I was watching Growing pains TV shows, one scene is that Carol is watching a show called "the sturgeons of Pitt Street", and her mom was watching too and asked Carol "why is the butler on all fours? " then Carol answered the family dog died, and they didn't have the heart to tell their grandma.   I don't understand why Carol's mother ask "why is the butler on all fours? " and the meaning of it. Anyone could help? Thanks.   Ref: it is from Growing pains TV shows, first season，5th episode."super dad".
Immediately, his insides started writhing as though he'd just swallowed live snakes -- doubled up, he wondered whether he was going to be sick -- then a burning sensation spread rapidly form his stomach to the very ends of his fingers and toes -- next, bringing him gasping to all fours, came to a horrible melting feeling, as the skin all over his body bubbled like hot wax -- and before their eyes, his hands began to grow, the fingers thickened, the knuckles were bulging like bolts -- his shoulders stretched painfully and a prickling on his forehead told him that his hair was creeping down toward his eyebrows -- his robes ripped as his chest expanded like a barrel bursting its hoops -- his feet were agony in shoes four sizes too small      Harry potter and the chamber of secrets   It is the description of the feeling of drinking Polyjuice Potion, which makes someone into a different person, from the point of view of Harry Potter turning into Gregory Goyle.  And I don't understand what 'bring him gasping to all fours' means, especially 'four'. Does four here mean number 4?
Shadows along edges of mesh in 3D View Python Split String Lets Say we have Zaptoit:685158:zaptoit@hotmail.com   How do you split so it only be left 685158:zaptoit@hotmail.com Is there any practical difference between saving at 300ppi or 72ppi? I often see statements in discussions about web displayed image quality that go something like this: "I only upload pictures at 72 dpi and 1200 pixels on the long edge, so if someone copies and prints the image it won't look as good as if it were 300 dpi."  What? Have I missed something here?  Does an image edited and saved/exported with 1200x800 pixels at 300 ppi look any different online than the same image saved/exported with 1200x800 pixels at 72 ppi? Other than the metadata regarding ppi, is there any difference in the two images at all? If so, what is the difference? If I tell my printer to print the images at 4R (4X6 inches) will there be any difference at all in how the printer creates a print from the 1200x800 @ 300 dpi image versus the 1200x800 @ 72 dpi image? Why and how can you hear explosions in space in Star Wars? Considering that sound can't travel through vacuum. When is unbalanced data really a problem in Machine Learning? We already had multiple questions about unbalanced data when using , , ,  and a number of other similar questions, what makes it a very popular topic! Unfortunately, each of the questions seems to be algorithm-specific and I didn't find any general guidelines for dealing with unbalanced data.  Quoting , dealing with unbalanced data     (...) heavily depends on the learning method. Most general purpose   approaches have one (or several) ways to deal with this.   But when exactly should we worry about unbalanced data? Which algorithms are mostly affected by it and which are able to deal with it? Which algorithms would need us to balance the data? I am aware that discussing each of the algorithms would be impossible on Q&amp;A site like this, I am rather looking for a general guidelines on when it could be a problem. The direct sum $\oplus$ versus the cartesian product $\times$ In the case of abelian groups, I have been treating these two set operations as more or less indistinguishable. In early mathematics courses, one normally defines $A^n := A\times A\times\ldots\times A$; however in, for example, the fundamental theorem of finitely generated abelian groups, we normally write that every such group is isomorphic to one of the form $$ \mathbb{Z}^n \oplus \mathbb{Z}_{r_1} \oplus \cdots \oplus \mathbb{Z}_{r_t}  $$ where $\mathbb{Z}^n$ now means $\mathbb{Z}\oplus\mathbb{Z}\oplus\cdots\oplus\mathbb{Z}$.  From an intuition perspective, and in the sense of sets, is this more or less the same as $\mathbb{Z}\times\mathbb{Z}\times\cdots\times\mathbb{Z}$? (Bear in mind I am normally using these ideas in relation to homology groups.) Spacing before and after section titles "It was my op" what does it mean? I heard this in  movie. It was my op. What does it mean? Googling gave me : 'Original Poster'. But that doesn't seem very meaningful. I know that each new tab on Google Chrome have its own process, but I have 14 chrome.exe processes running actually as I can see it on the Task Manager, and only two tabs are opened on Google Chrome.    Could it be due to Chrome extensions? What other reason can open more chrome.exe process and how to avoid it? Best way to build a Plugin system with Java How would you implement a Plugin-system for your Java application?  Is it possible to have an easy to use (for the developer) system which achieves the following:   Users put their plugins into a subdirectory of the app The Plugin can provide a configuration screen If you use a framework, is the license compatible with commercial developement? Why didn't Harry Potter tell Aunt Petunia he was rich to improve how he was treated by Dursleys? This is a follow-up question to   One reason Aunt Petunia mistreated Harry was that she did not know he was rich. If she knew, she would naturally have treated this golden goose nicely. Her retirement would be secured if Harry financially supported her in old age.  Why didn't Harry tell Aunt Petunia he was rich? Surely every boy wants to be treated nicely by his family. \ifmmode doesn't seem to work correctly inside an array environment I’m struggling with getting \ifmmode to work correctly when used inside an array environment which is inside a displaymath environment.  Here is a minimal example:  \documentclass{article}  \newcommand{\signal}[1]{%   \ifmmode     1#1   \else     2$#1$   \fi }  \begin{document} \begin{displaymath}   \begin{array}{cc}     \signal{a} \signal{b} &amp; \signal{c} \signal{d} \\   \end{array} \end{displaymath} \end{document}   This example generates the following output:        Why doesn’t all invokations of \signal detect math-mode? Solution check: Let $f_n$ be fibonacci numbers. Prove: $\sum_{k=0}^{n-1} \binom{n+k}{2k+1} = f_{2n-1}$ and $\sum_{k=0}^n \binom{n+k}{2k} = f_{2n}$ There are many, many old posts on meta asking for suggestions on how to better organize favorites.  ,  and , among others.  This is not meant to be an open discussion on how to improve favorites, but rather a specific feature request that I'd like feedback on.      I would love to see a feature added that would let users arbitrarily create "groups" of favorites, and drag individual favorited questions under these groups.  I have about 2 pages of favorites (I know others have much more), and finding an individual one is quite difficult, especially since the specific question title is usually forgotten.  I just added  to my favorites, since I liked Andrew Whitaker's answer, and might want to come back and look at it later; I'd love to add this to a group called, say, "Useful Code".    I've favorited other posts since they had neat tricks in them, or because there were answers written on interesting theoretical computer science topics.  Having different groups for all these areas would be immensely helpful in finding posts later. The close dialog says there are two off-topic votes, but none of the off-topic reasons have votes next to them I've found strange behavior when closing this  - I definitely see that there are 3 closing votes and 2 of them are at "Off-topic" section:   -but there are no explanations on section itself:   -while, normally, it's expected that it will appear. In custom comments section there are also no closing-votes displayed.   Perhaps it's just my browser (which is FF 26 x64 under Win) - so marking this as a "possible bug". Thank you for your attention. Orange squares appearing on render? I'm trying to render a scene in Blender, and as of yesterday (it was not doing this when I was working on it 2-3 days ago), I am seeing orange squares dancing around the rendered image. Google tells me that these are render tiles (I think), but what are they, why are they there, and how do I get rid of them? How to upgrade only core with drush? Is there an integer $N>0$ such that $\varphi(n) = N$ has infinitely many solutions? Let $\varphi: \mathbb{N} \to \mathbb{N}$ be the totient function.   Is there an integer $N &gt; 0$ such that there are infinitely many integers $n &gt; 0$ such that $$\varphi(n) = N?$$ Getting random row through SQLAlchemy Kinematics with non constant acceleration A particle experiences an acceleration described by  $$ a=kx^{-2} $$ where x is the displacement from the origin and k is an arbitrary constant.  To what value does the velocity v of the particle converge to as x approaches infinity if the particle starts at some point x0?  If I approach this problem with energy, then $$ W = \int F \mathrm{d}x $$ $$  = \int_{x_0}^\infty mkx^{-2} \mathrm{d}x $$ $$  = mk(-\infty^{-1}+{x_0}^{-1}) $$ $$ W = K = mk{x_0}^{-1} $$ $$ \frac{1}{2}mv^2 = mk{x_0}^{-1} $$ $$ v = \sqrt{2k{x_0}^{-1}} $$  How would I solve this problem with pure kinematics? (there appears to be some sort of cyclical dependency where acceleration affects velocity, velocity affects displacement, and displacement affects acceleration)  Likewise, two particles experience accelerations described by $$ a_1=k_1x^{-2} $$ $$and $$ $$ a_2=-k_2x^{-2} $$ where x is the distance between the two particles  What two velocities do the particles reach as x approaches infinity if the two particles are initially separated by some x0?