Big bang singularity in an infinite universe If the spacetime of the universe is infinite now, then it must have been infinite at every point in its history, right? How then can Big Bang be an expansion of space and time? Can somebody show the compatibility of the idea of a singularity and the possible infinity of spacetime extent.
Did the Big Bang happen at a point? TV documentaries invariably show the Big Bang as an exploding ball of fire expanding outwards. Did the Big Bang really explode outwards from a point like this? If not, what did happen?
I have been looking at the plugin API a bit more in depth recently and I was wondering what real differences there were between action and filter hooks. They both are events that receive data as a parameter and they seem to both be able to do the same things.  Obviously I see that actions are called when actions take place and filters are called when data is manipulated, but it seems to just be a semantic naming difference.  Besides semantics and what they are used for, what real differences are there between them? I am tired of always trying to guess, if I should escape special characters like '()[]{}|' etc. when using many implementations of regexps.  It is different with, for example, Python, sed, grep, awk, Perl, rename, Apache, find and so on. Is there any rule set which tells when I should, and when I should not, escape special characters? Does it depend on the regexp type, like PCRE, POSIX or extended regexps? What is the correct formula for gravitational time dilation for a satellite in a circular orbit? In the Wikipedia article on  I see two formulae for the gravitational time dilation. One contains $\sqrt{1 - r_0/r}$ but the other $\sqrt{1 - 1.5 r_0/r}$. What formula should I use to calculate the time dilation due to gravity inside a satellite? The speed induced time dilation is of course just special relativity.  With the first of these two formulas I can perfectly reproduce the graphs on time dilation as a function of $r$,  I find that the two contributions to time dilation cancel at 1.5 Earth radii, all numbers are OK... But why not the second formula? Children’s books, one in space setting, the other in a jungle When I was little I remember getting these two books from the library.  Both books were paperback and flimsy.  The pages were wide.  Each book had full page illustrations with puzzles and mazes in them, but it was like you were immersed in this setting completely.  They were also like choose-your-own adventure books, but only in the way that you go through the book in a different order based on your results in the puzzles/games.    For example, there is a bridge to cross, or you can take this path.  If you choose to cross the bridge you go to page x.  On page x you have to pretend to cross the bridge but some planks are broken.  You can't skip more than a certain number of planks, but you also cannot "step" on a broken plank.  One book was in a jungle setting with rope bridges, alligators, quick sand, etc. The other was in space, with all kinds of aliens and weird stuff.  I have faint memories of these books but I REALLY want to track them down because I remember loving them. While writing a proposal at work today I needed to mention a list of things and within that list were multi-part items. It seems like replacing the comma with a semi-colon in this situation would make the sentence easier to understand, but is it correct usage?  With standard punctuation this could get confusing:       Some of my favorite things to do are   camping, playing football and   baseball, watching Laurel and Hardy   Movies, and traveling.   Proposed alternative. Is this acceptable usage?       Some of my favorite things to do are   camping; playing football and   baseball; watching Laurel and Hardy   Movies; and traveling. Autofilling fields based on another field Proper subspaces of $ R^n $ I'm trying to prove that proper subspaces of $ R^n $ are closed and have empty interiors.  To prove that they are closed I'm trying to use the fact that inverse images of closed sets are closed sets by continuous functions. So I'm trying to find a linear map such that a proper subspace of $ R^n $ is its Kernel but I don't know how to express it so that it would work on all dimensions.  Regarding the fact that they have empty interiors, I really don't know what to do.  Thanks in advance. During kill Bill, we learn that all the black mamba had to do to get Hanzo to build her a sword, was to mention Bill's name.  When black mamba meets Bill at the end, she tells him that all she did was mention his name. Bill responds with, "that'll do it!"  So what was it that Bill did to Hanzo to make him come out of retirement and make another weapon of death? Can we insert or update FieldSets using apex code? View history of commands run in terminal Is there a way to save all my typed terminal commands and view it like history in a log book? Bound for the correlation of three random variables In the last 30 years, human technology has developed massively.  Every year a new smartphone is released with a faster processor, more memory, better features.  Why hasn't the same level of progress happened in the Star Wars universe?  In The Phantom Menace, we see a number of droids - R2 units, C-3PO, Pit Droids, etc.  In Return of the Jedi - the droids we see pretty much have the same capabilities.  I would have thought that technology would still be progressing in the Star Wars universe - but it appears to have stopped.  During wars on Earth, our technology capabilities grow - so it can't just be the effect of a massive war which is causing the stagnation of development.  So, what gives? unable to reset root password of mysql I need to reset the root password of my local mysql installation but it woudln't let me. I've tried this:  $ sudo /etc/init.d/mysql stop  * Stopping MySQL database server mysqld                                                                                                              [ OK ]  [1]-  Exit 1                  sudo /usr/sbin/mysqld --skip-grant-tables --skip-networking [2]+  Exit 1                  sudo /usr/sbin/mysqld --skip-grant-tables --skip-networking reg@regDesktopHome:~$ sudo mysqld --skip-grant-tables &amp; [1] 13651 reg@regDesktopHome:~$ 140627 19:02:02 [Warning] Using unique option prefix key_buffer instead of key_buffer_size is deprecated and will be removed in a future release. Please use the full name instead.  reg@regDesktopHome:~$ mysql -u root mysql ERROR 1045 (28000): Access denied for user 'root'@'localhost' (using password: NO) reg@regDesktopHome:~$ sudo mysql -u root mysql ERROR 1045 (28000): Access denied for user 'root'@'localhost' (using password: NO) [1]+  Exit 1                  sudo mysqld --skip-grant-tables   How can I get the password reset? edit 1 I got this:  $ ps ax| grep mysql 16515 ?        Ssl    0:00 /usr/sbin/mysqld 16551 pts/23   S+     0:00 grep --color=auto mysql reg@regDesktopHome:~/semios/v3upgrade$ sudo kill -9 16515 reg@regDesktopHome:~/semios/v3upgrade$ ps ax| grep mysql 16678 ?        Ssl    0:00 /usr/sbin/mysqld 16715 pts/23   S+     0:00 grep --color=auto mysql reg@regDesktopHome:~/semios/v3upgrade$ mysql -u root ERROR 1045 (28000): Access denied for user 'root'@'localhost' (using password: NO)   looks like a process is automatically restarting mysql as soon as I kill it... Every planar graph has a vertex of degree at most 5. Could new users be prompted to edit instead of commenting? It's very common to ask for additional information on a question.  This is perhaps most common with new users who are a little unfamiliar with the need to put all relevant information in their question to start with.  To be blunt, I'm a little tired of explaining to new users that an edit is better than a comment, particularly where we ask "please add the output of..." I note that some users have taken to explicitly asking OPs to edit their question and adding an edit link in their comment.  But still this is missed.  More recently, adding a comment to a new user's question displays a little note saying:     ... is a new contributor. Be nice, and check out our Code of Conduct.   Could there be a similarly formatted note to new contributors commenting on their own question or answer:     If you need to add more information please  your [question][answer] instead of adding a comment. How to use mirror ball to light a scene? Fake small caps with XeTeX/fontspec? Using XeTeX and fontspec, I use the Liberation font family in of my documents. Unfortunately those fonts (esp. Liberation Serif) do not natively support small caps.  Is there a way to enable fake small caps in fontspec? Get total amount of time between records when changed state I have a table, showing the status (healthy, broken) for each device at a given timestamp. I need to get the total amount of time of a whole breakdown.  So the data is stored like this:  device_owner   device_id    timestamp          status owner1         device_1     2001-01-01 09:00   0 owner1         device_2     2001-01-01 09:15   0 owner1         device_1     2001-01-01 09:30   1 owner1         device_2     2001-01-01 09:45   1   and so on.  The example above shows    device_1 was down from 09:00 to 09:30 (total 30 mins),   device_2 was down from 09:15 to 09:45 (total 30 mins)   What I need  Need to calculate the total amount of time for the whole breakdown for owner_1 will be 45 mins (from 09:00 to 09:45) instead of 60 mins (30 + 30).  device_owner   total_breakdown_min owner_1        45   What I've done  Currently I can define a breakdown time for each device separately (device_1 = 30mins, device_2 = 30mins). For this I transformed the table using LEAD over partition by device_owner, device_id and date part from timestamp:  device_owner  device_id     timestamp        status lead_timestamp   lead_status owner1        device_1     2001-01-01 09:00   0     2001-01-01 09:30     1 owner1        device_1     2001-01-01 09:30   1     NULL                 NULL owner1        device_2     2001-01-01 09:15   0     2001-01-01 09:45     1 owner1        device_2     2001-01-01 09:45   1     NULL                 NULL   So the datetime difference between timestamp and lead_timestamp in sum gives me the total breakdown time for a device.  ;WITH LeadStatus AS (     SELECT         D.*,         lead_status = LEAD(D.status) OVER (PARTITION BY D.device_owner, D.device_id, D.date ORDER BY D.datetime ASC),         lead_timestamp = LEAD(D.datetime) OVER (PARTITION BY D.device_owner, D.device_id, D.date ORDER BY D.datetime ASC)     FROM         #DeviceStatus AS D ) SELECT * FROM LeadStatus   It is the same device list for any owner. The data snapshot is to be taken between 2 dates (StartDate, EndDate). The records are written to a DB each n seconds and also when the device status changes. Fastest way to clamp a real (fixed/floating point) value? Is there a more efficient way to clamp real numbers than using if statements or ternary operators? I want to do this both for doubles and for a 32-bit fixpoint implementation (16.16). I'm not asking for code that can handle both cases; they will be handled in separate functions.  Obviously, I can do something like:  double clampedA; double a = calculate(); clampedA = a &gt; MY_MAX ? MY_MAX : a; clampedA = a &lt; MY_MIN ? MY_MIN : a;   or  double a = calculate(); double clampedA = a; if(clampedA &gt; MY_MAX)     clampedA = MY_MAX; else if(clampedA &lt; MY_MIN)     clampedA = MY_MIN;   The fixpoint version would use functions/macros for comparisons.  This is done in a performance-critical part of the code, so I'm looking for an as efficient way to do it as possible (which I suspect would involve bit-manipulation)   EDIT: It has to be standard/portable C, platform-specific functionality is not of any interest here. Also, MY_MIN and MY_MAX are the same type as the value I want clamped (doubles in the examples above). Why do we need a diagonal matrix? Apart from simplifying matrix powers, why do want to diagonalize a matrix? Do they have any appealing application which can be used to motivate to study diagonal matrices.  Thanks for any answers.