This has never been clear for me. Modern CPUs have the addressable space of 64 bits. The most expensive part of adding more memory is obviously the memory hardware itself, chips on them, etc. But why do motherboards also always impose the limitation? Is there a downside in supporting all 64 bits to pass the signal between CPU/controller/physical memory?
My specific question is with the ASUS M3N78-VM motherboard that my home server uses. I currently have 4x2GB installed for a total of 8GB but I was hoping to upgrade to say 16GB (4x4GB). The official specifications of that motherboard says it only supports up to 8GB but it was released back when only 2GB sticks were available. What, if any, would prevent it from working with 4GB sticks now that 4GB sticks are available?  My general question is with motherboards in general... what would prevent a motherboard from working with bigger sticks if its all just the same type (DDR2 for example and same speeds) of memory?
Looking for Scifi Short Story in a Jerry Pournelle edited Anthology I'm looking for the title of the short story, and any of the volumes of anthology it may have appeared in. I know for SURE it's in one of Jerry Pournelle's anthologies, either Star Empires and There will be War, but as I have all the eBook version of THere will be war, I'm almost certain it wasn't there.   Anyway, the book is about a Commodore who went back to the academy to visit. I'm not sure what his name was, but I'm pretty sure he lived at "Mercer Hall". He had 2 roommates, and a butler to take care of all their needs, like putting away their stuff. (He even tried to argue with the hall monitor) The butler once took away their bottle of booze UNTIL they study for mid-term, and only gave it back AFTER they wrote to their mother AFTER the exam.   The book also goes heavily into "Bless you!" or the translated version, "May the great cosmic magnificence be benevolent toward you" or something like that. Basically, it's about as inoffensive as possible, and if you say it enough, and the aliens are reasonable, they will give up and things will resolve peacefully.   My Google-fu is weak and I can't find this particular story, or which volume of anthology was it in.   Little help? How can we sum up $\sin$ and $\cos$ series when the angles are in arithmetic progression? How can we sum up $\sin$ and $\cos$ series when the angles are in arithmetic progression? For example here is the sum of $\cos$ series:  $$\sum_{k=0}^{n-1}\cos (a+k \cdot d) =\frac{\sin(n \times \frac{d}{2})}{\sin ( \frac{d}{2} )} \times \cos \biggl( \frac{ 2 a + (n-1)\cdot d}{2}\biggr)$$  There is a slight difference in case of $\sin$, which is: $$\sum_{k=0}^{n-1}\sin (a+k \cdot d) =\frac{\sin(n \times \frac{d}{2})}{\sin ( \frac{d}{2} )} \times \sin\biggl( \frac{2  a + (n-1)\cdot d}{2}\biggr)$$   How do we prove the above two identities? Boggle: What is the dice configuration for Boggle in various languages? This is the dice configuration for the English Boggle:  Other variants and discussions concerning letter distributions for English can be found here:  , , ,  (Wikipedia).  I am interested in the 16 dice configurations for also other languages (Spanish in particular) and I am unable to find it anywhere online.  Versions I have managed to find so far:  ,  English 25 dice version:   Spanish 25 dice version:   Italian 25 dice version: In Harry Potter and the philosophers stone Harry was "receiving" his letters in a way that was so labour intensive. First, one was sent in the mail, and the others where then sent, either shoved into the letterbox or through the door cracks. It then it got, "out of hand," as twenty four letters found their way inside the house. The letter sender (Minerva, I do believe, Deputy Headmistress) must, obviously have known they were not getting to Harry, so why keep sending them? I cannot even believe Minerva sending more than thirty letters! Why not either,  A) Send the letters directly to Harry  OR  B) Show up at the house, to explain everything.  Why not do a more logical way of sending/explaining Harry's being? Notify-osd notifications appear unthemed in top-left corner How does Python evaluate the expression 1+++2?  How many ever + I put in between, it is printing 3 as the answer. Please can anyone explain this behavior  And for 1--2 it is printing 3 and for 1---2 it is printing -1 I'm looking for a site, similar to StackOverflow, but with possibility to ask opinion based questions Since opinion based questions are not allowed neither here nor on stackoverflow, I would like to ask if any of you, know some other web page (outside Stack* ecosystem), where we can ask questions like:  "Which Java Web framework would you recommend to learn"   or any other, which by nature are opinion based.  EDIT1:  Allow me to explain a bit more - I know there are webgroups, forums and mailing lists BUT most of those are for single programming language or framework and I'm looking for something more generic. Stackoverflow is great because there are experts from all sort of programming languages and frameworks, so if it would be allowed to ask:   "Best web frameworks similar to ASP.NET MVC4"  I would get a lot of opinions, from different languages and frameworks, and that exactly what I'm looking for. How can you find and replace text in a file using the Windows command-line environment? I am writing a batch file script using Windows command-line environment and want to change each occurrence of some text in a file (ex. "FOO") with another (ex. "BAR"). What is the simplest way to do that? Any built in functions? Clipboard.GetText returns null (empty string) My clipboard is populated with text, but when I run  string clipboardData = Clipboard.GetText(System.Windows.Forms.TextDataFormat.Text);   I get back an empty string. I've toyed with various forms of the call including:  string clipboardData = Clipboard.GetText(); string clipboardData = Clipboard.GetText(System.Windows.Forms.TextDataFormat.UnicodeText);   But with the same result.  Am I missing something obvious? $\aleph_0$ is the cardinality of the set of natural numbers, $\aleph_0 = |N|$. $c$ is the cardinality of the continuum, i.e. the set of real numbers $c = |R|$.  I know that $|P(A)| = 2^{|A|}$. This means that the cardinality of the power set of a set is 2 raised to the power of the cardinality of that set.  This basically means that to prove  $2^{\aleph_0} = c$, I need to prove $c = |P(N)|$. I've seen the Cantor diagonal argument, although I have no idea on how to use it to prove this.   Could anyone suggest ideas of the simplest way to prove that $2^{\aleph_0} = c$? Houston, we have a porblem Since  in titles, and there's not even a way  (or ) we all know users just get around that filter by typing various permutations of the word "problem".  The filter has . The bottom line there was:     "Hacking around" the filter is in fact very very rare.   I beg to disagree. I tried searching Stack Overflow for the following variations of the title:  problme probelm probeml probmle probmel prolbem prolbme prolebm prolemb prolmbe prolmeb proeblm proebml proelbm proelmb proembl proemlb   These are just a couple of permutations from 5040 possible ones. I also tried searching for variations with left out letters, like proble, or prblm. Here's just a graph of a subset from maybe 20 searches—but in reality, there might be more ways to get around the filter:    Was this ever intended? I know it saves a lot of bad titles from being created, but on the other hand it enforces even worse titles as well. 3% based on the  aren't much, but they're 3% crap the filter actively provokes.  Now, my questions up for discussion are:   What are we going to do about this large number of porblematic posts? It seems almost impossible to fix all those. We now have a really good review system that allows people to dig through low quality posts the entire day, so that'd be a way to address this of course. Are there any plans of getting rid of the filter again? This, at least, would give you a good indicator of poor quality. If a post title contains the word "problem" you instantly know something's off. Why not have it reviewed? I understand that some people will choose a better title after being blocked, but I don't even want to start looking at the number of those who merely did a s/problem/issue, or even worse, just used "problems" (because that's not blocked, just sayin').   In the end I'm just thinking if there was a way to clean up the back log on this, or how to prevent more posts of this sort in the future, even with a title filter in place if it has to be. Childrens fantasy, blind monk leading boy who can control the elements There has been a significant drop (90%) in traffic from Google to one of my well-established sites (6+ years) in the last week. Searches show that the top 3 wide keywords all dropped 4 spots. Searches for other keywords do not show ANY results in the first 10 to 25 pages of results, while previously one 1st or 2nd page at most.  Since there are , the question really is:  What steps are necessary to figure out what caused such a drop?  There have been no major changes during this period or the last month on the site and certainly not in the homepage which has dropped in rank. Over all the years of running this site and plenty of others, I have never experienced this. There are is duplicate content on my site and I have rigorously used canonical links for the last few years to ensure it is not misinterpreted as such. Good color palette, usable for the color blind. I'm designing a chart right now, that will slowly have more items added to it. I'd like to create an list/order of colors for the items, that will be most usable for the color blind to differentiate between each item. Any ideas how/where to start? inequality with three variables and condition Manually calculated $R^2$ doesn't match up with randomForest() $R^2$ for testing new data I know this is a fairly specific R question, but I may be thinking about proportion variance explained, $R^2$, incorrectly. Here goes.  I'm trying to use the R package randomForest. I have some training data and testing data. When I fit a random forest model, the randomForest function allows you to input new testing data to test. It then tells you the percentage of variance explained in this new data. When I look at this, I get one number.  When I use the predict() function to predict the outcome value of the testing data based on the model fit from the training data, and I take the squared correlation coefficient between these values and the actual outcome values for the testing data, I get a different number. These values don't match up.   Here's some R code to demonstrate the problem.  # use the built in iris data data(iris)  #load the randomForest library library(randomForest)  # split the data into training and testing sets index &lt;- 1:nrow(iris) trainindex &lt;- sample(index, trunc(length(index)/2)) trainset &lt;- iris[trainindex, ] testset &lt;- iris[-trainindex, ]  # fit a model to the training set (column 1, Sepal.Length, will be the outcome) set.seed(42) model &lt;- randomForest(x=trainset[ ,-1],y=trainset[ ,1])  # predict values for the testing set (the first column is the outcome, leave it out) predicted &lt;- predict(model, testset[ ,-1])  # what's the squared correlation coefficient between predicted and actual values? cor(predicted, testset[, 1])^2  # now, refit the model using built-in x.test and y.test set.seed(42) randomForest(x=trainset[ ,-1], y=trainset[ ,1], xtest=testset[ ,-1], ytest=testset[ ,1]) What is the "correct" way of embedding text into math mode? Lets say I have something like:   \[ Let x = number of cats \]   (This is a contrived example, but pretend we are actually inside a long align environment block...) "Let" and "number of cats" need to be written like normal text, while x= needs to be math type text.  I've seen this:  \[ \mbox{Let } x = \mbox{ number of cats} \]   and this:  \[ \textrm{Let } x = \textrm{ number of cats} \]   They seem to produce equivalent output, but I'm not sure which is the "correct" one. Also, they are not ideal in that the extra space needs to be placed inside the text mode block, otherwise it is ignored as math mode and butts the text right up against the math.  Ideally there would be some command which allowed embedding text into an equation, which correctly inserted leading and trailing space around the block as required without adding space inside the text block.  How does one do that "correctly"? Is spacetime discrete or continuous? What constitutes an observation/measurement in QM? Can I transfer or sync purchased as well as non-purchased songs from my iPhone to my computer?