I just watched  explaining the difficulty of measuring the one-way speed of light.  The presenter explains that a round-trip will always average out to $c$ even if the speed in one direction isn't always the same as the speed in a different direction.  He used the example of an astronaut on Mars synching his clock with Earth, and how different aberrations would still always make it end up looking like it was consistently $c$. But the example of Mars got me thinking.  Mars has two interesting properties: it's far enough away from Earth that there's a very noticeable time delay, and it's in a different orbit around the sun than we are, so its direction relative to us is constantly changing.  So here's an experimental proposal that doesn't require any synchronization:  Put a radio beacon on Mars that pulses in a regular, well-defined rhythm, then observe it from Earth for a Martian year or three. No clock synchronization is necessary; just observe the rhythm.  If the speed of light is not constant in all directions, this will create a Doppler effect in the pulses that can't be explained simply by the movement of the two planets.  If no such Doppler distortion is detected, we can safely conclude that the speed of light is invariant in different directions.  (Or at least in all the directions along the essentially 2-dimensional orbital plane of Sol.) Is there anything that would cause this experiment to not produce correct results, if it were tried?
I recently watched  by Veritasium where he talks about the One Way Speed of Light and talks about the limiting case where in one direction the speed of light is $c/2$ while it's instantaneous in the other. He also says this is perfectly fine according to our Physics theories. He also points at Einstein's assumption in his famous 1905 paper where he assumes that the speed of light is same in all directions. This made me ask this question is taking the speed of light same in all directions an axiom of some sort? As I've often read no information can be sent at more than the speed of light but here one-way taking the speed to infinite makes no difference. So are all of our physics theories based on the assumption and what would happen if light turns out to be moving at different speeds in different direction? Will that enable transfer of information faster than the speed of light and is there any way for us knowing that the transfer happens faster than the speed of light? The video takes a Earth Mars case where he says it isn't possible for us to every realize this discrepancy but is there a more general proof which says it isn't possible
Can I learn Dual Talent Specialization? World of Warcraft has an ability to have two different talent builds and switch between them with a button press.  Does this exist in Star Wars: The Old Republic?  If so, where (and when) do I learn it and how much does it cost to learn? AWK: Nested Conditional Subset of Rows I have a pretty specific question, and have been able to find lots on conditional subsetting using awk but none that lends enough explicit code for me to generalize to my situation. I have a file 'keys' and a file 'features'. The 'keys' table contains two variables, KEY and GROUP, toy example below.      KEY        GROUP     ---        -----     1          GROUP0     2          GROUP0     3          GROUP1     4          GROUP1     5          GROUP2     6          GROUP2     The file 'features' contains a list of features of widgets like so      ID          FEATURE      VALUE     --          -------      -----     A           num_user     10     A           KEY          4     B           num_user     2     B           KEY          2     B           battery      Large     C           num_user     10     C           KEY          15     D           num_user     2     D           KEY          2     D           battery      Small     E           num_user     2     E           KEY          7     E           battery      Small   I am trying to select all rows for an ID which has a value of 'KEY' that is in the 'KEY' column of 'keys' for a hardcoded list of 'GROUP' values. The desired result is      ID          FEATURE      VALUE     --          -------      -----     A           num_user     10     A           KEY          4     B           num_user     2     B           KEY          2     B           battery      Large     D           num_user     2     D           KEY          2     D           battery      Small   Any ideas? use contradiction to prove that the square root of $p$ is irrational How can I charge my iPhone without waking up my MacBook Pro? If I take a sponge and place it in a shallow dish of water (i.e. water level is lower than height of sponge), it absorbs water until the sponge is wet, including a portion of the sponge above the water level. In other words, it seems the sponge pulls some water from the bath up into itself, doing work, and the water gains some gravitational potential energy.  Where does the energy required to do this work come from? My suspicion is that the answer involves physical and/or chemical bonds between the water and the sponge, or possibly the change in the surface area to volume ratio of the water. Expected Value of Max of IID Variables What is the expected value of the maximum of 500 IID random variables   with uniform distribution between 0 and 1?   I'm not quite sure of the technique to go about solving something like this. Could anyone point me the right direction?  Thanks In my resume, I'm describing several projects I've worked on in the past. Most of them were done in teamwork. What is the best way to say this?  Examples:  Together with XY, I built ... OR  In collaboration with XY, I built ... OR  XY and I built ...  Are the first two examples grammatically correct? I'm unsure since first I state that something has been done in collaboration with a second person, but then I use "I built ...". Finding Radii of Convergence for $\sum a_n z^{2n}$ and $\sum a_n^2 z^n$ Setting: Let $\sum a_n z^n$ have radius of convergence $R$.  We have that  $$ R = \frac{1}{\underset{n \rightarrow \infty}{\limsup} \left|a_n \right|^{1/n}} $$  via Hadamard's formula for the radius of convergence.  Question: What are the radii of convergence for (i) $\sum a_n z^{2n}$ and (ii) $\sum a_n^2 z^n$?  Attempt for $\sum a_n^2 z^n$:   For ease of notation, let $R_1$ and $R_2$ denote the radii of convergence for power series $\sum a_n z^{2n}$ and $\sum a_n^2 z^n$ respectively. From Hadamard's formula, we then have  $$ R_2 = \frac{1}{\underset{n \rightarrow \infty}{\limsup} \left|a_n^2 \right|^{1/n}} = \left( \frac{1}{\underset{n \rightarrow \infty}{\limsup} \left|a_n \right|^{1/n}} \right)^2 = R^2 $$   But what about $R_1$? Is the uncertainty principle just saying something about what an observer can know or is it a fundamental property of nature? I ask this question because I have read two different quotes on the  that don't seem to match very well. There are similar questions around here but I would like an explanation that reconciles these two interpretations specifically:   Feynman talks about the uncertainty principle in one of his lectures and mentions it as the reason why electrons don't crash into the atom's nucleus: If they did they would have an exact location and momentum which is not allowed by the uncertainty principle. In saying this it is clear that the uncertainty principle is a fundamental property of nature because it has an effect on where an electron can reside. Recently I read - somewhere else but I forgot where exactly - an account of the uncertainty principle where there was explained how we can measure position of a particle by firing another particle into it, the collision disturbs the velocity of the observed particle therefore we can not know its momentum anymore.   Now, 2) very much seems like a limitation of what the observer can know, while 1) attributes a fundamental property of nature to it (electrons don't crash into the nucleus). What is the correct way to think about this? I need to get MODIS NDVI (MOD13A3), but output from EarthExplorer or Daac2Disk HDF format is a numerical range is -2000 to 9996.   But I need for futher work basic range -1 to 1.   Is there any conversion method? What is the normal operating temperature for the MacBook (2016 generation)? I need a robust and simple way to remove illegal path and file characters from a simple string. I've used the below code but it doesn't seem to do anything, what am I missing?  using System; using System.IO;  namespace ConsoleApplication1 {     class Program     {         static void Main(string[] args)         {             string illegal = "\"M&lt;&gt;\"\\a/ry/ h**ad:&gt;&gt; a\\/:*?\"&lt;&gt;| li*tt|le|| la\"mb.?";              illegal = illegal.Trim(Path.GetInvalidFileNameChars());             illegal = illegal.Trim(Path.GetInvalidPathChars());              Console.WriteLine(illegal);             Console.ReadLine();         }     } } It is known that all $B$, $C$ and $D$ are $3 \times 3$ matrices. And the eigenvalues of $B$ are $1, 2, 3$; $C$ are $4, 5, 6$; and $D$ are $7, 8, 9$. What are the eigenvalues of the $6 \times 6$ matrix  $$\begin{pmatrix} B &amp; C\\0 &amp; D \end{pmatrix}$$ where $0$ is the $3 \times 3$ matrix whose entries are all $0$.  From my intuition, I think the eigenvalues of the new $6 \times 6$ matrix are the eigenvalues of $B$ and $D$. But how can I show that? For every generation of Excel I can remember (including 2010, which I'm using now), Excel's "Auto Size Row" features sometimes fails to actually auto size a row when the cell contains wrapped text. When it works properly, all the text is revealed and there is no additional space below the last line of text. When it fails, it adds extra space below the text. To make matters worse, what you see is not always what you get, i.e., text that appeared okay on screen gets cut off when it's printed. You also get different sizing depending on whether you are zoomed in/out or at actual size.  Simple test case:  Why is there a one-line gap after the text in cell A1 but not in A2?  (To reproduce: set width of column A to 17.14 (125 pixels), text wrap on, and cell alignment top.)  (I double-checked that I applied Auto Fit Row Height to both rows. Zoom level is 100%.)    Is there any known remedy for this without resorting to manually adjusting the row heights (which is not practical for more than a handful of rows)? App drawer icon gone from Cyanogenmod dock I have a Samsung Galaxy S2, running the latest CM10.1.  I lost the app drawer icon on my Dock; I must have deleted it. The app drawer icon lets you go to the app list, and the widget list.  How do I get the app drawer icon back? The icon looks like a circle with 6 dots inside it. Blender image output is greyish and not white dynamic does not contain a definition for a property from a project reference I am getting really confused now. I installed Tex Live 2012 on my Xubuntu 12.04 with a backport and I installed TexMaker.  I could user PdfLatex right away and it generated everything I needed except my bibliography. I read that Tex Live 2012 comes with biblatex so I just changed the bibtex command in TexMaker from "bibtex" to "biblatex". However, that does not exist. So I did  sudo apt-get remove biblatex sudo apt-get install biblatex   The package is installed but I don't find the binary. Using bibtex the whole thing crashes. Which does not surprise me since I want to userbiber:  \usepackage[backend=biber]{biblatex}   Btw does biber come with biblatex? So far I couldn't get any clear explanation what biber and biblatex are to each other.  EDIT: I had to remove texlive completely and install it with the install script form . Apparently the newest version of biber does not work with the older version of biblatex I had. Comment authors are not getting migrated Expected value as a function of quantiles?