All the volcanoes in middle earth are a throw back to Melkor trying to trash middle earth (executive summary of this ).  Would any other volcano contain enough 'power' from Melkor to do likewise? Or was mount Doom merely the closest?
I was recently reading some Lord of the Rings/Stargate SG-1 crossover fanfiction. It is a guilty pleasure, I admit :) In this story, it was suggested by Col. O'Neill to destroy the Ring using a nuclear device. Truth be told I stopped reading at this point, as it was getting to be a little much even for me.  Obviously, this is not canonical in either universe, but it made me wonder: When Elrond said that "only in the fires of Mt. Doom may it be unmade," was he speaking literally? Or was this merely the only known active volcano in Middle Earth? In other words, was whatever magic that protected the One Ring from damage location-based or did it just make it very resistant to destructive force, and Mt. Doom just happened to be hot enough to do this? I know there is (understandably) little information about such technicalities of how magic works in Middle Earth, but I'll accept any reasonable conjecture/consensus as an answer.
Optimal estimation of a single parameter given data at different scales Let $A,B,C,D$ be independent normal random variables distributed according to $\mathcal{N}(0,\sigma^2)$ and $E = A+B+C+D$.  The goal is to provide an optimal estimate of $\sigma^2$ given samples of $A,B,E$ but not $C,D$.  In this case optimal refers to minimising the root-mean square deviation of the estimate $\hat{\sigma}^2$:  $$RMSD(\hat{\sigma}^2) = \sqrt{\mathbb{E}\left[\left(\hat{\sigma}^2-\sigma^2\right)^2\right]}$$  I can think of a simple approach to estimate $\sigma^2$ given samples of $A,B$ which is to simply compute the sample variance. Also I know that the variance of $E$ is $4\sigma^2$ so I could compute the sample variance of $E$ and divide it by 4 to get an estimate of $\sigma^2$. However it should be possible to combine the information from both $E$ and $A,B$ to improve estimation $\sigma^2$. Could you outline the approach to use both sets of information? Syntax highlighting language hints Do you think it would be worthwhile to provide hints as to what language to use for the syntax highlighting?  Sometimes I find the highlighting on SQL or VB.NET answers is more distracting than helpful; for example:       to pick the two I've been looking at recently. Why does Jack let Walt go? In Breaking Bad S5 E14, Jack not only lets Walt go, but also leaves a barrel of money to him after killing Hank. I don't understand why he would do this. Jack says that, with 7 barrels of money, he doesn't need to cook meth any more, so there is no reason to keep Walt (the witness of the killing) alive, let alone to give him so much money. What's the rationale behind this? Or it's just mercy or respect? How to install X11/xorg? My 12.04 x64 system won't boot into GUI, but I can still use virtual console with my own account, so apparently it's the Windows Management System that's causing it, how can I reinstall it from tty, what's the apt-get command? QGIS area calculation differs when on the fly CRS transformation enabled When I open QGIS, add the layer, and calculate the areas of the shapefile via field calculator I get a different area than when I open QGIS and check "Enable on the fly CRS transformation" and calculate the area. This is despite making sure that the project and the layer have the same Coordinate system (same EPSG number). What am I doing wrong?   I have a shapefile with area calculations made with ArcGIS (not be me, the data was handed to me and I have no clue for which CRS the area was calculated with ArcGIS). The shapefile layer CRS is EPSG: 21781 (Switzerland). In QGIS, if I do not change the OTF settings and leave the project CRS as EPSG:4326 (WGS84) I get the same value as the ArcGIS area value. However, if I change the OTF before adding the layer to EPSG: 21781 I get different area values. As I understand this suggests that ArcGIS Area was calculated with the CRS EPSG: 4326.  First workflow:   open QGIS  project CRS: EPSG 4326  add layer  project CRS adapts automatically and is EPSG 21781 now  calculate $area with field calculator    Second workflow:   open QGIS  project CRS: EPSG 4326  Turn on OTF, set project CRS to EPSG 21781  add layer  calculate $area with field calculator    Step 5 of the first and second workflow DO NOT produce the same area. How can one prove that the series $\displaystyle \sum\limits_{n=1}^\infty \frac{1}{(n!)^2}$ converges to an irrational number? There's no need to use Taylor expansion, integrals or any advanced/professional techniques. It can be proved using only basic techniques. My first attempt was to assume that the series does converge to a rational number $ \frac{p}{q}$ and then it follows by definition that for every positive epsilon there exists an integer k such that $ {\sum_{n=1}^{k} \frac{1}{(n!)^2} -\frac{p}{q}}&lt;=\epsilon$ I tried to get a contradiction but I failed. No "waiting for review" for comment flags Let me explain using screenshot and Free Hand Red Circles and Arrows:        As comment flags are now fully showing in the summary, I would expect the same behavior by showing how many are still active. Flawed proof that all positive integers are equal White screen of death: Fatal error: Allowed memory size of X bytes exhausted I have a issue with my Drupal installation, for example:   when I enable or disable the modules, It redirects me to a blank page, when I create a new content type and save it, redirects me to a blank page, when I add a new view and save it, it redirects me to a blank page, when I try to clear the cache, it redirects me back to a blank page, or in similar cases.   Basically all the confirmation pages redirect me to a white screen. When I refresh it again, it shows me the page. I tried to increase the PHP memory value but it doesn't help.  Are there any other solutions for this?  The error which I'm having:      Fatal error: Allowed memory size of 100663296 bytes exhausted (tried to allocate 8192 bytes) in sites/all/modules/views/plugins/views_plugin_localization_none.inc on line 1 How should I phrase a question that must be answered with an ordinal number (e.g., the third prime)? I want to make a question having an answer as follows:     5 is the third prime number.   The bold part is the answer. How to phrase the question? How do I use reflection to call a generic method? Should I upgrade to the "mainline" kernels? Newer "mainline" versions of the kernel are available from the , e.g. 3.4 and 3.5, while Ubuntu 12.04 is on 3.2.   What are the mainline kernels? Are they better than my existing kernel? What are the pros and cons of upgrading to a mainline kernel? Will I easily be able to go back? Proof or disproof that every integer can be written as the sum of a prime and a square. I'm refreshing some algebra and in the beginning chapters of my book I'm presented with the following simple looking problem that I got stuck on:      Prove or disprove: If $n$ is a positive integer, then $n=p+a^2$, where $a$ is an integer and $p$ is prime or $p=1$.   At first I thought $n=13$ would give a nice counterexample, but then I noticed my book defines primes to include the negative primes. Now $13=-3+4^2$ is a solution.   I am allowed to use the fundamental theorem of arithmetic and the division and euclidean algorithms. I tried to express $n$ and $a$ by their prime factorizations, but I didn't get anywhere from there. I would like a hint which direction to take. Am I just missing something silly? Photons in expanding space: how is energy conserved? If a photon (wave package) redshifts (stretches) travelling in our expanding universe, is its energy reduced?  If so, where does that energy go? There's a way to safely try KDE on top of an Ubuntu installation, keeping the possibility to revert the changes in case I dislike how it runs? After most recent kernel update (4.15.0-44-generic) my tablet freezes whenever plugged into docking station I performed the most recent kernel update on my Dell 5290 2-in-1 earlier today.  But moments after I plug it into its docking station, the screen flickers, blanks and freezes.  The only item left on the screen is the mouse pointer, and it is stuck.   If I leave the tablet not plugged in, it runs just fine.  It seems to be the docking station that triggers the freeze.  That said, I can log into the tablet via ssh even with the screen frozen.  So the system is still running.  But if I try to reboot the tablet via the reboot command, nothing appears to happen. sudo reboot -f will reboot the system, while sudo reboot will not.  Any ideas where I should start looking to identify this problem? How to derive the formula for the sum of the first $n$ odd numbers: $n^2=\sum_{k=1}^n(2k-1).$ How to derive this formula?   $$n^2=\sum_{k=1}^n(2k-1).$$ For $a,b,c>0$, prove that $\frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{a}\ge a+b+c+\frac{4(a-b)^2}{a+b+c}$ What determines how much experience I get from a hearthstone match in play mode? Sometimes I win handily and get a little experience, sometimes I squeak out a victory and get a lot.  How is experience earned? How can I override the OnBeforeUnload dialog and replace it with my own? I need to warn users about unsaved changes before they leave a page (a pretty common problem). window.onbeforeunload = handler  This works but it raises a default dialog with an irritating standard message that wraps my own text. I need to either completely replace the standard message, so my text is clear, or (even better) replace the entire dialog with a modal dialog using jQuery. So far I have failed and I haven't found anyone else who seems to have an answer. Is it even possible? Javascript in my page: &lt;script type=&quot;text/javascript&quot;&gt;        window.onbeforeunload = closeIt; &lt;/script&gt;  The closeIt() function: function closeIt() {   if (changes == &quot;true&quot; || files == &quot;true&quot;)   {       return &quot;Here you can append a custom message to the default dialog.&quot;;   } }  Using jQuery and jqModal I have tried this kind of thing (using a custom confirm dialog): $(window).beforeunload(function () {     confirm('new message: ' + this.href + ' !', this.href);     return false; });  which also doesn't work - I cannot seem to bind to the beforeunload event.