I understand that the terms snap, crackle and pop aren't exactly official terms but I needed a compact title about various derivatives of position with time.  A body at rest has all it's time derivatives of position equal to $0$. When it starts to move it gains velocity. So it's velocity has changed implying acceleration. Acceleration has changed implying jerk and so on. So even the $1,000,000th$ derivative is not 0. Am I right about this or is there some flaw to my method?  If I'm right about this. So once the body starts to move why is it that we only consider the derivatives up to acceleration, hardly consider jerk and rarely mention higher derivatives? Intuition tells me that one the body starts to move, any change in speed can be attributed to acceleration and that takes care of everything and we need not consider anything beyond. But I would like to have a feel of the real answer. An amateur like me told me that higher derivatives are not considered for such problems and not even for some differential equations as the derivatives are small and ignoring them will result in a negligible error. The answer feels sound for engineering but not for theoretical physics. Is she right to say it's okay to ignore tiny values?  Also does it signify anything interesting when derivatives up to the 1000th derivative are all varying?   Either this is a valid question or I'm fundamentally flawed. Forgive me for wasting your time if it's the latter.  EDIT:  this is not a duplicate in any way. The question similar to mine assumes advanced knowledge of lagrangian mechanics and the category it came under was differential geometry and field theory. My question is on Newtonian mechanics and neither do I have the mathematical background to understand the answers to the other question. In fact I don't know enough Mathematics to understand the other question itself. ;-)
What is the reason for the observation that across the board fields in physics are generally governed by second order (partial) differential equations?    If someone on the street would flat out ask me that question, then I'd probably mumble something about physicists wanting to be able to use the Lagrangian approach. And to allow a positive rotation and translation invariant energy term, which allows for local propagation, you need something like $-\phi\Delta\phi$.  I assume the answer goes in this direction, but I can't really justify why more complex terms in the Lagrangian are not allowed or why higher orders are a physical problem. Even if these require more initial data, I don't see the a priori problem.  Furthermore you could come up with quantities in the spirit of $F\wedge F$ and $F \wedge *F$ and okay yes... maybe any made up scalar just doesn't describe physics or misses valuable symmetries. On there other hand in the whole renormalization business, they seem to be allowed to use lots and lots of terms in their Lagrangians. And if I understand correctly, supersymmetry theory is basically a method of introducing new Lagrangian densities too.   Do we know the limit for making up these objects? What is the fundamental justification for order two?
Ubuntu 16.04 has been hanging on me ~1x per day.  This happens when I am in the middle of web browsing or using a desktop application, not when booting.  When it does, the mouse pointer will still move freely, but clicking or keystrokes have no effect on my system until I do a hard reboot.  What is the best way for me to debug this?  Here is some information:  selah@selah-Precision-Tower-5810:~$ uname -a Linux selah-Precision-Tower-5810 4.4.0-59-generic #80-Ubuntu SMP Fri Jan 6 17:47:47 UTC 2017 x86_64 x86_64 x86_64 GNU/Linux   Also, in case it is relevant, I have a "very big" monitor, a Dell 42" at 3840x2160 resolution.  selah@selah-Precision-Tower-5810:~$ lspci | grep VGA 03:00.0 VGA compatible controller: NVIDIA Corporation GM107GL [Quadro K2200] (rev a2)     UPDATE:  Following Artyom's advice I found the following message in my error logs:   Apr 27 09:47:25 selah-Precision-Tower-5810 kernel: nouveau 0000:03:00.0: fifo: SCHED_ERROR 0a [CTXSW_TIMEOUT] Apr 27 09:47:29 selah-Precision-Tower-5810 kernel: nouveau 0000:03:00.0: fifo: SCHED_ERROR 0a [CTXSW_TIMEOUT] Apr 27 09:47:33 selah-Precision-Tower-5810 kernel: nouveau 0000:03:00.0: fifo: SCHED_ERROR 0a [CTXSW_TIMEOUT]   Which has let me to this bug which describes similar behavior: Does $a\mid bc$ imply $a\mid b$ or $a\mid c$? I am not sure I understand this I just to an explanation to this question:  If $a, b, c \in \Bbb{Z}^+$ and $a\mid bc$, does it follow that $a\mid b$ or $a\mid c$? Break a long command to multiple lines I got a shell script and inside I got the command as below #!/bin/sh sh ../jboss/bin/standalone.sh --server-config=standalone-full.xml -Djboss.node.name=node1 -b 0.0.0.0 -bmanagement 0.0.0.0  How can I break the line to multiple lines for better understanding and management #!/bin/sh sh ../jboss/bin/standalone.sh    --server-config=standalone-full.xml   -Djboss.node.name=node1   -b 0.0.0.0   -bmanagement 0.0.0.0  Tried with backslash at the end of each line and it doesnt work. I am trying to understand the permission usage for the cp command in unix.   What are the permissions required for copying a file into a directory What are the permissions required for copying out of a directory?   I'm assuming for my first question, the directory will need execute permissions to perform the operation and the file will need read permissions to read the binary of the file and then the output file will need write permissions.  For the second the directory itself would need execute permissions to perform the copy operation and the file would need read permissions to extract the data from the file.  Can anyone tell me if my logic is flawed? How do I close a connection early? I'm attempting to do an AJAX call (via JQuery) that will initiate a fairly long process. I'd like the script to simply send a response indicating that the process has started, but JQuery won't return the response until the PHP script is done running.  I've tried this with a "close" header (below), and also with output buffering; neither seems to work. Any guesses? or is this something I need to do in JQuery?  &lt;?php  echo( "We'll email you as soon as this is done." );  header( "Connection: Close" );  // do some stuff that will take a while  mail( 'dude@thatplace.com', "okay I'm done", 'Yup, all done.' );  ?&gt; Why wouldn't the `which` command work for `cd`? I can't find the executable for `cd` either! I tried which cd and it didn't give a path but instead returned the exit code 1 (checked with echo $?). The coreutil cd itself is working, so the executable should be there, right? I also ran a find for cd, but there was no executable file shown. How is it implemented then?  Update:  I don't know if I should ask this in another post but since I think it is good here, I'm expanding (?) the post... So the answer was actually quite simple, there's no executable for that — because it's a builtin — But I've found some builtins (bash shell in Fedora) have the executable files! So builtin -> no executable isn't right I suppose? Maybe an answer explaining what builtins actually are (builtin commands?), which actually is the matter here, rather than focusing more on cd... Some good links posted previously indicate that builtins are not programs... so what are they? How do they work? Are they just functions or threads of the shell? Max Planck, arguably the leading theoretical Physicist of his day, apparently used of experimental data to formulate his equation for , which was a major step in the birth of quantum mechanics. For this seminal event of the 20th century, I would expect a detailed explanation of how Planck arrived at his conclusion that energy MUST be quantized. I've even read his Nobel lecture but was non the wiser.  Can some kind person please explain it, or give me even just a hint? How to Evaluate $\int e^{2x}\sin(3x)\ dx$? Integration by parts - unless I'm not thinking straight - doesn't seem to help here.. If I pick either of the functions $e^{2x}$ or $\sin(3x)$ to be $u$ or $dv$, they don't change to anything easier... $e^{2x}$ stays in the form $e^x$ and $\sin(3x)$ flip-flops between $\sin(3x)$ and $\cos(3x)$, neglecting the constant that gets introduced.  So how can I approach solving this? $u$-substitution doesn't seem to be something I can use either. Show that not all 5 cycles in $A_5$ are conjugate in $A_5$ This is a practice question (not assignment). One thing I am wondering is what this question exactly means. From my understanding, the conjugate of $a \in A_5$ is $gag^{-1} \in A_5$ where $g \in A_5$. I was trying to look at a similar question here on MSE and someone mentioned $(12345) \in A_5$ is not conjuagte in $A_5$. So does that means there exists a $g \in A_5$ such that $g(12345)g^{-1} \notin A_5$ (I am guessing this is incorrect since $A_5$ is a group). I am also away of the property that $g(12345)g^{-1} = (g(1)g(2)g(3)g(4)g(5))$. What is the current state of apple device (iPhone, iPod, etc.) support? My sister, cousins, and other relatives speculate that my mom's grandmother was Jewish (for various reasons). I've heard people say at times things like, for example, "I'm 50% German" or "I'm 25% Swedish." This has to do with their ancestry. But, how exactly is this calculated? Say for example that my mother's paternal grandmother was indeed 100% Jewish, what would that make me and my siblings, and how is it calculated? What is the easiest way to export just the selected objects in Illustrator? The title says it all, I want to know what the simplest way to export the selected objects.  In Inkscape, there is a menu option called export selected which does just this.    The aforementioned option lets you export the selection as a composite image or as a batch of individual images.  Both would be nice, but in this scenario I want to export the selected objects as a single image.  I can already create a new document, and paste in the selected items.  I am looking for a way that is easier than this.  How can I save / output / export only the objects I currently have selected, to an image file, in Adobe Illustrator CS5? From :  Error propagation It was common to discuss the &quot;error propagation&quot; properties as a selection criterion for a mode of operation. It might be observed, for example, that a one-block error in the transmitted ciphertext would result in a one-block error in the reconstructed plaintext for ECB mode encryption, while in CBC mode such an error would affect two blocks.  I read  similar post before. And I can understand that in CBC decryption, only two blocks are affected due to error propagation (error in 1 block). But, for the same case in CBC encryption, why are still only two blocks affected? It looks like all the following blocks will be affected. I have to do some manual reordering or rows in Excel and cut/paste is too hard to use. I'm looking for something that would enable me to use drag'n'drop or to add some buttons to move-up/down move-top/bottom. Casting nines and elevens in other bases (radix) and doing check sums for binary What is the difference between a symbolic link and a hard link? Recently I was asked this during a job interview. I was honest and said I knew how a symbolic link behaves and how to create one, but do not understand the use of a hard link and how it differs from a symbolic one. An example of a sequence of Riemann integrable functions $(f_n)$ that converges pointwise to a function $f$ that is not Riemann integrable. Where did the pardon come from? In the  episode  (S04E08), Barristan Selmy is presented with a Royal Pardon supposedly signed by the late Robert Baratheon for Ser Jorah Morment by a lowly boy of Meereen.  However, it is a bit confusing to me as where this actually came from.  Is this the same pardon that Jorah had towards the beginning of the series while Robert was actually alive, or is this pardon one that Tywin actually forged and wrote in a previous episode (remember he asks Mace Tyrell for a quill after learning about Dany's recent actions and allies).  It being from Tywin makes sense but this point is brought up by Jorah and then defeated a sentence later as he himself states it is not a forged Pardon.    So which is it and why would Jorah say it is not a forged copy if it indeed is? Can we know the fundamental nature of space and time? Ability to retract reopen/delete votes It seems that now we can retract close votes but we cannot retract reopen votes or delete votes.  I am trying to retract my reopen vote  but it does not allow me to.  Can we have that ability?