My question concerns an aspect of the pole-barn paradox that, to my knowledge, has not been discussed so far. So rejecting the question as &quot;duplicate&quot; is incorrect, in my view. Here is the edited version: Einstein's 1905 postulates entail that unlimitedly long objects can be trapped, in a compressed state, inside unlimitedly short containers: &quot;These are the props. You own a barn, 40m long, with automatic doors at either end, that can be opened and closed simultaneously by a switch. You also have a pole, 80m long, which of course won't fit in the barn. [...] So, as the pole passes through the barn, there is an instant when it is completely within the barn. At that instant, you close both doors simultaneously, with your switch. [...] If it does not explode under the strain and it is sufficiently elastic it will come to rest and start to spring back to its natural shape but since it is too big for the barn the other end is now going to crash into the back door and the rod will be TRAPPED IN A COMPRESSED STATE inside the barn.&quot;  One of the comments on the previous version of the question is as follows: &quot;Note that the pole is not compressed by the Lorentz-FitzGerald contraction, it's compressed by colliding with the back door at 0.866c&quot; Not true. The compression occurs before colliding - the long object is still flying inside the short container when the doors are closed. That is, the compression is purely relativistic. Then the trapped object will &quot;start to spring back to its natural shape&quot;. How much energy will be released if a 1 km object, compressed to 1 cm, restores its original length? Even the question sounds absurd, let alone the answer. If such trapping is absurd, we have reductio ad absurdum: the absurdity of the logical consequence shows that at least one of the postulates is false. Is trapping unlimitedly long objects, in a compressed state, inside unlimitedly short containers absurd?
Suppose the proper length of a train is longer than that of a bridge, and the bridge can't bear the total weight of the train but can bear it partially. As the train goes very fast, it becomes shorter than the bridge and it can be entirely on the bridge. As a result, the bridge will collapse. However, in the train's frame, the train is even longer than the bridge, and it is only partially on the bridge; so the bridge will not collapse. What is the solution to this paradox?
How do I boot from ISO file stored on hard disk? New figure environment I am writing my PhD thesis. In my manuscript I have Figures in the text and Photographic plates (a figure of figures) in the annexes. The two elements are different and I would like create a new environment of Plate that follows the same structure of the Figure environment. Where can I find the Figure environment to modify it?  The new environment table should have exactly the same structure than the figure environment but replacing the word figure by the word Planche (in French). What are the zero divisors of $C[0,1]$? Suppose you have a ring $(C[0,1],+,\cdot,0,1)$ of continuous real valued functions on $[0,1]$, with addition defined as $(f+g)(x)=f(x)+g(x)$ and multiplication defined as $(fg)(x)=f(x)g(x)$. I'm curious what the zero divisors are.  My hunch is that the zero divisors are precisely the functions whose zero set contains an open interval. My thinking is that if $f$ is a function which is at least zero on an open interval $(a,b)$, then there exists some function which is nonzero on $(a,b)$, but zero everywhere else on $[0,1]\setminus(a,b)$. Conversely, if $f$ is not zero on any open interval, then every zero is isolated in a sense. But if $fg=0$ for some $g$, then $g$ is zero everywhere except these isolated points, but continuity would imply that it is also zero at the zeros of $f$, but then $g=0$, so $f$ is not a zero divisor.   I have a hard time stating this formally though, since I'm only studying algebra, and not analysis. Is this intuition correct, and if so, how could it be rigorously expressed? I know than an ellipsis can be used to show a broken sentence, the same way an em dash can be used. What I don't know is that if the two are interchangeable and it is writer preference or if different meaning is conveyed by their use.  Are ellipses and em dashes commutable? What registers to save in the ARM C calling convention? It's been a while since I last coded arm assembler and I'm a little rusty on the details. If I call a C function from arm,  I only have to worry about saving r0-r3 and lr, right?  If the C function uses any other registers, is it responsible for saving those on the stack and restoring them? In other words, the compiler would generate code to do this for C functions.   For example if I use r10 in an assembler function, I don't have to push its value on the stack, or to memory, and pop/restore it after a C call, do I?  This is for arm-eabi-gcc 4.3.0. How do I connect to a MSSQL database using Perl's DBI module in Windows? How do I connect to a MSSQL database using Perl's DBI module in Windows? I wonder if it is possible to consider $\mathbb R$ as a Cartesian product $X\times X$ for some set $X$. From the point of view of the dimensionality, there are spaces with a Hausdorff dimension $1/2$ (sort of Cantor sets), but I guess there are other problems in this construction  unrelated to the dimension.  Edited: replying on the comment by Asaf. I want that for all $r\in\mathbb R$ there exists a unique representation $r=\langle x,y\rangle$ where $x\in X$ and $y\in X$. Also, what if we want to have $X$ to be a topological space and $h:X\times X\to\mathbb R$ to be a homeomorphism? Prove or show a counter example for: $\forall a, b, c \in \mathbb Z$, if $ab\mid c$ then $a\mid c$ and $b\mid c$ I'm working on my Discrete Mathematics homework and they are asking me this:  Prove or show a counterexample for: $\forall a, b, c \in \mathbb Z$, if $ab\mid c$ then $a\mid c$ and $b\mid c$  I'm not completely sure how to prove it. I was thinking to find a counterexample like zero but I'm not sure if that it's going to work. Or maybe try to approach it backwards?   I'm a little bit lost What formula would you use to add up a column based on results from two drop down menus? e.force:navigateToURL: [Cannot read property 'setParams' of undefined] Hungerford's book of algebra has exercise $6$ chapter $3$ section $6$ [Probably impossible with the tools at hand.]:     Let $p \in \mathbb{Z}$ be a prime; let $F$ be a field  and let $c \in  F$. Then $x^p - c$ is irreducible in $F[x]$ if and only if $x^p - c$   has no root  in $F$. [Hint: consider two cases: char$(F) = p$ and   char$(F)$ different of $p$.]   I have attempted this a lot. Anyone has an answer? "Fatal error: Cannot redeclare " Can I pass arguments to an alias command? I want to know if I can pass an argument with an alias command.  for example:  alias d="dmesg|grep -iw usb|tail -5"    Now d will print the last 5 lines. If I want to use d to print a different number of lines, I have to make change in the alias command declaration of d again.  Is there any way I can modify the declaration of an alias so that I don't have to retype the declaration to change the number of lines. Like incorporating passing the number of lines as an argument while declaring alias for d? Or is there some other method to solve this? apt-get stuck at 0 [Connecting to us.archive.ubuntu.com] When I do upgrade it gets stuck here:  user@plato:~# sudo apt-get upgrade Reading package lists... Done Building dependency tree        Reading state information... Done Calculating upgrade... Done The following packages will be upgraded:   bind9-host coreutils cpio curl dnsutils libbind9-90 libc-bin libc-dev-bin   libc6 libc6-dev libcgmanager0 libcurl3 libcurl3-gnutls libdns100   libdrm-intel1 libdrm-nouveau2 libdrm-radeon1 libdrm2 libisc95 libisccc90   libisccfg90 libjasper1 liblwres90 libplymouth2 libsepol1 libssl-dev   libssl-doc libssl1.0.0 linux-libc-dev mime-support multiarch-support ntp   ntpdate openssl plymouth plymouth-theme-ubuntu-text python3-distupgrade   ubuntu-release-upgrader-core unzip 39 upgraded, 0 newly installed, 0 to remove and 0 not upgraded. Need to get 16.0 MB of archives. After this operation, 12.3 kB of additional disk space will be used. Do you want to continue? [Y/n] y 0% [Connecting to us.archive.ubuntu.com (2001:67c:1562::15)] ░   When I do update it gets stuck here:  user@plato:~# apt-get update 0% [Connecting to us.archive.ubuntu.com (2001:67c:1562::14)] [Connecting to sec░   I'm able to ping us.archive.ubuntu.com just fine:  user@plato:~# ping us.archive.ubuntu.com PING us.archive.ubuntu.com (91.189.91.23) 56(84) bytes of data. 64 bytes from economy.canonical.com (91.189.91.23): icmp_seq=1 ttl=54 time=81.5 ms 64 bytes from economy.canonical.com (91.189.91.23): icmp_seq=2 ttl=54 time=81.5 ms 64 bytes from economy.canonical.com (91.189.91.23): icmp_seq=3 ttl=54 time=81.5 ms 64 bytes from economy.canonical.com (91.189.91.23): icmp_seq=4 ttl=54 time=81.4 ms ^C --- us.archive.ubuntu.com ping statistics --- 4 packets transmitted, 4 received, 0% packet loss, time 3004ms rtt min/avg/max/mdev = 81.425/81.528/81.582/0.355 ms   What can i do to fix this?    What I have tried so far.  I've tried following directions on this blog:   To force apt-get to use IPv4 exclusively   Create a file in /etc/apt/apt.conf.d/99force-ipv4 Add this line to newly created file Acquire::ForceIPv4 false; Apt-get will now use IPv4 exclusively Orthogonal complement examples Trim string in JavaScript? How do I trim a string in JavaScript? That is, how do I remove all whitespace from the beginning and the end of the string in JavaScript? What if the universe is rotating as a whole? Which view is the "Current view"? I have got a SharePoint 2010 website with a WebPart-page and a few WebParts on it.  One of the WebParts displays a list/a view of a list.  The views of that list have been updated due to business needs - but the view in the WebPart on the WebPart-page is not updated.    If I edit "Modify Shared Web Part" (the one with the list / list view),  the "Selected view" is set to "&lt;Current view&gt;".  My question is now: Which view of the list is the "&lt;Current view&gt;"? Is it any view of the list at all - or has the WebPart some kind of its own view to that list? How to edit Parameters for an Object after it is created? java.lang.NullPointerException at org.glassfish.hk2.classmodel.reflect.impl.TypesImpl.getType