I'm a Dungeon Master, and I can't figure out how passive wisdom works. In the Player's Handbook it says:      A passive check is a special type of check that dose not use any dice rolls.   That is good to know, but it does not say how you determine if something is a failure or a success!
For Christmas my kiddo got the D&amp;D Starter Set and we've been going though it and the full rules we downloaded online. I'm having a hard time figuring out how the example listed in the rules gets to a final value of 14.  The example is a level 1 character with wisdom of 15 and a proficiency in perception.  I understand that you start with  10 (base) + 2 (character level) + 2 (wisdom 15) which gets you to 14 but then how does the "proficiency in perception" help or factor in?   What gets more confusing is on one of the pre-generated character sheets has a level 1 character with wisdom of 10 but a passive perception value of 10. If I follow the math from above shouldn't it be 10 (base) + 2 (char lev 1) + 0 (wisdom 10 = 0 bonus) for a final score of 12?  How to calculate passive perception?
Are "white" and "black" ever capitalized when referring to people? How to replace ${} placeholders in a text file? I want to pipe the output of a "template" file into MySQL, the file having variables like ${dbName} interspersed. What is the command line utility to replace these instances and dump the output to standard output? How to backup an Android device? Can anyone recommend a good way to backup Android devices? Ideally I would like to do this wirelessly and, not only backup my data, but also my user settings. Is it possible to backup an image of an Android device - so that one doesn't even need to reinstall apps? It would be particularly useful to hear from users that have restored backups, as to how easy, and complete, their processes were. Thanks Fig.1: A typical prompt, asking user for feedback/rating in iOS Background Any serious smartphone users must have seen a message similar to Fig.1 above at least once. Variations of such prompt include: &quot;Please give us 5 star ratings if you love this app!&quot;, &quot;Rate us :)&quot;, &quot;Your rating helps improve this app!&quot;, etc. Basically, Fig.1 asks user to leave a (nice) feedback/rating for the app on its AppStore(or equivalents).  The Shorter Question  When and how often should a mobile app user be asked to leave a feedback/ratings?   The Longer Question #1. Which User-statistics? What are the significant user's behavioral statistics that should be based on to generate Fig.1? For example:  Number of runs since install/reinstall of the application Time elapsed since current application run Time elapsed since first application run Time elapsed since first application install Certain events (e.g. after certain number of stages are cleared for a game app)  #2. When to Ask? If multiple user-statistics are chosen to be calculated to generate Fig.1, specifically how should the user-statistics satisfy the condition of the event? For example:  Form a unified equation (e.g. X^2+Y^2=Z^2) with all significant user-statistics partaken fairly to trigger the event. Create (multiple of) &quot;absolute&quot; event triggers (e.g. every 10th app run; elapsing 2 hours since current application run). Both of the two. Generate Fig.1 whichever comes true first. Neither of the two. &quot;There's a better way!&quot;  #3. How often? What would be the optimal min/max frequency of Fig.1 generation? By optimal, I mean users are not to be bothered too much, yet developers gain maximum output of great feedbacks from users? #4. &quot;Don't bother me again :(&quot; Should users have an option to opt-out from receiving Fig.1 at all? #5. Universal User-statistics for All Mobile Apps? Should apps under different categories be based on different user-statistics? There are significant differences in size and type of user-statistics in apps under different categories. For example, a &quot;Flashlight&quot; app is not typically run for one hour straight, while a music/movie streaming app may be run for over one hour. #6. &quot;This app does not need more feedback.&quot; Should every app of all kinds of user base ask this message? If any, should any mobile app stop generating Fig.1 when target conditions are met (e.g. downloads count, active user count, feedback count)? #7. Feedback/Rating Before Deletion Should users be asked to leave a feedback before deleting as seen in Fig.2 below? Users are more likely to leave very critical review on app deletion, but this kind of feedback will be very helpful for the developers to strengthen their app's weakness for next version release.                                                                                                 Fig.2: Asking user for rating before app deletion Is it possible to double your proficiency bonus twice? Let's say I'm a multiclass rogue/ranger and I have taken Expertise in survival checks. Now, if a ranger is in their favored terrain it says they double their proficiency bonus in intelligence and wisdom checks relating to you environment. If I am in my favored terrain and use my already doubled survival check, will it double again? Can a full version of Ubuntu be Installed on a USB Drive? Drawing visibility polygons in Unity (for vision cones with occlusion) I'm currently trying to create an effect like the one displayed below in Unity:    However, it seems that I can't do this with any of Unity's built-in light objects, and I simply cannot find anything online that talks about this. Is there a way to achieve this in Unity? 2D or 3D solutions are fine, as I'm sure that they're both very similar to each other, How are answers with the same vote score sorted? When a new question is asked how are the answers sorted?  I just answered a question and there were two other answers.  All three answers have 0 votes and no edits.  Immediately after I answered my answer appeared first.  Now the order refreshed,  it appears they are sorted by reputation. What was Natsume hiding in her closet in episode 11? In episode 11 of Tokyo Ravens, what was Natsume hiding in her closet? Let $z_1,z_2,\ldots,z_n$ be complex number such that $|z_i|&lt;1$ for all $i=1,2,\ldots,n$. Show that we can choose $a_i \in\{-1,1\}$, $i=1,2,\ldots,n$ such that $$\left|\sum_{i=1}^n a_iz_i\right|&lt;\sqrt3.$$ optimality of the Carnot cycle It is well-known and is stated always and everywhere that the Carnot cycle is the most efficient thermodynamic cycle. Although stated as such it is rarely proven. One proof is in the article &quot;Engine Efficiencies and the Second Law of Thermodynamics&quot;, (AMERICAN JOURNAL OF PHYSICS VOLUME 37, NUMBER 11 NOVEMBER 1969), Tobin proves that among all engines performing a cycle, so that the engine returns to its starting state, the Carnot cycle is the most efficient where efficiency is defined as $\epsilon= 1-\frac{Q_{rejected}}{Q_{absorbed}}$, and the Carnot cycle is defined as one consisting of an isothermal-adiabatic-isothermal-adiabatic segment. The proof assumes the Clausius equality, that is in a reversible cycle $\oint \frac{\delta Q}{T} = 0$. Then using the geometry of the picture below a simple argument over the areas enclosed in the cycles IABCDJI vs. IAEFGDJI (heat absorbed) or IJDAI vs. GHEAIJDG (heat rejected) will show that any other cycle working between the same temperature limits such as EFGHE will have lower efficiency than the Carnot cycle ABCDA. But this proof assumes tacitly that pieces EFG and GHE are such that $dS&gt;0$ and $dS&lt;0$, respectively. Here I am thinking of a nasty cycle such as shown in the next figure in red where the cycle cannot be neatly separated into two and only two monotonic parts having $dS&gt;0$ or $dS&lt;0$. There is no obvious reason why that restriction should hold in general. Clearly this monotonicity should hold if the engine has only temperature as its independent &quot;force&quot; but if the engine's state needs more than one independent force variable than the situation is more complicated. Instead it is reasonable to assume that any physical cycle should have finite number of monotonic pieces, kind of a &quot;thermodynamic Dirichlet condition&quot; but it could also have self intersections, little loops, and other ugly features when projected on the TS plane. How would then one prove the optimality of a Carnot cycle? Or ugly cycles on the ST plane are non-physical even if there are more than one thermodynamic variables? [] [] $f(x)$ is a strictly increasing, and continuous, function on $[0,+\infty)$. Consider the integral,  $$\int_0^a f^{-1}(x) dx.$$  Reasoning  The interval $[0,a]$ is "reflected" across the line $y=x$ onto the interval $0 \leq y \leq a.$  $f(x)$ and $f^{-1}(x)$ are symmetric across the line $y=x$. So, the integral is equivalent to the area bounded by $y = 0$, $y=a$, and $f(x)$.  So, "integrating $f$ along an interval on the $y$-axis" is the same as integrating $f^{-1}$ along the same interval on the $x$-axis?  Question  Is my reasoning correct? What autofocus zone selection mode should I use for action/event shooting? I have a Canon 7D, and typically shoot everything I do in its single-point autofocus zone select mode, because I usually want fine control over exactly what the camera is focusing on and I often find that its two automatic focus zone select modes don't focus on what I want in focus.  For most of the photography I do, this is fine -- I have enough time that I can compose the shot the way I want, use the joystick on the back to select the right focus point, and take the shot at my leisure.  However, recently I've been doing more event/action photography, and I've been running into issues with this mode of operation.  Too often, I will see a person start to do something interesting, but my autofocus point is not in the right place -- so by the time I get the camera up, adjust the settings, and move the autofocus point, the opportunity to take the shot has passed.  My question is, what autofocus zone selection mode and workflow should I use for this type of photography?  I could use the 5-zone partial-auto mode (which gives me a choice of top, middle, bottom, left, or right, and then the camera chooses the points within my selected region), but I find that the time needed to switch in between that mode and the single-point mode is similarly prohibitive, and I have to hope that the camera chooses the right thing to focus on. It looks like this guy  without even knowing it.  I don't get the impression that he was trying to harm anyone with this process.  What about a warning message that triggers after a person upvotes (or downvotes) the same person X times within Y time span (with X and Y being thresholds that are well below the limit that actually results in a vote fraud reversal)?  Say, twice within 15 minutes?  Maybe display a warning pop-up that says:     Whoa, Camel!  It looks like you're starting to perform serial voting on a particular user.  Did you know that    I have little doubt that this guy would have stopped had he been (gently) warned.  Perhaps others will stop, too. jQuery - auto size text input (not textarea!) Do virtual particles actually physically exist? I am confused by the orientation of a topological manifold. My understanding is: An orientation of a topological manifold is a choice of generator of the $H^n(M,\mathbb Z)$. So given a manifold, we could have 2 orientation defined on the manifold. For $\mathbb{CP}^2$ on orientation is determined by the complex structure, the other orientation is denoted by $\overline{\mathbb{CP}}^2$. And it is well known that there is no orientation reversing map from $\mathbb{CP}^2$ to itself.  My question is: are they homeomorphic? I guess they are not homeomorphic. But I am confuesed, doesn't the orientations defined on the same manifold, how come after reversing the orientation they become not homeomorphic? Borel-Cantelli-related exercise: Show that $\sum_{n=1}^{\infty} p_n < 1 \implies \prod_{n=1}^{\infty} (1-p_n) \geq 1- S$. This is supposed to be related to the  (my justification for the independence tag). In Williams' Probability with Martingales, 2BCL is proven and then the following is given as an exercise:  Prove $S \doteq \sum_{n=1}^\infty p_n &lt; \infty \implies \prod_{n=1}^\infty (1-p_n) &gt; 0$ assuming $0 \leq p_n &lt; 1$. Hint: Show that $S &lt; 1 \implies \prod_{n=1}^\infty (1-p_n) \geq 1 - S$.   Proving the hint: I tried to find $\{a_n\}$ s.t. $$\prod_{n=1}^\infty (1-p_n) \geq \prod_{n=1}^\infty e^{a_n} = e^{\sum_{n=1}^\infty a_n} \geq 1 - \sum_{n=1}^\infty a_n \geq 1 - S &gt; 0$$ That is, find $\{a_n\}$ s.t.: 1a. $1 - p_n \geq e^{a_n}$ 1b. $a_n \leq p_n$ I thought of $a_n = \ln(1-p_n)$ (a reason why $p_n &lt; 1$, I guess) Is that right? Edit: Actually, assuming my proof is right, is $S &lt; 1$ used in the proof? If so, where?  From Williams book: I have the following code that will remove lines with the pattern banana and 2 lines after it:  sed '/banana/I,+2 d' file   So far, so good! But I need it to remove 2 lines before banana, but I can't get it with a “minus sign” or whatever (similar to what grep -v -B2 banana file should do but doesn't):  teresaejunior@localhost ~ &gt; LC_ALL=C sed '-2,/banana/I d' file sed: invalid option -- '2' teresaejunior@localhost ~ &gt; LC_ALL=C sed '/banana/I,-2 d' file sed: -e expression #1, char 16: unexpected `,' teresaejunior@localhost ~ &gt; LC_ALL=C sed '/banana/I,2- d' file sed: -e expression #1, char 17: unknown command: `-' Is it possible in PHP to do something like this? How would you go about writing a function? Here is an example. The order is the most important thing.  $customer['address'] = '123 fake st'; $customer['name'] = 'Tim'; $customer['dob'] = '12/08/1986'; $customer['dontSortMe'] = 'this value doesnt need to be sorted';   And I'd like to do something like   $properOrderedArray = sortArrayByArray($customer, array('name', 'dob', 'address'));   Because at the end I use a foreach() and they're not in the right order (because I append the values to a string which needs to be in the correct order and I don't know in advance all of the array keys/values).  I've looked through PHP's internal array functions but it seems you can only sort alphabetically or numerically.