By meaningful I mean experimentally falsifiable.
I was surprised to only recently notice that      An object of any density can be large enough to fall within its own   Schwarzschild radius.   Of course! It turns out that supermassive black holes at galactic centers can have an average density of less than water's.  Somehow I always operated under the assumption that black holes of any size had to be superdense objects by everyday standards.  Compare the Earth to collapsing into a mere 9mm marble retaining the same mass, in order for the escape velocity at the surface to finally reach that of light.  Or Mt. Everest packed into one nanometer.  Reading on about this , it increases proportionally with total mass.  Assuming matter is accumulated at a steady density into a spherical volume, the volume's radius will only "grow" at a cube root of the total volume and be quickly outpaced by its own gravitational radius.  Question: For an object the , what would have to be its diameter for it to qualify as a black hole (from an external point of view)?  Would this not imply by definition that:   The Earth, Solar system and Milky Way are conceivably inside this black hole? Black holes can be nested/be contained within larger ones? Whether something is a black hole or not is actually a matter of perspective/where the observer is, inside or outside?
Not getting any reading from FTDI UMFT201XB USB-to-I2C module I got the  in order to interface with an I2C peripheral through a USB port on my Windows 7 computer.  The VCP drivers seem to install correctly, and a COM port is assigned to the module, and can be opened by a terminal emulator. However, I cannot seem to get any signal in or out of the module. That is, I see no activity when I send data through the port, or receive any data when I connect an I2C device to it (this was debugged using a scope). I have also verified that the RESET isn't on.  I found very little helpful information out there on how to get this module to work, so if anyone has experience with it, or with similar FTDI modules, my question is: what are the steps that I need to take in order to get the module to communicate? In a case of mine a very high (compared to the video stream) resolution graphical frame (saying "access denied" (when my IP changes)) can appear instead of a video stream, which makes VLC window to resize, getting bigger than my screen is. This annoys me. Can I set up VLC to never resize its window when I don't do it myself and resize content instead? Is there any way to get the windows cmd shell to expand wildcard paths? Occasionally, the cmd shell's inability to expand wildcard paths can really be an inconvenience. I had to pass 100 files in a directory to a program, and couldn't type *.ext. Instead, I used mingw's 'ls' to dump the list to a file, then replaced newlines with spaces, copied and pasted into cmd. Quite a nightmare.  I suspect the answer will be no, but has anyone dealt with this or come up with any way to make this easier? How can I change Win 10 protected registry entries? SQL query to convert columns into rows Is it possible to resize an image in an answer? For example,  has  that should have the image in the answer, but it's too big.  Is there a way to handle resizing? How do I remove the Unity launcher? How can we remove the launcher that come with Unity on this new Ubuntu version ? Theoretical proof of the constant of speed of light $c$ in vacuum in all frames of references Is there any theoretical proof for the constant speed of light in all frames of references? I know it is experimentally proven but just curious. biblatex: separator for citing multiple sources, some of them with page, some not I'm using biblatex for my references.  Normally, if I use \cite{source1, source2, source3}, I get a citation like  [3, 45, 98]   If I now want to give a page number for one of them, it looks confusing imho, as I should get (did not try it out up to now, honestly)   [3, 45, 78, p. 23f, 98]   So imho it would make sense to change one of the separator from a comma to e. g. a semicolon like:  [3; 45; 78, p. 23f; 98]   Question 1: Does that make sense, or are there other conventions for citing sources with and without page numbers together?  (Up to now I collected the citations without page number in one cite command and added singular \cite[][p. xy]{} commands for those with page numbers., so I'd get:   [3, 45, 98][78, p. 23f]   )  the \cites[]{}[]{}[]{} could also do that, but it also uses the same separators for entries and postnotes.  Question 2: How could I change the separator globally for those number-citations from comma to semicolon in biblatex? Does the derivative of a continuous function goes to zero if the function converges to it? Physicist here. I am puzzled by a question: looking at a continuous function $g :\mathbb{R} \rightarrow \mathbb{R}$ that goes to zero at infinity, I am interested in the behavior of its derivative $\beta = g'$. Precisely, does it go to zero too? By writing on paper it looks like: $$ \beta(+ \infty)=\text{lim}_{x\rightarrow \infty}\text{lim}_{h\rightarrow 0} \frac{g(x+h)-g(x)}{h}$$ And if I can invert the two limits, I get what I expect: $\beta(+\infty)=0$, so I was curious about the hypothesis behind this permutation. Is the requirement of continuity enough? Thanks. From Geneva airport to Lausanne station On September 4, I will be arriving in Geneva by airplane at approximately 11 AM. After that, I need to go to Lausanne. I have two questions:   Do I need to buy a train ticket online, or can I buy it directly at the station without any problems? (Problems such as: the trains are always full, it's not permitted to buy a ticket etc.) Moreover, are the tickets only for a specific train or it is like "you can board any train from Geneve to Lausanne with this ticket"? How do I get from the airport to the Geneva train station (as low a budget as possible, I guess walking is not an option though), and how much does it cost?   I'd appreciate answers from people who have been there, but if you're able to find an exhaustive link from any website that's okay too. How can I check for an empty/undefined/null string in JavaScript? I have a question related to modeling short time-series. It is not a question , but how. What method would you recommend for modeling (very) short time-series (say of length $T \leq 20$)? By "best" I mean here the most robust one, that is the least prone to errors due the fact of limited numbers of observations. With short series single observations could influence the forecast, so the method should provide a cautious estimate of errors and possible variability connected to the forecast. I am generally interested in univariate time-series but it would be also interesting to know about other methods. How can I account for a nonlinear variable in a logistic regression? How can I account for a nonlinear independent variable in a logistic regression?  For example, consider this data set:  b1  b2  b3  b4  b5 1   1   0   0   20 0   1   0   0   20 1   0   0   0   13 1   1   1   0   8 1   1   0   1   5 0   1   0   1   4 1   1   0   1   5 0   0   0   0   8 0   0   1   0   13 1   0   0   1   20 1   0   0   0   29 1   1   0   1   40 1   0   0   0   53 0   1   1   0   68   Suppose I gathered some data like the above (suppose I had 10,000 rows) and I want to use them to predict future sets of similar data with an equation generated by a logistic regression. I get the above data. My independent variables are b1 through b5. By looking at the data, I can clearly see that independent variables b1 through b4 are binary (maybe they are male/female, rent/own, etc).   However I see that b5 is clearly not binary. Upon graphing it and looking at the numbers I determine that the b5 variable has a bathtub shaped U curve with an equation of b5=(x-4)^2+4.   I understand that using the b5 variable as it is would screw up my logistic regression - since any interval independent variables must have a linear relationship with the dependent variable.   Yet, I must account for the variable b5 in my data set while doing a logistic regression for it to be accurate and predict well (right?).  Given the above data, how would I go about making a predictive model with a logistic regression? Any references online or in books would greatly be appreciated as I am having trouble finding a good explanation of the above.  Cheers =)  EDIT:  Sorry if my question is unclear.  Consider this: Suppose we had the following data on many people:  Y: Whether they had a stroke before the age of 50 or not 1. Whether they own a pet or not. 2. Whether they graduated college or not. 3. Whether they are male or female. 4. The number of hours they exercise every week.  We want to train a logistic regression model based on historical data to predict if someone in the future with the same data will be more apt or not to have a stroke before the age of 50.  The problem I am having is with the last variable. A continuous ratio variable like "number of hours exercised each week."  Exercising more each week may have diminishing returns on health and thus having a stroke. For example decreasing an increasing rate. Or maybe (totally made up) exercising a little bit is really good for you, exercising a moderate amount is really bad for you, and exercising a lot is really good for you again. We might have a U shaped curve like (x-4)^2+4 for example when plotting health to exercise.   I would image that having a curved, non-linear independent variable in a logistic regression like the one I described above would cause problems. Am I right? And if so, what kinds of things can you do to still include the variable in the logistic regression. Perhaps a transformation? Is that all? Cycle Normal Pass in Camera Space For me, it is pretty clear that $a + \overline{a}*b = a + b$, because the first $a$ in the or will make sure that if the second term must be 'evaluated', $a$ will always be false, and therefore won't matter in the and - probably because I'm a programmer and it is very common to see this unnecessary cluttering in long if-else structures.  I can easily prove it with the truth table as well, just make both expressions', and turns out they are identical.  But I was looking for a 'algebraic' way to prove it. That is, something using the basic operations properties like the fact that they are transitive, commutative, associative, etc. For example, if I was to prove this other simple identity $a + a*b = a$ I would simply do something like:  $a + a*b = a*(1 + b) = a*1 = a$.  Is there a way to also prove the former using this algebraic operations, without resorting to the truth table? Bottom of tool shelf grayed out how do I get my code to use the value of the $HOME variable? I'm trying to put together a generic script that will check the existence of several key directories for various users on different servers. Additionally, I want to leverage each user's $HOME variable.  For eg, let's say this were true:   on server 1: jdoe's home is /home/jdoe  on server 2: jdoe's home is /opt/jdoe2 server 3 hasn't been built yet; we won't know where they build his $HOME until the server is built. on server 4: mysql's home is /opt/home/mysql   This is what I have for my important directories (ordered from most to least impt):  $ cat mylist.txt $HOME/most_impt_dir1 $HOME/most_impt_dir2 $HOME/most_impt_dir3 $HOME/misc $HOME/junk   ...I want to find the most impt dir owned by this user.   Here's what I'm trying:  for i in `cat mylist.txt` do    if [[ -O $i ]] &amp;&amp; [[ -d $i ]]; then     echo "found it: $i"     break   else     echo "$i is not it."   fi  done   The above code does not work for anything in my list because it is literally checking for dirs beginning with $HOME. How do I get my code to use the value of the user's $HOME variable? Sync folder with Android device I would like to have a folder with all my music which is automatically synced on my Android device (Wifi only, plugged in only, like in SugarSync). Is there any hope for this feature to be implemented in the near future.  This would actually make me pay for U1. I am not experienced in Number Theory but what I know is that some results of this filed are applicable in other areas, e.g. algebra. For sure FLT made (and makes) people be interested in Number Theory leading to the development of new methods which can be themselves applied not only for the proof of FLT (like financial problems motivated somehow development of stochastic analysis). I am interested - if there are applications or implications of FLT itself?  More precisely: if the fact "for each $n\geq3$ there are no integer solutions of $a^n+b^n=c^n$" leads to solutions of problems which are not in the field of Number Theory?   I would specify that I wonder about some problems which are already formulated: since FLT is known for more then 300 years I am pretty sure that there were formulated hypothesis which follow from FLT directly (if there are such hypothesis not in the field of Number Theory).