I am wanting to know who rules Canada. Should I ask: &quot;By WHAT monarch is Canada ruled?&quot; or &quot;By WHICH monarch is Canada ruled?&quot; (The answer would be: &quot;Canada is ruled by the British monarch Elisabeth the second.&quot;)
What are the grammatical rules determining whether to use which or what?  I usually go by intuition. It's "What car are you looking at?" and "What bicycle do you like most?" but "Which song did you sing?" Quite often, I don't know whether to use what or which.  How can I tell?
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. I would like to know where to find the source code of Ubuntu. I'd like to see how far it is "open source". Replacing a font in many illustrator files I have several hundred Illustrator files that are formatted similarly, and for legal reasons I need to replace a font in all of them. Even with the 'Find font' tool, that's a hell of a lot of fonts to replace by hand.  Is there some way of automating it? For example, using Bridge? Illustrator (CS5) doesn't offer many options in Bridge, compared to the automation options offered by Photoshop. I also don't see any option for running actions on multiple Illustrator files.  Also, creating a repeatable action for replacing the font doesn't seem to work: instead of repeating my action, it brings up the dialog box an waits for me to tell it to replace them.  As a programmer I'm prepared to edit the files directly if it can be done without breaking them.    Update: The 'Batch...' menu item from Illustrator's actions panel menu allows the same action to be performed on a folder of files. It doesn't fix the Find Fonts action waiting for input though. Toggling the dialog off makes the action do nothing at all. Struggling with Plural/Singular? Which of the following is a grammatically correct statement?   The value of cars depreciate over time.   The values of cars depreciate over time. The value of cars depreciates over time.   Thanks! Slit screen and wave-particle duality Repeating something with (1/n)th chance of success n times Theorem 13.9 in these  is the polynomial spectral mapping theorem:     Theorem 13.9 For a polynomial $p$ we have $\sigma(p(T)) = p(\sigma(T))$.     My questions:   First direction: Why would $q(T) (p(T) - p(\lambda) I)$ be an inverse for $T - \lambda I$? Update: @RobertIsrael said that instead $(p(T) - p(\lambda) I)^{-1} q(T)$ should be $(p(T) - p(\lambda) I)^{-1}$ be? According to the lines in the proof above, we have $$ (p(T) - p(\lambda) I)^{-1} = ((T - \lambda I) q(T))^{-1} \overset{?!}{=} q(T)^{-1} (T - \lambda I)^{-1}, $$ but as $\lambda \in \sigma(T)$ by assumption, $(T - \lambda I)^{-1}$ doesn't exist, right? For the second direction: Why does $x_i \in \sigma(T)$ imply that $p(x_i) - \mu = 0$? I thought that $x_i \in \sigma(T)$ only implies that $T - x_i I$ is not boundedly invertible. Since $\mu \in \sigma(p(T))$ we have that $p(T) - \mu I = c \prod_{k = 1}^{n} (T - x_i I)$ is not boundedly invertible but how does that help?   In both statements there seem to be a notion of "a product of operators is not invertible iff all factors aren't invertible", but how can that be true? Consider i.e. shift operators on a sequence spaces such that $ST = I$, i.e. the left and right shift operators, then the above mentioned notion doesn't hold, right? Inverse Fourier transform of Gaussian I need to calculate the Inverse Fourier Transform of this Gaussian function:  $\frac{1}{\sqrt{2\pi}} exp(\frac{-k^2 \sigma^2}{2})$  where $\sigma &gt; 0$, namely I have to calculate the following integral: $\int{\frac{1}{\sqrt{2\pi}} \exp(\frac{-k^2 \sigma^2}{2})} \exp(ikx) dk$.  How can I do that? If I am not wrong (in which case please correct me) the result should be $\frac{1}{\sqrt{2\pi}\sigma}exp(\frac{-x^2}{2\sigma^2})$...but I don't know how to get there! how to make a regex string reject a blank field Query standard input of lightning-input I want to query standard HTML textarea which is wrapped by lightning-textarea. How can I get it?  &lt;lightning-textarea name=&quot;secret_field&quot; label=&quot;Secret&quot; value={secretFieldValue}&gt;&lt;/lightning-textarea&gt; What is the easiest way to swap occurrences of two strings in Vim? Rounded caps on a Bezier Curve pipe This may be a simple question.  Essentially I am procedurally generating random 3D figures using a bezier curve and bezier circle bevel object, however, one of the only things I can't figure out how to do is how to round the end caps of the object.   I have tried using a taper object like suggested  but have had only limited success.  This is about as close as I've gotten:   I should note that all of this is done through Python and I'm not modeling any of this by hand. So any suggestions for how I can make the rounded caps programmatically would be greatly appreciated. How to reduce the number of authors above >3 to 'First Author et al., (year)'? How to perform a true GIS clip of polygons layer using a polygon layer in R? Find the minimum value of $f(x,y,z)=\frac{x^2}{(x+y)(x+z)}+\frac{y^2}{(y+z)(y+x)}+\frac{z^2}{(z+x)(z+y)}$. Find the minimum value of $f(x,y,z)=\frac{x^2}{(x+y)(x+z)}+\frac{y^2}{(y+z)(y+x)}+\frac{z^2}{(z+x)(z+y)}$ for all notnegative value of $x,y,z$.  I think that minimum value is $\frac{3}{4}$ when $x=y=z$ but I have no prove. I've a friend that booked a round-trip journey. He booked A-to-B and B-to-A. Somehow he needed to be earlier at location B, so he took a train and did not take the flight from A to B.  When he went to the airport to take the "back home" flight (B-to-A), he was informed that his ticket was canceled because he did not take the A-to-B flight. They canceled the ticket and sold it to someone else.  Is this normal? The company said it was their right to do so, and he could not get the flight back. The company was Iberia. Gilbert, MacWilliams, and Sloane defined a solution to "perfect integrity" in , unconditionally secure message authentication, not vulnerable to any cryptanalysis on its own even by an adversary with unbounded computational power, provided you have a key chosen uniformly at random the same length as the message. It sounds counter-intuitive that a MAC could have perfect integrity, any hash function can be broken with enough computational power. How does their solution have "perfect integrity"? Inhumans vs. Mutants in the Marvel Universe What's the difference between those two? Aren't Inhumans supposed to be an evolution of the human race "forced" by the Kree? Which is almost the same as Mutants, the natural evolution of the human race...  What exactly am I missing? Didn't Harry have any other family he could have searched for? You'd think that as soon as Harry met someone who was friends with his dad, he'd have asked about his family.  Certainly Lupin or Sirius could have told him something of his family, given that they were James' closest friends, and Sirius was "always welcome at the Potters".  Obviously there's nothing in the books, but did J.K. Rowling ever explain why there was no mention of any living relative other than Aunt Petunia, or even what happened to Harry's grandparents? How to pass arguments to addEventListener listener function? The situation is somewhat like-  var someVar = some_other_function(); someObj.addEventListener("click", function(){     some_function(someVar); }, false);   The problem is that the value of someVar is not visible inside the listener function of the addEventListener, where it is probably being treated as a new variable.