What did Mace Windu mean when he said that Anakin is too old to become an apprentice?
How old should you be when you begin Jedi training?
Why is the subject omitted in sentences like "Thought you'd never ask"? "Thought you'd never ask" is "I thought you'd never ask" with "I" omitted. "Hope this helps" is "I hope this helps" with "I" omitted.   In English grammar, normally every sentence should have a subject, right?   My first thought is that these two examples are so often used that they are like set phrases. But these are not really set phrases. You can alter the words after "thought" and "hope".  Another possible explanation is the tendency to drop the subject if it is the first person pronoun. It seems that in many languages, such as Spanish, Italian and Japanese, the first person subject is usually omitted. Maybe English is going the same way? (Not exactly the same, since in Italian, verb forms change according to the person, so the subject is not necessary to understand who one's referring to.)  And, apparently, such omission is more common in spoken English than in written English.  Are there more examples of such first person subject omission? How frequent is it? Deseasonalizing count data I used stl() in R to decompose count data into trend, seasonal &amp; irregular components. The resulting trend values are not integers anymore. I have the following questions:   Is stl() an appropriate way to deseasonalize count data? Since the resulting trend is not interger valued anymore, can I use lm() to model the trend components? Why isn't dark matter just ordinary matter? There's more gravitational force in our galaxy (and others) than can be explained by counting stars made of ordinary matter. So why not lots of dark planetary systems (i.e., without stars) made of ordinary matter? Why must we assume some undiscovered and unexplained form of matter? Automorphism group of the quaternion group Why does the atmosphere rotate along with the earth? I was reading somewhere about a really cheap way of travelling: using balloons to get ourselves away from the surface of the earth. The idea held that because the earth rotates, we should be able to land in a different place after some time. As we all know, this doesn't happen.  Someone said that the reason why this doesn't happen is because the atmosphere (air, clouds etc.) also revolves around the earth (with the same angular velocity as the earth's rotation). Since we are also part of the atmosphere, our position doesn't change relatively.  Well, I'm not convinced with that answer. Why does the atmosphere rotate along with earth?  Gravitational force is towards the centre of the earth, but I don't see how it's making the atmosphere rotate. Where can I find a repository for older unsupported releases? How can I get exactly 5 logarithmic divisions of an interval? Show that function $f$ has a continuous extension to $[a,b]$ iff $f$ is uniformly continuous on $(a,b)$ Let $E \subset F \subset X$ and $f:E\rightarrow Y$. We say that the function $g:F\rightarrow Y$ is an extension of $f$ if $g(x) = f(x)$ for all $x \in E$.   Let $f: (a, b) \rightarrow \mathbb{R}$. Show that $f$ has a continuous extension to $[a, b]$ if and only if $f$ is uniformly continuous on $(a, b)$.   $(X,d)$ is a metric space.  Hint: To prove $\Leftarrow$ start by showing that $f$ maps Cauchy sequences to Cauchy sequences. Then how should you define $g(a)$ and $g(b)$?  The $\Rightarrow$ part of the proof was quite simple, but even with the hint, the other way seems a bit difficult. Doesn't the first part of the "hint" follow from the way we defined $f$? If so, how do I prove this? Help/Hints appreciated! Why are bias nodes used in neural networks?  How many you should use?  In which layers you should use them: all hidden layers and the output layer? Margin on child element moves parent element Possible to do a MySQL foreign key to one of two possible tables? Well here's my problem I have three tables; regions, countries, states.  Countries can be inside of regions, states can be inside of regions.  Regions are the top of the food chain.  Now I'm adding a popular_areas table with two columns; region_id and popular_place_id.  Is it possible to make popular_place_id be a foreign key to either countries OR states.  I'm probably going to have to add a popular_place_type column to determine whether the id is describing a country or state either way. Show that the boundary of a set equals the boundary of its complement $\newcommand{\bdy}{\operatorname{bdy}}$  I'm trying to show that $\bdy(A) = \bdy(A^c)$.  I know that $\bdy(A) = \operatorname{closure} A \setminus \operatorname{int}(A) = (\operatorname{int}(A^c))^c \setminus \operatorname{int}(A)$, but I don't know where to go from there.  Any help or hints would be very much appreciated. A geometric reason why the square of the focal length of a hyperbola is equal to the sum of the squares of the axes? When I teach conics, I give a simple geometric argument for the Pythagorean relation for ellipses. (By "Pythagorean relation" I mean the fact that the square of the focal length $c$ is the difference of the squares of the semimajor and semiminor axes, i.e. $c^2=|a^2-b^2|$ for the ellipse defined by $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$.) The picture argument goes as follows: just draw the obvious isosceles triangle from the two foci to one of the two points at the end of the minor axis. We see two right triangles; in each, one leg is the focal length $c$ and the other leg is the semiminor axis, while the hypotenuse is the semimajor axis. The result follows from the Pythagorean theorem applied to this right triangle.  But when it comes to the Pythagorean relation for hyperbolas, I can't think of an equally convincing picture to draw. Instead I have to give a rather inelegant algebraic argument for the relation $c^2=a^2+b^2$ (for the hyperbola defined by $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$, with focal length $c$), directly from the definition of the hyperbola. The messy details are below.*  Now, obviously there is an asymmetry between the argument for the ellipse and the argument for the hyperbola: the ellipse argument is almost trivial and doesn't involve working straight from the locus definition, but the hyperbola argument is tedious and does require working straight from the definition. So, my question:     Is there an equally persuasive picture I could draw to convince high   school students of the Pythagorean relation for hyperbolas -- without having to get technical with points at infinity, say?   The natural triangle to draw is the right triangle with legs from the center to a vertex and from that vertex to an asymptote, which has legs of length $a$ and $b$; but then the problem becomes why the length along the asymptote should be equal to $c$. I doubt there is a purely (Euclidean) geometrical reason because this triangle lies on the asymptote, not on the hyperbola itself; I suspect some sort of limiting procedure will be required.    [*] The tedious algebraic details:     The foci lie at $(\pm c,0)$.   Say $a&gt;b$. Then hyperbola is the locus of points $(x,y)$ such that       $$\left|\sqrt{(x+c)^2+y^2}-\sqrt{(x-c)^2+y^2}\right|=2a$$      Assume for simplicity the expression between the absolute value bars   is positive. (The algebra is even more tedious if we don't make such a   simplifying assumption.) Then moving the right root to the other side   and squaring gives      $$(x+c)^2+y^2=4a^2+(x-c)^2+y^2+4a\sqrt{(x-c)^2+y^2}$$      Simplifying gives      $$xc-a^2=a\sqrt{(x-c)^2+y^2}$$      and upon squaring again we have      $$x^2c^2-2xca^2+a^4=a^2(x^2-2xc+c^2+y^2)=a^2x^2-2xca^2+c^2a^2+a^2y^2$$      which reduces to      $$x^2(c^2-a^2)-y^2a^2=a^2(c^2-a^2)$$      Defining $b^2:=c^2-a^2$ brings the equation into the form   $x^2/a^2+y^2/b^2=1$, and the Pythagorean relation follows from the   definition of $b$. Android: How to draw route directions google maps API V2 from current location to destination When computing the covariance matrix of a sample, is one then guaranteed to get a symmetric and positive-definite matrix?  Currently my problem has a sample of 4600 observation vectors and 24 dimensions. How precisely do I need to post close to 7:00 (somewhere) to get hero of time? Timezones... are complicated. We have full hour offsets, half hour offsets...  And time keeping isn't always accurate. So does the Hero Of Time hat assume full or half hour offsets (or literally any timezone) and how close to 7:00 at somewhere do I have to post for my hat? Trouble enabling Cube surfer addon Every time I have tried to enable the Cube Surfer addon but this error message comes up. FYI I have the correct versions of everything.  I have had this problem with some other add ons as well. Sometimes it's when I have tried to click a button in an addon (after 'successfully' installing) PlotLegends disappearing with list of functions Why doesn't Java have compound assignment versions of the conditional-and and conditional-or operators? (&&=, ||=) Mobile phones and mobile internet in Italy Buongiorno! Suppose I step down from the plain in Fiumicino. What is the fastest way to get hold of Italian SIM-card with some talking minutes and some Internet? The latter is more important than the former.  So, my requirements:   Good coverage in main cities (Rome, Venice, Milan, Florence) Good for 2 weeks (after that I'm going to leave the country, the SIM is going to lose its value anyway) Good for massive internet usage is in store for maps, orientation, etc. Cheap. :)   Now, I know that there are 3 main communication providers in Italy: Vodafone, Wind and the third one. :) Which one? Which one won't leave me destitute and won't sue me over the border months after for some unknown reasons? What I have to look for?