A different question about truly spherical objects in nature (Do spheres exist in nature?) made me think of a lecture I had been at where, as I recall, it was mentioned that the most perfectly spherical object in nature is in fact (the event horizon of) a black hole. In the comments of the aforementioned question, I was informed that any deviations from a spherical shape of such an event horizon would be damped out within a very short time, related to the characteristic timescale of the system. So I was wondering what order of timescales exactly we're talking about here, I would appreciate some elaboration on this. And something I thought of just now: would it be possible for some wave (periodic) phenomenon to occur in this horizon, periodically distorting the spherical shape?


Does speed of pressurized gas escaping through a narrow nozzle into vacuum depend on the pressure? I've asked a question on Space.SE regarding utilizing gas at extreme pressures for propulsion. My idea was that the higher the pressure of the gas, the higher specific impulse would be achieved, because it would increase speed of the escaping particles. An answer cites the Choked Flow article, claiming The exhaust speed of a rocket is limited by the speed of sound. The answer was criticized as the linked article only gives the case of atmospheric pressure on one side and vacuum on the other as where this would apply, and my question was about way higher pressures. I'm finding this answer difficult to accept too, because speed of sound should be relative to the medium; a co-pilot of a supersonic plane can still communicate with the pilot, because the air enclosed in the cockpit moves with them. So, in a long pipe, speed of sound in decompressing gas should be relative to the local speed of the gas. Still, I don't have any solid background or source to back it up - thus the question. Is the speed still limited to speed of sound in case of very high pressures? If so, what effect limits it?


Heat can be evolved or absorbed when two dissimilar liquids are mixed together at constant temperature and pressure. This is called the heat of mixing of the mixture. I'm trying to understand the molecular "picture" associated with this process. Here is my current attempt: Initially, there are two pure substances each with its own "like-like" intermolecular forces. During mixing, these forces have to be overcome in order to "break-up" the similar molecules to "make way" for the dissimilar molecules. This requires energy and so is endothermic for both pure substances, correct? It would be like boiling the liquid (energy input) to achieve an ideal gas (no interactions) of each pure substance. The second component of the net energy change is the release of energy when forming the mixture. Now, we have to accomodate both the "like-like" interaction forces (presumably at different intermolecular distances than the pure substance) and the "like-unlike" interaction forces. Overall, this direction is exothermic since formation of the solution with interaction forces is lower energy overall than the non-interacting ideal gas mixture, right? So I have two offsetting directions in the two components of energy change associated with mixing. The net effect (endo or exothermic) obviously will depend on the quantitative forces associated with the each component of the process. Do I have the basic molecular picture correct?


If we have a perfect Schwarzschild black hole (uncharged and stationary), and we "perturb" the black hole by dropping in a some small object. For simplicity "dropping" means sending the object on straight inward trajectory near the speed of light. Clearly the falling object will cause some small (time dependent) curvature of space due to its mass and trajectory, and in particular, once it passes the even horizon, the object will cause some perturbation to the null surface (horizon) surrounding the singularity (intuitively I would think they would resemble waves or ripples). Analogously to how a pebble dropped in a pond causes ripples along the surface. Is there any way to calculate (i.e. approximate numerically) the effect of such a perturbation of the metric surrounding the black hole?, and specifically to calculate the "wobbling" of the null surface as a result of the perturbation,maybe something analogous to quantum perturbation theory? Or more broadly, does anyone know of any papers or relevant articles about a problem such as this?


Recently I was told of a job offer to analyse astronomical data. The job offer states that they want somebody with knowledge of astronomical data analysis software and it will be a plus somebody who has experience with programming languages, giving as examples: IDL and Fortran. My first question is: Is Matlab a good programming language? I mean, to treat astronomical data and any other things that they might want? From what I see IDL is comparable to Matlab, both have pros and cons but basically they both do the job. For my second question, and I'm sorry if I should post this on a different post but are very closely related, the selection for this job will be made by analysing data from some surveys on the optic, millimeter and infrared frequencies from the Hubble, Spitzer, Herschel and Apex telescopes. My other question is: what kind of data is this and what kind of treatment I may have to do? If somebody could indicate me somewhere online where free data is available I would be deeply thankful. My experience on this kind of job is, clearly, limited, but I believe I have all the theoretical knowledge to tackle the problem, I just need to know what to study and train.


As an example of someone who has discovered maths at a later point in my life than average, and who has (perhaps unusually?) proven the point that it is perfectly possible to study undergraduate mathematics with almost no prerequisites, I am now having to accept that fluency in mathematical techniques is in the end extremely important in the long run. I am curious about the extent to which having a rich exposure to elementary maths techniques must influence creativity in research later on? At the moment I have taken on a full-time programming job, and I am looking for optimal methods for improving fluency in elementary maths, that could work in such a limited time frame. Any suggestions? Could it be feasible to multi-task- say, for example, practice methods of mental arithmetic at the same time as doing something else?


Consider these two sentences, one with a contraction, one without: I didn't check my voicemail. I did not check my voicemail. didn't is expanded to did not. Now consider: Why didn't you check your voicemail? If you want to write this without a contraction, you must write it as: Why did you not check your voicemail? The word you comes in between did and not when didn't is expanded. This: Why did not you check your voicemail? is probably not correct at all. I've never heard anyone speak like that, and never seen that written, even though didn't is expanded directly into did not. This came up during discussion the other day, and I was wondering if there was a term for this situation where a contraction cannot be expanded into what might seem the most obvious form.


So I was trying to figure out the reason why my old (and probably sufficiently damaged) needle on my phonograph (turntable) was not working like it was a little while ago. With my headphones on, I was playing around with it and happened to touch two of the leads on the underbody of the needle. All of a sudden, a man's voice was speaking to me in a muffled, mid-pass tone, slightly audible but definitely discernible (talking about the "nightmares of the Obama regime" or something odd like that). The voices only occurred when I was in contact with both leads. Why is this? Did I turn myself into a giant watery antenna? I know phonographs have some interesting physics to them, but this is a new one. Why is it so clear? I can hardly get old analog radios to focus cleanly, let alone my own body. Is there a natural resonance that caused such a clear audio frequency to be heard?


In Texmaker, I like using the shortcut to enter math mode. This shortcut creates two dollar signs, and allows you to immediately type text in between the two. My problem is that I would like to be able to continue typing outside of this block immediately upon finishing with my math text. I would like to, say, hit "tab" and be able to start typing outside the math block, one space after the latter dollar sign. How do I do this? Is there a shortcut for this? If not, can I create one? Alternatiely: Can I edit the Math shortcuts that come with Texmaker? I don't mean that I want to edit the keys I press to obtain the code -- rather, I would like to change the code that is available from the Math menu.


Let's suppose you go to Ikea to buy a wardrobe, but you have to make sure it fits in your room. You find two that are really nice and since you like them so much you decide to buy both of them. So you measure their length, width and height (just to be sure they fit in your room). For the width you have no problem: They could be thicker or narrower and would still fit. However the first wardrobe length is not good. It's too long so you write in comments: Please provide a shorter one. The second wardrobe length is good but its height is not. This one is too tall so you write in comments: Please provide a shorter one. Wardrobe A is too large so it must be shorter. Wardrobe B is too tall so it must be shorter. Because shorter has two meanings you end up receiving both wardrobes with incorrect sizes. Now the question: Is there a pair of words for length and height that avoid using the same word to mean less magnitude?


According to the current Big Bang with inflation cosmological model? I was under the mistaken impression that there was very low volume, very high temperature/pressure, very low entropy and the Big Bang (perhaps prompted by the high pressure) resulted in an expansion of volume where energy didn't change much so temperature went down and entropy went up. Now I've learned about inflation and how there is no conservation of energy at cosmological scales and that the universe gained an exponential amount of energy during the inflationary period. How did this happen with a decrease in temperature? Inflation was a period of supercooled expansion, was it not? Why was positive pressure not enough to cause inflation such that we need a negative pressure in the form of the inflaton field (or later dark energy) to explain the expansion of the universe? Thanks for your time


You can obviously move a solid at a different speed along the surface of another solid, so how come the velocity of the fluid at the fluid-solid interface must be equal to that of the solid? What physical property dictates that the no-slip is valid for fluids but not solids? The Wikipedia page has the following: Particles close to a surface do not move along with a flow when adhesion is stronger than cohesion. At the fluid-solid interface, the force of attraction between the fluid particles and solid particles (Adhesive forces) is greater than that between the fluid particles (Cohesive forces). This force imbalance brings down the fluid velocity to zero. which didn't make sense to me since I'm not sure how they prove that this is true for any fluid-solid interface.


A long time ago I was thinking about how the Imperial system of measurements is arbitrary and annoying, and I decided to design the best system of units ever (I wasn't very old then). I worked on this idea occasionally for years without making any progress. When I finally got serious about it, I discovered Planck Units and that seemed to settle the issue. Now my problem is that Planck Units are so small that they can't be used for "normal" things without huge exponents, most of these being very different depending on the quantity being measured. Solving human-scale equations with these units by computer would thus either be very inaccurate due to floating-point errors (for numbers that are even within range) or very slow due to the need for extended precision. They also go "up" but not "down", which renders almost half of the possibile signed floating-point values as useless. I considered the idea of creating a new system by raising each Planck Unit with a standard exponent or multiplier, but I think this would bring some into an acceptable range but not others. So what I want to know is whether a system of natural units exists that uses units that are appropriate for work with technology that humans can interact with, or can be made appropriate without introducing too many arbitrary elements.


My friend has a tendency to wear mismatched socks, because he "Can't be bothered wasting time matching them, so he just pairs them up at random". One day I noticed he was wearing matching socks, which was apparently not on purpose. This got me thinking, if you have N different pairs of socks and you start matching them at random, what is the probability of putting together at least one correct pair? What first came to my mind was the famous Hat-checking problem, which I cannot generalize to answer this question. I tried programming the problem though and noticed that the chance of getting a correct pair becomes significantly lower with large inputs. It does seem to converge though, but I'm not sure how to find the limit analytically.


I'm currently writing a simulation in python with scipy and matplotlib to reproduce an one dimensional driven diffusive system described in this paper from M.R. Evans et al. The system consists of positive, negative and hole particles. On the left side of the system the positive (negative) particles are produced on the left (right) side with a possibility a and destroyed at the right (left) side with the possibility b. In some cases the system should show a flip between positive and negative high density states and I'm trying to reproduce this behaviour with my simulation. But all I can see is an increasing current within my simulation and I can't find any problems in my code explaining such behaviour. Does anyone here have some experience simulation such or similar systems? Cheers, Florian


Sorry if this question is naive. It is just a curiosity that I have. Are there theoretical or experimental reasons why gravity should not be an emergent property of nature? Assume a standard model view of the world in the very small. Is it possible that gravity only applies to systems with a scale large enough to encompass very large numbers of particles as an emergent property? After all: the standard model works very well without gravity; general relativity (and gravity in general) has only been measured at distances on the millimeter scale. How could gravity emerge? For example, it could be that space-time only gets curved by systems which have measurable properties, or only gets curved by average values. In other words that the stress-energy tensor has a minimum scale by which it varies. Edit to explain a bit better what I'm thinking of. We would not have a proper quantum gravity as such. I.e. no unified theory that contains QM and GR at the same time. We could have a "small" (possibly semi-classical) glue theory that only needs to explain how the two theories cross over: the conditions and mechanism of wave packet reduction (or the other corresponding phenomena in other QM interpretations, like universe branching or decoherence or whatnot) how this is correlated to curvature - how GM phenomena arise at this transition point. Are there theoretical or experimental reasons why such a reasoning is fundamentally incorrect?


Reading about intellectual history and the history of natural science, I have very often come across the expression to come-to-be as a synonym for to come into being, to start to exist, to originate, and so on. I also see commonly used such verbal expressions as to come to know (for to learn, to acquire knowledge of) or to come to see (for to realize), and so on. My question now is twofold: If one is allowed to write to come-to-be and to come-to-know and to come-to-see, is there some definite end to this or am I allowed also to write to come-to-converge, to come-to-acquire, to come-to-X? If I am allowed also to use other combinations, then what about the dashes/hyphens in these expressions. I usually see come-to-be with dashes, but the to come to know without (I think). Why is that so? Should one be consistent? Or has to come-to-be become a lexical entity that warrants a particular use of dashes, whereas the other expressions are simply compound verbs that do not warrant an equal use of dashes? What about "to-come-to-converge` and other less usual instances of such combinations?


Feynman Path Integrals are a way of calculating the wave function of quantum mechanics. It usually integrates every possible path through all of space. I wonder if there is any study of Feynman path integrals through a space with holes in it - with regions of space excluded from the integration process. More specifically, I'm wondering about points or regions of space where the amplitude must be zero. I assume that a point or region that is exclude from the path integral means that the amplitude will be zero there. I've heard described elsewhere that a space with holes in it can result in curvature in that space. And I wonder if the classical limit of a particle path will become curved due to nearby holes. This might result in the curvature of general relativity. So I wonder if there has been any study on this.


I think the wave function of a free electron is nonzero almost everywhere. In particular there are regions of space arbitrarily far away where the electron has positive probability of being found. If I prepare an electron in a particular position, then wait a small amount of time and then check to see if it has appeared in a region that is too far away for it to reach even if it traveled at the speed of light, there is a positive probability that I (or my assistant, who is coordinating with me) will find it there. What have I missed? This seems a lot like spooky action at a distance, but with spooky action no matter/information actually moves faster than light, wheras in this situation the electron actually moves a greater distance than light could in a given amount of time.


I'm working on ray tracing and I'm trying to understand the impact of the angle at which a light-path intersects the surface of a light source on the amount of light that source delivers to the path (per unit time, of course). My assumption for an ideal diffuse light source is that light rays leaving a particular point on the surface of the light source are uniformly distributed, in which case the angle of the path is irrelevant. I think that in essence, this assumption models each point on the diffuse surface of the light as an individual point-light source. Is that a fair assumption for something like a frosted light bulb, where I'm modeling the light as coming directly from the surface of the bulb, not the filament? Or alternatively, if I wanted to actually model the filament itself, would the same assumption be relatively valid? Are there any light sources for which this assumption would not work? I'm assuming lasers would not work this way, with most of the light leaving in one particular direction, but I'm not really worried about modeling laser light. For spot lights, I believe this is still just an ordinary "diffuse" light source which uses mirrors, an aperture, and lenses to direct the light once it has already left the light source so I could model it this way (though I suppose a more efficient model would encapsulate all of this and take the angle of the path into account).


Is there a game which is perfect, that is: always provides a decisive victor, and involves no component of luck Possible games which would be perfect or near-perfect might involve the pie rule. https://en.wikipedia.org/wiki/Pie_rule For the purposes of this question, a 'decisive victor' means that there is no tie, draw or stalemate- the game always ends with one player winning and another losing. 'Luck' includes any arbitrary decision outside the strategy of the players, such as deciding who gets to go first by flipping a coin. In other words, what I'm asking is: is there a strategy game in which neither player has an advantage due to luck, but one of them must win. It seems to me that there cannot be, because otherwise if two 'perfect' players played against each other, what could be the result?


In an electric circuit, how does the excitation of the free electrons to higher energy levels translate into net forward motion of the electrons to the positive terminal? My concept of electrons being excited by the electric field is that they have a higher orbital but they are still localized around the nucleus of a few atoms (especially in a more resistive element). But I know there must be a small net forward motion for there to be current. I need to marry the classical model of the colliding electrons and atoms of the medium with the Quantum principles involving the excitation of charges to higher energy bands and emission of photons. Also, a second question is what causes the electric field in the conductor to be practically zero (compared to that in the resistor) in a non - electrostatic model (i.e., when there is a current). Thank you so much for your help. I have scoured the internet for insight but I have not found a site that marries the classical to modern theory clearly for me.


For class I'm supposed to create a PDA state diagram that is capable of generating an infinite language with no state q such that q is reachable from the start state, there is no cycle within the diagram that starts at q and ends at q, and there is not path from q to and end state. Essentially, I'm trying to prove that a PDA does not need looping states to create an infinite language but I do not know the first place to start. I know that a PDA can make use of lambda transitions which could possibly be to my benefit, and I know that there can be multiple paths resulting from the same transition but I cannot wrap my head around an infinite number of possibilities without any sort of loop. I suppose I'm not looking for a definitive answer, more so something to get me pointing in the right direction. Thanks!


I have the following question, and given few proofs (provided by friends, professors, and my myself) which seem to work, I suspect the answer is yes: But I am still not completely sure. The question is: (A): "For any given value x, are there uncountably many (countably infinite) binary sequences (ones and zeroes) whose limiting relative frequency is x" Is this an open question? I ask this because all of those whom I've asked, had either not thought about the question nor knew the answer until they came up with their own proof. So has (A) been proven in the literature, and if so where? I am interested because if the answer to (A) is no, it can be easily shown that the Kolmogorov formalization/calculus of probability is undermined. This holds because the Kolmogorov calculus seems to require that (A) is true. That the Kolmogorov calculus requires (A) can be easily shown given its axiom of countable additivity, and its theorem: the strong law of large numbers (ie, simply consider that any infinite sequence of independent and identical random variables/trails has probability zero, if the individual outcome probabilities on each trial is less than one). Even if non-standard analysis is applied (so that infinite sequences composed of individual independent and identical random variable with non zero probability are assigned infinitesimal probability values, rather then zero probability values), it appears that this result (ie (A)) is demanded by the Kolmogorov calculus


I am struggling with the concept of tension in a rope. Below specific questions. I am understanding tension to be an elastic force between rope molecules. If so, is it fair to say the net tension on each rope molecule is zero (if rope is in rest) but there is a net tension for the rope whose direction is opposite to applied force? What is the direction of the tension. I am reading conflicting answers for it. If a mass attached to rope is hanging. I think tension in rope is equal and opposite of weight. is that true? Kleppner seems to mention that tension has no direction which is confusing me. Also, does the tension vary. Mass attached to rope and hanging. does value of tension vary throughout the rope?


Here is an old but interesting task from a math book, but I'm completely clueless: A teacher stands at the chalkboard and draws a line, starting from the left side of the board, towards the right. The line is ten centimeters long. Then he draws, without interruption, a second line with half of the length of the first line towards the right. Then a third, with a third of the length of the first. Then a fourth with a quarter of the length, and so on and so forth. The teacher works very carefully. With pointed chalk, he adds a new line per second. The chalkboard is one meter and ninety centimeters wide. How long the teacher needs, to arrive at the right side of the chalkboard? As the teacher finished, he constructed a square on each line. The side length of the squares corresponds to the length of the respective lines. How big is the surface area of all the squares together, approximately? Can't even tell if it is about a convergent respectively divergent series. Can you help? Thank you!


I'm using LyX for writing my article. And I want to add a bibtex library to add references for it. I can do that and then add citations from that library without a problem. But the thing is, I'm writing the article and adding references as I write. I don't have a ready-made library of references beforehand. On every paragraph I would like to add a citation that was not there before. But as far as it works in LyX, you add the bibtex library to your file and then add its citations to your article. So by every new reference I want to add, I have to remove my bib library and reload it for the new citation to be added and this is a bit tiresome because I'm going to have a lot of references. So I was wondering if there's something I don't know or is there another way of doing that. Would appreciate it.


I know how to use LaTeX (not an expert, but still quite some experience - wrote couple of papers and my thesis, can make TikZ pictures etc.), but I don't have the slightest idea, what XeTeX, LuaTeX, etc. are. For an invitation card I'd like to design I found this beautiful font named zapfino. But it's for XeTeX or LuaTex. This website has a nice example: http://nitens.org/taraborelli/latex#glyph I downloaded that tex code, but I can't compile the code on my ubuntu machine (with texlive) - neither using LaTeX (no surprise there), nor xetex, nor luatex, nor xelatex. I always have issues. Best works xelatex, it only complains about the font not being found before it exits. I downloaded the font from <removed> and put the .otf file into /usr/local/share/texmf (where the TEXMFLOCAL variable points to), but that does not change anything. What do I do wrong? Is there a possibility to make zapfino work with latex? and if not, how can I compile that small example on my machine, what do I have to do? Furthermore - is there a way of combining XeTeX (for the font) with LaTeX (for TikZ-tricks)?


Let A and B be linearly independent subsets of a finite dimensional vector space. I want to show that if |A|>|B| then there exists an x in A s.t. B union {x} is linearly independent. My proof is ' Let |A|=n and |B|=r. Suppose B union {x} is linearly dependent for all x in A then span A is in span B. Since |B|=r , vector space spanned by B has dimension at most r. And vector space spanned by A has dimension at most r , since span A is in span B. But then it is contradict to A is linearly independent , since |A|=n > r implies A is linearly dependent. Therefore our assumption is false ' Is that right? And, someone have another proof? I want to prove it by using linearly independent but dimension of vector space.


There're other previous questions about using a color background with fancyhdr so that you get a colored header and/or footer. However, they discuss either using a different color box for each part of the header, or working with a single part header (i.e: a header with just the center part, for example). But what if I have a complete header with three parts (left, center, and right), and I want all the three parts inside a single colored box? Ideally, the colored box should have no margins, but the three header parts should keep their original margins, so I guess I cannot use the fancyhdr margin parameters for that. I really need to use fancyhdr for the header. I can add more packages if necessary, but the header must still be created with fancyhdr.


In short, I'm hoping for some reading recommendations. I'm starting to do some work with Calabi-Yau manifolds, though my prerequisites are fairly minimal in differential geometry. I've taken a relaxed reading course on differential geometry, hopping around Spivak, and I'm taking a full course this semester. I've also taken a reading course on elliptic curves and a full course in algebraic geometry, building up to Riemann-Roch, in case there are some reads that build from that angle. So, does anyone have any recommendations for good reading material for my situation? Mostly I'm asking because I've been informed I have to read papers and present (relaxed) talks on the material, and I'd like to not fall flat on my face on the very first talk! Thanks! (Also, any recommendations on presenting material you very not familiar with is welcome.)


Please note that I am posting this question because I'm still not sure if I understand the difference although I did a comprehensive study of a great number of answers to the "for versus to" questions. This issue turns out to be much more complicated than I expected. I chose to pick this among many and different questions still to be made. (A) It is important FOR me to speak proper English. (B) It is important TO me to speak proper English. (A) It is important FOR me to speak proper English. Could this imply that he or she is an English learner and wants to improve his or her English very much, making it possible to rephrase it as "it is important that I speak proper English?" (B) It is important TO me to speak proper English. Could this imply that he or she, presumably a native English speaker, expects English to be spoken properly no matter who the speaker is, making it possible to rephrase it as "it is important to me that English be spoken properly" or "speaking proper English is important to me?" My guess is that they wouldn't be interchangeable and could have different meanings as above. I would appreciate any advice, hopefully including any rule of thumb.


Consider the following sentence: I have a lot to talk about with John about his project. Since I can swap the position of the first about to make it 'I have a lot to talk with John about', then I would end up with: I have a lot to talk with John about about his project. My question is, can I consolidate the two instances of about, giving me: I have a lot to talk with John about his project. Or do I have to keep two prepositions there, but change the second about to something else in order to make it sound less-awkward, as in: I have a lot to talk with John about regarding his project. Related question (now that I'm thinking more...er...about this): is the first about really an adverb, in which case, of course, I cannot ever consolidate the two?


I'm studying the first chapter of Hartshorne's Algebraic Geometry by myself and I found this book really hard for a beginner like me, but my advisor said to me that I had to study Algebraic Geometry by this book during my vacations. Then any part of the Hartshorne's book which I find very dry or superficial I search the same subject in another books or notes available online which are easier to read and have more examples. So my question is if there is some book or pdf to accompany Hartshorne's book? I mean the same contents but more detailed, if there isn't such book, it can be a book for each section of the first chapter. In this way, the first chapter of Hartshorne's book for me would be more a route to follow for an introduction of algebraic geometry, than a book to study. Remark: I know there are a lot of posts asking requests of books in algebraic geometry on this site, my question is more specific, I'm only asking this because I couldn't find any good resources with I need. Any suggestions would be really appreciated. Thanks in advance


Notes for context: I am a native BrEng speaker. I have read "Each of these is" vs. "each of these are", How does "each" change "are" to "is"?, and What should I use between "triple" vs. "all"? and I understand the general concept of "Each of them is" and how "each" always takes the singular. Reading my daughter's bedtime story this evening, I came across the phrase "They each have a bag of equipment". It made me wonder why the following seems naturally (to me at least) to be true: (Correct) Each of them has an X (Correct) They each have an X (Correct) Each of them is a Y (Incorrect?) They each are a Y I would never say (to use the examples from one of the posts I linked) "I have three pens. They each are green.", but "I have three pens. They each have a lid." is fine. Is "to have" different from "to be" when it comes to using it with "each"?


The other day I saw this life-hack: And I was wondering how true it is. First of all, I always thought(listening to weather forecasts) that low-pressure atmosphere is what correlates with rain; although I never learned the argument behind it. Anyway, even if low atmospheric pressure correlates with storms and rain; how much(and in what sense) does this affect the bubbles in my morning coffee(if any)? My initial guess is that there should be a threshold pressure that will differentiate whether the bubbles will stick to an edge or suspend in the middle. Since this is an everyday-life question, I should say that experimental answers are welcome as well as rigorous theoretical ones. Also, I am wondering if we can make a barometer based on the bubbles in a mug of coffee? If so, how sensitive it would be?


Consider the following exchange: Alice: Did Charlotte send you that email? Bob: No, but I'm sure she'll send it eventually. In this case, there's no upper bound on the period of time in which Charlotte can send the email to Bob for his expectation to be met. Suppose I want it to be limited by some point in the past or in the future: Alice: Did Charlotte send you that email last month? Bob: No, but I'm sure she sent it eventually. Can Bob say that? What about: Alice: Did Charlotte send you that email last month? Bob: No, but I'm sure she sent it eventually-by-one-week-ago. And what about: Alice: Did Charlotte send you that email last month? Bob: No, but I'm sure she has sent/did send/will send it eventually-by-one-month-from-now. How can Bob express his certainty that the email was sent, or will be sent, at some point in time between the day Alice mentioned and the limit time Bob is referring to?


Here's the situation: You and your spouse are talking with a third person who is of the opposite gender as yourself. e.g., my wife and I are talking with a woman named - let's call her Joan. If I'm talking to Joan about my firstborn son, I don't want to say "my son" because it may imply that he is not also my wife's son. I also don't necessarily want to say "our son" because it may imply that Joan is the co-parent, even though everyone present knows that's not the case (it could be even more awkward with a couple talking to a man, and the wife is talking, because there might be a little more doubt about the biological parentage in that circumstance). Of course, I could gesture at my wife while saying "our son," but is there a verbal way of indicating the child belongs to myself and my wife without saying something long and awkward like "the son of my wife and myself" or "I and my wife's son" or "me and my wife's son" etc.? UPDATE The comments make sense; I guess I should have presented the scenario as my wife not being there; if in the course of the conversation I mentioned my wife, and then later my son, but said that ("my son" -- or "our son") those expressions would seem even awkwarder to me (without my wife present). But the commenter is probably right that I'm overthinking it.


The OpenStreetMap Sign Up page advises new users on its password policy: With OpenID a password is not required, but some extra tools or server [sic] may still need one. I've added [sic] immediately after the error in the middle of the sentence. When I read the sentence, I immediately thought "Which extra tools or servers need a password?" How do I express this while quoting the original text, so that I may bring attention to the error? Do I put [sic] inside the quote like this: Which "extra tools or server [sic]" need a password? Or put it outside the quote like this: Which "extra tools or server" [sic] need a password? Or do something else? (Would it be petty to call out a small error in this way?)


I was curious earlier about the use of various pronouns / possessives in English (primarily first person), so I chose a selection of them and was surprised to discover that, among other oddities, "I" has apparently undergone a rather drastic shift in use over the last century. I was wondering whether any further statistical analysis of usage had been done to describe these trends. Specifically, whether there's any statistical (so, not anecdotal or simply convincing-sounding) explanation for what patterns of use of the word might be responsible? What constructions fell out of use so markedly? What constructions have been revived, and which new ones are most responsible? P.S: This may be too broad a question, but since (as per the help center) it does appear to fall under the site's remit, I thought I might as well ask. Plus, my own research was getting me nowhere; somewhat unsurprisingly, adding the most common words in the language to a search string doesn't really narrow down results significantly.


Temperature is just an indication of a combined property of the masses of the molecules and their random motion. In principle, we can explain "no effective energy transfer between two conducting solid bodies in contact" via a condition in terms of the masses of the molecules and their speeds such that due to the collisions of molecules of two bodies, net energy transfer between two bodies is zero. But it would be a complex calculative work to derive this condition analytically so we use the temperature scale just as a phenomenological parameter to easily determine the condition of "no net energy transfer between conducting solids" for practical purposes. But it does not denote any fundamentally new property of the body separate from the already known mechanical properties of the same. Then why do we call it a fundamental quantity, e.g. in the SI list of fundamental quantities?


I always notice this weird thing and try to overcome it but cant. As shown in the image when I ride the bike by just one hand and pull the handle back say from the right side so as commonly the handle should rotate towards right and the bike should turn to right. But that doesn't happen. No matter what I do the handle turns to left and the bike always go to left. And when I try to push it forward so that it turns to left then the handle turns to right and so the bike also turns to right. As from how much I know about laws of motion I don't know why it happens. Please explain as it is too much weird and interesting for me.


What benchmarks or useful signs can be found to declassify neologisms? Obviously, inclusion in a dictionary is as likely as anything to declare a neologism a word but what happens just before that point? Note that I am not asking how long it takes to convert a neologism. I am asking if there are there any good indications of neologisms about to phase into the lexicon. The flip side is also interesting: When is it safe to say that a neologism is not likely to catch on without some drastic intervention? For instance, kipple is an interesting word with a distinct meaning but it seems so far outside of the cultural sphere that it seems safe to claim it will never become a recognized word. I suspect that answers to the first part (what makes a neologism stick) are likely to answer the second part via absence. As in, if a certain thing is a good sign for a neologism, its absence is evidence against the neologism.


I have never really found a way to comfortably comprehend the idea of time shift even though I know its not the hard part of relativity theory. In that light, can someone point out what is wrong or right about the following logic I'm thinking of here: The scenario is: There are four things in my universe: a wallclock, a flashlight, my wrist watch and myself. I shine the flashlight at my wrist which is in the same line of sight as the wallclock and see they two clocks are synchronized. Now my wristwatch, my flashlight and myself begin traveling away from the wallclock along the line of sight. It seems to me that logically the light I'm running away from will take longer to reach my eye, so that means I would see the wall clock run slower, no? But according to what I think I know, when a minute passes for me, more than a minute passes for the wall clock. I just feel like I must be looking at it wrong. Any pointers are appreciated. This is just recreational thinking...


So a company has n available projects and k employees on the bench. Each project has a "number of hours" associated with it. Each employee has an hourly rate that the parent company gets paid gets paid if he is on a project. Not all employees can be assigned to any project i.e. each employee has a subset of the n projects he can work on. I want to assign the employees to projects so that I can maximize what the company makes from the assignment. Each project can be assigned to only one employee. I am thinking of using dynamic programming but am unable to reach a recursion which I can use to fill a table. I am thinking along the lines of: Max_profit= max(For each employee -> {assign him to each of the projects on his available list and recurse with the remaining projects on the remaining employees or do not assign him to any project and recurse}. Any help will be appreciated!


Imagine a situation where one sees a woman without being aware of her surroundings and concludes wrongly something about her and the group she is a part of. For example, the person sees the writings on woman's face and proceeds to conclude that the she is part of a protest group, but is soon told otherwise. Now the person sees the bigger picture and learns that it was actually a football match. What may he respond? I'm looking for the right response. "Sorry, I was ... by that woman" "The woman ... me" maybe: "Sorry, I was misled by that woman" "That girl tricked me (into thinking it was a protest)" "I was deceived by that woman" There must be a more fitting word. I'm looking for a verb which describes the woman's unintentional misleading of a person into concluding wrongly. She was the reason why the person came to the wrong conclusion, because women rarely attend football matches so one concluded it was something more plausible. As if the person was tricked into believing something based on a single characteristics which turned out to be the one which can't represent the entire group.


My problem concerns a finite set of points in a space, for example (A,B,C,D,E). The information I have on the points is the distances of separations between the points and it comes in two sets. The distance of A from all of (B,C,D,E) and the distance of B from all of (A,C,D,E). The values of these distances are impossible if the points were to lie in a two dimensional space. To determine the minimum dimension that these points could lie in it has been suggested to me to try running an algorithm by the name of Multidimensional Scaling, MDS for short, that maps points in high dimensional space to lower dimensions. This algorithm that takes as input the pairwise distances between all of the points has a "stress" function can be evaluated to see how well these distances are maintained when mapped to the lower dimension. Therefore one possible way of solving my problem could be to to run the algorithm and start from the second dimension and increment upwards until the stress function approaches zero closely enough at which point I will have the answer for what dimension the points lie in. However the pairwise distance data I have is not complete and plugging in zeros for the missing data does not make sense because we believe the all of the points in question to be distinct.


In Russell's famous paradox ("Does the set of all sets which do not contain themselves contain itself?") he obviously makes the assumption that a set can contain itself. I do not understand how this should be possible and therefore my answer to Russell's question would simply be "No, because a set cannot contain itself in the first place." How can a set be exactly the same set as the one that contains it? To me it seems unavoidable that the containing set will always have one more additional level of depth compared to all the sets which it contains, just like those russian matryoshka-dolls where every doll contains at least one more doll than all the dolls inside it. Of course one can define something like "the set of all sets with at least one element" which of course would include a lot of sets and therefore by definition should also include itself, but does it necessarily need to include itself just because its definition demands so? To me this only seems to prove that it's possible to define something that cannot exist beyond its pure definition.


During my teenage years I got into arts and slowly but surely I continue to pursue different art forms (poetry, music, painting, photography, etc) but it was just recently that I got interested in mathematics. I used to hate it in high school, mostly because it was thought as formulas to memorize and the results were only right or wrong with no room to understand why. I was reading about mysticism & occultism which turned me on to numerology, and from there found myself mesmerized by pure mathematics. I'm not interested in applied mathematics, I just find it mundane and trivial while pure math is eternal, abstract and creative. Right now I'm reviewing my high school topics so I can go into more complex ones. Being using a college algebra textbook I found in a public library and reading Basic Mathematics by Serge Lang. I'm really a beginner still so if anyone can give me some tips or suggestions to grow into this divine pursuit of abstraction I'll appreciate it. Which topics would I need to have a good foundation to build my studies in pure, theoretical math?


I understand that water boils at lower temperatures at lower pressures, but I want to know what happens when external heat is supplied to a body of water at low pressure. Suppose I have a hot object in an enclosed chamber. I then cover the hot object with water, then vacuum the air out so the pressure drops. I know that with out the help of any additional heat the water can boil at low temperature because i have dropped the pressure, but what happens when I introduce the hot object? Does the water boil even faster because of the exchange of heat between the water and the hot object? What is the boiling point of the water at low pressure and the help of additional heat VS. the boiling point at just vacuum pressure?


When a person is employed by a company, they are normally issued some sort of equipment or tools that they are supposed to use in a regular course of their work. If they decide to quit the job or they are laid off they will have to return the tools or equipment in proper and working condition. The tools will be inspected, their number and condition, and in case anything is missing or broken that person will have to bear the cost of replacing that tool or instrument. But what word or phrase could I use to say that someone who is quitting his job is required to account for the condition of a larger, immovable piece of machinery that he worked on. Clearly I can't say that he was "issued with the machine" or that he "returned the machine", but he's still responsible that the machine is in proper and working condition. For example, there must not be missing parts, or defects due to his negligence or anything like that, for which he could be held responsible, and would need to pay for. How can I say that he was "put in charge of the machine" when he started working for the company and also that, on quitting the job, and inspection of the machine he is "relieved of the responsibility for it".


I am a casual TeX user. Mostly I have used it to type up some reports/homeworks for class in my graduate engineering work. In the past I have used document type "article". And then kept all the defaults. I need to self publish something online. At the highest level I would like to know: How do you setup a TeX document to self publish a book online? Some more low level questions: Is there a document type for "book" and what is its name? I am looking at Amazon Createspace. Amazon Createspace's requirements are: filetype=pdf, trim size, margins (gutter and outside margins). All of these various trim size, margins gutter/outside can be adjusted in the Tex document? Has anyone seen any good TeX templates for Amazon Createspace? If you could demonstrate how to tweak a specific "book" document type that would be very helpful also. Other than the above questions, please feel free to offer any other sort of help since I am completely new to this process (advice, links to good tutorials, links to wikibooks).


In the definition of an algebra over a field in the wiki entry , it states that an algebra over a field is a vector space equipped with a bilinear product. Question: Does anyone know how a bilinear product is defined? Then a unital associative algebra is defined: An algebra such that the product is associative and has an identity is therefore a ring that is also a vector space, and this equipped with a field of scalars. Such an algebra is called here a unital associative algebra. Question: It is stated that the associativity of the product and identity makes it a ring that is also a vector space. What about the left and right distributivity of multiplication over addition which is required for a ring? How is that guaranteed to be satisfied?


In ZFC, a cardinal is an isomorphism class of sets. However ZFC doesn't explicitly have classes; NBG, which is a conservative extension of ZFC does. There is no largest cardinal by Cantors Theorem There is no set of all sets - it is in fact a class. Classes do not have cardinalities, as these have been only defined for sets - but if one could define a cardinality for classes - wouldn't this, in some sense be a 'limit' of all cardinals in Set, including all large cardinal axioms? Thus, is it possible to extend the notion of cardinality in any significant way to classes? Apologies for the loose phrasing of this question. It was originally going to be a posting on Philosophy.SE, but I thought I would get better answers here.


Before I proceed, let me first say I have done research and understand the general idea between the two: summed up crudely reversible happens in a slower continuous manner while irreversible happens immediately due to a sudden change in conditions. Or mathematically, I suppose you could say the irreversible change isn't continuous and therefore the entropy formula is not integratabtle. But I was given an example of a box with a partition and gas in only one chamber. The removal of the partition and the expansion of the gas is a form of irreversible entropy because the gas fills the chamber almost instantaneously. So I'm left with the question: what if the partition doesn't disappear but is simply disconnected from the walls and the gas is able to push the wall as if the gas was doing work on a piston. This would then be seen as reversible correct? As you would be able to see the partition move in a continuous path across the box. If I am correct in my beliefs up to this point, then... What if the partition is made the size of an atom, wouldn't work still be done on the atom? Wouldn't it still take a continuous path across the box? So is this reversible or irreversible?


Suppose we are considering some fluid. As I currently understand, viscosity exists because of the following: supposing we draw one infinitesimal surface on the fluid, then the fluid parcels on either side have different momentum. Since a fluid parcel is made up of a large number of molecules and its velocity is the average velocity of those molecules if some molecules cross the surface into the other fluid parcel they will change the average velocity of the fluid parcel they migrated into. In that case, this will change the momentum of the fluid parcels and since change of momentum is related to force this will give rise to one kind of force which will be the viscosity force. Is that understanding right? I thought at first there was something to do with the collisions of molecules but what I said above is what I understood when I read about it on the book. If it's not like that, how we should think about viscosity qualitatively?


Not sure where else to put this as I did not see a StackExchange for legal questions. Will gladly remove if someone can suggest a more appropriate place. We are submitting a proposal in response to a government RFP. My client thinks that any and all uses of ensure, assure, or insure, (unless specifically about insurance) in any document (not just the specific proposal we are doing today) should be avoided as it exposes them to legal liability. So on a resume we can't say, "Mr. Jones utilized cutting edge technology to ensure optimal placement of gizmos". It is true that if we represent that we can do the work and then fail we will have some legal liability. But I don't believe the liability attaches in our proposal, it would be when we sign a contract. ETA: The done thing here is to use "make sure" in place of these words. Which would be legally identical, wouldn't it? Is it plausible that one could avoid liability by using "make sure" instead of "ensure"?


When a horse is being registered with the country's official registry, a clerk arrives to the stable to file the necessary paperwork. This process involves writing down the owner's data, the horse's parentage, measuring height at withers, and noting down locations of the special "fingerprinting features" that are unique to individual horse and remain constant through its whole life - the fur pattern along the mane. Specifically, the locations where the fur converges forming a small tip, diverges revealing a little skin, or forms a small whirl, clockwise or anticlockwise These are noted down with respective symbols on a chart of horse's neck, filed with the registry, and allow to uniquely identify the horse, say, in case of theft and dispute of ownership. What are these "features" called in English?


Apologies to all if this has been asked before, I searched but was unable to find one similar. This is a question that has been bugging me for a while that i haven't really been able to find a suitable answer for. I am aware that the space between an atoms nucleus and its electron cloud is teeming with virtual particles that allow the exchange of energy that give electrons an assigned energy level or 'shell' but what bugs me is about the space in between atoms. What is in between atoms? is it classifiable as a vacuum where nothing at all exists? I would find it hard to believe that atoms are pushed right up against each other at all times due to repulsive charges on the nucleus acting upon any other. I accept that the gap is unbelievably small but on the scale of atoms and electrons, how small are we talking? Is there even a gap at all? Do we know what is in between or is it unknown? is it a similar process to the virtual particles between nucleus and electrons? It is to my limited understanding that when particles "collide" there is no physical interaction, rather an exchange of energy through virtual photons. Is that what exists in all of these gaps? a constant exchange of virtual energy that acts as a consistent repulsion between all atoms?


This question is about how the ground state is chosen in a spontaneous symmetry breaking process. Say we have a Mexican Hat potential (e.g. the one for the Higgs field) and are sitting at the unstable equilibrium in the middle. My lecturer said that then the "state would decay into" a random one of the stable equilibria that are located on a circle around the origin. My question is now how exactly this "random" direction the symmetry is broken into is determined. To illustrate my problem: For the equivalent process in a superconductor I understand at least conceptually how that could happen. We have some thermal motion that is a statistical process, so the random choice of the direction of symmetry breaking really just comes from the chaotic dependence on the thermal initial conditions. What I don't understand is where such a random process could come from in the case of particle physics since I thought of the fields as fundamental. But maybe I am completely misunderstanding and such a decay from an unstable equilibrium to a Ground State never actually happens. EDIT From the comments knzhou seems to think that the breaking is an actual process while seeking_infinity says that it is just that you have to "expand your Taylor series" about a minimum. The latter would resolve the problem completely, but is it true that this only matters when we do perturbation theory?


I am performing a simulation involving growth of bacteria. This is an agent-based simulation where the solutes (glucose, oxygen etc.) are represented as a concentration field discretised over space, and the bacteria are discrete objects in a continuous space (spherical blobs with a size, mass and position). The concentration fields diffuse throughout space, and the bacteria provide the reaction by taking up (or releasing) these solutes. The rate of uptake at any position in space is proportional to the amount of biomass at that position. Hence this becomes a reaction-diffusion problem. The simulation is time discretised such that in one time step: concentration fields are solved to steady state by numerical integration of a reaction-diffusion equation for the current amount of biomass bacteria grow (biomass in the system changes) with respect to the updated concentration fields I want to know, how valid is this approximation? I have always justified it that diffusion happens on a much smaller timescale than growth of the bacteria. Is it worth creating a transient solver where the reaction-diffusion equation is solved over a finite length of time and the bugs are grown for the same amount of time in a leapfrog-like scheme?


I am trying to calculate an instantaneous merger of two rotating spheres into one. Two spheres each rotating around their own axis of rotation (which are generally not aligned) and moving relative to each other. Imagine two entirely inelastically colliding planets. While I can calculate their individual spin angular momentum and the orbital angular momentum, it is unclear to me how to combine this into one (spin) angular momentum for the resulting sphere. It seems to me I cannot simply add the four vectors together... or can I? After merging the two into a single body maintaining the initial momentum, can I calculate the released energy (in the inelastic collision) simply as the difference in kinetic energy, using the same reference frame? I realize this should be pretty trivial, but I have thus far not been able to neither derive nor locate and answer.


My professor of algebraic function fields class gave me a paper to make a project (give the proof details, fill some gaps, etc). As my previous question here suggests, the paper he gave me is hard for me. He says if I know another paper to work, it's ok. He is very busy and he doesn't care about me and leaves me to find another one. My background: I finished Fulton's algebraic curves book. I finished the third chapter of Stichtenoth's Algebraic function fields and codes. I've heard that if we finish the third chapter of Stichtenoth's book we're prepared to make some research in the area. However, as I said my ambition is much lower, is there some paper which I can read by myself with ONLY this background? I need some suggestions. I don't know if I have many choices, so ANY paper following these criteria not so old, it would be great, really. I hope not asking so much, I really need help, you're my last chance. Thanks very much in advance


I came across this question on Yahoo! Answers: Should M-theory read, M-hypothesis? It being limited evidence for further investigation, perhaps not yet a theory. I responded thus: (I realise the words "use" and "usage" are.. ahem.. overused. Please disregard this stylistic concern.) I believe this use of the word "theory" reflects an overlap in mathematics and theoretical physics. In mathematics, the word "theory" is used informally to refer to "a self-consistent body of definitions, axioms, theorems, examples, and so on" (reference). Examples of this usage include "field theory" and "group theory". This differs from the scientific use of the word "theory" to mean "an extensively tested hypothesis". I believe the use of the word "theory" here is a purposeful reference to the fact that the inventors were interested in laying a mathematical foundation for their model. Note that "string theory" has the exact same usage. In fact, the usage seems to be quite rampant throughout theoretical physics. However, that's quite possibly just a way to rationalise what is actually carelessness on the part of scientists using the terms. It may not even fit with the facts; my knowledge of theoretical physics is admittedly slim. Can anyone give any support for or against my explanation? I found this blog entry wherein commenter James Reed chalks it up to a combination of carelessness and an alternate definition of "theory" as "a model being developed by a theorist" (which is similar to the informal mathematical definition, I think).


If you're at the wrong place at the wrong time, is this actually a bad thing? Don't the two negatives words result in a positive meaning? For instance, being at the wrong place at the right time wouldn't be good, and being at the right place at the wrong time, that too would have a negative result. As I see it, being at the wrong place, at the wrong time, could result in the second negative cancelling out the first negative and therefore the phrase doesn't necessarily have a negative meaning, am I correct? As an example, take a sales appointment. You go to the right place at the right time, that's good, you've got there OK. However you go the right place at the wrong time, and that's not good as you aren't expected, and if you go the wrong place at the right time, well, you've missed your appointment. Go the wrong place at the right time, doesn't mean you've missed the appointment though does it? It doesn't mean that you didn't get to the appointment. Is this correct? Although it's generally seen as a negative phrase, it could be used positively? What would be the full implication of this, as all definitions I've seen give this phrase a completely negative meaning and don't take this into account.


What does it mean when a denomination or theological tradition is described to be "pietistic"? The definitions of Merriam-Webster for "pietistic" mean: of or relating to Pietism a : of or relating to religious devotion or devout persons b : marked by overly sentimental or emotional devotion to religion : RELIGIOSE I do not think the second definition is the one that is used when someone describes a theological tradition as pietistic, because that one seems to connote general piety or being a very pious person. I think the first definition is close, because it merely uses the adjectival form of Pietism. I have also done some reading in The A to Z of Lutheranism, looking for the entry on Pietism, and it characterizes Pietism as: ecumenical, emotional, lay-focused, and interested in institutions only if they are voluntary associations focus on the regeneration or conversion of the believer, and on living, active, heartfelt faith opposition toward [Lutheran] Orthodoxy for its overattention to the will and the intellect, seeing it as encouraging a barren and arid assent rather than living faith Later, Pietism opposed its own child, Enlightenment rationalism, for its overattention to reason, seeing it as setting skepticism above faith. I am aware that Pietism has greatly influenced other Christian denominations, but I am still not sure what it means essentially for a Christian denomination to be described as pietistic. Do all the definitions sum up to some sort of anti-intellectualism or something more?


This is what I'm trying to express [Foo] can be simplifiedly characterised as [bar]. However I am unable to find references for such as word as simplifiedly. What I want to say is that the following characterisation as [bar] is to be understood as being simplified for the sake of explaining [Foo] in the first place. How would you phrase it? I would prefer if the structure of the sentence would remain unchanged. But if there is no such word maybe this can be restructured without being too verbose. Edit: It's not a question of rhythm or aesthetics, it's a question of meaning. I'm not trying to say that the characterisation I'm making is simple to derive, I'm trying to say that I'm making a characterisation that is simplifying the matter of [Foo], which is in fact a bit more general/complicated than its representation as [bar] might suggest. For me "simply" has the taste of what I'm not trying to say (according to the above paragraph). Regarding the suggested "more simply", I have no gut feeling and will have to trust you as experts.


I am looking for a word or term that means something like: you are using previous results outside boundaries of the original experiment/observation earlier experience/results does not apply in all other cases you are extrapolating findings beyond original context those specific test results don't apply to every case there is no evidence that previous observations apply in all other cases those findings cannot be applied here it does not follow that... For example - someone has measured some attribute and concluded it increases efficiency (ignoring correlation and causality) - then extrapolate to claim that all other cases would benefit from increasing this attribute. I want to say that is not true, because the original observation applied to specific situation and it's faulty logic or extrapolating too much to assume the same thing works everywhere. I Found a list of fallacies on Wikipedia- the ones that I think are most appropriate are: Faulty Generalization, Hasty Generalization, Fallacy of Composition and Inductive Fallacy


There are a couple of idioms whose meaning is from time to time or occasionally. Every so often (Every) once in a while (Every) now and then/again Every actually is a determiner (or, broadly speaking, an adjective) specifying a noun or noun phrase and means that everybody or everything of the referred group is addressed, as in every day, every man, or every student. Obviously, every is also used when referring to a period or range of time, e.g., every thirty minutes or every week but, again, the time frame is given as a noun. I was looking at the entry in Etymology Online, as well at Merriam-Webster and Oxford dictionaries to get further information. Etymology Online doesn't address the matter at all. While the dictionaries at least define these phrases and list a couple of examples, they do not give any clue to answer my questions: what part of role is every playing in these expressions (from both a grammatical and logical point of view) and where did this usage come from.


I have a list of events. A few of them may be cancelled or they may be "moved" to another date. The latter are usually postponed but not necessarily. For cancelled events I add the state "Cancelled". What is the best word (or short phrase) to describe a date change of an event? Is it "Rescheduled"? I saw some answers here, but they referred to full sentences. Edit: As it has been asked for clarification. In the German sources usually only "verschoben" is used. In this case this can mean "date of event will be changed" but also "previous date of event has already been set to a new date". Im looking for such a word. But now I'm also thinking about introducing a new state in my data model to express the distinction between the state "to be rescheduled" and "rescheduled to/postponed to".


I am writing a dissertation and I have a two collections of data from my research which I would like to compare using graphs. I have the values for abscissa and ordinate and I am looking for some sort of tool into which I can input the values I have and which will plot and trace the graph so I can show the variations in both samples. Just something simple nothing very complicated. I have been searching the Internet for something like this for hours and I can't seem to find one. What I have found so far are tools which take a function before drawing the graph, but what I need is something which can take the values directly in order to draw the graph connecting them. I don't know whether my search terms are not accurate enough to describe what I need so I hope someone here may be able to help me out. Please, does anyone know a simple tool which I can use to achieve this? (Windows or - eventually - Linux would be highly appreciated)


I have always thought that colons were used to clarify, expand, provide evidence for the preceding sentence, or show an example. I have heard that this is not true. (Truly, it is a shame if it is so: colons are my favorite punctuation.) Which of the following sentences uses the colon correctly: There are three children in my class: two boys and one girl. There are three children in my class: Jack, Larry, and Susan. He is undoubtedly a true man: his beard is long and his hands are strong. It was a big fireplace: not one of those ornamental dainties you find in the houses of snobs, but a real fireplace that had a utility surpassed only by the greatest furnaces. She was a promiscuous fiend: she had seduced every guest who had dared to pass her threshold with her fiery eyes and her wealth. This is the problem with your stubbornness: if you happen to be wrong, it will be all the more embarassing. Never in my life have I been homesick: perhaps I am emotionally stronger than others, or perhaps they have a better home than I.


I am a user of LaTeX for about two years and I can see that almost every package which exists for TeX is free and these packages are maintained perfectly; packages are updated regularly and new packages or classes are developed when needed. Why people do such volunteer work? How do they benefit from the time they spend on creating and maintaining things related to TeX, LaTeX and friends? Do they do these just to have fun, fill their leisure time and learn something during the time they do not work or does working on these help people to develop their own business and work? I know that every person may have his own reason to work on open source/free softwares, but how should I answer this question and convince somebody asking such question and thinks that it is just waste of time spending time on something which has not any financial benefit? I personally really love TeX and LaTeX and spend some of my time learning about it but once somebody asked similar question and I had no answer to him.


As space-time is distorted in a gravitational field, relativistic effects such as time dilation and length contraction take effect. Time dilation is explained simply enough: closer to the source of gravity, slower the time passage. However, space contraction gives no such clear answer. for example, a single thread on the matter contains the following: gravitational field would produce a transverse expansion of distances gravitational fields produce increased distances in the direction perpendicular to the field [gravitational fields] produce decreased distances in the radial direction So, to pose the question as bluntly and directly as I can: Ignoring all other effects (relativistic or otherwise), which is shorter: a measuring stick closer to the source of gravity or a farther one? If the orientation of the stick plays a part, try to answer for both the case where it's pointing towards the source of gravity, as well as perpendicular. Similarly, if the position of the observer relative to source of gravity plays a part try to take that into account (but it doesn't seem to in the case of time dilation so I don't expect it here either)


Will a machine or a technique ever be possible that allows artificial gravity in interplanetary space? And I ask out of pure curiosity. I know there is the "Vomit Comet" that allows for a non-gravity 'simulation' (for lack of a better word) on Earth, and I was thinking about if there would be a way to reverse that and rather have gravity in space. edit: Say I was building a space shuttle because I'm dying to go to the moon (true story). Unlimited budget, the smartest people you can fathom helping me build my space shuttle. I get motion sickness and the whole "anti-gravity" thing wouldn't really work for me. Would there be a way to have gravity on my space shuttle? Perhaps by using a type of machine or magnets or something of the like?


I found some theoretical questions in an old test of my school, and would like some help with the ones I cant answer: It is said that the electric field is an intermediary of the electric interaction. What does this mean? Why the participation of this intermediate is necessary and can not establish direct interaction between charges ( as supposed by Coulomb ) ? Electrostatic field lines are open. How can you establish a relation between this and the fact that electric force is conservative? If a charge is placed inside a non-uniform electrostatic field, will it move alongside the field lines? (I think this is true, because the electric field is parallel to the electric force which is what causes the movement state variation, but I'm not sure...)


I realised, reading another Phys.SE question about balloons moving forwards in an accelerating car that I don't really understand how buoyancy works. Particularly concerning, for a SCUBA diver. The top answers to that question seem to claim that balloons get their "sense of down" from a pressure differential. They continue: when a car accelerates, the air at the back of the car becomes more dense, and at the front less dense, changing the plane of the pressure differential and so also, the balloon's sense of up. I find that extremely hard to credit. However, I realised that I don't really know why less dense things float in more dense things. I'm fairly sure it's something to do with displacement of heavier things by lighter things, and I think pressure acting on the lighter thing's surface has something to do with it, but that's about it.


I have a LaTeX document that works fine, but it does give a warning message every time I compile it. Here is the text of the warning message: LaTeX Warning: Label `' multiply defined. The name of the label that is multiply defined appears to be an empty string. I am confused about this, but I have had trouble searching for it online because the key element is the empty string, which does not make for a good search term. Does anyone know what this warning message could mean? I can post details of the document in question as needed, but at this point I have no idea what parts could be important. Got it. I guess I didn't realize that bibliography items counted as labels - since I never had any intention of referring to them anywhere, I left all of their labels blank initially.


I was reading Surtees' Young Tom Hall the other day, and came across this... Sir Thomas, whose father had been a great army tailor, was a Dublin Castle knight, but, like all truly great men, condescending withal - and no feast or fete, or wedding, or christening, in Fleecyborough, or within a radius of three miles, was considered perfect without Sir Thomas Thimbleton of Thimbleton Park (so he called his villa and twenty acres of land). Does anyone know what a Dublin Castle knight is? It doesn't sound terribly complimentary. Farmer & Henley, Partridge and Green have Dublin dissector, Dublin packet, Dublin trick and Dublin rules, but no knight. A search of the internet produces thousands of references to a song, whose lyrics I have perused but which doesn't appear to be relevant.


In the U.S. when someone orders a 'well drink' they are typically intending to order a drink (i.e. "vodka tonic, well") with the cheapest of the liquor the bar has available Where did the "well" come from? It is distinct from what is called a "call drink", which is when the customer specifies the brand (i.e. Stoli tonic). Since well liquor is also distinguished in contrast to middle- and top-shelf liquors, is "well" perhaps being used as a reference of altitude (e.g., a well is a subterranean water hole)? Is it coincidence or is it etymologically pertinent that the Hebrew word "be'er" means "well" in the sense of shaft/recepticle? To emphasize, this question is asking for information on the origin of the word "well" in its sense and usage behind a bar. Where does this usage of "well" derive from and how was it adopted for bar usage?


There are a few other topics I found that explore this idea from a different perspective: Is randomness deterministic? Can randomness exist? Is the universe fundamentally deterministic? My question is on similar lines but from the perspective of complexity and within the framework of classical mechanics. It would seem to me that what we typically describe as "random", for example in probability theory, refers to the unpredictability within a complex system. A coin flip has many different initial conditions: the size and shape of the coin, the way the hand moves when it flips it, the material of the surface the coin lands on, the movement of molecules in the air etc. It also has many many interacting parts, many of which exist on the atomic scale, and whose relationship with other parts change dynamically. Probability is a mathematical model that allows us to tell what possible average outputs the system can produce given all the internal variables that are unknown to us. Is this a fair characterization? However, if we were, in theory, to know all the initial conditions and had a way of describing all of the interactions of all variables in this dynamic system once it has begun, could we not predict the outcome (assuming theoretical computational power)? My main question: Is there any kind of dynamic system in classical mechanics in which the outcome would not be predictable and, if so, why not?


Consider these sentences: If you haven't got a fresh chicken, I'll take a frozen. If you haven't got a fresh chicken, I'll take the frozen. If you haven't got fresh cream, I'll take canned. If you haven't got (any) fresh cream, I'll take some canned. If you haven't got fresh cream, I'll take the canned. As you see, frozen and canned are adjectives that are used attributively but their accompanying nouns are left out. Is it grammatical to do so? Under what conditions? Does the phrase remain a noun phrase? Of course, the problem can be detoured by adding back the omitted nouns (frozen chicken/one, canned cream), but the question is, cannot the adjectives do alone? You can also share your native impression and tell us (preferably in the comment section) which of the sentences above you find acceptable and which unnatural.


I am writing a document which will contain many small (approximately a page) snippets of text, potentially organized in sections or subsections. To each such section, I would like to attach several "tags" from a predefined list. At a different place in the document, I would like to make a list of all tags and the sections which are associated with each. I have an idea how to make a very primitive tagging system if the tags list occurs in the end of the document (e.g. I can successively redefine a command adding text to it; later I can place this command to list the contents). Does anyone know a better solution? Ideally I would like to organize my tags in the beginning of the document, after the table of contents. I feel there might be a package which does this but I haven't been able to find one.


Suppose, sometime in the future I develop an experimental superweapon capable of blowing up the entire Moon. If I used it to break the Moon into multiple pieces of varying sizes, we would then have giant chunks of Moon rocks floating around. We all know the Moon is drifting away from us at a constant rate. But now, rather than there being a single concentrated mass we have multiple masses. If I understand Newtonian Gravitation correctly, the bigger the object the more gravitational pull it has. For example, if I landed on Phobos (if that is possible) and jumped, it would take a longer time for me to fall down than it would, say if I jumped while on Earth's Moon. After being broken up into smaller pieces, which of the following would happen to the Earth's Moon? A) The Moon remnants keep drifting away from us, regardless of the fact that the pieces are now smaller. B) The Moon now does not have the "power" to counter Earth's gravity due to not being the massive object it used to be, so the pieces all fall to the Earth and that ends everything. C) The Moon gets close to Earth but does not fall down on the surface. The pieces form an asteroid belt made of lunar remains much like the Jovian planets, which will never get away or closer to us and remain in a relatively perfect ellipse?


I am always surprised by the subtleties that are embedded in the wave/particle dualism. That is why I read again and again the paragraph in the Dirac's classical text dealing with the single photon interference. Here, it is clearly stated that any measurement of the kick-off of a mirror would cause the photon wave function to collapse, then completely spoiling the quantum interference of the probability distribution. So I wonder if here some ad hoc definiton of measurement is assumed, since in general terms, no matter how I chose to support the mirror, that support will experience a momentum transfer (or radiation pressure) therefore its kick-off will be definitely measured. To be precise, I found no reason to assume that, provided I have a sensitive enough device, I could not measure the single photon radiation pressure (gravitational wave interferometers actually can do that). So the point is that I could, but I don't do it? Subsequent inspections of the Dirac's text unfortunately did not improve my understanding.


First of all, English is my foreign language. I've never thought of this until the release of the film Dr. Strange the supreme sorcerer. My co-worker argued that Dr. means Doctor (as a job), while I translate it to Dr (as a title, like Master, bachelor, doctor). I think Dr is, of course, short for Doctor, which can be both a title or a job. However, I'm not so sure if they have the same meaning (when using as a prefix). The question is: Does Dr. as a prefix could mean both as a job and a title or only one? If it has only one meaning, how do I distinguish those two? How do I know if it's being used as a job or as a title? P/S: Also, does Dr. as a title has anything relate to those in {Master, Doctor, Bachelor}?


The class of words called 'words of comparison' includes words such as 'higher' and 'highest'. The words 'higher' and 'highest' express comparative height. The term for the class of words that includes 'higher' is 'the comparative'. The term for the class of words that includes 'highest' is 'the superlative'. Is there a linguistic term that denotes the class of properties that words of comparison compare? I'd appreciate whatever answers people can offer, but I'd prefer answers that include a completion one of these two similes. The word 'higher' and the word 'highest' are to the word 'height' as the phrase 'the comparative' and the phrase 'the superlative' are to '_____'. The word 'higher' and the word 'highest' are to the property called 'height' as the phrase 'the comparative' and the phrase 'the superlative' are to _____. Thank you, -Hal


Is there an adjective that can express the concept of a law that supersedes other laws? I would prefer a single adjective that has legal connotations, although a present participle will suffice. The phrases supreme law and overruling law approximate this concept, but supreme merely seems to indicate significance, and overruling implies direct contradiction, rather than "displacement in favor of another" as supersedure indicates (the laws do not run completely contrary to one another, but one is more appropriate and takes precedent). Also, the phrases the law which has primacy over other laws and the law which supersedes other laws are too wordy and awkward for my intended usage in a paper about a certain contentious Supreme Court decision. Is there an adjectival form of "primacy" or "supersedure", or another adjective which accurately describes this legal usage? Here is the sort of context in which I intend to use such an adjective: The ruling demonstrated disregard for the ________ constitution/law/legal right.


I want to fill the holes in my knowledge and get to a masterful level at undergraduate material, so I am looking for books to help me with that. I recently took the GRE Math Subject test and I focused on calculus problems. I am not sure how I did and I will be happy getting into just one graduate school, but what I really want to do is get better. I do not have much to do for the next few months, so I want to become expertly proficient in calculus, linear algebra, ODE, abstract algebra, number theory, and any other core subject. I have taken classes on these subjects so I am looking for books that do the following: Cover material in a concise and complete manner Have advanced questions that help me prepare for future learning Have answers to the questions Thanks!


Tchrist's comment here on my answer to an etymology question brought the following to mind: Ox (from Old English oxa) maintains the same vowel in the plural oxen that it has in the singular. But child has a different vowel (an English short vowel) in the plural. Brethren, an archaic or specialized form of the plural of brother, is a similar case; it changes its vowel in the plural as well, through i-mutation. (Yet brothers does not.) I've looked at http://etymonline.com to find these two words, as well as looking briefly in an introduction to Old English published by the Medieval Institute at Western Michigan University, and discovered that child has an older plural, which might be childer in Modern English. But I'm still not entirely clear on its history; and I'm confused about what the text says about brother. Why do these two words with (standard, archaic, or alternative) plurals ending in -en have vowel changes in the plural, when ox does not?


I just had a conversation where the sentence 'The system is broken because it's fixed!' was correctly spoken under the pretense where fixed means that it's rigged. Assuming that context of rigged matches as a weak synonym for broken, the question came up - what's the word for a pair of words that are simultaneously synonyms and antonyms? I am not asking about autoantonyms. I am not even looking for a single word. I am trying to find a term to describe the relationship of two different words, where one is an autoantonym and where one of its definitions is synonymous with the second word, causing the two words to be synonyms and antonyms at the same time. In my example: fixed = rigged: fixed and rigged are synonyms fixed = repaired: fixed and rigged are antonyms What is the label given to the relationship between fixed and rigged?


In the Hindi language there is an equivalent phrase which is widely used when a common man who is trying to suggest an idea to a person in power or some higher authority respectfully without challenging the latter's incompetency to 'not see the flaw' in the system. Example: A head of the police department being addressed by a common man (person of a lower stratum) giving an intellectual suggestion. I have translated a suggestion which was originally in Hindi. Common man: Small mouth big words but Sir, wouldn't it be a better idea to install wireless communication systems in police station too? Is this phrase used in a similar fashion in English too? The only phrase I have seen is 'in my humble opinion' used at the start of sentence in such cases. Another phrase I know is 'Small mouth, big talk' but I haven't seen it used as a prefix in sentences. Any other appropriate suggestions are also welcome.


I am a physics undergrad, wishing to pursue a PhD in Math. I am mostly self taught in the typical math undergrad curriculum. I am looking for more input, in ways I can improve my mathematical thinking. So, my question is once you read a proof of a particular theorem, what should be the important things that you are looking for in the proof. How should you approach it? So, one of the things I have learnt to do is to look at every hypothesis of the theorem, and see its effect on the proof, or how do the subsections of the proof correspond to parts of the hypothesis, and how they fit together. However, what I find difficult is to recognize how the proof fits together in the general scheme of things. What should I ask or explore after the proof? How can I learn to solve problems more quickly and effectively through proof - reading? I am very slow are problem solving and wish to improve that. Lastly, I am terrible at coming up with new examples, and I don't even seem to remember examples beyond very typical ones. How can I improve this ability through reading of proofs? I hope this question is welcome here. Otherwise, please feel free to close it. I understand this is a vague and difficult question, but any kind of input (however small) will be highly appreciated.


I've learned that there is no authoritative dictionary for English. I wonder on what juristic basis students are corrected when making mistakes in an English class. How can someone say that whatever the student did wrong is not considered correct English by other people. In German schools, students may only be "punished" (by getting a bad mark) when they had the chance to know better. For example when they have violated a rule in the official German dictionary. That is impossible when there is no official dictionary. How do schools in Britain or the US handle that issue? Note: There is no official reference of the German language either. However, authorities in Germany are advised to use the German language as specified in a dictionary called "Duden". Pupils in Germany are graded using the "Duden" dictionary. Other German-speaking countries may use other dictionary.


On our sister site a user recently used the term "tags" in relation to taxis in China. I thought it might mean some kind of official authorization to operate a taxi. But upon clarification I was told "tags" actually means "License plates and stickers that show the registration is currently valid". I'm a native speaker of Australian English and I've travelled in almost every English speaking country and didn't know this use of "tags", though I guess this is not a topic that's come up in conversation in my travels often either. In which countries would this sense be known? Just USA? USA and it's neighbours in Canada and Belize? All English speaking countries other than Australia? Even in Australia and I somehow remained ignorant of it despite having classic cars as a hobby for a number of years?


I am working on a Project and one of the major part of it is a GAS Detector, The GAS Detector detects the large number of flammable gases, but in order to test the Detector I am required to release certain gases in a room from the GAS cylinder with different flammable gases. There is no such thing in a room which could cause ignition, still i wonder if the Static electricity produces in a room somehow, can it cause the fire or some harm due to this gases ?? Is there even the slightest possiblity that it could be harmful ? I just want to know if it may cause so that I could tell my Professors why I am testing the GAS sensor with the Hydrogen gas present in air.


Let us assume that we want to describe the full process of photon emission by electron A and absorption by electron B. Therefore electron B must be on the forward lightcone of electron A. In the normal forwards in time description a virtual photon propagates from A to B depositing a certain amount of energy and momentum onto electron B. But does this process alone also describe the recoil of electron A? Should one also include the backwards-in-time virtual photon which propagates from B to A depositing an equal amount of negative energy and momentum back onto electron A? Between measurements no-one is "looking" at a quantum system so in the spirit of "what isn't prohibited is compulsory" maybe it evolves both forwards and backwards in time. One could say that the product of the forward-in-time and backward-in-time propagators give the full probability of photon emission by A and absorption by B. Is this where the Born rule comes from (as in John Cramer's TIQM)?


Let q be a generalized coordinate with a conjugate momentum p and a potential resulting in a periodic motion of q. What is the meaning of the Fourier transform of q(t) over its period? Can this be interpreted as the distribution of momenta? I know this is the case in QM but what happens in the Classical case? For instance for a particle in a box (classical) with an initial velocity of p/m, the motion is a triangle wave. The Fourier transform is a squared sinc function. As the triangle wave gets smaller, the F transform spreads out and vice versa. Very nice but the only two momenta for the particle are p and -p as the particle either moves up with constant speed or moved down at constant speed.


Complex analysis, and in particular contour integrals and the residue theory have proved a very powerful tool in computing a large class of real function integrals which would be quite troublesome to compute if only within the scope of real calculus. There are a great many techniques designed for this purpose, for instance, both the choice of the complex variable function and the choice of an appropriate contour is critical to our success of computation. I want to study these techniques systematically, so I want recommendations for tutorials that cover them in a systematical way, the more inclusive the better. In a word, I want to learn as many those techniques as possible, so I think such a tutorial is a must. Any advice is welcome. Thanks! Ps: the tutorial I currently have at hand is Stein's Complex Analysis, it is good but covers too few exercises about such techniques.


S.E friends, Due to my genuine interest to Goldbach's conjecture, I decided to self-study the subject of additive number theory on this upcoming Fall. Before jumping to such fascinating field of mathematics, I decided to self-study "introductory" number theory as I never took a number-theory course in past. While browsing through websites and libraries, I found books like Ireland/Rosen, Apostol, Nathanson,Hardy/Wright, Sierpinski, and Niven/Zuckerman/Montogomery. I really like them but I am not sure what book would be best for my plan to study additive number theory. Ireland/Rosen looks like it emphasizes algebraic aspect and assumes familiarity with elementary number theory from readers, Hardy/Wright and Apostol looks like an introduction to analytic number theory (which I am doubting if it is better idea to just start with additive number theory), etc. Currently, I fear that choosing wrong book might kill my curiosity to the number theory. What books do you recommend to prepare for analytic number theory?


I hope this is the right word to use. To me, these forces seem kind of fanciful (except for General Relativity and Gravity, which have a geometric interpretation). For example, how do two charged particles know that they are to move apart from each other? Do they communicate with each other somehow through some means? I've heard some people tell me that they bounce together messenger photons. So does one electron receive a messenger photon, go, "Oh hey, I should move in the direction opposite of where this came from, due to the data in it", and then move? Aren't photons also associated with energy, as well? Does this type of mediation imply that electrons give off energy in order to exert force on other electrons? Every electron is repelled by every other electron in the universe, right? How does it know where to send its force mediators? Does it just know what direction to point it in? Does it simply send it in all directions in a continuum? Does that mean it's always giving off photons/energy? I'm just not sure how to view "how" it is that electrons know they are to move away from each other. These questions have always bugged me when studying forces. I'm sure the Standard Model has something to shed some light on it.


Is it possible to let LaTeX manage minipage placement similar to how LaTeX manages figures and tables to be placed? This question comes from my previous question. I could move the minipages around manual for the best use of space but this becomes a hassle as the number of minipages increases. If possible, it would convenient for LaTeX to handle this task. Can this be done? Note: I want management like a float environment but not a float. As I stated in the linked post, I want to place minipages that butt up against each other across three columns. I dont want wasted white space (like a float would induce). I do want the the minipages to be able to rearrange themselves for the best use of the page without me going in and placing them higher or lower in the document.