{equation*} %\begin{array}{ll} \sum_{m=0}^{\infty} \sum_{n=m}^{\infty} \frac{n!}{m!(n-m)!}(b-a)^{n-m}c_n(x-b)^m = \sum_{n=0}^{\infty} \sum_{m=0}^{n}\frac{n!}{m!(n-m)!}(b-a)^{n-m}c_n(x-b)^m %\end{array} \end{equation*} and thus  $$=\sum_{n=0}^{\infty} c_n(x-a)^n$$ However, I do not know how to perform this step rigorously in case of infinite summation. What Is Energy? Where did it come from? No non-trivial clopen sets in $\mathbb{R}$? How to give a direct proof? How to give a direct proof of the following result?     Let $A$ be a subset of $\mathbb{R}$ such that $A$ is both open and closed. Then $A$ is either empty or all of $\mathbb{R}$?   My work:   If $A$ is not empty, let $u \in A$. Then there is some open interval $(a,b)$ such that $$u \in (a,b) \subset A.$$  Now if $\mathbb{R} - A$ is not empty either, then let $v \in \mathbb{R} - A$. Then there is some open interval $(c,d)$ such that  $$v \in (c,d) \subset \mathbb{R} - A.$$  Suppose that $u &lt; v$.   Since $$\emptyset \subset (a,b) \cap (c,d) \subset A \cap (\mathbb{R} - A) = \emptyset,$$ we must have $$(a,b) \cap (c,d) = \emptyset.$$ So we can conlclude that $$b \leq c.$$ But $b \in A$ and $c \in \mathbb{R} - A$. So we must have $$b &lt; c.$$  What next? Can anybody here please help complete the proof from here on?  An edit based on a comment by Marc Paul:   Let us assume that the set $A$ is a non-trivial clopen set in $\mathbb{R}$. Let us define a function $f \colon \mathbb{R} \to \mathbb{R}$ as follows:  $$f(x) \colon= \begin{cases} 1 \ \mbox{ for } \ x \in A; \\ 0 \ \mbox{ for } \ x \in \mathbb{R} - A. \end{cases}$$   Let $V$ be an open set in the range space $\mathbb{R}$. We show that the inverse image set $f^{-1}(V)$ is open in the domain space $\mathbb{R}$.   The following cases arise:   If $0, 1 \in V$, then $f^{-1}(V) = \mathbb{R}$.   If $0 \in V$ but $1 \not\in V$, then $f^{-1}(V) = \mathbb{R} - A$.   If $1 \in V$ but $0 \not\in V$, then $f^{-1}(V) = A$.   And, if $0 \not\in V$ and $1 \not\in V$, then $f^{-1}(V) = \emptyset$.   Thus, $f^{-1}(V)$ is open in the domain space $\mathbb{R}$.   Hence the function $f$ is continuous.   What next? How does this lead to our desired conclusion?   [Yet another edit, again based on valuable comments from Marc Paul: ]  So if both $A$ and $\mathbb{R} - A$ were non-empty, then let's suppose $a \in A$ and $b \in \mathbb{R} - A$, and we can assume without any loss of generality that $a &lt; b$.   Then $f(a) = 1$ and $f(b) = 0$. So by the intermediate value theorem there is a real number $c \in (a,b)$ such that $f(c) = 1/2$, which is a contradiction because the image set of $f$ does not contain $1/2$. YA book about a young powerful female caster attending a school that trains in magical arts and duels I read a young adult novel around the turn of the century. This story features a young female protagonist that is very naturally gifted in magic. She is attending a  to learn mastery and control over her gifts.  A lot of her school revolves around magic dueling. The participants are taught to extend their inner aura like a second magical skin, possibly referred to as creating a shield, or . The user can increase the strength of the shield by focusing harder on it, but doing so means you have less ability to be offensive. The amount of energy needed to create a shield was half the energy a foe would need to focus at you to break it.  Ex: Mage A and B are equally matched. Mage A focuses half his power into a shield. Mage B would then need to focus 100% of his power to break A’s shield.  Another aspect I remember is that when dueling, a school master would extend a personal shield on to one of the combatants as a sort of secondary shield that goes underneath the combatants. When one mage broke the others mages personal shield, the school masters shield protects the losers life from harm, and the breaker of the shield is declared the winner.  I distinctly remember one match in which the protagonist is having a duel with another strong student. She creates a wind storm around herself that picks up the sand from the arena floor and makes her impossible to see and thus makes it hard for her opponent to focus on her shield to break it. She then lashes out at her opponent with incredibly powerful strikes with the final strike being so hard it shatters the opponents shield and then breaks the school masters shield as well and stops just shy of killing her dueling partner.  Any assistance on this one? I think my daughter would love to read it. I made chili and it's too hot! If I cook it longer will the heat calm down?