my understanding of a singularity is that it is a 'point' in the universe with an infinite energy density. I have also read on the internet that a singularity is one-dimensional.  This is a concept that troubles me. using my (very limited) knowledge of what dimensions are and how they work, I have made the following assumptions:   we live in a three-dimensional world with length, width and height (excluding time which  I am confused about and am unsure as to whether it is a dimension or not)  so a two-dimensional object would have only length and width (sort of like a flat shape in an area question in a textbook). so a one-dimensional object would only have length and would be a sort of 'line'.   But a 'line' is not a 'point', therefore in order to have a pointlike singularity it would need to be zero-dimensional. another aspect of the one-dimensional 'linear' singularity that I find difficult to understand is that for the finite amount of energy in the universe to be infinitely dense, it cannot be spread out along one or more dimensions, but rather it must be contained in zero dimensions. Hence the energy is 'X' joules per zero metres so the density is undefined.  are singularities one or zero-dimensional and why/how?   if the above reasoning is wrong, why is it wrong?
General relativity is expressed in terms of differential geometry, which allows you to do interesting things with the coordinates: multiple coordinates may refer to a single point, eg. the  has whole lines at the top and the bottom that correspond to the North and South poles, respectively; or a single coordinate may refer to multiple points, for example by using inverse geometry the origin refers to all the points infinitely far away.  So, is the singularity just a single point in the curved spacetime, or can it be a more extended object, described by a single coordinate?
I know that the emergency services can be called FREE in the UK by dialing 999 and in the US by dialing 911.   What I don't know is the number to call in other countries and if there is a cost involved. This is something I think most people should find out before travelling but many don't (including me). Hopefully this will help me and other people. unsigned int vs. size_t Can Conjure Animals beasts be used as mounts? Is it possible to use the animals that are summoned using Conjure Animals as mounts?  As an example: Summoning Giant Eagles to carry a group up the mountain or over a wall. datetime conversion to CDT Can anyone please help me how to convert the given time into CST timezone.  Input timezone will change dynamically, so i want to convert the given timzone into CST and then need to get the hour from that CST timezone in apex. Linux ACL behaviour: settings the mask changes 'ls' output, but not actual permissions It might be the time of night, but this is puzzling me. Picture the following.  [root@node1 acltest]# getfacl foo/ # file: foo # owner: root # group: testuser user::rwx group::r-x other::---  [root@node1 acltest]# ls -la . total 24 drwxr-xr-x  3 root root     4096 Feb  9 21:53 . drwxr-xr-x 25 root root     4096 Feb  9 21:54 .. drwxr-x---  2 root testuser 4096 Feb  9 21:53 foo [root@node1 acltest]# setfacl -m m::rwx foo [root@node1 acltest]# getfacl foo/ # file: foo # owner: root # group: testuser user::rwx group::r-x mask::rwx other::---  [root@node1 acltest]# ls -la . total 24 drwxr-xr-x   3 root root     4096 Feb  9 21:53 . drwxr-xr-x  25 root root     4096 Feb  9 21:54 .. drwxrwx---+  2 root testuser 4096 Feb  9 21:53 foo [root@node1 acltest]# su - testuser [testuser@node1 ~]$ cd /acltest/foo/ [testuser@node1 foo]$ ls -la . total 16 drwxrwx---+ 2 root testuser 4096 Feb  9 21:53 . drwxr-xr-x  3 root root     4096 Feb  9 21:53 .. [testuser@node1 foo]$ touch bar touch: cannot touch `bar': Permission denied   In words: I create a directory foo, with mode 0750, root as owner and testuser as the group. (testuser is the private group of testuser, but that doesn't matter.)  The getfacl command correctly shows no ACL's on this directory and there is not mask yet. The mask will be set accordingly to the group permissions if I would add a named group or user now.  If I explicitly set the mask to rwx now, the group permissions as shown by ls change too. I know it happens the other way around (the mask changes when the group permissions change), but this seems puzzling.  The more puzzling because the getfacl output does not show the group permissions as rwx but - as said - ls does.  Which one is right? Apparently, the output of getfacl is right, because testuser cannot write to foo. As expected, by the way, because I did not grant the testuser group any permissions to do so.  It goes on. I cannot allow the testuser group write permissions on foo by just using chmod. I have to explicitly set an ACL using setfacl -m g:testuser:rwx foo to allow testuser to finally touch foo/bar.   Can someone explain the rationale behind the difference in the outputs of getfacl and ls? I know it can be tricky to have normal permissions go together with ACL's, but this seems plain wrong. (Though I expect to be missing something glaringly obvious ;))  I have already seen Concurrently interleaving execution of Lua and TeX in LuaTeX The usual way to interleave Lua and TeX in generating documents is by invoking Lua from Tex through the \directlua facility and generate Tex from Lua using tex.print().  For example, consider the Plain LuaTeX:  \directlua{     es=""; someluatex = function () tex.everypar="PAR!" end     tex.print("one", es, "two")     someluatex()     tex.print("three", es, "four") } five\bye   Looking at the document LuaTeX generates for that input, we see that someluatex() is run before the Tex backend does anything with the output: the PAR!s will be inserted before "one" and "two", as well as after "three".  Is there best practice for ensuring that TeX code issued by some Lua code is issued before some other LuaTeX code?  There are several ways to do this: with some code I am working with I am trying the following scheme:   Wrap the code executed by the \directlua in a coroutine, call it myco; At the point we want to ensure the Tex so far tex.print-ed is executed, use:  tex.print("\\directlua{coroutine.resume(myco)}") coroutine.yield()  If everything is in order, the Lua will resume after the Tex is processed.   This is not ideal, however: we must ensure that the TeX backend is in the right state to understand the \directlua command, which may not always be the case.  Is there a better way to achieve this? What are sentences like "the longer X, the more Y" called and can they be used in formal written English? What is the type of sentence exemplified below called? Is it appropriate to use it in a scientific paper and formal written English in general?     1. The more pronounced the variation, the   more the waste.      2. The more you give, the more you get.      3. The longer I live, the more I realize the impact of attitude on life. How to make Gnome's "Activities" bar always visible? How does Austria's suspension of Schengen affect travellers (both EU and non-EU)? I'm an Italian citizen. Next Sunday I'm going to Austria. I have a national ID card but no passport. Recently Austria suspended Schengen. So can I enter Austria? tables with lots of columns I have a table that lists various attributes of an individuals personal development plan; objective, time to complete objective, comments etc. The table is editable so the user can directly add comments without having to go to an intermediate form. The problem is that the client wants to add more columns and this is messing up the visual display.   The alternatives I have are:   allowing columns to expand out on click keeping essential attributes in table, rest in 'advanced edit option form' or somesuch I don't know - have you any ideas?   One more thing to add: I think the addition of extra columns is based on user feedback ...  edit: here is what I have gone for Why can a 1 element set be a member of another set but not a subset of it? I have came across this in a textbook:     $\{2\}\nsubseteq\{\{2\}\}$ but $\{2\}\in\{\{2\}\}$   I understand that $\{2\}$ is an element (member) of the other set but considering $\{2\}$ is a set itself, why is it not a subset? I am flying from the US to Edinburgh, UK. My layover is at Heathrow. Will I need to go through customs and check bags again at Heathrow before I take the next flight? I've tried to install Ubuntu on a VMWare Virtual Machine, but it never gets past the  bootloader :  ISOLINUX 4.01 debian-20100714 ETCD Copyright (C) 1994-2010 H. Peter Anvin et al No DEFAULT or UI configuration directive found! boot: _   I've also tried to burn this .iso image to a CD and go from therem but I got the same problem.  Some more details :   VMWare Server 2.0.2 Build 203138 on Windows 2008 R2 ubuntu-10.10-desktop-i386.iso image used (downloaded yesterday evening) What function satisfies $ f(x)+f\left(\frac{1-x}x\right)=x$ ? How to run a program on a remote pc via command line? How can I run a program on a remote Windows PC in our network without the need of killing an existing remote-desktop-connection? I only need a command line for running the program and getting its results. Thank you! What's the bad magic number error? What's the "Bad magic number" ImportError in python, and how do I fix it?  The only thing I can find online suggests this is caused by compiling a .py -> .pyc file and then trying to use it with the wrong version of python. In my case, however, the file seems to import fine some times but not others, and I'm not sure why.  The information python's providing in the traceback isn't particularly helpful (which is why I was asking here...), but here it is in case it helps:  Traceback (most recent call last):   File "run.py", line 7, in &lt;module&gt;     from Normalization import Normalizer How to find regression coefficients $\beta$ in ridge regression? In ridge regression, the objective function to be minimized is: $$\text{RSS}+\lambda \sum\beta_j^2.$$   Can this be optimized using the Lagrange multiplier method? Or is it straight differentiation? Why does  get a pass, but I can't ask my own book recommendation question? Can I ask my own book recommendation question in a way that is acceptable to the community, like the C++ book list question? Addons: Only some .zips will install Evaluate  $$\int\frac{e^xdx}{(e^{2x}-1)(e^x+1)}$$  I tried to decompose the integrand into A and B partial fractions.  No success.