What can happen if a magnitude of such huge force is applied over the sea water of earth? Force applied will be average mass of each person *7 billion *9.8 .
What would happen if every person in the world gathered at a minimum possible area and jumped all at once? Would that have any effect on Earth?
Knitr: opts_chunk$set() not working in Rscript command I was given a laptop with a totally dead display. I do not want to pay to replace the broken display, but I would like to use the laptop as a server and connect to it via SSH to control it.  I have pulled out the internal hard drive from the broken laptop, and I want to install Debian GNU/Linux and the SSH server onto this HDD using a working Debian laptop.  However, the hardware in the two laptops is very different, and I am wondering what kind of problems I would run into when I plugged the drive back in to the laptop with the broken display because of this?  How would I make this work? What is the proper way for me to install a bootable copy of Linux onto a HDD that will be used by a computer with different hardware? Earlier today, I was talking with my friend about some "cool" infinite series and the value they converge to like the Basel problem, Madhava-Leibniz formula for $\pi/4, \log 2$ and similar alternating series etc.  One series that popped into our discussion was $\sum\limits_{n=1}^{\infty} \frac{1}{n^n}$.  Proving the convergence of this series is trivial but finding the value to which converges has defied me so far. Mathematica says this series converges to $\approx 1.29129$.  I tried Googling about this series and found very little information about this series (which is actually surprising since the series looks cool enough to arise in some context).  We were joking that it should have something to do with $\pi,e,\phi,\gamma$ or at the least it must be a transcendental number :-).  My questions are:   What does this series converge to? Does this series arise in any context and are there interesting trivia to be known about this series?   I am actually slightly puzzled that I have not been able to find much about this series on the Internet. (At least my Google search did not yield any interesting results). I'm new to Linux and Ubuntu. People keep using ~/filename in their answers to my questions. What does ~/ mean? What kind of node is this?    Image from this Subsample of a random sample: random sample? Let's say you have a large random sample of soccer players in Europe but you are only interested in what happens in Spain. Could you reduce your sample to players in Spain and still call it a random sample (but of a different population)? If not, how would you call that subsample and which specific precautions should you take to be able to make inferences on the population of spanish soccer players?  My feeling is that using that subsample would be fine as long as it is large enough, but maybe I am missing something. "To be subject to" vs. "to be subjected to" What's the "official" explanation for Harry's (and everyone else's) absence from muggle school? Why is area of a surface of revolution integral $2\pi y~ds$? not '$dx$'? How can you check for a #hash in a URL using JavaScript? How to use exclamation marks in Minecraft commands? I know that you can use exclamation marks in Minecraft commands to check for an entity that does not have a specific tag. For example, you can use /kill @e[type=!Player] to kill all entities except for the player. I have, however, encountered two problems with using exclamation marks that I can't find a solution for.  For my first problem, I've set up a series of command blocks to summon shootable fireballs above the player’s head when a certain item is being held;  /scoreboard players add @a Fireball 1 {SelectedItem:{tag:{display:{Name:"Summon Fireball"}}}} /execute @a[score_Fireball_min=1,score_Fireball=1] ~ ~ ~ /summon Fireball ~ ~2.5 ~ {direction:[0.0,0.0,0.0]} /scoreboard players set @a Fireball 0   I used a comparator and a redstone torch so that the last command would activate when the first command would deactivate, that is, when the player is not holding the item.  The problem is, that when I move far away from the setup, the redstone stops working, leaving me unable to summon any new fireballs. Instead, I'm trying to use a command block to check when anything except for item is being held;  /scoreboard players set @a Fireball 0 {SelectedItem:{tag:{display:{Name:!"Summon Fireball"}}}}   I’ve either put it at the wrong place, or you simply can’t use exclamation marks in NBT tags. Could someone tell me where I should put the exclamation mark, or in the latter case, how I can check for anything except for a specific item?  Further, I’ve tried using exclamation marks to set the score of all entities, including the ones with a blank score, but except for the ones with a score of 2 or higher, to 0;  /scoreboard players set @e[score_arrows_min!=2] Arrows 0 /scoreboard players set @a Arrows 1 {SelectedItem:{tag:{display:{Name:"Rain of Arrows"}}}} /scoreboard players set @e[type=Arrow] Arrows 2 {inGround:1b}   The code does change the scores of entities without scores to 0, but it doesn’t exclude the arrows with a score of 2. Could anyone tell me what I’m doing wrong here? Intuition for Rayleigh PDF We have ground-truth data $\mathbf{x}^* = (0,0)^T \in \mathbb{R}^{2}$. Furthermore, we have $N$ measurements $\mathbf{x}_i \in \mathbb{R}^{2}, i\in \{1,\ldots,N\}$. We calculate the $N$ error vectors $\mathbf{e}_i = \mathbf{x}_i - \mathbf{x}^*$. We assume that the two components of $\mathbf{e}_i = (e_{x,i}, e_{y,i})^T $ are independent of each other and normally distributed with equal mean $\mathbf{\mu} = (0,0)^T$ and variance $\sigma^2$. The absolute errors $e_i = \sqrt {e_{x,i}^2 + {e}_{y,i}^2} $ follow a Rayleigh distribution, is that correct?  The probability density function (PDF) of the Rayleigh function is zero at a value of zero. Why is this the case (intuitively)? I would assume that our errors should most likely be 0 (i.e. PDF should be highest at 0)... Can I use lens brand X on interchangeable lens camera brand Y? I've got some lenses of brand X, but I've just got a new camera of brand Y. How can I tell if it's possible to use my lenses on my camera? I accept that I may lose a lot of automatic functionality like autofocus, aperture control and metering when using an adapter to connect the two. Big tilde in math mode How do I get a really wide tilde?  I need to cover at least  abcdefghijklmnopqrstuvwxyz  The \widetilde command does not work. Nor using \stackrel with \sim. Choosing whether to include PDF or PNG in PDFLaTeX Can I tell graphicx somehow which graphic format to choose when I omit the file extension in includegraphics and both a PDF and a PNG version of the same image exist? The reason is that I have some very large PDF vector graphics (in terms of file size/drawing primitives) that take a pretty long time to load each time I view the document. I would like to convert them to PNGs while working on the document and only use the PDF versions in the final document. Therefore, a global option that I can switch in the end would be great.  An additional plus would be to do the conversion to PNG on the fly during the LaTeX run if there is a PDF that has not been converted to PNG yet, if a tool for that exists. (I know how to use convert, but not how to include it automatically in LaTeX.) Is there a package of Ubuntu drivers as driver pack solution? I tried to search for it, but I did not find it. If there is, how can I easily get it? Prove that $a^2(b+c-a)+b^2(a+c-b)+c^2(a+b-c) \leq 3abc.$ A friend offered me a brain teaser to which the solution involves a $195$ pound man juggling two $3$-pound balls to traverse a bridge having a maximum capacity of only $200$ pounds. He explained that since the man only ever holds one $3$-pound object at a time, the maximum combined weight at any given moment is only $195 + 3=198$ pounds, and the bridge would hold.  I corrected him by explaining that the acts of throwing up and catching the ball temporarily make you 'heavier' (an additional force is exerted by the ball to me and by me onto the bridge due to the change in momentum when throwing up or catching the ball), but admitted that gentle tosses/catches (less acceleration) might offer a situation in which the force on the bridge never reaches the combined weight of the man and both balls.  Can the bridge withstand the man and his balls? What Topology does a Straight Line in the Plane Inherit as a Subspace of $\mathbb{R_l} \times \mathbb{R}$ and of $\mathbb{R_l} \times \mathbb{R_l}$ Given a straight line in the plane, what topology does this straight line inherit as a subspace of $\mathbb{R_l} \times \mathbb{R}$ and as a subspace of $\mathbb{R_l} \times \mathbb{R_l}$, where $\mathbb{R_l}$ is the lower limit topology?  So trying to figure this out definitely made my brain hurt.  I believe that as a subspace of $\mathbb{R_l} \times \mathbb{R}$, all non-vertical straight lines just inherit the lower limit topology $\mathbb{R_l}$, while vertical lines inherit the standard topology on $\mathbb{R}$.  As for $\mathbb{R_l} \times \mathbb{R_l}$, as far as I can tell, the only difference is that now all straight lines, including vertical ones, inherit the lower limit topology.  My reasoning was basically that for $\mathbb{R_l} \times \mathbb{R}$, open sets on the line all have an initial left end point, since the x-coordinate of this left end point is always captured by the open sets [a,b) in $\mathbb{R_l}$, and this in turn drags the y-coordinate of the initial left end point along for the ride (so to speak).  This is true in all but the vertical line case where there is no shift in the horizontal direction and thus the topology is inherited strictly from $\mathbb{R}$.  As for $\mathbb{R_l} \times \mathbb{R_l}$ it's basically the same argument except now the vertical lines inherit from $\mathbb{R_l}$ as well.  Can someone let me know whether I've reasoned correctly?  Thanks. I am relatively new to Java, and often find that I need to sort a Map&lt;Key, Value&gt; on the values.  Since the values are not unique, I find myself converting the keySet into an array, and sorting that array through array sort with a custom comparator that sorts on the value associated with the key.  Is there an easier way?