We know that newtonian mechanics is described by a set of second order differential equations. This leads also to the principle of determinism that every trajectory is determined by initial conditions on position and velocity. How good is the experimental evidence on that that there is no third derivative term? (In the same spirit like ppl try to look for an electric field inside a conductor to test Coloumbs law).  Edit: to the downvoters: please comment what is the problem with this question? Using experiments to determine null-results is part and parcel of physics.  Edit: my question is not a duplicate of  but related. The other question asks about theoretical grounds. I am asking about experiments conducted and the limits they impose on higher order derivative terms.  Edit: To clarify the question: we generally accept Newtons second law of motion $$ m \ddot {x}  = F(x, \dot{x}, t) $$ this implies that specification of position and velocity uniquely defines a solution (so called principle of determination).  How precisely do we know this to be true in the sense of what if we assume instead $$ const\dddot {x} + m \ddot{x} = F $$ then what are the experimental limits on the constant 'const'. How close to zero is it determined from actual experiments.  Note: I still diagree this is a duplicate. For example one answer which goes in the direction from the linked question:  is 'Because the second derivative is fully determined by the external force, it is an experimental fact.' This goes in the right direction, but my question really is: which experiment gives the highes accuracy on this, where was it published and to what precision does it prove this fact. My question is in the same spirit like questions 'what is the current upper bound on the photon mass' except for a different topic in physics.   Thought experiment to test this: build a rail-gun, place it in a vacuum-chamber and shoot a parabola using the earth gravitational field. Use constant acceleration while still on the rail. Now place the object at a different start position on the rail but also change the constant acceleration so that at the release point (exit nozzle of the gun) the object has the same velocity. Will the object alway hit the same spot? (of course, if the equation of motion is a second order differential equation; it wont if the trajectory depends on the initial acceleration). Of course we know that it will not depend on initial acceleration, but to what precision do we know that?
Why is the Lagrangian a function of the position and velocity (possibly also of time) and why are dependences on higher order derivatives (acceleration, jerk,...) excluded?  Is there a good reason for this or is it simply "because it works".
We are provided with a string A (may contain repeated characters as well ). One needs to make all possible permutations of A , and find out how many pairs of strings chosen from these permutations are not similar.  Two strings are similar if we can make both of them exactly same by carrying out at most 1 swap in each of them .  Example :- if we are provided with string abcd  , then for permutation abcd , the permutations which are not similar to it are bcda , bdac , cadb , cdba , dabc , dcab . Similar is the case for other permuations as well. So overall number of desired pairs are 24*6=144 .  I tried solving it for each possible pair by approach mentioned here     But as the permutations can be large enough , I need a better approach of solving this. Similar to this question posted in August 2014:       Has the fact that  (as  in The Fires of Pompeii, and  in Torchwood’s Children of Earth season) yet been addressed/explained either in, or out of universe? Screen brightness isn't taking effect on a Lenovo Z570 My Lenovo Z570 has two GPU's, nVidia and Intell. Brightness control has no effect what so ever over the screen brightness, and because I've had some major issues in the past when I was trying to fiddle with nVidia drivers and settings, and I wanna be cautious now. I haven't find similar questions referring 14.04 LTS with similar configuration as mine.   I've read that it could be fixed by adding/changing content in xorg.conf but when I run  sudo gedit /etc/X11/xorg.conf   the file comes out to be absolutely empty. What do I need to do, what do I need to add to it and not get my laptop screwed with a black screen again? I have an ex who has posted nude photos of me online in the past, linked to my online social media, and posted my full name and where I live. I am concerned he may do so again once he finds out I'm now in a PhD program (he's very jealous of any success I have), and may link to my school bio page, or worse.   Revenge porn is illegal in my state, and the case against him is currently pending. I have also gotten the photos taken down with a DMCA letter (I hold the copyright over the photos in question). At this point, I am concerned with how a future attempt could affect my career.  I can handle the embarrassment now that I've been through it once, so if that's the biggest concern, I can deal. I just don't want to lose a career over it, given how small academia really is and how a reputation might follow one around.  My question is, if I don't change my name (I've considered this, assuming I can keep him from finding out) and my photos are circulated and discovered by faculty or students, how likely am I to be thrown out of my PhD program or later lose a job as an untenured prof? Is a name change worth it?   (If it makes any difference, they are essentially just topless portraits; I'm not engaged in any sexual activity or anything weird, and were taken 10 years ago when I was very young and foolish.) What's wrong now with fwupd? It was OK since May 1st, 2020 on newly installed Ubuntu 20.04 The following packages have been kept back:    fwupd  0 upgraded, 0 newly installed, 0 to remove and 1 not upgraded. I frequently cross this issue, and always have to google for an answer. Does anyone have a permanent fix for BADSIG errors from apt-get?     W: GPG error:    lucid   Release: The following signatures were   invalid: BADSIG 54422A4B98AB5139   Oracle Corporation (VirtualBox archive   signing key) Generally accepted root mean square (RMS) error for rectifying topographic maps This is a generic inquiry on the common practice/standard for determining the acceptable values of RMS when georeferencing topographic maps.  Is there an absolute value?  Some literature suggests that it should be "less than or equal to 1/2 of the side of a cell which make up the total resolution of the image." How to get the current time in Python What is the module/method used to get the current time? How to install Microsoft fonts on Ubuntu 16.10? Linking search box to dataset column in Carto? The search box in a published map of CartoDB isn't linked to the dataset which is shown in the CartoDB map. How can I link the search box to a certain column of a dataset? On iOS, while watching a video in YouTube app, when I go to the Home Screen, the video stops playing. I found no setting to enable it.  I know it is available for Android, but is there a way to do so in iOS? Is there any setting, or a 3rd party app that I can use? I recently changed my username to Undo. I was amazed when I pressed Submit and saw that it actually went through - surely someone somewhere was using this same username.  Out of curiosity, I then search the SO user list for Undo - and found  with Undo as thier name. They have 50 rep. I have around 1,500.   Is there some kind of pecking order, I.e. a high-rep user can 'steal' a low-rep user's name? Or is this a bug?  Or can two users have the same username without causing the SO servers to go down in a burning ring of fire? I added this to /etc/crontab on a few different linux &amp; freebsd systems:  # monthly reboot: 3rd Tuesday of every month 56 07 15-21 * 2 root /sbin/shutdown -r now   I want a reboot on the 3rd TUESDAY of every month.  However, all the systems rebooted on the 3rd Wednesday of this month (the 19th).  What am I doing wrong?  Update: Thanks to Ranon's answer below, looks like the below revision will work, can anyone confirm or is there an even better way of doing it?  # monthly reboot: 3rd Tuesday of every month 56 07 15-21 * * root test $(date +\%u) -eq 2 &amp;&amp; /sbin/shutdown -r now Two different expansions of $\frac{z}{1-z}$ This is exercise 21 of Chapter 1 from Stein and Shakarchi's Complex Analysis.  Show that for $|z|&lt;1$ one has $$\frac{z}{1-z^2}+\frac{z^2}{1-z^4}+\cdots +\frac{z^{2^n}}{1-z^{2^{n+1}}}+\cdots =\frac{z}{1-z}$$and   $$\frac{z}{1+z}+\frac{2z^2}{1+z^2}+\cdots \frac{2^k z^{2^k}}{1+z^{2^k}}+\cdots =\frac{z}{1-z}.$$  Justify any change in the order of summation.   [Hint: Use the dyadic expansion of an integer and the fact that $2^{k+1}-1=1+2+2^2+\cdots +2^k$.]  I don't really know how to work this through. I know that $\frac{z}{1-z}=\sum_{n=1}^\infty z^n$ and each $n$ can be represented as a dyadic expansion, but I don't know how to progress from here. Any hints solutions or suggestions would be appreciated. I have a WordPress site which is 90% based on images.  I've installed Wp-Super-Cache, now it seems to load a little bit faster.   I've made a speed test on Pingdom Tools:   Page size 4.7MB Load time 5.09s Requests 153 Perf. grade 74/100   And also the Time Spent per Content Type:   Image    88.23%     So the problem is obviously the images.   My plan is to try as much as I can to optimize the images in terms of size, and then to add CDN support.  Is this enough in terms of improving the loading of images? How can I install a different version of Python using apt-get?  Obviously I realise I can install using the source tar ball, however I would prefer not to install from source and instead use the package manager, as that's what it's there for. Surely somewhere reputable builds .deb files for the latest Python releases (why python.org don't is beyond me) that I can reference.   What do I need to do to reference them and what issues might it create when upgrading to the next version?  If there is no way except for building from source, is there a (pseudo) package that I can can install that will provide all of the dependencies needed without having to find and install each individually? So that I don't get:  The necessary bits to build these optional modules were not found: _bz2                  _curses               _curses_panel       _dbm                  _gdbm                 _lzma               _sqlite3              _ssl                  _tkinter            readline              zlib Shortest path from points in one layer to points in another layer via roads in QGIS I'm looking for a way to calculate the shortest path from addresses to subway stations via a network of roads.  I have the , however, the addresses and subway stations are point layers that do not overlap with vertices in the roads layer.  In QGIS, is there a way to calculate the shortest distance from the address/subway station points to the roads, create vertices at those locations, then calculate the shortest distance via the roads network?   black squares - addresses white circles - subway stops gray lines - roads Image uploads from the editor strip preceding line breaks Recently, using the image uploader in the post editor has starting stripping preceding line breaks; placing the image directly after any previous text instead of at the current cursor position. This means that the inserted image is placed inline as part of the previous line of text rather than in a new paragraph as it did previously...  Before inserting the image (note the cursor position):        After inserting the image:        This also happens after the Markdown for a horizontal rule, which destroys the rule and gives us a bunch of hyphens followed by an image instead:        Seems the behaviour is a bit inconsistent... Sometimes I get the behaviour shown above and sometimes it leaves a single newline, I'm not sure when or why but single line breaks are ignored in Markdown so the rendered result is the same regardless.  Obviously it's useful to be able to have inline images, but I'm pretty certain most images aren't intended to (and shouldn't) be. Student missing exam for “medical reasons” I posted a comment to a duplicate question on . But I decided to delete it. Afterwards I voted as duplicate and thought a comment would be generated like     possible duplicate of ...   But it didn't. My guess is that the duplicate-comment won't be generated if a comment exists with that link, even if deleted.