There was some discussion on  about whether ambient humidity could cause a normally good shortcrust recipe to come out dry and crumbly.  Is this possible? How strong of an effect might be expected from going from "average" humidity to extremely dry? Would it affect all types of pastry dough similarly?
Cooking lore places a lot of importance on air humidity for doughs. When a dough fails, people quickly point that out as a possible factor, .     Is it really true? I don't doubt that the actual flour moisture content changes, but is it noticeable in the dough preparation, or is the difference too small to matter?  If it makes a difference, what can I do about it?
My PC has a build-in VT1828S chip. The connection between PC and monitor (which has built-in speakers) is through an HDMI cable.  Audio preferences shows 2 devices for audio output: analog stereo and RS880 Audio Device [Radeon HD 4200] digital stereo (HDMI).  When I plug a headphone in the rear jack and I choose the former device, everything works. When I choose the latter device, instead, no sound is heard, and video playback is too fast. It is as if video frames want to synchronise with the audio timing, but the audio timing information is wrong.  HDMI audio worked perfectly with Ubuntu 11.04, but stopped after 11.10 upgrade. What are the complexity guarantees of the standard containers? How to see what's going on during Windows shutdown/logging off process? Windows 7 msconfig lets users select the options No GUI boot and OS boot information to have a list of drivers being loaded during boot. Is it possible to have similar detailed messages during shutting down/restarting/logging off? Here's the screen I want disable or give me more details: Proof of the equality $\sum\limits_{k=1}^{\infty} \frac{k^2}{2^k} = 6$ Show that for $k$ running over positive integers  $$ \sum_{k=1}^\infty \frac{k^2}{2^k}=6 .$$ We can use finite calculus. How do I configure Apache 2 to run Perl CGI scripts? I would like to configure Apache 2 running on Kubuntu to execute Perl CGI scripts. I've tried some steps that I came across by googling, but nothing seems to work.  What is the right way of achieving this? A question about E12 series resistors I'm trying to calculate E12 resistor series myself.  Above is an illustration of the idea where such equation can be written:  x = r3 + r3 * %tol = r4 - r4 * %tol  form that we can derive:  r4 = r3* [(1 + %tol)/(1 - %tol)]  hence in generalized form we can write (%tol = 0.1 for E12 series);   r(i+1) = ri* [(1 + %tol)/(1 - %tol)]  But when I iterate the above formula in a for loop I obtain the following results for the first resistor values:  1.0000    1.2222    1.4938    1.8258    2.2315    2.7274    3.3335    4.0743    4.9797    6.0863    7.4388  Then I take [(1 + %tol)/(1 - %tol)] = 1.2 rounded value instead of 1.222222 and write the formula as:  r(i+1) = r(i)*1.2  But again when I iterate the above formula in a for loop I obtain the following results for the first resistor values:  1.0000    1.2000    1.4400    1.7280    2.0736    2.4883    2.9860    3.5832    4.2998    5.1598    6.1917  But the real values for E12 should be as:  1.0, 1.2, 1.5, 1.8, 2.2, 2.7, 3.3, 3.9, 4.7, 5.6, 6.8  What am I doing wrong here? How do I get adequate depth of field in macro photography? I have been messing around with some Macro Photography using the techniques (and a reversal ring) described in a  by @ My main issue is that I am having a hard time getting the subject into focus. There are times when the center is blurred and the outside is in focus or the center in focus and the outside out of focus. What are ways to get as much of the subject in focus?   I am using a Nikon D5100, I have a 18-55mm kit lens but I find the 55-200mm lens easier to use for shooting. Arrays, linked lists and other data structures in cmd.exe (batch) script Space after LaTeX commands Closing Etiquette: Why Do Some Answer *and* Close? I've noticed quite a few cases () where people not only vote to close a question, but then also answer said question. At best this is just silly, and at worst it is totally hypocritical and seems almost like rep whoring (since often the closers answers are the only ones that remain to be voted on since no new answers can be given).  If you want to close a question, it makes more sense to simply add a comment if you feel the need to say something. This also leaves the option open for the author of the question to delete it if they want to. If the author realizes they've asked a duplicate, or they want to avoid the onslaught of downvotes that can often accompany a closed question, they should be allowed to delete it. However, if any answers to the question have upvotes, the author can't delete it.  So why do people answer and close? Should we try to crack down on this sort of thing, via either new features, clearly stating it in the FAQs, or just getting the word out through commenting when we see it?  EDIT: Just to clarify, I'm asking this in relation to SO, not MetaSO. How does update work with programs installed from .deb file I'm having some difficulties exactly understanding how the the whole update thing work in Ubuntu and good practice for installing software.  I understand I have a  /etc/apt/sources.list file where all my repositories are listed, and that these repositories are queried when I use apt-get update - to later be used with e.g. apt-get upgrade.  This makes perfect sense and I recently installed spotify by adding deb http://repository.spotify.com stable non-free to this "sources" list.    But then I got confused...  When I went to download Google Chrome I merely had to download and grab a .deb file, and Chrome installed with no problem... but I don't see any new entry in /etc/apt/sources.list...  So how does apt-get update know where to query concerning Chrome updates?  Has it somehow been added to one of the already listed repositories in the sources file?  I would like all my installed software to be encompassed by the update function. I have looked at other questions on this site (e.g. "why does space expansion affect matter") but can't find the answer I am looking for.  So here is my question: One often hears talk of space expanding when we talk about the speed of galaxies relative to ours. Why, if space is expanding, does matter not also expand? If a circle is drawn on balloon (2d plane), and the balloon expands, then the circle also expands. If matter is an object with 3 spatial dimensions, then when those 3 dimensions expand, so should the object.  If that was the case, we wouldn't see the universe as expanding at all, because we would be expanding (spatially) with it.  I have a few potential answers for this, which raise their own problems:   Fundamental particles are 'point sized' objects. They cannot expand because they do not have spatial dimension to begin with. The problem with this is that while the particles would not expand, the space between them would, leading to a point where the 3 non-gravity forces would no longer hold matter together due to distance Fundamental particles are curled up in additional dimensions a la string theory. These dimensions are not expanding. Same problems as 1, with the added problem of being a bit unsatisfying. The answer seems to be (from Marek in the previous question) that the gravitational force is so much weaker than the other forces that large (macro) objects move apart, but small (micro) objects stay together. However, this simple explanation seems to imply that expansion of space is a 'force' that can be overcome by a greater one. That doesn't sound right to me. Fixed Field of $\sigma, \tau$ Let $k$ be a field and let $K=k(x)$ be the rational function field in one variable over $k$. Let $\DeclareMathOperator{\aut}{Aut}\sigma, \tau \in \aut(K)$ s.t. $$\sigma\left(\frac {f(x)}{ g(x)}\right)=\frac {f(1/x)}{g(1/x)}\qquad \&amp;\qquad \tau\left(\frac {f(x)}{ g(x)}\right)=\frac {f(1-x)}{g(1-x)}.$$ Find the fixed field $F$ of $&lt;\sigma, \tau&gt;$. Determine $\DeclareMathOperator{\gal}{Gal}\gal(k/F)$. Find an $h \in F$ so that $F=k(h)$.   Now for the first automorphism $\sigma$, I think if I concentrate on $k[x]$ it will give me some idea. Now, if $f(x)=a_0+a_1x+a_2x^2+ \cdots + a_nx^n \in k[x]$ then if $x^n \sigma(f(x))=f(x)$ the case will be $a_i=a_{n-i}$ $\forall i=0(1)[n/2]$. So all the funtions in $K$ which will be fixed by $\sigma$ are of the form $\frac {f(x)}{ g(x)}$ where $f(x)=a_0+a_1x+a_2x^2+ \cdots + a_nx^n$ and $g(x)=b_0+b_1x+b_2x^2+ \cdots + b_nx^n$ such that $a_i=a_{n-i}$ $\forall i=0(1)[n/2]$ and $b_i=b_{n-i}$ $\forall i=0(1)[n/2]$.   Please check whether am I right or not?  And any ideas for the rest of the part? Birthday Problem applied to collisions I'm trying to extend the birthday problem to detect collision probability in a hashing scheme. Here is my problem. I use the letters and numbers [A-Z][a-z][0-9] to make a set of keys by randomly choosing from that set 10 times and concatenating them all together. So A24cv30kf2 could be one key for example. This implies that the base set has $62^{10}$ possible keys. Next, I want to compute the probability that I would see a collision if I picked a key from that set and issued it to $n$ users. If $M$ represents the size of the set (= $62^{10}$) and $P(M,n)$ the probability then  $$P(M,n) = \frac{M!}{M^{n}(M-n)!}$$  This follows by replacing 365 in the well known birthday problem shown   What I want to understand is the following: I want to check and see if my choice of concatenating 10 is right, when I know that my $n$ is of the order of a few millions and my $1 - P(M,n)$ needs to be less than 0.0001 or some small number. The large values of M &amp; n make the above intractable to compute. Is there an easier way to compute this? Often while playing Pathfinder, my group will run into problems where rules for 3-dimensional play simply don't exist, so far as we can find. Arguments will come up over things like carrying-capacity, movement speed, area-effects, and a variety of other things.  Simply put, are there rules for 3D play for Pathfinder, and if so where can I find them? "OpenID 2.0 for Google Accounts is going away"; will this affect Stack Exchange? Covariance of binary and continuous variable Suppose $y$ is a continuous random variable and $d$ is a binary random variable that takes the value $1$ with probability $p$ and $0$ with probability $1-p$.   How do I show that $\text{Cov}(y,d)=(E[y|d=1]-E[y|d=0])p(1-p)$? Merge pdfs sequentially I would like to merge 4 pdfs, pdf1.pdf, pdf2.pdf, pdf3.pdf pdf4.pdf together so that the pdfs are spliced, i.e. the first page will be the first page of pdf1, the second the first of pdf2, the third the first of pdf3, etc.  The pdf files are with plain images, no table of contents.  How would I accomplish this? It would be nice to do it from Terminal as well. How do you empty the buffers and cache on a Linux system? Glossary with entries without reference Is there a command so that the glossary will also display elements without links (an equivalent of \nocite in BibTeX)?