Looking for a story, from maybe the 1960's, in which an experimental world is rapidly evolved to solve problems
Man creates miniature population on different time-scale; uses them to invent the 'absolute protection' dome
80s/90s book where boy stumbles on game where aliens gamble their planets I don't remember much about it other than the setting. It's about a boy who one night stumbles upon some different alien races playing a game in which their civilizations will end if they lose. He gets involved in the game somehow and is hunted. The security guard problem There was a security guard in a bank. In front of him were 100 lockers in rows of 10. He thought of something as he saw all the lockers were closed. He started opening all the lockers whose lock numbers were multiples of 1, then closed all lockers whose number was a multiple of 2,and did the same for 3 and so on. If the locker was open, he closed it, if closed, opened it. He went to open multiples of 1 (all),then 2,4,6,8...and then 3,6,9.. And then finally reached 100.  After all the opening and closing,in the end, how many lockers are open and how many closed? Before upgrading to 14.04 when I clicked on a file in the dash, it opened the file.   This still happens on my 12.04 machine.  In 14.04 when I click on a file in dash search results, it offers me 3 options: 'Email', 'Open' and 'Show in Folder'.  How can I get back the previous behaviour - i.e. to immediately open the files on the first click? This is a problem from Introduction to Representation Theory by Etingof et al. I have no idea how to approach it. My friend wrote a program that uses Gaussian elimination to find a basis, which starts with x, y, [x, y], [y, [x, y]], ... but freezes once it gets to elements with 9 or more occurrences of x, y.  I expect that there is some way to characterize the nonzero elements of this Lie algebra (i.e., elements that are "immune" to being shown to be zero through repeated application of the Jacobi identity) which could be turned into a way to enumerate them. I don't see what it is, though.  It's also totally unclear to me how to show that some set we know spans the Lie algebra (proven using some criterion as described in the previous paragraph) is actually linearly independent, unless we find a faithful representation... but I have no idea how to find a faithful representation for an infinite-dimensional Lie algebra.  Hints would be greatly appreciated.  Edit: After looking at the partial output, we can form the "straightforward" conjecture that:   If $n \geq 4$ is even, then there is one basis element of grade $n$, namely $\mathrm{ad}([x, y])^{(n-4)/2}[y, [y, [y, x]]]$. If $n \geq 5$ is odd, then there are two basis elements of grade $n$, namely $[x, z]$ and $[y, z]$ where $z$ is the single basis element of grade $n-1$.   I also have a different conjecture, which is mutually exclusive with the above: that if we flatten out all nonzero elements into the form ${\rm ad}(e_1) {\rm ad}(e_2) \ldots {\rm ad}(e_{n-1}) e_n$ using the Jacobi identity, then in the sequences $e_1, \ldots, e_{n-1}, e_n$ and $e_1, \ldots, e_n, e_{n-1}$, any span containing two x's must contain at least two y's and any span containing five y's must contain at least two x's, otherwise we can use the Jacobi identity to rearrange the element somehow to show that it vanishes. If this is true, then the long-range behaviour must be:   For $n \geq 8$ there is exactly one basis element of grade $n$, namely $[... [y, [x, [y, [y, [x, y]]]]] ...]$ (the pattern $y x y$ repeats).   I still don't see an approach to proving that none of the elements in this sequence actually vanishes, though.  Edit 2: Here is the hint given by Etingof in an email:     No, there are no published solutions, since these problems are used as   a homework for classes. This is indeed a nontrivial problem.      This is the positive part of the affine Kac-Moody algebra of type   A_2^2, which is the twisted loop algebra for sl(2). So what you need   to do is to relate this Lie algebra to loops into sl(2). I see from   your post that you are on the right track. I am wanting to find a latitude and longitude point given a bearing, a distance, and a starting latitude and longitude.  This appears to be the opposite of this question ().  I have already looked into the haversine formula and think it's approximation of the world is probably close enough.  I am assuming that I need to solve the haversine formula for my unknown lat/long, is this correct? Are there any good websites that talk about this sort of thing? It seems like it would be common, but my googling has only turned up questions similar to the one above.  What I am really looking for is just a formula for this. I'd like to give it a starting lat/lng, a bearing, and a distance (miles or kilometers) and I would like to get out of it a lat/lng pair that represent where one would have ended up had they traveled along that route. How can I record my screen on Ubuntu?   The app I'm looking for has ideally all of these features:   Can record in a format that can be played back easily on any platform and/or accepted by YouTube or another popular video site Can record just a window (instead of the whole screen), possibly selecting it with a mouse click Can start recording after a configurable delay (e.g., I launch the app and have time to do arrangements to my desktop/window before actual recording starts) How can I remove launcher drive icons? How to find out what's accessing a particular hard drive on Windows? Possible Duplicate:          My HDD on a dock just started making noises like it's being accessed but I don't see any program accessing it.  Is there a program that shows which HDD is accessed by which program in percentages similar to how the task manager shows which programs use the most CPU? Using CSS to affect div style inside iframe What is the most convenient way to read definitions of in-memory symbols when we don't have the source files? (Spelunking tools) So I was writing up a simple binary tree in Python and came across [...]  I don't believe this to be related to the Ellipsis object, more it seems to have something to do with an infinity loop (due to Python's shallow copy?). The source of this infinity loop and why it doesn't get expanded while expanding when accessed is something I'm completely lost to, however   &gt;&gt;&gt; a [[[[[], [], 8, 3], [[], [], 3, 2], 6, 3], [], 1, 4], [[], [], -4, 2], 0, 0] &gt;&gt;&gt; Keys(a)#With a+b [0, 1, 6, 8, 3, -4] &gt;&gt;&gt; Keys(a)#With [a,b] [8, [...], [...], 3, [...], [...], 6, [...], [...], 1, [...], [...], -4, [...], [...], 0, [...], [...]] &gt;&gt;&gt; Keys(a)[1]#?? [8, [...], [...], 3, [...], [...], 6, [...], [...], 1, [...], [...], -4, [...], [...], 0, [...], [...], 8, [...], [...], 3, [...], [...], 6, [...], [...], 1, [...], [...], -4, [...], [...], 0, [...], [...]]     Version using a+b  def Keys(x,y=[]):     if len(x):y+=[x[2]]+Keys(x[0],y)+Keys(x[1],y)#Though it seems I was using y=y[:]+, this actually outputs an ugly mess     return y   version using [a,b]  def Keys(x,y=[]):     if len(x):y+=[x[2],Keys(x[0],y),Keys(x[1],y)]     return y   So what exactly is [...]? Eclipse says: “Workspace in use or cannot be created, chose a different one.” How do I unlock a workspace? I am currently visiting the USA from the UK (I am a UK citizen) and am intending on staying here for the full 90 days under the Visa Waiver Program.     How long would I have to stay out of the US at the end of this period before returning again?    Would I have to return to the UK, or could I stay with friends in another country (such as Canada) for a while? I have a big pot full of chicken necks and backs on the stove which I need to separate into (a) stock and (b) everything else.  I'm wondering the best way to go about doing this. I've previously laid cheesecloth into a fine-mesh strainer and poured it through that, but the cheesecloth always seems to kind of clog up, making straining 4 litres of stock a very lengthy process. I also tried a coffee filter laid inside a strainer and got more-or-less the same results.   Alternatively, I ditched the cheesecloth and just used the fine-mesh strainer by itself, but, unsurprisingly, this method leaves some bits I'd rather not have.   I'm wondering: is there a better way? Or should I stick with the cheesecloth and work on being more patient? Deriving the Coulomb force equation from the idea of photon exchange? requireJS optional dependency How can I avoid SSH's host verification for known hosts? Make browser window blink in task Bar How do I make a user's browser blink/flash/highlight in the task bar using JavaScript? For example, if I make an AJAX request every 10 seconds to see if the user has any new messages on the server, I want the user to know it right away, even if he is using another application at the time.  Edit: These users do want to be distracted when a new message arrives. Perturbation property of Orthonormal basis for Hilbert space Can compact sets completey determine a topology? Suppose that $\tau_1$ and $\tau_2$ are two topologies on a set $X$ with the property that $K\subset X$ is compact with respect to $\tau_1$ if and only if $K$ is compact with respect to $\tau_2$. Then is this enough information to determine whether $\tau_1 = \tau_2$?  If not (which is suspect to be the case) is there a nice counterexample, and what is the minimum amount of extra information required for $\tau_1 = \tau_2$?  I feel like there would be an issue regarding 'points at infinity.'