At school I learnt the  to remember the resulting direction of different phenomena, such as geometrical cross products, mechanical torque, or the direction a screw will move when turning it. This directions are however decided by humans, and we could have easily defined the directions in the opposite way.  However the right hand rule also predicts phenomena which is not arbitrarily set by humans, but is intrinsic to the nature. If you have a coil in which you put some current, and the nature creates a magnetic field in a direction perpendicular to it, the direction depends on the right hand rule.  My question is, why this direction and not the opposite? Nature tends to be symmetric and not have apparent preferences for two equal options, so in a so why is one direction preferred over the other one? Why doesn't a "left hand" rule apply?
In definition of vector multiplication, the direction of the resulting vector is given by the right hand rule. However I don't know any mathematical requirement to pick right hand instead of left for this purpose. Is there any?
Why is FIFA against adding instant replay to the game? Is there any evidence or reason why FIFA is so against adding instant replay to soccer? I find myself seeing many unlucky or just plain wrong decisions made by refs that could be corrected with instant replay. Case insensitive searching in Oracle Suppose, I want to refer multiple equations (1), (2), (3), (4), (5) and (7) so that they appear as (1-5, 7):  \documentclass[fleqn,preprint,10pt]{article} \usepackage{amsmath} \usepackage{amssymb} \usepackage{amsfonts} \begin{document} \begin{align} \label{1}\psi([e_1,e_2]) = \psi(e_2) = e_2 = (e_2,2e_3) = (-2e_3,e_2) = (\psi(e_1), \psi(e_2))\\ \label{2}\psi([e_1,e_3]) = \psi(2e_3) = 2e_1 = (e_1,2e_3) = (-2e_3,e_1) = (\psi(e_1),\psi(e_3))\\ \label{3}\psi([e_2,e_3]) = 0 = (e_2,e_1) = (\psi(e_2),\psi(e_3)),\\ \label{4}\left\{e_4, e_1\right\},\,\,\,\left\{e_4, e_2\right\},\,\,\,\left\{e_4, e_3\right\},\,\,\,\left\{e_4, e_1+\epsilon\,e_2\right\},\\ \label{5}\left\{e_1, e_2\right\},\,\,\,\left\{e_3, e_1\right\},\,\,\,\left\{e_3, e_2\right\},\\ \label{6}\left\{e_4, e_1\right\},\,\,\,\left\{e_4, e_2\right\},\,\,\,\left\{e_4, e_3\right\},\,\,\,\left\{e_4, e_1+\epsilon\,e_2\right\},\\ \label{7}\text{Nor}_{L_4\oplus L_3}\left(\{e_2\}\right)/\{e_2\}=\,\{e_1, e_3, e_4\} \end{align} \end{document} I don't understand philosophy very well, and so I am wondering whether you can "prove" anything in philosophy. It always seems you can go a layer down, and find another question, almost endlessly until you get to the question of "why/how/are we here?"  Can you prove, absolutely, and 100% that something is true, in the field of philosophy? After update, get "error: file not found." followed by "grub rescue> _" Is there any noun in English which changes the first letter in the plural? Plenty of nouns change the second letter to become plural (man->men, goose->geese) but does anything change its first letter.  I've hunted high and low over the internet, and spent ages browsing the questions at  but I can't find anything. Best WPF open source projects I have programmed with WPF for more than a year. When I started there weren't so many examples and guidelines to follow, now the situation is much more better.  I would like to ask you some help in listing the best WPF (open) source code examples or projects that you suggest to study in order to learn more about project structure, best practices, etc.  Thank you, Marco Is every open subset of $ \mathbb{R} $ uncountable? Is every open subset of $\mathbb{R}$ uncountable?  I was crafting a proof for the theorem that states every open subset of $\mathbb{R}$ can be written as the union of a countable number of disjoint intervals when this question came up.  I feel like the answer is yes, but I'm not sure how to go about proving it or whether there is a crazy construction (like the Cantor Set)  that creates a countable, open subset of $\mathbb{R}$. Any ideas? How to redirect users to custom lostpassword page? How to modify an invalid '/etc/sudoers' file? How do I edit an invalid sudoers file? It throws the below error and it's not allowing me to edit again to fix it.  Here is what happens:  $ sudo visudo &gt;&gt;&gt; /etc/sudoers: syntax error near line 28 &lt;&lt;&lt; sudo: parse error in /etc/sudoers near line 28 sudo: no valid sudoers sources found, quitting Overflow to left instead of right I have a div with overflow:hidden, inside which I show a phone number as the user types it. The text inside the div is aligned to right and incoming characters are added to right as the text grows to left.  But once the text is big enough not to fit in the div, last characters of the number is automatically cropped and the user cannot see the new characters she types.  What I want to do is crop the left characters, like the div is showing the rightmost of its content and overflowing to the left side. How can I create this effect? Can I open Microsoft Word and Excel files with Ubuntu? I needed to create a list of lists in Python, so I typed the following: my_list = [[1] * 4] * 3  The list looked like this: [[1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1]]    Then I changed one of the innermost values: my_list[0][0] = 5  Now my list looks like this: [[5, 1, 1, 1], [5, 1, 1, 1], [5, 1, 1, 1]]    which is not what I wanted or expected. Can someone please explain what's going on, and how to get around it? The problem   I have tens of thousands of small polygons for which I want to create buffer/doughnuts for, but I don’t get the units right. I want meters and not degrees, and changing to (what I think is) the right CRS my layer doesn’t longer show. The polygons are small farming plots. I work in QGIS 3.4.15.   Let me take you through it  I start by adding a vector layer. I opt for ‘Directory’ as a source type (Encoding: UTF-8 by default) and under Source (Type: UK. NTF2 by default) I point to the folder in which I store the shapefile.   The default CRS is set to EPSG:4326 – WGS 84, for both layer and the project (checked in bottom right), and unit is thus in degrees. I add the layer world map (EPSG:4326 – WGS 84 by default) by taping “world” in the coordinate box in the middle bottom, I also add Open street map (EPSG:3857 – WGS 84 / Pseudo-Mercator by default) from XYZ Tiles. The polygons appear nicely on the map considering some are just adjacent to the nearby lake, many nicely adjacent to roads, etc.   When attempting to do buffers the distance is obviously set to degrees. I have tried to change the CRS, both for the layer(s) and the projects, but without luck. After researching (e.g. here: ) I believe that the correct CSR would be Arc 1960 / UTM zone 36S EPSG:21036 (it is my understanding that either 36N or 36S would work as the polygons appear both south and north of, but close enough to the equator). When setting the mentioned CRS for my polygon layer, the polygons disappear from the map, and remain gone even after setting the project CSR (by bottom right) to the same. It seems that whenever I try with different CRS in UTM, the layer doesn’t show. Does this mean that the polygons are somehow not compatible with units in meter? Is there an issue with importing the .prj file?  Other things I've tried:   I have made a good attempt searching for solutions. I have ensured that the polygon layer is on top of the layers list. I have ensured the file names are identical and tried all different suitable CRS I can think of. I have seen similar questions been solved by saving the .shp 'as', but I don't think that's my issue as it's already a .shp file. Can it be the case that I need to perform a datum transformation? I gave it a shot using a transformation code (1122) provided by above link, but then the polygons were projected on the Antarctica on the world map, so obviously something went quite wrong...   Note that when I have changed to what I believe is the right CRS I can execute buffers in units of meters, however, they do not appear on the window… We are developing a C# application for a web-service client. This will run on Windows XP PC's.  One of the fields returned by the web service is a DateTime field. The server returns a field in GMT format i.e. with a "Z" at the end.  However, we found that .NET seems to do some kind of implicit conversion and the time was always 12 hours out.  The following code sample resolves this to some extent in that the 12 hour difference has gone but it makes no allowance for NZ daylight saving.  CultureInfo ci = new CultureInfo("en-NZ"); string date = "Web service date".ToString("R", ci); DateTime convertedDate = DateTime.Parse(date);               As per :     UTC/GMT Offset       Standard time zone: UTC/GMT +12 hours   Daylight saving time: +1 hour   Current time zone offset: UTC/GMT +13 hours     How do we adjust for the extra hour? Can this be done programmatically or is this some kind of setting on the PC's? Is cancer caused by vitamin B17 deficiency? How do you get JavaScript/jQuery Intellisense Working in Visual Studio 2008? How to remove extra start item from boot menu? I bought a laptop recently. While Windows 7 was installing, the battery died. So I plugged in the charger and re-installed Windows 7 Home Basic from the start. After completion of the procedure I now have 2 Windows folders in my C:\ drive, so I deleted the old Windows folder.  The problem is, while booting time it shows two Windows 7 options, although I already deleted the old Windows folder.  How can I remove old Windows 7 option from my boot? How to define orbital angular momentum in other than three dimensions? How to inline expand wildcard in bash? I remembered bash can do the following:  Suppose there are 3 files: a,b,c in the current directory, when I input:  $&gt; somecommand *   and then press a key or key combinations or a key sequence, the wildcard * online expanded as:  $&gt; somecommand a b c   but I cannot remember and cannot google out the key sequence! help!