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Energy conservation of Virtual Particles - Quantum Fluctuation? I (as a middle-school student) was wondering how virtual particles even conserve energy of the entire system? I don't mean just the particle's energy, but conservation with respect to the surroundings?  Let me explain more, Einstein proved that $E = mc^2$ and equivalently, we can say $m = \frac{E}{c^2}$ . We however know mass causes curvature in space-time (gravity well). Now that statement being completely valid we can use Quantum Fluctuation, implying energy and time can be related by the relation:  $\Delta{E}\Delta{t}\approx\frac{\hbar}{2}$ and by that simple relation we can make the following points:   As the energy increases, the time allowed to be "borrowed" decreases, before it gives it back to the universe. As time increases, the energy allowed to be "borrowed" decreases.    These are completely satisfactory points I've made, I believe.  Now, I have read that the vacuum is filled with constantly bubbling virtual particles that get created from the energy "borrowed" by the above relation and is destroyed again, which satisfies the energy conservation laws.   This seems to imply that  in the short time the virtual particle exists, they must have a very small mass which is: $m_{1} = \frac{\Delta{E}}{c^2}$ and using basic classical mechanics rather than GR (for sake of simplicity) we calculate that the gravitational force mediated by this short-lived virtual particle;  $F_{g}= G\frac{m_1 * m_x}{r^2}$   where $m_x$ is an particle\mass in question. Nevertheless since we know the force set upon an object moves the object in a direction, we can say it would increase its kinetic energy by this factor: $F_g = \frac{1}{2}mv^2$ which is equal to $G\frac{m_1 * m_x}{r^2} = \frac{1}{2}mv^2$.  Surely, this implies that every time quantum fluctuations happen, energy of real-particles\masses increases and therefore violates energy conservation, but what prevents this violation from taking place?  If virtual particles are not really present and interact with objects like I thought, how can Hawking radiation (currently a large concept in black hole physics) then be accepted in physics community? In the 3d-view workspace, we can use a random color to give our separated object a distinct look.  What if I don't like the result and I want to randomize the color again?   Swapping the setting doesn't change the random seed in color.    (Blender 2.80.64.) In PHP you can do:  print_r($var) or vardump($var)   which prints "human-readible" information about variable.  Is there equivalent functions / helpers for those in Ruby / Rails ? Why is volatile needed in C? Why is volatile needed in C? What is it used for? What will it do? Arriving at a different port of entry in the same state in USA? I am a girl in my early twenties traveling to USA from India and in my visa application I have provided the contact address for a relative in San Francisco, and their invitation letter. I would like to visit LA first. Will I face problems during immigration if I land in LA (with an immediate on wards ticket to SF)? I dont plan to get on the flight from LA to SFO.  Initially I was planning to fly to SFO from India and then fly to LA immediately after completing immigration at SFO airport. What did Hegel mean by 'world spirit'? I understand that Hegel intends to justify the history of mankind by stating that every town and society that has existed has been a test indirectly arranged by the 'world spirit' in order to eventually create a town in which people would live ethically, and that this process has been done in order for the 'world spirit' to become aware of its freedom. But what exactly is this 'world spirit'?   In the last quiz of a course I'm taking (I´ve taken this year a philosophy course at college), I wrote that the 'world spirit' was some kind of parasitic entity which inhabits every human being that has existed and is going to exist. Does this seem right? Mental estimate for tangent of an angle (from $0$ to $90$ degrees) Does anyone know of a way to estimate the tangent of an angle in their head? Accuracy is not critically important, but within $5%$ percent would probably be good, 10% may be acceptable.  I can estimate sines and cosines quite well, but I consider division of/by arbitrary values to be too complex for this task. Multiplication of a few values is generally acceptable, and addition and subtraction are fine.  My angles are in degrees, and I prefer not have to mentally convert to radians, though I can if necessary. Also, all angles I'm concerned with are in the range of [0, 90 degrees].  I am also interested in estimating arc tangent under the same conditions, to within about 5-degrees would be good.  Backstory  I'm working on estimating the path of the sun across the sky. I can estimate the declination pretty easily, but now I want to estimate the amount of daylight on any given day and latitude. I've got it down to the arc cosine of the product of two tangents, but resolving the two tangents is now my sticking point. I also want to calculate the altitude of the sun for any time of day, day of the year, and latitude, which I have down to just an arc tangent. Why does the buffer take up whole screen? I am trying to create buffers around the Hurricane Sandy path I created in QGIS (points are lat/long).   I have both points from each day she was tracted and the line I created from it with Points2One.   When I go to make buffers around either the line or the points, the buffer takes up the whole screen. Its all just one color.   I have made buffers before but from data I did not create.   Right now all of my projections are set to WGS 84 EPSG 4326. Recovering an accidentally deleted  folder in OSX - no Time Machine or backup available I am a longtime Windows user, recently switched to Mac. I replaced folder with another folder (they had the same name) thinking that OS X will merge the contents of both folders. But OS X deleted the original folder and replaced it with the new one. Windows merges both the folders (I do this often in Windows). I have now lost hundreds of files. I haven't enabled Time Machine. I've tried using Finder's Undo, but that doesn't work.  Currently, I am trying to recover my data using . It shows estimated time as 7 hours, 31 minutes. Does anyone know any free data recovery software that's faster and more powerful? Decision Tree in LaTeX with TikZ Grid line doesn't have to be included     \documentclass[10pt]{beamer}  \usetheme{default}  \usepackage{graphicx}  \usepackage{amssymb,amsmath}  \usepackage{tikz}  \usetikzlibrary{matrix}  \usepackage{adjustbox}  \usepackage{caption} \ usepackage{subcaption}   \setbeamercolor{title}{fg=black}  \setbeamercolor{subtitle}{fg=gray}  \setbeamercolor{footlinecolor}{fg=white,bg=green}  \setbeamertemplate{footline}[text line]{% \parbox{\linewidth}{\vspace*{-10pt} \textit{Where Wall Street Goes to School} \hfill \insertpagenumber} } \setbeamertemplate{navigation symbols}{} –  \begin{tikzpicture}[&gt;=stealth,sloped][scale=0.8]  \matrix (tree) [matrix of nodes, minimum size=0.25cm, column sep=2cm, row sep=1cm, ]  { &amp; $C_{i+1,j+1}$ \\ $C_{i,j}$ &amp;$C_{i+1,j}$ \\  &amp; $C_{i+1,j-1}$ \\   };  \draw[-&gt;] (tree-3-1) -- (tree-1-3) node [midway,above] {};  \draw[-&gt;] (tree-3-1) -- (tree-3-3) node [midway,above] {};  \draw[-&gt;] (tree-3-1) -- (tree-5-3) node [midway,below] {};  \end{tikzpicture}  \end{adjustbox} – Two of my friends are getting married. They're both huge Doctor Who geeks, and actually met through a DW RPG. Their wedding invitation contained a very subtle DW reference (you wouldn't have been able to tell unless you were very familiar with the show yourself.)   Doctor Who's been running long enough that there are quite a few nice quotes for basically every occasion in life. I was hoping someone would know a nice wedding-related one, or maybe one about love, that I could include in a wedding card? Java: splitting a comma-separated string but ignoring commas in quotes This is a problem from Introduction to Representation Theory by Etingof et al. I have no idea how to approach it. My friend wrote a program that uses Gaussian elimination to find a basis, which starts with x, y, [x, y], [y, [x, y]], ... but freezes once it gets to elements with 9 or more occurrences of x, y.  I expect that there is some way to characterize the nonzero elements of this Lie algebra (i.e., elements that are "immune" to being shown to be zero through repeated application of the Jacobi identity) which could be turned into a way to enumerate them. I don't see what it is, though.  It's also totally unclear to me how to show that some set we know spans the Lie algebra (proven using some criterion as described in the previous paragraph) is actually linearly independent, unless we find a faithful representation... but I have no idea how to find a faithful representation for an infinite-dimensional Lie algebra.  Hints would be greatly appreciated.  Edit: After looking at the partial output, we can form the "straightforward" conjecture that:   If $n \geq 4$ is even, then there is one basis element of grade $n$, namely $\mathrm{ad}([x, y])^{(n-4)/2}[y, [y, [y, x]]]$. If $n \geq 5$ is odd, then there are two basis elements of grade $n$, namely $[x, z]$ and $[y, z]$ where $z$ is the single basis element of grade $n-1$.   I also have a different conjecture, which is mutually exclusive with the above: that if we flatten out all nonzero elements into the form ${\rm ad}(e_1) {\rm ad}(e_2) \ldots {\rm ad}(e_{n-1}) e_n$ using the Jacobi identity, then in the sequences $e_1, \ldots, e_{n-1}, e_n$ and $e_1, \ldots, e_n, e_{n-1}$, any span containing two x's must contain at least two y's and any span containing five y's must contain at least two x's, otherwise we can use the Jacobi identity to rearrange the element somehow to show that it vanishes. If this is true, then the long-range behaviour must be:   For $n \geq 8$ there is exactly one basis element of grade $n$, namely $[... [y, [x, [y, [y, [x, y]]]]] ...]$ (the pattern $y x y$ repeats).   I still don't see an approach to proving that none of the elements in this sequence actually vanishes, though.  Edit 2: Here is the hint given by Etingof in an email:     No, there are no published solutions, since these problems are used as   a homework for classes. This is indeed a nontrivial problem.      This is the positive part of the affine Kac-Moody algebra of type   A_2^2, which is the twisted loop algebra for sl(2). So what you need   to do is to relate this Lie algebra to loops into sl(2). I see from   your post that you are on the right track. Optimal tiling of polygon using ArcGIS Desktop? I am trying to tile a polygon with a minimal number of fixed sized squares.  Currently I am creating a fishnet over my polygon then spatially joining the squares that intersect the polygon. This is not optimal.  Also note the squares can be shifted vertically/horizontally but not rotated.  My end goal: The polygon represents a clipped image and I want a tiling of the clipped image. Where each tile is 300px by 300px. Some overlap is fine if that makes the problem easier.  Current    Manually optimized    Are there any tools or algorithms that would help with this? I am proficient with Python and ArcMap.  The polygon was created from line features so I also have access to those segments. Maybe that would will help for generating the squares.  The entire polygon must be covered. 500 Error on index.php file Is a block of cotton heavier than a block of iron? if i have a block of cotton and a block of iron each containing a weight of 100 kg when measured on a weighing machine, in reality which one is heaver than the other, which one is heavier and why?  This question was in my physics worksheet. The teacher gave the following answer: the apparent weight of both of them is the same, but the buoyant force of cotton is high since the volume of cotton is more than iron. Therefore, true weight of cotton is more. Does this answer make sense? What is the right answer? Some Git commands take commit ranges and one valid syntax is to separate two commit names with two dots .., and another syntax uses three dots ....  What are the differences between the two? Single word describing a person new in something What is a word for someone who is totally new in something or participates in something for the first time? What Hogwarts classes are taught to two houses at once? I remember from my mumble about nine mumble rereads of the Harry Potter series that the following classes Harry took were taught to more than one house in the same lesson:   Potions with the Slytherins  Herbology with the Hufflepuffs  Care of Magical Creatures with the Slytherins  broomstick riding with at least the Slytherins (maybe other houses, too?)    I don't remember any student from a house that isn't Gryffindor being mentioned in the sections on Transfiguration, Charms, Defense Against Dark Arts, History of Magic, or Divination. That would mean McGonagall had to teach twice as many classes as Snape, if both subjects got the same number of lessons (which I think I recall).   Were any subjects other than Potions, Herbology, and Care of Magical Creatures taught to more than one house in the same lesson? And do we know why some subjects are taught to more students at the same time than others? I was a member of a study team that produced a couple of research papers. The authors of the paper are, for example:      Michael Jordan, Tiger Woods, John Smith and The ABC Study Investigators   In the acknowledgements, it reads:     The ABC Study team consists of members from Harvard University (James Bond, Thomas Harper, David Price, and Jason Jolly)   (Suppose that my name is David Price.)  Can I list such papers in the publication list of my CV? If not, how can I show that I participated in these research papers?  In PubMed, my name was listed as one of 'collaborators.'