how do you prove the existence super natural
Is any aspect of the supernatural testable? What level of proof is possible for the supernatural?
I've been trying to develop an intuition based understanding of Bayes' theorem in terms of the prior, posterior, likelihood and marginal probability. For that I use the following equation: $$P(B|A) = \frac{P(A|B)P(B)}{P(A)}$$ where $A$ represents a hypothesis or belief and $B$ represents data or evidence. I've understood the concept of the posterior - it's a unifying entity that combines the prior belief and the likelihood of an event. What I don't understand is what does the likelihood signify? And why is the marginal probability in the denominator? After reviewing a couple of resources I came across this quote:     The likelihood is the weight of event $B$ given by the occurrence of $A$ ... $P(B|A)$ is the posterior probability of event $B$ , given that event $A$ has occurred.   The above 2 statements seem identical to me, just written in different ways. Can anyone please explain the difference between the two? Can crumbled feta cheese last almost a year? talks about feta cheese in a brine or milk bath lasting up to three months.  What about crumbled feta?  I was looking through the fridge, and found a 1/2 pound open container of crumbled feta.  I have only used about an ounce of it.  There is no sign of mold on it, and it smells like feta cheese.  A small sample tasted okay.  The amazing thing is that I bought it in October or November: 8-10 months ago!  I have a recipe that calls for almost a 1/2 pound of feta, and I will be the only one eating it (so I'm not trying to impress anybody!).  I dislike wasting food, but I dislike being sick even more!  Is it safe to use dry crumbled feta that is so old? When should I not kill -9 a process? Can I travel to the UK on different dates from those on my entry clearance? I have a "Standard Visitor Entry Clearance" for the UK and will be traveling there from Saudi Arabia.    Is it necessary to travel on the same date I provided on my application?  Will the Immigration Officer check?  Will it make problems if I travel on a different date? Computing the integral of $\log(\sin x)$ How to compute the following integral?  $$\int\log(\sin x)\,dx$$    Motivation: Since $\log(\sin x)'=\cot x$, the antiderivative $\int\log(\sin x)\,dx$ has the nice property $F''(x)=\cot x$. Can we find $F$ explicitly? Failing that, can we find the definite integral over one of intervals where $\log (\sin x)$ is defined? How are Contacts in Marketing Cloud counted? Salesforce bills Marketing Cloud on total number of Contacts within the system. I'd like to know what exactly is used to count these? Is this the Email Studio > All Subscribers list or the Contact Builder > All Contacts list?  When we have Marketing Cloud connector and synchronise the Contacts object, is this counted towards that number? (or only when they have been inserted into the All Subscribers / All Contacts list, as they are not done so automatically) Accessing the index in 'for' loops? How do I access the index in a for loop like the following?  ints = [8, 23, 45, 12, 78] for i in ints:     print('item #{} = {}'.format(???, i))   I want to get this output:  item #1 = 8 item #2 = 23 item #3 = 45 item #4 = 12 item #5 = 78   When I loop through it using a for loop, how do I access the loop index, from 1 to 5 in this case? Creating random numbers with no duplicates When I use ssh -X on my Mac (running OS X 10.6.7) to connect to my Ubuntu (11.04) box, I get the following warning:     Warning: untrusted X11 forwarding   setup failed: xauth key data not   generated Warning: No xauth data;   using fake authentication data for X11   forwarding.   Is there something I can do to make this warning go away?  If not, can I safely ignore it?  X11 forwarding seems to work fine, though I do see this message:     Xlib:  extension "RANDR" missing on   display "localhost:10.0".   Is that related to the warning?  (I'm guessing not.  If it's not, I'll file a new question about that.) Time Manager (QGIS) date format I've been through associated answers but cannot quite seem to find something which works!  I'm having trouble getting TimeManager to recognise a simple data field (this is in QGIS2 - but I've had this error in earlier versions). I have these fields formatted in what appears to be one of the acceptable formats:    ... here is a screenshot of the field properties:    The format appears to be recognised in QGIS as I've worked out days difference between two dates (the "Time on Market" field shown in the image).  However ... I always end up with:   The Twitter.shp file works fine as a test, so I don't think this is an issue with the install / phyton conflict.  Any thoughts welcome! I have read several introductory texts about LSTM online, but none of them give a rigorously mathematical explanation of what the model actually does. For instance, why does the forget gate forget any more than any of the other gates in the LSTM unit?  Which papers and/or books should I read if I want to get a deeper understanding of LSTM? Java Array, Finding Duplicates Do you think that "was going to be" or "would be" could be used as past tense of will?     I thought this book was going to be your choice.        I thought this book would be your choice.   Do these two sentences basically mean the same thing or are they slightly different? How does Hextech Crafting work? How do you earn free loot?  What's the deal with essences and why are they so important?  What do the different options mean when dealing with Redeeming Rerolling Disenchanting and Upgrading?  How does it all work? Complete residue system proof I was given a proof of this in class, but it does not make sense to me, can someone provide a better proof, or explain the one I have provided, thanks.  Suppose $\gcd(a,n) = 1$, where $a$ and $n$ are natural numbers. Prove that $0$, $a$, $2a$, $3a,\ldots, (n-1)a$, is complete residue system modulo $n$.  Proof given in class:  \begin{align*} ka &amp;\equiv ra \pmod{n}\\ &amp;\Rightarrow  k \equiv r \pmod{n}\\ &amp;\Rightarrow  \text{$k-r$ divides $n$}\\ &amp;\Rightarrow \text{$k=r$ because $0\leq k\lt n$, $0\leq r\lt n$} \end{align*} Maximal order of an element in a symmetric group If we let $S_n$ denote the symmetric group on $n$ letters, then any element in $S_n$ can be written as the product of disjoint cycles, and for $k$ disjoint cycles, $\sigma_1,\sigma_2,\ldots,\sigma_k$, we have that $|\sigma_1\sigma_2\ldots\sigma_k|=\operatorname{lcm}(\sigma_1,\sigma_2,\ldots,\sigma_k)$.  So to find the maximum order of an element in $S_n$, we need to maximize $\operatorname{lcm}(\sigma_1,\sigma_2,\ldots,\sigma_k)$ given that $\sum_{i=1}^k{|\sigma_i|}=n$. So my question:      How can we determine $|\sigma_1|,|\sigma_2|,\ldots,|\sigma_k|$ such that $\sum_{i=1}^k{|\sigma_i|}=n$ and $\operatorname{lcm}(\sigma_1,\sigma_2,\ldots,\sigma_k)$ is at a maximum?   Example  For $S_{10}$ we have that the maximal order of an element consists of 3 cycles of length 2,3, and 5 (or so I think) resulting in an element order of $\operatorname{lcm}(2,3,5)=30$.  I'm certain that the all of the magnitudes will have to be relatively prime to achieve the greatest lcm, but other than this, I don't know how to proceed. Any thoughts or references? Thanks so much. An init-script does not get called on shutdown I have set up an init-script to control the state of a VirtualBox VM:  #!/bin/sh #chkconfig: 35 99 5 #description: vTiger virtual machine  ### BEGIN INIT INFO # Provides: vtigervm # Required-Start: $local_fs # Requider-Stop: $stop_fs # Default-Start: 3 5 # Default-Stop: 0 1 2 6 # Short-Description: Manage vTiger virtual machine # Description: Utility to start and stop vTiger virtual machine on VirtualBox ### END INIT INFO  start() {     echo -n "Starting vTiger"     echo     su myuser -c '/usr/bin/VBoxManage startvm "vTiger" --type headless'     echo "Started virtual machine" &gt;&gt; /var/log/messages }  stop() {     echo -n "Shutting vTiger down..."     echo     su myuser-c '/usr/bin/VBoxManage controlvm "vTiger" acpipowerbutton'     while [ ! -z "`su - juhani -c '/usr/bin/VBoxManage list runningvms | grep vTiger'`" ]; do         echo -n "."         sleep 1     done     echo "Done."     echo "Stopped virtual machine" &gt;&gt; /var/log/messages }  status() {     echo -n "Running VMs: "     su myuser -c '/usr/bin/VBoxManage list runningvms'     echo     if [ -z "`su - juhani -c '/usr/bin/VBoxManage list runningvms | grep vTiger'`" ]; then         RETVAL=3         else         RETVAL=0     fi     echo "Queried virtual machine status" &gt;&gt; /var/log/messages }  echo "Called virtual machine management script with: $1" &gt;&gt; /var/log/messages case "$1" in   start)         start    ;;    stop)         stop    ;;    restart|try-restart|condrestart|reload)         stop         start    ;;    status)         status    ;;    *)         echo $"Usage: $0 {start|stop|restart|status}"         exit 1    ;; esac  exit $RETVAL   The system is CentOS 6.5. If I manually run service [start|stop|status] vtigervm, it works as I expect it to. If the VM is running, $? after the service vtigervm status returns 0, and 3 if it is stopped. I installed it with chkconfig and it created among a few others rc5.d/S99vtigervm and rc0.d/K05vtigervm.  The problem  When I start the system it starts the "service", but on shutdown it does not even run the scripts.  grep "virtual machine" /var/log/messages shows:  *[machine starting]* Called virtual machine management script with: start Started virtual machine *[shutdown -h now]* *[machine stopped]*   What I expect:  *[machine starting]* Called virtual machine management script with: start Started virtual machine  *[shutdown -h now]* Called virtual machine management script with: status Queried virtual machine status Called virtual machine management script with: stop Stopped virtual machine *[machine stopped]*   File permissions &amp; etc:  # ls -lah /etc/rc0.d/ lrwxrwxrwx. 1 root root 13 7.2. 17:49 /etc/rc0.d/K05atd -&gt; ../initd.d/atd lrwxrwxrwx. 1 root root 18 9.2. 00:06 /etc/rc0.d/K05vtigervm -&gt; ../initd.d/vtigervm I have a list of requirements for a program, but I don't know what program meets these criteria. That's about general-purpose software, for example, not a programming IDE or statistical workbench, questions about which would certainly go to respective sites.  Is this question appropriate on Stack Overflow? Where should I ask about it? On Super User or elsewhere? What is the process for a moderator to request reinstatement or appeal a removal? How to disable copy in shared folder I am trying to make folder that everyone can view and can't copy,modify.    For all answers.I thinking about specially ms office files. I tried following methods  Software  - copy protect    - anti copy    This method can't protect save as and upload  MS office macro    Users can enable,disable macros.  MS office restriction    This is best choice but can't protect from file uploading.   Almost I found the solution. Way is combination of MS office restriction and restrict access from browsers using firewall or antivirus. But I don't exact how to do this.