Please no hate for lack of knowledge:  I am somewhat fascinated with the subject of black holes. However, I do not understand a concept which is constantly attributed with black holes: that a black hole can attract light and therefore light cannot escape it. What I don't understand is, how? Gravity, as far as I understand, only attracts matter. However, light has no mass (right?), so how can a black hole attract light?
Light is clearly affected by gravity, just think about a black hole, but light supposedly has no mass and gravity only affects objects with mass.  On the other hand, if light does have mass then doesn't mass become infinitely larger the closer to the speed of light an object travels. So this would result in light have an infinite mass which is impossible.  Any explanations?
Find the sum of two elements in a matrix Given $[a_{ij}]_{10\times10}=\left[ \begin{array}{ccc}   1&amp;2&amp;4&amp;7&amp;...&amp;...&amp;...\\   3&amp;5&amp;8&amp;...&amp;...&amp;...&amp;...\\   6&amp;9&amp;...&amp;...&amp;...&amp;...&amp;...\\   10&amp;...&amp;...&amp;...&amp;...&amp;...&amp;...&amp;\\   ...&amp;...&amp;...&amp;...&amp;...&amp;...&amp;...\\   ...&amp;...&amp;...&amp;...&amp;...&amp;...&amp;98\\   ...&amp;...&amp;...&amp;...&amp;...&amp;99&amp;100\\ \end{array} \right]$, what's $a_{7,3}+a_{7,7}$?  Is there a better way than write down all the elements? It's not easy to find the formula of $a_{i,j}$ As I am seeing this,  the man and boat will have different displacement from ground frame,  so there should be a net work done by friction .  The books says,  total work done by friction is zero when friction is static and internal to system. Please explain.. I can get the element like this $("#txtEmail") but I'm not sure how to get the actual value. Rules for forming demonyms Are there specific rules / conventions at play when creating demonyms? Or are they merely formed organically over time - the most popular winning out?  There are many suffixes to choose from, but I cannot find concrete guidelines as to which is proper to use in which instance. Is there a difference between "==" and "is"? When & why I need to use web.AllowUnsafeUpdates = true Defining commands/abbreviations that contain numbers I tend to use \newcommand to define macros for symbols I use often, e.g. \newcommand{\hankel}{H^{(1)}_0}.  One inconvenience of this approach is the fact that command names cannot include numbers.  What I ideally want is to map something like \H0 to H^{(1)}_0.  I imagine this could be done with some macro expansion/snippet package, or one might use \newcommand to define a command that takes a parameter, etc.  Before I start experimenting, though -- is there a canonical way of dealing with this problem? Your visa application has been concluded - what does this mean? I got two mails from the UK embassy in Abu, saying your visa application has been concluded. I'm really confused, did I get the visa or not? What could the possible results be? Sum of digits of repunits I've read a number of the helpful Q&amp;As on photons that mention the mass/mass-less issue. Do I understand correctly that the idea of mass-less (a rest mass of 0) may be just a convention to make the equations work?  From a layperson's view, it's difficult to understand how a particle of light (photon) can be mass-less. A physical object (everyday world-large or quantum-small) must have a mass. Yet, if my understanding is correct, the mass of a moving object/particle increases in proportion to its speed/velocity...so that at the speed of light, its mass would be infinite. A photon travels at the speed of light, but it obviously doesn't have infinite mass, right? Can someone formulate a practical explanation that can be understood by middle-school to high school kids? Much thanks for the help.    Wow--your answers to my original Q below clear up much of my confusion. I now have the daunting task of going over these nuggets and working up an equation-less (hopefully) explanation of the mass-less photon for non-physicist types.  Yes, from a layperson's view, it does seem remarkable that an existing piece of matter-- which has to be made of physical substance--could have zero mass at rest (though a photon is never at rest). It would be almost understandable if a piece of matter made of nothing had zero mass, but that  seems to be an oxymoron, and "nothing" would equate to nonexistent, right?  In case you might find it interesting: I'm working on a writing project that posits we inhabit a universe that consists of matter (physical stuff) only, and that the NON-physical (aka supernatural) does not (and cannot) exist. For instance, if a purported supernatural phenomenon is found to actually exist, then by definition, its existence is proof that it is mundane/natural. All it would take to disprove this premise is reliable proof that ONE supernatural event has occurred. Despite thousands of such claims, that's never yet happened.  Who else better than physicists to confirm my premise? However, I do wish the TV physicists would explain the terms they throw about, some of which mislead/confuse their lay viewers. Case in point: "The universe is made up of matter and energy" (without properly defining the term "energy" as a property of matter).  The result is that laypersons are left with the impression that energy must therefore be something apart from or independent of matter (ie, nonphysical). Their use of the term "pure energy" without specifying exactly what that means adds to the confusion. (Thanks to your replies on this forum, I now understand that "pure energy" refers to photon particles.) However, "psychics" and other charlatans take advantage of such confusion by hijacking terms like energy (as in "psychic energy"), frequencies, vibrations, etc to give perceived scientific legitimacy to their claims that a supernatural spirit world, etc., exists. As you may realize, the majority of people in the US (per 2009 Harris Poll) and around the world believe in the existence of nonphysical/supernatural stuff such as ghosts and spirits.  My purpose is to give laypersons the information they need to distinguish what's real from what's not.  Thanks so much for help...And, PLEASE, add any further comments you think might be helpful/insightful to better inform laypersons. Sometimes a suggested edit is  because of a concurrent direct edit that takes precedence.  Since this is no fault of the edit suggestor, such rejections should not count against the suggestor when counting .  Here are some examples where it happened: I posted a question recently regarding my Windows 10 upgrade which ended up with a black screen and cursor.   I reverted back to Windows 8.1 using the "Revert to previous build" option in recovery, and all seems fine, except that Virtualisation is disabled.  I tried to open BIOS settings but it just boots into Windows. I've tried the usual F2 key and Shift F2, all the other F keys, tried pressing B and Shift+B but no luck.  I tried pressing the Lenovo key on the laptop when it is powered down, which shows a menu to either boot into BIOS, recovery, or show boot menu. I choose BIOS and it just boots into Windows.  I tried going into advanced startup options from Windows (Shift+Restart) and choosing "UEFI FIRMWARE SETTINGS" but it just reboots back into Windows.  Before the Windows 10 upgrade it was working perfectly.  Lenovo G580 laptop - Core i3 with Intel 4000 graphics. 8GB of RAM and a Crucial MX100 512GB SSD (replaced the original hard drive with this SSD). memoryless property of exponential distributions with random variables It is true that $P(X&gt;t+s|X&gt;t)=P(X&gt;s)$ for certain values $t$ and $s$.  However, how can I show that this still holds if:   $T$ is a continuous random variable. That is $P(X&gt;T+s|X&gt;T)=P(X&gt;s)$ Both $T$ and $S$ are continuous RVs: $P(X&gt;T+S|X&gt;T)=P(X&gt;S)$   All the random variables are independent. There are five boxes consisting of several identical coins. There are five boxes consisting of several identical coins. The first box contains 4 coins, the second box contains 9 coins, the third box contains 7 coins, the fourth box contains 10 coins, and the fifth box contains 3 coins. Some coins are taken from the boxes such that at least a coin taken from each box. In how many ways in taking the coins, such that the numbers of the coins taken are 12?  My attempt was solving it using repetition combination of which, there are only seven coins remaining considering that at least a coin taken from each box. By using the repetition combination, i.e. taking 7 from 9 (five boxes and four borders), resulting in 36 ways. However, there is no 36 ways in the choices. Suppose that $V, W$ are closed in $X$ and that $V\cap W, V\cup W$ are connected. Show that $V$ and $W$ are connected.  My attempt: Suppose that $V=U_1\cup U_2$ where $U_i$ are open in $V$, not empty and $U_1\cap U_2=\emptyset$. This induces a separation for $V\cap W$: $$ V\cap W = (U_1\cap W)\cup(U_2\cap W).$$  $U_i\cap W$ is open in $V\cap W$  $(U_1\cap W)\cup (U_2\cap W)=\emptyset$ as otherwise $U_1\cap U_2 \ne \emptyset$.  Now, I need to show that both sets are not empty. We know that $V\cup W$ is connected and closed in $X$. So, for all $x\in V\cup W=U_1\cup U_2\cup W$ and all neighborhoods $Z$ (in $X$!) of $x$ we have that $Z\cap (V\cup W) \ne \emptyset$. We can choose $x\in U_1 \subseteq V\cup W$. But then I would have to find a neighborhood of $x$ in $X$. I can't find one... How can I complete this bullet point?   Thanks. R linear regression categorical variable "hidden" value Why do games run slow on CPU Maybe my question sounds naive because I'm not a game developer but I dont see objective reasons for this. An average cpu is in times more powerful than an average gpu like a few graphics cards in one. The most repeated reasons in internet:  the GPU isn't as busy as the CPU  If the gpu renders the screen how it can not be busy The modern cpus are powerful enough. They are not busy most of time. For example my cpu's usage is 3%.  many GPU's are designed to process graphics commands in parallel, CPU single threads them  What bothers the games to run a few parallel processes even on one cpu core? In my opinion its not correct to tell that the gpu is better if games never use 100% of the cpu's capacity. To be specific they dont use even 50%.  To clarify my question based on responses in the comments:  Did you mean to ask &quot;Why do games render more slowly on the CPU?&quot;  Yes I mean why the cpu cant do the whole work for games when it is underloaded and especially if it does the largest part of work in any case.  You can not compare GPUs and CPUs directly, because they do different things.  What bothers them to do the same things?  The CPU isn't as well suited to performing rendering calculations  I dont understand what &quot;suited&quot; means. And why the cpu is not suitable for primitive tasks aka paint roller.  adding additional parallel processes doesn't improve performance  Then why do you produce multicore graphics cards and multicore central processing units? Just give various parts of one task to a few processes if one process is slow and 100% of the capacity is not used. What bothers to emulate the gpu? Its also unclear for me why when you play without a separate graphics module the games see only one cpu core when you play with the gpu they see and use all the cpu cores. May be some magic. Where should I put software I compile myself? I would love to identify a sci-fi novel I read in the late 60s or 70s.  It followed a group of young space cadets through their training in the Space Academy.  The training culminated in small groups of cadets being sent through a gateway in the space station, into different worlds where they had to survive whatever conditions they met beyond the gateway, as part of their training.  One such trip went wrong and the group ended up stranded in a hostile world for days, hoping to be rescued by their trainers.  I can't remember much about the story or protagonists so this may be too vague, but I remember descriptions of a vast space station hall and these young cadets bringing whatever kit they hoped they might need - some brought breathing apparatus and full survival gear, but others came with very little as they believed they would not be sent into conditions where they could die without the right equipment.  They hadn't bargained for the power surge or whatever it was that misdirected them as they passed through the gateway!  I also remember rivalry between the cadets - I think the hero was male and quietly heading for top cadet of the year award... and I think at least one of the group died in the unknown planet before they were rescued.  Does this ring a bell with anyone?  I remember the mood and tension more than the details but it was a long time ago!  I have a 10-year old son who I think would love this kind of story.  If anyone can help you have my thanks! LWJGL—How to Animate and Render Characters Using a Sprite Sheet I'm making an RPG similar to Super Nintendo RPGs in the early '90s. I'm handling movement much like Squaresoft's Final Fantasy IV.   Notice that the player never actually changes his x and y positions on screen. What I'm asking, to be precise, is how could I, in LWJGL through user input (say, the arrow keys), take the sprite sheet I have of my character's movement animations and render them in a [partially] fluid animation like above?  I've been perusing the internet for hours, and I've not found a surefire way to do this. I don't have any code as of yet; I'm more or less looking for a guideline or some pointers in the right direction concerning how I might tackle this.  And, to note, this'll be a rather large game, so I want to focus partially on speed and efficiency—that meaning that I don't want to dive into Slick2D and libGDX unless absolutely necessary.