Note: I am NOT asking if moonlight can be used to start a fire. I am asking whether these particular arguments in support of the claim that it cannot are correct. i.e. I'm looking for an answer that addresses the physics of these arguments specifically.  On , the following claims are made:  You can't start a fire with moonlight no matter how big your magnifying glass is.  General rule of thumb: You can't use lenses and mirrors to make something hotter than the surface of the light source itself. In other words, you can't use sunlight to make something hotter than the surface of the Sun.  Lenses and mirrors work for free; they don't take any energy to operate. If you could use lenses and mirrors to make heat flow from the Sun to a spot on the ground that's hotter than the Sun, you'd be making heat flow from a colder place to a hotter place without expending energy. The second law of thermodynamics says you can't do that. If you could, you could make a perpetual motion machine.  (more claims which I'll omit here)   I neither believe the claim nor follow any of the reasoning. First, I don't get the thing about the perpetual motion machine:  If this is regarding the first law of thermodynamics (conservation of energy), then it's perfectly possible to lose energy while still heating up an object, which would avoid perpetual motion, so I don't get the argument.  If this is regarding the second law of thermodynamics (increasing of entropy), then it's also invalid because the disorder in the system is still increasing.  If this is about something else, then I don't know what that is.   Second,  is a video of a guy using a mirror he can hold in his hand to light paper on fire. Clearly the mirror itself isn't getting as hot as he's making the newspaper, and clearly the mirror is the one reflecting the sunlight. So how can one claim that the paper fundamentally can't get hotter than the reflecting surface? Why can't the moon's surface fundamentally behave similarly (albeit with poorer reflectivity)? Can someone explain? Is Randall confusing heat with temperature? Or maybe conduction with radiation? Or am I missing something subtle (or perhaps not so subtle)?
You can start fire by focusing the sunlight using the magnifying glass.   I searched the web whether you can do the same using moonlight. And found  and  - the first two in Google search results.  What I found is the thermodynamics argument: you cannot heat anything to a higher temperature using black body radiation than the black body itself, and Moon isn't hot enough.  It may be true, but my gut feelings protest... The larger your aperture is, the more light you collect, also you have better focus because the airy disk is smaller. So if you have a really huge lens with a really short focus (to keep Moon's picture small), or in the extreme case you build a Dyson-sphere around the Moon (letting a small hole to the let the sunlight enter), and focusing all reflected light into a point it should be more than enough to ingnite a piece of paper isn't it?   I'm confused. So can you start fires using the Moon?
What desktop environments can group window icons in the taskbar like Windows 7? I find it much faster to identify a window in the taskbar (window list) by its icon,    rather than by its text:    The problem with most graphical interfaces I've  is that they don't group windows, and if you have more terminals or file managers, they'll just clutter the taskbar and you won't know which is which. Windows 7 offers a relatively elegant solution to this by grouping similar window icons together.  Question: What Linux  have this functionality? If addons exist that provide it, that's alright.  For reference, a Cinnamon applet that sort of does this is . I want to subtract a constant number from my data to get new data file. For example, I want to subtract  10 from my data.   data.txt  Id  a   b   c   d   e 1   1   2   3   4   5 2   2   3   4   5   6 3   3   4   5   6   7 4   4   5   6   7   8 5   5   6   7   8   9 6   6   7   8   9   10 7   7   8   9   10  11 8   8   9   10  11  12 9   9   10  11  12  13 10  10  11  12  13  14 11  11  12  13  14  15 12  12  13  14  15  16 13  13  14  15  16  17 14  14  15  16  17  18   Required output:  out.txt   Id  a   b   c   d   e 1   -9  -8  -7  -6  -5 2   -8  -7  -6  -5  -4 3   -7  -6  -5  -4  -3 4   -6  -5  -4  -3  -2 5   -5  -4  -3  -2  -1 6   -4  -3  -2  -1  0 7   -3  -2  -1  0   1 8   -2  -1  0   1   2 9   -1  0   1   2   3 10  0   1   2   3   4 11  1   2   3   4   5 12  2   3   4   5   6 13  3   4   5   6   7 14  4   5   6   7   8 Set HDMI sound output automatically on connect/disconnect I have a dual screen setup on my laptop (using 12.04 LTS) using a HDMI connected display. Everything works fine, but everytime I connect/disconnect the cable I have to go to Sound preferences and change the sound output device manually.  Is there any way to change the sound output device on connect/disconnection of cable, so when I connect my display the sound output is set to HDMI and when I disconnect it the sound goes back to laptop speakers? Is there a clever way to show that  $$|x| - |y| \leq |x-y|$$  I believe I can think of a way to solve this using cases, but the book I'm working out of said that "A very short proof is possible if you write things in the right way" which has motivated me to figure out this quick way, but I've failed thus far and any help would be appreciated Should "each" be followed by a singular or plural possessive? If a possessive noun, which is plural, is preceded by "each", then should it use the singular or plural possessive form?  For example, which of the following is correct?    spend time in each other's presence spend time in each others' presence How to check if a point is inside a rectangle? There is a point $(x,y)$, and a rectangle $a(x_1,y_1),b(x_2,y_2),c(x_3,y_3),d(x_4,y_4)$, how can one check if the point inside the rectangle? Questions link almost unreadable when active on meta If you click on  the font color is almost unreadable on the main site here.  Is it possible to make it a slightly different color? (I cannot say if darker or lighter is better) Allow rejected editors to be @replied to Basically on my site I have a bunch of song lyrics and in a static page I want to show them listed by album  and album position of the song and I have two custom fields with that data, sd_album_title and `sd_album_track_n. Plus some of the songs don't have an album yet, so both values are void, and I wish to list those ones at the foot of the others, sorted by alphabetical order.  The latest thing I tried at least to sort everything by the two field is this one:  $key = 'sd_album_title'; $themeta = get_post_meta($post-&gt;ID, $key, TRUE);  add_filter( 'pre_get_posts', 'my_get_posts' ); function my_get_posts( $query ) {     if ($themeta != '') {         $query-&gt;set( 'post_type', 'lyric' );         $query-&gt;set( 'meta_key', 'sd_album_title' );         $query-&gt;set( 'orderby', 'meta_value' );         $query-&gt;set( 'order', 'ASC' );         $query-&gt;set( 'meta_query', array(               array(                     'key' =&gt; 'sd_album_title'               ),               array(                     'key' =&gt; 'sd_album_track_n',                     'value' =&gt; 'target_value',                     'compare' =&gt; '&gt;=',                     'type' =&gt; 'numeric'               )         ));     }     return $query; }  $getlist= 'my_get_posts'; $posts = get_posts( $getlist );   And my intention was to put an else at the end of it with an array ordered by title for the other songs, but it returns nothing as it is. Could something like this work with some corrections or am I on a totally wrong path? How to say that something is (not) random I want to compare two things, one of which is random and the other is not, in favor of the latter. I'd like to do it in a more sophisticated way than simply using the word "random".  Like, for example,     In this case, your pay will not depend on the roll of the dice.   But Google Ngrams doesn't find a single occurrence of "depend on the roll of the dice", so I guess there's something wrong with this particular phrase. What would be a better substitute? I'm trying to transition from a list of pros to a list of cons, and would like to have some sort of transition quote. Something in the form of,  "But, alas, (((something something quote quote)))"  Everything that has a beginning has an end, something along the lines of that. Syntax highlighting language hints Do you think it would be worthwhile to provide hints as to what language to use for the syntax highlighting?  Sometimes I find the highlighting on SQL or VB.NET answers is more distracting than helpful; for example:       to pick the two I've been looking at recently. A sequence of real numbers such that $\lim_{n\to+\infty}|x_n-x_{n+1}|=0$ but it is not Cauchy Can Muggles publicly establish the existence of a magical community? Open Attachment on Create of Child Record How can I import Opera bookmarks into Chrome? showing $\psi: R\to \mathbb C$ is ring isomorphism. Why is sample standard deviation a biased estimator of $\sigma$? According to the Wikipedia article on  the sample SD   $$s = \sqrt{\frac{1}{n-1} \sum_{i=1}^n (x_i - \overline{x})^2}$$  is a biased estimator of the SD of the population. It states that $E(\sqrt{s^2}) \neq \sqrt{E(s^2)}$.   NB. Random variables are independent and each $x_{i} \sim N(\mu,\sigma^{2})$   My question is two-fold:   What is the proof of the biasedness? How does one compute the expectation of the sample standard deviation    My knowledge of maths/stats is only intermediate. Combination with repetitions. Prove the inequality $\frac{a}{c+a-b}+\frac{b}{a+b-c}+\frac{c}{b+c-a}\ge{3}$