In Interstellar, how did humans survive the first time in order to communicate?
Bootstrap Paradox in Interstellar
Our production server (2012, VM + SAN) has 32 GB of RAM, the database size is ~80GB. The application uses TempDB heavily - disk is hit ~100 MBps both reads &amp; writes.  Seeing tons of SQL compilations/sec .. 95% of all batch requests are compilations.  Ideally would like to increase the RAM to 64GB or 128GB, but need to 'prove' to team that it's required.  Buffer Cache Hit Ratio (BCHR) is 99.9%, but Page Life Expectancy (PLE) is only ~400. What's the explanation for this ? I though PLE &amp; BCHR had a linear relationship (i.e. they increase or decrease together)  On other VMs with larger databases and lot more RAM, both BCHR &amp; PLE are high.  Current wait stats and perf counters Styling multi-line conditions in 'if' statements? What is the physical significance of dot & cross product of vectors? Why is division not defined for vectors? I get the physical significance of vector addition &amp; subtraction. But I don't understand what do dot &amp; cross products mean?   More specifically,    Why is it that dot product of vectors $\vec{A}$ and $\vec{B}$ is defined as $AB\cos\theta$? Why is it that cross product of vectors $\vec{A}$ and $\vec{B}$ is defined as $AB\sin\theta$, times a unit vector determined from the right-hand rule?   To me, both these formulae seem to be arbitrarily defined (although, I know that it definitely wouldn't be the case).   If the cross product could be defined arbitrarily, why can't we define division of vectors? What's wrong with that? Why can't vectors be divided? This is a homework question. But I am completely stuck.  My only intuition was to go about it inductively from a "greedy algorithm" maybe know as the deletion-contraction algorithm. And to somehow use the information about the jth cycle to solve the j+1th. But I'm not sure how I'd do it. Thank you very much for looking this over. Bind an element to two sources I currently have two text boxes which accept any number. I have a text block that takes the two numbers entered and calculates the average.   I was wondering if there was a way I could bind this text block to both text boxes and utilize a custom converter to calculate the average? I currently am catching the text changed events on both text boxes and calculating the average that way, but I am under the assumption data binding would be more efficient and easier. Error - SqlDateTime overflow. Must be between 1/1/1753 12:00:00 AM and 12/31/9999 11:59:59 PM I have a front end module that generates an (ECG) signal that varies from +/-2.5 V. I want to shift this signal to 0 - 5V. What is the best way to do this? Would a summing amplifier like the below circuit good enough? With R1 = R2 and V1 = 2.5V, V2 = my signal, V3 = V4 = GND I'm from Central Pennsylvania, and apparently, we have a strange language construct in this area. I was recently talking about how "my car needs washed" to a friend from NJ, and she told me that my sentence was grammatically incorrect.   I realize she's right, and I realize my options are "my car needs to be washed" or "my car needs washing". But I'm not clear on the precise rule being invoked. Will ArcGIS for Desktop run on Windows 10? Will ArcGIS 10 run on the new windows 10 technical preview?  I am setting up an interface on my Mac and there is the free option of downloading the Windows 10 technical preview, some sort of beta version, I'm assuming.   Just wanted to see if 10.1 will run ok on Windows 10 (ignoring the Mac aspect), as this is all I am using my windows interface for? How can I show that $n! \leqslant \left(\frac{n+1}{2}\right)^n$? Show that $$n! \leqslant \left(\frac{n+1}{2}\right)^n \quad \hbox{for all } n \in \mathbb{N}$$  I know that it can be done by induction but I always find line where I do not know what to do next. What are the advantages and disadvantages of using the GAC? And on top of that, are there cases where one has to use the global assembly cache or where one cannot use it? I am currently developing a website which is going to take some time to finish. I need to move some 'stuff' to production frequently, while maintaining a under construction status. My front page will clearly mention that my website is under construction.  I know crawlers will access my URL before I am ready to go live. Should I tell them my site is under construction (no need to index)? If yes how?  P.S.: Eventually, I am ok to let them see my under construction front page. Can I permanently block an update (non-driver) that will not install on my machine on Win10 pro? I have an update to Visual Studio 2010 that will NOT update and has failed hundreds of times. Manually installing it also fails, and no source has been found for manually getting this very old patch to install on Windows 10. I believe the problem is that Microsoft simply hasn't re-tested KB2890573 at all and it doesn't install on Win10 ver 1511 at all, anymore.  I do not want to use the MS utility that will postpone this update for a while. I want to permanently block it so it does not appear in the windows update list ever again. Calculate the last digit of $3^{347}$ I think i know how to solve it but is that the best way? Is there a better way (using number theory). What i do is: knowing that  1st power last digit: 3 2nd power last digit: 9 3rd power last digit: 7 4rh power last digit: 1 5th power last digit: 3    $3^{347} = 3^{5\cdot69+2} = (3^5)^{69} \cdot3^2 = 3\cdot3^2=3^3=27 $ so the result is $7$. Unable to boot into Windows after installing Ubuntu, how to fix? What command(s) would you use to extract all of the usernames from a database called /etc/passwd and then sort this output alphabetically in reverse order? Limits involving factorials $\lim_{N\to\infty} \frac{N!}{(N-k)!N^{k}}$ I am trying to calculate the following limit  $$\lim_{N\to\infty} \frac{N!}{(N-k)!N^{k}}$$ where $k$ can be any number between $0$ and $N$.  I thought of the following:  If I take the logarithm of the expression then I get:  $$\lim_{N\to\infty} \left(\log(N!)-\log((N-k)!)-k\log N\right)$$    Using the Stirling formula this can be approximated as:  $$\lim_{N\to\infty} \left(N\log(N)-(N-k)\log(N-k)-k\log N\right)$$  Now there are two cases: If $k$ is $N$, then the second term vanishes and the remaining terms cancel. If $k$ is smaller than $N$, then I can drop the $k$ inside the second logarithm and all the terms cancel. So the limit $$\lim_{N\to\infty} \log\left(\frac{N!}{(N-k)!N^{k}}\right)=0$$ Which means that: $$\lim_{N\to\infty} \frac{N!}{(N-k)!N^{k}}=1$$ I don't know if this is mathematically rigorous. Would like some help. Thanks Can I use an "if" clause without "then"? Rules of thumb for divisibility Given a number presented in decimal form $n=\sum_{k=0} d_k10^k$ there are some nice thumb rules to decide whether it is divisible with a prime number  $p\in\{7,11,13,17,19,23,29\}$.   For each of this numbers there is a number  $a_p$ such that $p|n\iff p|(a_p\cdot d_0+\sum_{k=0} d_{k+1}10^k)$.  $a_7=-2,\;a_{11}=-1,\;a_{13}=4,\;a_{17}=-5,\;a_{19}=2,\;a_{23}=7,\;a_{29}=3$  E.g. $\;19\cdot 17=323$ and $32+2\cdot 3=38=2\cdot 19$ and $32-5\cdot 3=17$.  Is there a number $a_{31}$ that works the same way? Or $a_p,\;p\ge37$? What are some examples of manifolds that do not have boundaries and are not boundaries of higher dimensional manifolds?  Is any $n$-dimensional closed manifold a boundary of some $(n+1)$-dimensional manifold?