Since muggles know nothing about Hogwarts and the wizards inside don't want any muggles finding it, what would happen if a muggle had discovered it by accident (For example, plane crash or hiking)? What would the wizards do to the muggle?
I've been informed by those who know much more about Harry Potter than I that Hogwarts is protected with a Disillusionment Charm so all muggles will see is ruins with a "Danger: Keep out!" sign around them.  (Apparently this was in one of the first three books, but I'm not sure where it was.)  My first thought was, "Well, a danger sign would encourage some muggles to investigate!"  Which leads to what I think is an obvious question: Will a disillusionment charm on a place like that still work when a person is real close to the location?  Will it work from inside the location?  For example, if a curious muggle made it to the gates of Hogwarts and started walking around inside, would they still see it as abandon and in ruins, or once they entered, would they see it as it is?
What is the physical significance of dot & cross product of vectors? Why is division not defined for vectors? I get the physical significance of vector addition &amp; subtraction. But I don't understand what do dot &amp; cross products mean?   More specifically,    Why is it that dot product of vectors $\vec{A}$ and $\vec{B}$ is defined as $AB\cos\theta$? Why is it that cross product of vectors $\vec{A}$ and $\vec{B}$ is defined as $AB\sin\theta$, times a unit vector determined from the right-hand rule?   To me, both these formulae seem to be arbitrarily defined (although, I know that it definitely wouldn't be the case).   If the cross product could be defined arbitrarily, why can't we define division of vectors? What's wrong with that? Why can't vectors be divided? Cardioid in coffee mug? Can Mjolnir "stick" to anything? Need advice on flavoring/sweetening my homebrew cider I've just finished my primary fermentation and have produced a cider that is coming in at 5.2%. I am about to bottle my cider and add some priming sugar to give it a bit of a fizz. I would like to try and flavor some of the ciders with a fruit coulis. am I correct in thinking that the natural sugar in the fruit should give the cider a natural fizz and I don't need to add any sugar? Also, I am a fan of a sweeter cider, I have been advise not to add more than a teaspoon of priming sugar, and to use a sugar substitute at the same stage if i wish to sweeten it. I have purchased Xylitol, I plan on trying a few combinations with the priming sugar/Xylitol &amp; no additive fruit coulis. Does this all sound like it makes sense or am I just going to ruin my cider. Avoid footnotes from appearing before mark I am using gdal_rasterize to create a raster of a huge file containing polygons. I managed to generate the raster file with the right color and with the minimum size to tile it after with the gdal2tile.  gdal_rasterize -of GTiff -co COMPRESS=DEFLATE  -b 1 -b 2 -b 3 -burn 136-burn 46 -burn 17 -co PREDICTOR=2  -co ZLEVEL=9 -ot Byte  -a_nodata 255  -a Niveau  -ts 500000 500000  -l layer W:/layer.shp W:/layer.tif   Tile will be used to overlay Google Maps so the polygon must be transparent.  Has anybody experimented with this usage of gdal_rasterize and succeeded in setting the opacity of the output raster? Check tag classes with watir? Best Practice for Forcing Garbage Collection in C# Simple excel math wrong Firstly I do not want to round my numbers, I am using base 10 figures so excel should have no bother doing simple add and subtract.  A|  665.110000000000000000000000000000 B|  4.990000000000000000000000000000 C|  =a1+b1 D|  670.790000000000000000000000000000 E|  1,335.890000000000000000000000000000 F|  =e1-(c1+d1)   I should get -5 however F1  returns   -4.999999999999770000000000000000   It is a financial document therefore I want to avoid rounding, more to the point. Why should I need to? I've put cell formatting to Currency with 2 decimal placed and I will get the correct display value but for all calculations I will still get -4.9999...7 which leads to further errors with conditional formatting etc. Using special auto start servlet to initialize on startup and share application data How to adopt SD card as internal storage on Samsung devices? Recently I saw a widget on the Stack Overflow website which says Stack&nbsp;Overflow now has its own currency called "unicoins". According to this widget, a user can earn reputation, customize Stack Overflow by changing its colors and the user can also remove the vote down button from their questions and answers by spending "unicoins".  This widget does not look real, because this is out of standard of the Stack Overflow website.  Also today is 1st April. Is Stack Overflow fooling us?  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; After upgrading to 12.10 quantal, the packaged version of fglrx no longer works. I discovered that this is because there is a separate 'legacy' fglrx driver for the HD 2k-4k series cards, but it is incompatible with the xorg server on 12.10.  This is the most current version of the driver for HD 2000 through HD 4000 series cards. You can't use the non-legacy fglrx driver, but you can use the open-source radeon driver if you prefer your WM compositing to be laggy and your YouTube videos to play like they would on a Pentium MMX series:    Usually this driver can be installed in the following way, necessary because apt-get install fglrx would pull in the non-legacy driver:  wget http://www2.ati.com/drivers/legacy/amd-driver-installer-12.6-legacy-x86.x86_64.zip unzip amd-driver-installer-* sudo sh ./amd-driver-installer-*.run --buildpkg Ubuntu/quantal sudo dpkg -i fglrx*.deb sudo aticonfig --initial -f   If you use a different version of fglrx (for example, a newer 12.9 that doesn't support those cards) then the final command will give you an error no supported hardware detected or something similar. However, everything works at this point and you will get a reasonable xorg.conf:  ... other stuff  Section "Device"         Identifier  "aticonfig-Device[0]-0"         Driver      "fglrx"         BusID       "PCI:1:5:0" EndSection  ... other stuff   At this point you're supposed to reboot and everything will be working with the fglrx driver. However, upon rebooting, you'll be treated to the following errors in Xorg.0.log when fglrx attempts to load:  (EE) Failed to load /usr/lib/xorg/modules/drivers/fglrx_drv.so: /usr/lib/xorg/modules/drivers/fglrx_drv.so: undefined symbol: noXFree86DRIExtension   Some searching around will show that this is a problem with the legacy ATI drivers not supporting xserver 1.13 or newer. () ATI has released a fixed driver for its most recent (HD 5000 series or later) cards, but not for the 'legacy' cards yet. The non-legacy ATI drivers can't be used with the old cards.  What should an Ubuntu user, using one of these HD 2000-4000 series cards, do?    Wait for an updated 'legacy' ATI driver that properly works with xserver 1.13?   Downgrade back to 12.04 Precise, which uses xserver 1.11? Try to downgrade xserver on 12.10 Quantal to 1.12, which could possibly break Unity and GNOME? Forced upgrade to HD 5000 series or later card? (Not possible with integrated graphics...) Some other 1337 action that fixes this problem painlessly? How to update Ubuntu terminal? How to update Ubuntu terminal? Do I need to activate the firewall? I only use Ubuntu for a home desktop use? Without appealing to the axiom of choice, it can be shown that (Proposition:) if $X$ is well-orderable, then $2^X$ is totally-orderable.  Question: can we show the stronger result that if $X$ is well-orderable, then so too is $2^X$?  Proof of Proposition. Pick any well-ordering of $X$. Then the lexicographic order totally orders $2^X$.  More explicitly: for any two $f,g \in 2^X$, define $f &lt; g$ iff   there exists $x \in X$ such that $f(x) \neq g(x)$, and if $x \in X$ is minimal such that $f(x) \neq g(x)$, then $f(x)=0$ and $g(x)=1$.   It can be shown that $&lt;$ totally-orders $2^X$. I know that hardly any information is passed to the PDF when a .tex file is compiled.  But is there a tool that can convert a PDF document back to (La)TeX? Too many requests? I went to stackexchange.com and clicked on SO.  After a few minutes I got a message saying "We have detected too many requests from this IP.  If this is an error contact us."  That was the second SE page I tried to visit.  Second only to SE.com  I moved to another machine and it's working now.  The first machine usually works, I don't know if a got assigned a blacklisted IP or what.  Anyone know what's going on?  EDIT: I would really rather not post my IP on the web, but if a diamond or dev asks I'll email it.  EDIT 2: I looked at badp's dupe suggestion and can verify that I have no scripts frequently calling SO. I just deleted a file on my Nexus S that I really need back. (It was actually part of an app using a sqlite database that did a drop table when upgrading to a new version.)  Presumably I need to root the phone first (which I hear is easy on Nexus phones) but am I in a catch-22 here? Namely, does rooting the phone mean wiping/overwriting the partition where the data lives?  If not, what do you recommend for data recovery tools? Presumably the file was just unlinked and not actively overwritten (per usual when "deleting" a file) so technically the data must be there... How to prevent a background process from being stopped after closing SSH client in Linux