How far and how clear could the &quot;Eye of Sauron&quot; see? Could it see through the whole of Middle-earth or is it limited to only Mordor? Could it distinguish the human face, the small artifacts like rings, or not? Saruman says the &quot;Eye of Sauron&quot;  &quot;sees all — his gaze pierces cloud, shadow, earth and flesh. You know of what I speak, Gandalf — a great Eye… lidless… wreathed in flame&quot;  when he is intimidating Gandalf. This implies that Sauron could see everything, just like Superman. If this is true, how could the One Ring escape his gaze? Sauron just needed to scan the land of the Shire. I am afraid that the meeting in Rivendell is also under Sauron's sight. When Frodo brings up the One Ring and Gimli wields his axe, Sauron will see. And once he saw the Ring, he can see it always. Does this mean that Saruman is exaggerating? What is the true limit of the &quot;Eye of Sauron&quot;?
I am aware that the "Eye of Sauron" in Peter Jackson's movies was not Sauron's actual physical form.  What the answers at '' don't indicate is, despite this, what abilities of vision Sauron may have had.  Did he have the ability to see from afar? If so, what are his limitations or details of this power? Is it some kind of Elvish-sight like Legolas but stronger? Was it a magical power? Or perhaps with the help of the Palantir (I'm not sure of this last one because I dont remember if the Palantir could only see what other Palantíri were seeing or anything he wanted)?
When is the new ball due for all forms of cricket? Is there a standard time fixed in Test, ODI and T20 formats of Cricket, when a fielding side captain can ask for a new ball?  If the captain of the fielding side doesn't ask for a new ball, will he be forced to have it mandatorily after a certain point by the match umpires? Corrupt Backupt GPT Table Ways of getting a number with $n$ dice, each with $k$ sides Assume the dice are numbered from $1$ to $k$. My hunch is that this will form a normal distribution with a median at $n\cdot\frac{k}{2}$. However, I have no idea as to    turn this fact into an answer (I have a minimal knowledge of stats, but I know that I am missing the standard distribution) and this is probably the wrong approach   How can I approach and solve this problem? (Aside, this is not for a class, stats or other, so any and all approaches welcome).  *Edit: * I want to find the number of ways that the sum of the numbers that are rolled has a particular value, if $n$ dice are rolled, and each has $k$ sides, numbered $1$ to $k$. Why does English spelling use silent letters? Why have a letter in a word when it’s silent in pronunciation, like the b in debt?  Can anyone please clarify my uncertainty here? looks like someone got happy with the CSS - you can now no longer tell what tab is active, e.g. answer tabs:        Even if you hover over an option - it wont show you what tab is currently selected - it only shows you what tab you are currently hovering over: Let $ Y = \{ (1,1),(0,0\} \subset \mathbb A_k^2$. Find the $ \mathbb I(Y)$.   As if $f(x,y) \in \mathbb I(Y)$ then as $f(0,0)=0$ hence constant term of $f$ is zero and as $f(1,1)=0$ therefore sum of the coefficients of $f(x,y)$ is zero. But how can we describe this set properly? I have seen some hypotheses that the recent series corporate actions and statements are a sign of SO/SE being in the process of being, or about to be, sold. Arguments cited include the corp statements being made in paywalled areas and addressed to an audience that seems very distinct from the community, the choice of CEO, the push for a 'service sector' flavour of tensely smiling hospitality, and surely some more I can't recall in a coherent form.   Just how plausible and implausible, and how founded or unfounded, is such a hypothesis? Is it, as far as people more knowledgeable either about business in general or about the specific case of SE/SO, strategically consistent or even outright connected with the corp's behaviour (and a likely cause thereof)? Is there a LaTeX/TeX preprocessor/inliner that replaces only selected macros with their definitions? Why can't I just think the spin as rotating? I'm going mad about the problem.  I really don't understand why do electron have 1/2 spin number, why they are not actually spinning.  I can accept that the electrons have their own magnetic field, which is certain, but why do they have $\hbar\sqrt3/2$ of angular momentum, and I don't know what the heck is spin number.  I've read the definition of  and  more than a hundred times but there is no betterment. I've smashed my head in my desk more than a hundred times either.  My question is the title. Why can't I just think the spin as rotating?  What I've saw recently,     electron's hypothetical surface would have to be moving faster than the speed of light in order for it to rotate quickly enough to produce the necessary angular momentum. How does Edo Tensei Madara get back his Rinnegan? Madara gave his Rinnegan to Nagato. But after Kabuto brings him back using Edo Tensei, he still has the Rinnegan. How is this possible? My Developer Account cannot be activated because I used a relative's credit card In C# check that filename is *possibly* valid (not that it exists) Is there a method in the System.IO namespace that checks the validity of a filename?  For example, C:\foo\bar would validate and :"~-* would not  Or a little trickier, X:\foo\bar would validate is there is an X: drive on the system, but wouldn't otherwise.  I suppose I could write such a method myself, but I'm more interested in a built-in one. Intuition on the Kullback-Leibler (KL) Divergence proof that on a compact manifold a vector field is complete I would like to know if my proof of the following statement is correct     If $M$ is a compact manifold, then every vector field $X$ over $M$ is complete.   Proof:  I take $p\in M$ and $(\gamma_p,I_p)$ a maximal integral curve through $p$. $I_p$ is open and non empty so if $I_p$ is closed, it is equal to $\mathbb{R}$.  So take $s\in \text{Adh}(I_p)$. There exists $t_i\rightarrow s, t_i\in I_p$. Define $q$ as $\text{lim}(\gamma_p(t_i))$ and take a maximal integral curve passing by $q$ as $(\gamma_q,I_q)$. Then since the vector fields are $C^\infty$, $\gamma_q(I_q)\cap\gamma_p(I_p)$ is nonempty (intuitively, this is clear but don't really know how to show it).  On the intersection, $\gamma_p$ and $\gamma_q$ coincide. So we can extend the maximal curve $\gamma_p$ to include $\gamma_q$. This implies that $q\in\gamma_p(I_p)$ and is actually equal to $\gamma_p(s)$  I think the main idea is there even though it probably lacks a bit of rigour. Is something similar to Robin's theorem known for possible exceptions to Lagarias' inequality? Robin's theorem says that if $$\sigma(n)&lt;e^\gamma n\log\log n$$ holds for all $n&gt;5040$, where $\sigma(n)$ is the sum of divisors of $n$, then the Riemann hypothesis is true, but if there are any counterexamples, then they are colossally abundant numbers, and there are infinitely many counterexamples.  Lagarias' theorem says $$\sigma(n)\leq H_n+e^{H_n}\log(H_n)$$ holding for all natural numbers $n$ is equivalent to the Riemann hypothesis, where $H_n$ is the $n$th harmonic number, the sum of the reciprocals of the first $n$ positive integers. It looks like Lagarias' inequality is sharper than Robin's, so any counterexamples to Robin's inequality must also be counterexamples to Lagarias'. Is known to be impossible for integers that aren't colossally abundant numbers or of some similar more general type to be exceptions to Lagarias' inequality? Is there really no way to power a DSLR by USB? Do I need a flight ticket or a flight reservation for my UK visit visa application Am compiling documents for my visa application and I read that I need to present go and return flight tickets to prove that I will return at the end of my visit. Then a while ago I got to know that I can just get a flight reservation with out buying the flight tickets because the visa application can be refused and you have already bought the tickets.  So l request to know which of the two , having a flight ticket or flight reservation is more compelling to the visa officer and more convenient me because I would buy a flight ticket and my application is refused As mentioned in the , Ubuntu 18.04 LTS will not have a 32 bit Desktop Image Installer. But in the  it has  32bit Desktop Images.  This is little off topic, but I'm confused. How to prove that 2017 divides $1^{2017}+2^{2017}+\dots+2017^{2017}$? How can I prove that $2017 \mid 1^{2017}+2^{2017}+\dots+2017^{2017}$? I tried proving it with the use of modulo, however it was to no avail. Afterwards, I  tried researching, for possible theorems, that may help, but that bore no fruit, either. Can you guys please help me proving it, as I am stuck? Thanking you in advance. I tried to install Tor on my new version of Ubuntu, but it seems that Tor is not available in the repositories.  How else can I install and use Tor?