Is the linearity of transformation of intervals postulate in SR?
Interval preserving transformations are linear in special relativity
What's the added value of SD line over regression line when examining association between 2 variables? I'm trying to incorporate different practices to use when exploring a new data set. Especially, how to examine the association between two variables.  Steps for example (not necessarily by order):   plot a y-by-x scatter plot of the raw data to see the relationship visually. compute summary statistics for each variable (mean and sd) compute correlation coefficient r draw the OLS regression line, compute its slope and intercept etc....   I've come across the "SD line" in Freedman's Statistics book, which is defined as:     "the line that goes through the point of averages and climbs at the rate of one vertical SD for each horizontal SD" Freedman, D., Pisani, R., &amp; Purves, R. (2007). Statistics (4th edn).   Since this book ("Statistics") is a canonical textbook, I consider its choice to discuss the SD line as an indication for the line's importance. However, a simple google search for the term "SD line" doesn't yield as many independent results. Most of them come directly from Freedman's book. This tells me it's not a central concept in bivariate analyses in general.  When comparing the SD with the OLS regression line, it seems like the regression line is more informative (than the SD line) for predicting y from x. Therefore, I'm wondering if bothering to plot the SD line has any benefit or added value that I would not already have when plotting the regression line.  Example using mtcars dataset, focusing on association between weight and mpg  data(mtcars)  ## calculate means mean_wt &lt;- mean(mtcars$wt) mean_mpg &lt;- mean(mtcars$mpg)  ## calculate standard deviations sd_wt &lt;- sd(mtcars$wt) sd_mpg &lt;- sd(mtcars$mpg)  ## scatter plot plot(x = mtcars$wt, y = mtcars$mpg)  ## add the "point of averages" points(mean_wt, mean_mpg, col = "red", cex = 1.5, pch = 16)  ## calculate the slope of the sd line slope &lt;- -1*sd_mpg/sd_wt  ## plot the sd line curve(expr = x*slope + (mean_mpg - slope*mean_wt), add = TRUE, col = 'blue', lwd = 2, type = "l", lty = 2)  ## plot the regression line model &lt;- lm(mpg ~ wt, data = mtcars) abline(model, col = "orange", lwd = 2)  ## legend legend("topright",        legend = c("Regression line", "SD line"),        col = c("orange", "blue"),        lty = c(1, 2),        lwd = c(2, 2))     Thus, my question: how can the SD line increase one's understanding about the relationship between two variables, in a way that's either adding or complementing on what the regression line already tells? A man sits on a bench considering his woeful burden. He looks up at the stars and compares the distance from here to his house and here to the furthest visible star Deneb. Suddenly his problems seems pitifully faint and untroubling. He laughs and relaxes in his seat, staring at the ducks.     Look again at that dot. That's here, that's home, that's us. On it everyone you love, everyone you know, everyone you ever heard of, every human being who ever was, lived out their lives. The aggregate of our joy and suffering, thousands of confident religions, ideologies and economic doctrines, every hunter and forager, every hero and coward, every creator and destroyer of civilization, every king and peasant, every young couple in love, every mother and father, hopeful child, inventor and explorer, every teacher of morals, every corrupt politician, every "superstar," every "supreme leader," every saint and sinner in the history of our species lived there—on a mote of dust suspended in a sunbeam.   ~Carl Sagan      I really believe that if the political leaders of the world could see their planet from a distance of 100,000 miles their outlook could be fundamentally changed. That all-important border would be invisible, that noisy argument silenced. The tiny globe would continue to turn, serenely ignoring its subdivisions, presenting a unified façade that would cry out for unified understanding, for homogeneous treatment. The earth must become as it appears: blue and white, not capitalist or Communist; blue and white, not rich or poor; blue and white, not envious or envied. ~Michael Collins, astronaut   I'm looking for a noun or verb that describes this positive enlightening experience. I used node textures in a mesh I exported to .FBX.  I then imported it into Unreal Engine 4 and it didn't import any textures; I clicked the Upload Textures option in Unreal Engine.  Is there something I'm doing wrong or is it Blender? It is well established that:   'In quantum mechanics, the behavior of an electron in an atom is described by an orbital, which is a probability distribution rather than an orbit.   There are also many graphs describing this fact: : (hydrogen atomic orbital - one electron) In the figure, the shading indicates the relative probability to "find" the electron, having the energy corresponding to the given quantum numbers, at that point.  My question is: How do these symmetries shown in the above article occur?                 What about the 'preferable' axis of symmetries? Why these? Can I visit the US for tourism on a previously unused B1/B2 visa? Note: This is NOT a duplicate of  Difference: In both other questions, the posters traveled once to the US for the original purpose for which the B1 visa was obtained. Their question is about visiting again using the same visa. However, I've not traveled to the US yet, and I'm planning my visit. What I want to understand whether I can use this visa for a visit whose purpose is not the same as what was submitted along with the application.  Can I use a B1/B2 visa for tourism that was originally obtained for business purposes BEFORE I actually visit the US even once? I had applied for a business visitor visa for a valid business reason but by the time I got it stamped, my plan changed. So I've not visited the US even once. Can I now use this visa to visit as a tourist without having used that visa for its original intended purpose? PS: I live in India. normal subgroups of Alternating group Klein's $4$ group, $\{1\}$ and $A_4$ are three normal subgroups of $A_4$. I want to know about any other normal subgroups of $A_4$. Do these exist? Stack Overflow as a reference in a professional paper/presentation Suppose I'm doing an academic paper, journal article, or other professional presentation.  Would you say that it would be possible to use Stack Overflow as a reference?    Of course I'm pretty sure that the answer here would be "yes."   So here's the follow up: When, if ever, would it be a good idea to cite a Stack Overflow question as a reference in an professional paper/presentation of some kind? I would like to close some view windows that I opened accidentally.  See the image below:    Edit: another note: I tried searching for the solution, but only found things like "Join Area", which don't seem to work in this situation. Construct ideals in $\mathbb Z[x]$ with a given least number of generators Separable Hilbert space have a countable orthonormal basis I want to show that every an infinite-dimensional separable (contains countable dense set) Hilbert space has a countable orthonormal basis.  I know that every orthogonal set in a separable Hilbert space is countable, it is help me with the proof? View only the new entries in a growing log file GDAL HDF4 Driver on Linux System I'm running code that works with MODIS HDF4 datasets on a Debian Linux distribution.  I am also running this code on a Windows machine.  On both the Windows and the Linux machines, I have the most recent GDAL version (gdal 1.11.1, np19py27_1), however on the Linux machine, GDAL doesn't seem to recognize HDF4 Drivers... it won't load or process any of the HDF4 datasets that are easily processed on the Windows machine (unfortunately this machine doesn't have enough space to run the full code).  Has anyone else encountered this problem?  Do I need to install an additional module on the Linux system? Class method differences in Python: bound, unbound and static What is the difference between the following class methods?  Is it that one is static and the other is not?  class Test(object):   def method_one(self):     print "Called method_one"    def method_two():     print "Called method_two"  a_test = Test() a_test.method_one() a_test.method_two() I am trying to change the page size in the QGIS 3.0 Composer but I am not able to see the Composition tab.  I have right clicked an empty space in the toolbar but did not see anything about composition.  I am using Windows 7.  I tried looking at the QGIS docs but they are still in testing. Table of Contents with Chapter I'm attempting to modify the Table of Contents in my document. Currently, chapter one in my document is listed as   1   Introduction   What I would like to see is  Chapter 1   Introduction   Seems like an easy enough thing to ask for, but can't seem to find a good way to do this. Any feedback would be most appreciative. Time traveler asks archaeologist for help in transporting a girl from dinosaur Earth to present day Many decades ago, I read a short story about a time traveler who asks an archaeologist for help.  He convinces the archaeologist that he can time travel by bringing him back a freshly killed dinosaur (small one.)  The time traveler needs help because when traveling back in time to the age of the dinosaurs he met a girl and wants to transport her back to the present.  However only one person can travel in time at a time so he needs the archaeologist at the other end to wait for the girl.  The archaeologist agrees to help.  Unfortunately after the traveler goes back he and the girl find themselves in the middle of a battle between aliens on Earth.  They are chased by a dinosaur and never make it back to the present.  The archaeologist meanwhile is digging for evidence that the traveler went back in time and the story or my recollection of it ends with that. From :     Importantly, the DDH assumption does not hold in the multiplicative group $\mathbb {Z} _{p}^{*}$, where $p$ is prime. This is because given $g^{a}$ and $g^{b}$, one can efficiently compute the Legendre symbol of $g^{ab}$, giving a successful method to distinguish $g^{ab}$ from a random group element.   The only way I can think of to distinguish $g^c$ from $g^{ab}$ is:    If $\left(\frac{g}{p}\right)=-1$, then $\left(\frac{g^{ab}}{p}\right) = 1$ if and only if $a$ or $b$ is even (which is $3/4$ of the times). So if $\left(\frac{g^c}{p}\right) =-1$, probably $g^c\neq g^{ab}$. Nothing is certain.   How'd do you compute $\left(\frac{g^{ab}}{p}\right)$ given $g^a$ and $g^b$? PTR record won`t update When a player joins the server, this command block (containing gamemode 2 @a) puts them into gamemode 2/adventure mode. How can I change this so that only non-admin/not "opped" players' gamemode gets changed? I would like to revise the default new user registration form in Drupal 7. Rather than to requst "username", I want to request "full name" with helper instructions to enter the text "username is your full name as you would normally use it."  There may be some other minor formatting changes I would like to make as well.  I cannot find an admin menu item to access anything relating to this question. And I am unable to locate a file within any director that has any text that would indicate it is the source for the new user registration form.  I realize this is a bit unconventional, however it is useful for our needs. I am aware of a module that allows the input of First Name / Last Name, but in processing it changes the input to first initial/lastname, ie Tom Thumb = username of "tthumb". The module "Realname Registration" would be just what I am looking for if it would only translate the username the same as the input.   That wouldn't necessarily solve the other formatting edits, but I would be very happy just to be able to manually edit the registration form help text under the username field, instructing the new user to register using thier real name.  Thanks for any help that you can provide.  J.M.