I know that the speed of light, the universal constant of gravitation and the Planck's constant are considered to be the three fundamental constants of the universe. But, why is speed of light considered as a fundamental constant? The speed of light changes from medium to medium for satisfying Fermat's principle then, how can it be a constant?
Does it make sense to say, "The speed of light varies?"  Some may say right off the bat "Yes, it changes as a wave passes through a different medium."  However, I'd like to say no, because when I hear someone say the speed of light, I always think of the constant $c$ (unless the medium is specified to not be a vacuum, but then it isn't $c$ anymore), not the speed of a particular wave.  To me, it makes more sense to say something like, "The speed of a particular wave varies." What is the correct way to state this in the professional world? And in general, when professional physicists say "the speed of light," are they referring to the constant or the actual speed of the wave?
Choosing numbers without consecutive numbers. In how many ways can we choose $r$ numbers from $\{1,2,3,...,n\}$,   In a way where we have no consecutive numbers in the set? (like $1,2$) Alternative proof that $(a^2+b^2)/(ab+1)$ is a square when it's an integer Let $a,b$ be positive integers.  When $$k = \frac{a^2 + b^2}{ab+1}$$ is an integer, it is a square.    Proof 1: (Ngô Bảo Châu): Rearrange to get $a^2-akb+b^2-k=0$, as a quadratic in $a$ this has two values: $a$ and $kb - a = (b^2-k)/a$. (The second root is determined in two different ways from the expansion $(x-r_1)(x-r_2) = x^2 - (r_1 + r_2)x + r_1 r_2$.)  Now suppose we have $a,b$ such that $k$ is an integer but not a square, by the investigation about roots we have that the second root is a nonzero integer since $k,b,a$ are integers and $k \not = b^2$, futhermore it is positive which is easily seen from its defining equation.  WLOG assume $a \ge b$ so that the second root is strictly smaller than $a$. This leads to a decent, replacing $a$ with the second root.    Proof 2 (Don Zagier): Apply reduction theory (specifically, Sätze 1 and 2 of Section 13 of my book on quadratic fields) to the quadratic form $x^2 + kxy + y^2$, which is the unique reduced quadratic form in its equivalence class.    Note that Proof 2 is pretty much the same as Proof 1 when written out in explicit detail, but I could not read Zagier's book because I cannot read German.  I would like to know more approaches to this and other alternative proofs of this result if possible! Thanks in advance.  I would also be interested in related problems (especially easier ones of a similar nature) and texts which cover the reduction theory in English. SD card not showing files when connected to pc When my phone MOTOROLA G3(2015) is updated to Marshmallow, its not showing files when connected to PC. While connecting, it shows options as charing only, PTP, MTP, MIDI. When I select MTP, it shows the external card, but not showing the contents, where as internal memory is detected and all files are shown. Word style "keep with next" except on last item How should a bot earn enough reputation to perform the actions necessary for that bot? Converting GeoJSON to Shapefile using ogr2ogr? I have a GeoJson file that I want to convert to ESRI Shapefile using ogr2ogr in FWTools.  I tried using   ogr2ogr -F "ESRI Shapefile" filename.shp geojsonfile.json OGRGeoJSON   I got output      ERROR 6: Can't create fields of type StringList on shapefile layers. ERROR 1: Attempt to write non-polygon (POINT)   geometry to  type shapefile. ERROR 1: Terminating translation   prematurely after failed translation of layer OGRGeoJSON   GeoJSON input we are giving is in standard geojson format.  content of geojson are like  {to share I took only a part from features array }  {"id":1223, "properties":{"name":"3","level":2}, "map_version":11,"type":"FeatureCollection","x_id":1234,"obj_type":"LevelGeometry", "features":[  { "my_area":[131.40093253528894,33.58879853190332,6.515867411008615,3.490549810987222,-0.6237271428108215], "id":1984791, "location":{"type":"Point","coordinates":[131.4009325,33.5887985]}, "properties":{"display_name":"xyz"}, "type":"Feature", "geometry":{"type":"Polygon","coordinates":[[[131.4009508,33.5888314],[131.4008895,33.5887946],[131.4009148,33.5887653],[131.4009761,33.5888020],[131.4009508,33.5888314]]]}, "obj_type":"Geometry" }  ] } How to apply CSS to iframe? I have a simple page that has some iframe sections (to display RSS links). How can I apply the same CSS format from the main page to the page displayed in the iframe? While building things I want to see the overlays from other modes so I can make better decisions. Can I lock an overlay somehow?  For example: When building roads I want to see the natural resources overlay. When zoning I want to see the wind overlay Live CD asks for a username and password Why can´t we assign a new string to an char array, but to a pointer? Listen for incoming request on port on Linux, then run command I am after as lightweight as possible solution to listen on a port for a specific request, then run a command should the port be hit and the correct request be recedved.  Eg. Send a request to 192.168.0.10 on port 5432 with the string my_token. On the host (eg. 192.168.0.10), then run a command should that port be hit and the string matched.  I was initially thinking of using netstat (eg. nc -l 5000) then running the command on change. However, ideally a string or token of sorts would be ideal alongside this or similar, but without using a full-blown webserver - essentially something that can run in the background with few resources. If an effect would prevent a spell from doing damage, does it continue to prevent that damage after the spell changes zones? Anthony casts , targeting Nathan's .  Nathan casts and resolves , choosing to 1) prevent all damage that would be dealt by Searing Blood this turn and 2) put a +1/+1 counter on Elvish Mystic.  Searing Blood resolves, deals no damage, and goes to the graveyard.  Anthony casts and resolves  to kill Elvish Mystic.  Searing Blood triggers from the graveyard, because Elvish Mystic died. Does the prevention effect created by Dromoka's command still apply to it after it changes zones? In other words, will Searing Blood deal 3 damage to Nathan? How far can/should one press philosophical doubt? Should we keep on questioning until nothing is left to question or is there a point on which we need to stand (which we often tend to do)? Descartes used 'I think' as this fixed point where the skepticism abates, there may be others. But what is a rational way to find one, if any? How is this question addressed in modern philosophy? Is my US visa still valid after change in name? I'm a Malawian national and I got US Visa years back.  Recently, due to some reasons, I had to get my first name partially changed on my passport. I have got an affidavit certificate stating the reason and proof.  Since the visa on my old passport has still not expired, but there is a difference in first name, will I face any problem? $n$ choose $k$ where $n$ is less than $k$ How to use variable inside parameter $_GET? example: ($_GET[$my_var]) Prove that the sequence with $T(0)=1$ and $T(n) = 1 + \sum_{j=0}^{n-1}T(j)$ is given by $T(n)=2^n$ $T(0)=1 \\ T(n) = 1 + \sum_{j=0}^{n-1}T(j) \\ $  Show that $T(n) = 2^n$.  I know how to prove this by induction, but I would like to know how to show this using first principles.  Edit: The way I want to solve this problem is manipulate $T(n)$ in such a way that it ends up as $2^n$. How do I create a very long delay with Redstone? I know I'm asking for the close-to-impossible -- as a real full-backup certainly requires root permissions. But still there are many folks around not wanting to root their devices -- afraid of voiding their warranties or bricking their devices, or just not having their devices supported by any rooting method.  I also know there were a lot of questions asked already on this topic, and I checked all of them having the backup tag -- none covers the entire topic, all just have pieces, and especially people new to Android (but other non-power-users as well) would have a hard time figuring out the best way.  So I want a detailed canonical answer to the question:  Not involving root-solutions, how to achieve a backup as close as possible to a full backup?  Please do not give simple one-liner answers like "Use app xyz [full-stop]." If mentioning an app (and I doubt a single app would be the answer here), include what parts are covered by it -- as well as ideas on how to fill the gaps it leaves. (And to make it absolutely clear: I know the first thing coming to mind is Titanium Backup -- I use it myself, but this does not apply here: This question is strictly about methods for non-rooted devices!) Moreover, the answer should be as generic as possible in terms of applying to a wide range of devices (i.e. it should not be restricted to one device or manufacturer).  I already mentioned having investigated all questions here tagged backup. These will certainly be helpful providing details for answers here, so I will list up the topmost ones concerning my question:            All these provide some details for my question (so feel free to get inspired by them) -- but I feel there are still details missing. Also it would be helpful to have a summary -- say, an answer including the full description of "the maximum possible".  A last criterium: While I'd consider cloud-based solutions legit, I'd favour local solutions. If you can provide both: all the better. But some people value privacy quite high (I'm one of them), and thus would not trust their data to some cloud service.    Thanks to Ryan, we now have a solution for a really complete backup of all apps and their data -- which I didn't dare to hope for! The only disadvantage: His solution only works for less than 10% of all Android users; namely those whose devices are running at least with Android 4.x.  So again, I ask the close-to-impossible: Any solutions applicable at least on Gingerbread (2.3.x) or, better, even Froyo (2.2.x) -- so they cover the majority of current devices? These solutions may involve multiple tools (try to keep it as simple as possible though; think of your mother to follow your instructions ;)  And keep in mind: NO ROOT!    To further motivate high-quality answers (and hopefully avoid low-quality ones), I will be a harsh one here: As I rarely do, I will down-vote answers not fitting the mentioned criteria on one end -- but on the other end, I will setup a bounty for the best answer (which cannot be done immediately, but earliest after 2 days). Snapping in PyQGIS3.0 The following expression enables snapping for PyQGIS 2.0 :  QgsProject.instance().setSnapSettingsForLayer(layer.id(), True, 2, 1, 10, True)   What is the equivalent expression in PyQGIS 3.0?