This student doesn't learn by rote and is singled out as an individual thinker that can innovate.  He was fearful that he would not pass his exams about repairing space craft but in the end he proves to be much better than the other students.
In the story I'm trying to recall, everybody on their thirteenth birthday (?) is assigned by some kind of brain analysis method a profession and given some kind of pill (?) that instantly (?) grants them the required knowledge and skills to start working immediately. Some professions are more sought after than others, especially in view of the olympic (?) games regularly held on a profession-by-profession basis.  The protagonist, however, is turned down from this system and dismissed with some general reason and has to work his way to adulthood the boring old way: studying from books. Eventually he rejects from his status as a "special" student and goes on the run, hiding from the teachers and envying the normal people.      Eventually, it turns out that the protagonist was actually smart enough that being spoonfed premade information was a waste. What he actually was assigned to was advancing the bundles of knowledge themselves, as well as being front line in the technological progress.  "Somebody has to write those textbooks! You can infuse knowledge about how to use today's technology, but you can't do that for tomorrow's - people that get assigned a profession become tied with their assigned technology and are only as relevant as that. If you want more, you must learn how things actually work, and there's no shortcut for that." (not an actual quote, but a specific passage as I remember it.)  The troubles the protagonists underwent were actually planned and necessary for him to acknowledge and accept his role in society.   This story was certainly longer than a couple pages, but it wasn't very long either. If it's a short story, it was probably written by Asimov, but I can't be sure. It rings me of Brave New World given the theme of government-issued population planning, but it certainly doesn't fit with anything else in the actual plot. Any idea?
Explain how (or if) a box full of photons would weigh more due to massless photons I understand that mass-energy equivalence is often misinterpreted as saying that mass can be converted into energy and vice versa.  The reality is that energy is always manifested as mass in some form, but I struggle with some cases:  Understood Nuclear Decay Example  In the case of a simple nuclear reaction, for instance, the total system mass remains the same since the mass deficit (in rest masses) is accounted for in the greater relativistic masses of the products per $E=\Delta m c^2$.  When a neutron decays and you are left with a fast proton and a relativistic electron.  If you could weigh those two without slowing them down, you would find it weighed as much as the original neutron.  Light in a Box  This becomes more difficult for me when moving to massless particles like photons.  Photons can transmit energy from one heavy particle to another.  When a photon is absorbed the relativistic mass (not the rest mass) of the (previously stationary) particle that absorbs it increases.  But if my understanding is correct, the energy must still be manifested as mass somehow while the photon is in-flight, in spite of the fact that the photon does not have mass.  So let's consider a box with the interior entirely lined with perfect mirrors.  I have the tare weight of the box with no photons in it.  When photons are present the box has an additional quantifiable amount of energy (quantified below) due to the in-flight photons.  Say there are $N$ photons... obviously assume $N$ is large.  $$\Delta m = \frac{ E }{ c^2 } = \frac{ N h }{ \lambda c}$$  Interactions are limited to reflections with the wall, which manifest as a constant pressure on the walls.  If I hold this box in a constant gravitational field (like the surface of Earth) then there will be a gradient in the pressure that pushes down slightly.  Is this correct?  Wouldn't there still technically be mass as the photons are in-flight, which would cause its own gravitational field just as all matter does?  How is this all consistent with the assertion that photons are massless?  Is it really correct to say that photons don't have mass?  It seems to be a big stretch.  Please offer a more complete and physically accurate account of this mirror-box. Suggested edits in top-bar put flags over the winterbash snowflake Suggested edits in the top bar put the flag count right over the winterbash snowflake. Looks pretty ugly if you ask me... Noetherian property for exact sequence Let $0 \to M' \xrightarrow{\alpha} M \xrightarrow{\beta} M'' \to 0$ be an exact sequence of $A$-modules. Then $M$ is Noetherian is equivalent to $M'$ and $M''$ are Noetherian.  For the ''$\Leftarrow$'' case:  I guess if we let $(L_n)_{n\geq 1}$ be an ascending chain of submodules of $M$, then $(\alpha ^{-1}(L_n))_{n\geq 1}$ is a chain in $M'$, and $(\beta(L_n))_{n\geq 1}$ is a chain in  $M''$. For large $n$ both these chains are stationary. Then why we know the chain $(L_n)$ is stationary?   Thanks! Solution of limit $\lim\limits_{x\to 0} \frac {e^{-1/x^2}}{x} $ Small question, I'm trying to solve this limit but I just can't wrap my head around this problem.  $$\lim_{x\to 0} \frac {e^{-1/x^2}}{x} $$  L'Hopital just seems to make it messier.   It's probably pretty simple - I'd like to hear what I'm missing. How to perform orthogonal regression (total least squares) via PCA? I always use lm() in R to perform linear regression of $y$ on $x$. That function returns a coefficient $\beta$ such that $$y = \beta x.$$  Today I learned about total least squares and that princomp() function (principal component analysis, PCA) can be used to perform it. It should be good for me (more accurate). I have done some tests using princomp(), like:  r &lt;- princomp( ~ x + y)   My problem is: how to interpret its results? How can I get the regression coefficient? By "coefficient" I mean the number $\beta$ that I have to use to multiply the $x$ value to give a number close to $y$. Let $y_n$ be a sequence such that  $\lim_{n\to \infty} y_n= y$ then prove that     $ \lim \dfrac{y_1+y_2+...+y_n}{n}= y$   My try:  As  $\lim_{n\to \infty} y_n= y$ then given $\epsilon&gt;0$ there exists $N$ such that $\forall n\ge N ;||y_n-y||&lt;\epsilon $.  Now $||\dfrac{y_1+y_2+...+y_n}{n}-y||\le n^{-1}\{||y_1-y||+||y_2-y||+...+||y_n-y||\}$  How to make this limit tend to zero? Drawing text on an image background that has dark and bright parts Often, I want to write text over a background image. If the background image is bright, I use a dark color for the text, and vice versa. But, often the image has both dark and bright parts. So a dark text is unreadable on the dark parts, and a bright text is unreadable on the bright parts.  I currently use one of several solutions, all of them are imperfect:   Brighten the image and use a dark font, or darken the image and use a white font; the problem is that it reduces the beauty of the background image. Use grey text (as in this question:  ). But grey text often looks unappealing, and is still only barely readable. Use dark text, and try to position it on the bright spots of the image (or vice versa). This takes a lot of time because it requires me to position each word separately.   Are there better solutions to this problem?   In particular: is there an automatic tool that takes an image and a text, and positions the text only on the dark/bright parts of the image? I would like to add my bibliography to my presentation in IEEE format. What should I add to my preamble and code.  \documentclass{beamer} \setbeamertemplate{footline}[page number]  \usepackage{graphicx} \usepackage{booktabs} \begin{document} \section{Reference} \begin{frame} \frametitle{Reference}  \end{frame}   I'm using the same bibTex which I use to make the IEEE paper. I am getting FATAL_ERROR|System.QueryException: List has no rows for assignment to SObject. I know that it is because it is not returning any rows in the SOQL query but what I want is that if it returns any row, it should update ALO field on contact object, if it is null then ALO field should be set to null.  Here is my code:  ziptoLOD = [SELECT Id, Name, LOD__c             FROM Zip_3_to_LOD__c             WHERE Name =: contact.Extract_Zipcode__c ];  Zip_3_to_LOD__c ziptoLOD2 = (ziptoLOD != null) ? ziptoLOD : null;  if (ziptoLOD2 == null) {     contact.ALO__c = ' ';    } else {     System.debug(System.LoggingLevel.ERROR, 'Zip to LOD' + ziptoLOD2);     contact.ALO__c = ziptoLOD2.LOD__c; }   My code gets stuck at the SOQL query and gives me the list has no rows error. Split comma-separated values There is a way to add custom split normal use Python API? I can't find a way to achieve custom split normal effect. I want to use python (mesh normal/hard edge or soft edge) data collected from Maya then write to Blender mesh.    How to do it using the following Python API and how?  bpy.data.meshes[objName].normals_split_custom_set_from_vertices  bmesh module Show that if $a$ and $b$ are positive integers, then $$\left(a +\frac12\right)^n + \left(b+\frac{1}{2}\right)^n$$is an integer for only finitely many positive integers $n$.   I tried hard but nothing seems to work. :( What level is a spell if you cast it without expending a spell slot? There are ways to cast spells without expending a spell slot such as:  Master Transmuter (PHB 119):     Restore Life. You cast the raise dead spell on a creature you touch   with the transmuter’s stone, without expending a spell slot or needing   to have the spell in your spellbook.   Armor of Shadows (PHB 110):     You can cast mage armor on yourself at will, without expending a spell slot or material components.   Whispers of the Grave (PHB 111):     You can cast speak with dead at will, without expending a spell   slot.   See also: Channel Divinity: Read Thoughts (PHB 59-60), Mystic Arcanum (PHB 108), Beast Speech (PHB 110), Chains of Carceri (PHB 110), Eldritch Sight (PHB 110), Fiendish Vigor (PHB 111), Mask of Many Faces (PHB 111), Master of Myriad Forms (PHB 111), Misty Visions (PHB 111), Otherwordly Leap (PHB 111), Signature Spells (PHB 115), Spell Mastery (PHB 115), Shapechanger (PHB 119), Boon of Spell Mastery (DMG 232) and Boon of Spell Recall (DMG 232).  What level are these spells if you cast them without expending a spell slot? How do I expire a PHP session after 30 minutes? I need to keep a session alive for 30 minutes and then destroy it. Can less retain colored output? Can I get less not to monochrome its output?  E.g., the output from git diff is colored, but git diff | less is not. What can be said about the convergence on $|z|=1$? I already found the radius of convergence of the power series $:$ $$\sum_{n=1}^{\infty} \frac {(-1)^n} {n} z^{n(n+1)}.$$ What happens at the boundary of disk of convergence?  I found that the radius of convergence to be $1$ and hence the disk of convergence is $|z|&lt;1$. Now I found at $z=1$ the series converges. Now how can I proceed? Please help me. Thank you in advance. The case of the bleeding monospace font! Is exFAT now the best choice for an external hard drive that will be used for Windows, Mac, and Linux? Find all positive integers $a, b, c$ such that $1/a + 1/b + 1/c = 4/3999$ Find all positive integers $a, b, c$ such that $1/a + 1/b + 1/c = 4/3999$.  The contest is just ended, so you may freely answer. (I did not attend the contest: it is an Italian contest for schools and the groups may ask other people for hints. This is how I got involved, but of course asking on MSE would have been cheating)  I found three solutions: I am explaining below what I did. I would like however to know if there is a more general approach. How can you combine all lines that end with a backslash character? Using a common command line tool like sed or awk, is it possible to join all lines that end with a given character, like a backslash?  For example, given the file:  foo bar \ bash \ baz dude \ happy   I would like to get this output:  foo bar bash baz dude happy