darklight03/StackMIAsub huggingface dataset:
Everyone does know that the surface of a conductor is at equipotential during equilibrium. I was reading Feynman's lectures where I found this (bold)line: Suppose that we have a situation in which a total charge Q is placed on an arbitrary conductor. Now we will not be able to say exactly where the charges are. They will spread out in some way on the surface. How can we know how the charges have distributed themselves on the surface? They must distribute themselves so that the potential of the surface is constant. If the surface were not an equipotential, there would be an electric field inside the conductor, and the charges would keep moving until it became zero. This is a much good reasoning for the surface to be an equipotential one; if there were any region to be in higher potential, charges would flow towards them to neutralize and again make the surface equipotential. To understand his explanation, I thought of a positively charged surface that is not in equipotential status; so there would be an electric field which would prompt the free electrons inside the conductor to go there & nullify the field to make the surface equipotential, right? But what about the positive charges that are now inside the conductor? Okay, they would by repulsion move towards the surface. But what is the GUARANTEE that they would form the equipotential surface? What really happens when they go on the surface that compels them to make an equipotential surface?? [After all, you can't say:" since you are studying electrostatics, there must be equipotential region on the surface no matter what happens; that's it"-this is what my school-teacher said when I asked him.]
I'm thinking of writing a short story set on a version of Earth that is tidally locked to the Sun. I'm not exactly sure how to research the topic. Here's a number of questions about what would happen: How hot would the light side get? Are we talking ocean-boiling levels? I imagine that life would eventually flourish, given the massive constant energy source. Is this accurate? On that note, I imagine massive thunderstorms along all the coasts due to increased evaporation. How bad would they get? Would the ground ever see the Sun, or only rainfall? How cold would the dark side get? Is it conceivable that any life could still exist there? (Life has proven itself quite versitile in the past, i.e. life at the bottom of the ocean.) What wind speed would the twilight zone experience? I imagine the atmosphere would transfer heat from one side to the other, but would the wind speeds be bearable? In what direction would air flow? I hear that the oceans would recede into disjoint northern and southern oceans if the world stopped spinning. Would this also happen if the Earth became tidally locked? Would the Sun create a 'tidal' bulge in the ocean at the apex of the light side? Would this or the above dominate ocean behavior? Would we completely lose the magnetic field? Would life be able to survive without such shielding from magnetic radiation? Would the Moon eventually unlock the Earth? What state would the Moon have to be in for there to be both a locking between the Sun and the Earth as well as the Earth and the Moon? What other radical differences would exist between our Earth and a tidally locked alternative?
I was asking the other day how to find certain fonts of a document. Well at last it was easy. I came to the Mathematical Pi LT Std font and ITC New Baskerville Std results and for that part, I was pleased because I finally managed to get those fonts. So far, I have only used LaTeX for my documents and papers for the University and own projects and as most of us know, there are very few pleasant Math Fonts to use (at least for me). I have tried XeLaTeX and mathspec package to set the digits and latin to Baskerville and Greek to Mathematical Pi, but it turns out to be very clumsy when it comes to spacing and that stuff... and I ended up not liking the result. I have been checking the glyphs of Mathematical Pi and it contains a lot more than Greek Letters (obviously) but I don't know how to tell XeLaTeX to use for example the integral sign, relation signs, sums and everything else. I would like to know if there is any way to use Mathematical Pi font at full with any of the TeX systems and if that is not the case how to use that font other way, because I have been trying to use it in MS Word with its equation editor but I have not been successfull nor finding how to do it. Can anyone help me with this?, I'm sure there has to be a way since I have found that font in many books. Thank you all in advance.
It's not really clear to me how does QM attacks determinism. It sure attacks computability, which is a component of newtonian, naive determinism, but it's often claimed to destroy determinism itself (which says that we can't compute events, but they are determined anyway). A photon is both a particle and a wave; a particle doesn't have both speed and momentum defined values at the same time; some things are not a in a state, but in a superposition, until they are measured. It's cool, I get it. But aren't there a lot of macroscopical objects that can be described this way as well? A just published book is both a best-seller and a failure, until enough people buy it. It would be impossible to compute which state it is until the state itself 'happens'. I'm not sure I'm just referring to hidden variables. Where is the problem with observation exactly? It is obvious that the fact that a scientist decides to observe the particle as a wave is due to the fact that he's doing that experiment. And he's doing that experiment because he likes science, because it's written in his DNA or in his education. He's working because he needs to eat, because chemistry of his body tells him so, and so on. The impossibility to compute in advance which state is correct is due to the free will of the observer, in the exact same way in which the book is a best-seller or not (the decision of people to buy it). But it's just because it's too difficult to know everything: a God-like creature could perfectly know how many people would buy the book and also if the scientist decides to measure the photon as particle or as a wave at a given time. Is this just superdeterminism? (https://en.wikipedia.org/wiki/Superdeterminism) Looks like a pretty logical observation to me. What I am missing?
I have recently been studying continuous dynamical systems whose phase space can be divided into a number of regions. Inside each of these the flow is smooth, but there is a discrete jump in the flow just at the boundaries. In the mathematical description, the right hand side of the differential equation is different for different regions of the phase space of the dynamical variables. Note: I don't mean something trivial like systems which exhibit smoothness in different regions of physical space separated by boundaries, like differently heated gases in partitions, or water in contact with vapour etc. The different regions I mention are regions in the phase space of the dynamical systems. So imagine a set of continuous-time differential equations defining a flow which is segregated in its phase space into regions in which the evolution of the equations is piecewise smooth. I also don't mean phase transition. There is no variation of order parameter or bifurcations here. The piecewise smoothness exists in the dynamical phase space for a fixed value of the system parameters. I have been studying them in an engineering context of a mechanical device in which there is a sudden change in the velocity of a moving part when it hits something. But it struck me that such piecewise smooth systems should be found in many scenarios, from other areas of physics, maybe certain quantum phenomena, to biological systems that can be studied with the theory of dynamical systems. Some examples of the kind of systems I am looking for are: Quantum mechanics: the Muffin-Tin potential is a quantum model where the potential (the right side of the differential equation) is approximated to be piecewise defined. Classical mechanics: the hard impacting oscillator (oscillator with a rigid wall at an end restricting the amplitude, like the devices I was studying). Theoretical computer science: Hybrid automata and reachability problems which are further piecewise linear. I am curious to apply my understanding of the mechanical system to such systems. So, what are other dynamical systems in nature which exhibit piecewise smooth behaviour?
I posed a closely related question here but it received a tumbleweeds award. So I thought I would post it from a different angle to see if I can illicit at least some thoughtful comments if not answers. The modeling of many physical systems utilize the mathematical tools of calculus, by writing the relationship of physical quantities in the form of differential equations. Considering time dependent operations of integration and differentiation, the dynamics of a physical system may be expressed in terms of one form or the other. A good example are the Maxwell Equations which are often written in both differential and integral forms. Integral forms tend to express where the system has been up to where the system is at present while differential forms tend to express where a system is now and where it will be in the near future. So the two forms tend to imply a sense of causality. So this brings me to my question. Since we tend to observe a causal universe (at least at a macroscopic level) are integral forms a more natural approach to modeling systems? I'm using the word 'natural' in the sense that the nature of the universe tends to work one way vs another. In this case I'm saying nature tends to integrate rather than differentiate to propagate change. We can write our equations in differential form, solve them and predict, and they are useful tools. But isn't mother nature's path one of integration? I tend to believe this is so by my experience in simulating systems. Simulating systems in an integral form rather than differential form always seems to lead to better results.
Right now I'm writing an essay on Death in Venice, and I'm having trouble finding the right word or phrase to express how Aschenbach is parallel to the old man on the boat to Venice (both dress up to fit in with youth, some repetition of specific phrases in descriptions, youth from Pola vs youth from Poland, etc.). The closest word I can find to describe what is a "parallel". I see this word used a lot on the internet to describe (usually in TV shows) when something that one character did in a past episode is similar to something that a character (usually different, but I've also seen it used to point out character development via slight differences in the parallel). It kind of describes two completely separate scenes that have a much more powerful meaning when juxtaposed (usually very blatant mirroring, etc. to point this out to viewer/reader). In my case, it would be the scene with Aschenbach observing the man on the boat and the scene where Aschenbach applies makeup for Tadzio. Specifically, the man on the boat foreshadows the "endgame" for Aschenbach. In my essay, I've referred to it mostly as foreshadowing, but I think the depth of the connection that Mann makes warrants something a little stronger. The word foil came to mind, in terms of the intensity and how it's character specific, but obviously, it has the opposite meaning of what I'm going for. I did think about just using the word "parallel", but I when I looked it up, the definition for the word parallelism came up, and as a literary term it seemed from this definition, it seems that this word as a literary device refers to parallel syntax and a not to a broader similarity. I've come up with "symmetry" and "mirror" to describe individual aspects, but I was wondering if there is a proper term that encompasses the broad connection between the two characters.
I was looking at this question on SE and the answers seemed to say that the reason why matter doesn't expand along with space is because of forces like gravity, electromagnetism, etc. However, i feel like this has to mean the fields themselves don't "expand" along with space. Let me explain... From my understanding, the expansion of space is about the expansion of space itself, not about distances within space changing. For example it's about the space taken up by one meter increasing, not about the distance between entities increasing from one meter to two. If these assumptions are off please let me know. Keeping that in mind, look at redshifted light for example- This happens when the distance between crests of the light wave increases, changing the light's frequency. However, if space expansion doesn't increase distances within space, there should be no change of frequency, because there is no change in distance between crests. We do however see that the frequency does change with metric expansion. The only way i can think of to resolve this issue is to say that the expansion of space itself affects the wave. The only way for the expansion of space to affect the wave, is for the wave's field to not expand with space. The EM field "density" has to stay constant relative to the density of space (sorry for all the informal wording). Or in the case of gravity- if space expands, the distance (and therefore gravitational influence) between objects should remain unchanged. However, for gravity to keep mass from expanding along with the expansion of space, it would have to exert a force that isn't proportional to changes in space density. The behavior of gravity (relative to the distances that determine it's influence) changes based on the density of space. This would have to mean, like EM, the gravitational field does not expand with space. That's how we're able to deduce expansion, because the fields themselves are our reference points. This isn't about waves/excitations of a field, it's about the field itself, if that makes any sense. If this is true, how do we reconcile the expansion of space with fields remaining constant?
Having been an avid lover of Mathematics, it is my dream to become a mathematician one day. I have been learning some "Advanced Mathematics" (Real Analysis and some Abstract Algebra mostly, and a little bit of Linear Algebra). The first thing that anyone jumping from High School Math to proof based, rigorous math, should notice is how different they are from each other. Math that I am learning now is definitely not like the Math that I now do at school. This is the fist thing I realized when I started doing Real Analysis a few months back. Advanced Math, I noticed, is exceptionally beautiful and at times it is like art, utterly elegant and aesthetically pleasing. I don't know if others share this same feeling with me. I used to enjoy Math then, for sure, but nothing compared to the enjoyment I am having now. Because of the enjoyment I get while doing Math, I am pretty much sure that I would like to major in math someday and if possible go to a graduate school in mathematics. But this being said, I do have a small concern. Because Higher Math is so very different from grade-school math, I fear that as I dive in deeper and deeper into mathematics, I might realize that the Math I do then has changed so much that it was nowhere close to the Math that appealed me. How substantial is this fear? Is it legitimate? Because this community is full of Mathematicians, I figured this would be the best place to ask If you guys experienced such a feeling too? How and in what ways did you find math different from fairly lower level math that I am currently into. Any help is much appreciated!
I think the way that I've come to think about mathematics is becoming problematic and I'm wondering if I should abandon it. When I study mathematics, I find myself trying to compare the mathematical constructs, operations, entities, and even the basic terminology (which I have come to understand is incredibly elegant, precise, and deliberate) to real world, physical, even visible phenomena. I think under the pretense that the things I do in the mathematical world represent real, fundamental structures in this Universe. For example, the fact that terms can 'cancel' out in an equation has profound implications on the workings of the Universe and should be heeded and studied as such. In other words, I try to make sense of the things I learn in math classes by finding their analogs in the real word, because I assume they must have at least one. Thinking with this frame of mind has led me to appreciate mathematics in a deeply profound and beautiful way, and it's the mindset that I try to share with other people when explaining why mathematics should be studied and why people describe it as beautiful. When I learn something new in a math class, I try to understand and remember that these are not simply tedious equations and formulas that mean nothing and come from nowhere, but that they have real physical and, mostly, intuitive meaning. All that being said, I'm taking my first liner algebra course this term, and it's becoming harder to utilize this mentality, not simply because linear algebra deals with such things as infinite dimensionality which we obviously have no intuitive way of grasping or visualizing, but really just because the class seems more about computation and calculation than concept and philosophy. I worry that my thinking has led me astray, primarily because it becomes hard to focus on just doing sheer, brute force calculation without wondering and worrying about what these constructs really mean. This leads me to fall behind in lecture, take hours longer than is probably necessary on the homework, and add to an overall level of frustration that has been building for some time now because of it, which only clouds my understanding even more. My question is really more of a plea for advice. Should I abandon my way of thinking about mathematics as though it will become increasingly unhelpful in future courses and topics, or is linear algebra truly more about numerical gymnastics than tangible interpretation? Should I focus, currently, on simply learning the algorithms for computation now assuming that the philosophical groundwork will be exposed later on, after which the conceptual work that I'm looking for will yield itself? I'd really appreciate responses from the people that frequent this site. I've been nothing but overwhelmed at the level of quality, thought, and sincerity in the answers I've read here and throughout the conversations I've eavesdropped so far. Also, please direct me to similar questions if you know of any, and help me with the tagging of this question, as it is the first one I've ever asked on this site.
There's a poem in bahasa indonesia, titled "Aku Ingin (I want)" by Sapardi Djoko Damono, translated to english by John H. McGlynn. This is the english version: I want I want to love you simply, in words not spoken: tinder to the flame which transforms it to ash I want to love you simply, in signs not expressed: clouds to the rain which make them evanesce source What I want to ask lies on the last line, especially the word "make". This was originally being questioned in a blog post (in bahasa indonesia). The OP caught that make usage, and his post caught my attention, thus I asked it here to get more understanding of it. Seems like for Indonesian who reads the poem in bahasa indonesia, the last line interpreted as "rain that makes the clouds vanish". Just like the first verse interpreted as "fire that burns tinder to ashes". Thus, the word make on the last line should have be used by rain, that would make it makes. But in the poem's english version, make stayed make, make it looks like it's used by the clouds. Meanwhile on the first verse, both tinder and flame are singular, thus hard to know to which transforms is used. My question is, why is it make, without s? Is it a different interpretation, or is there some kind of poetic usage on that word, or is it a common usage for english poem (by english poem, I mean poem using english language)? Sorry for broken english, and in case I asked in a wrong place, please tell me where should I had asked.
I have never understood what measuring process (if any) is supposed to be continuously polling the quantum state of an unstable bound system subjected to decay via quantum tunnelling. The reason I reckon some kind of polling process should exist in the first place is the following: According to the QM postulates, the unitary evolution of such a system should by definition keep it reversible, so it is only when measured that a decay can be observed or not. But this would make the decay rate dependent on the measurement rate, while we well know that the decay probability is constant, and the decay deemed "spontaneaous". What am I missing? Edit: From the discussion in the comment section I gather I have not been clear about what I am asking here exactly. Let me try to reformulate the question. It is about how quantum tunnelling is supposed to explain the exponential dynamics of a decay process. I am not asking about the Zeno effect; quite the opposite, actually: why, in the absence of any measurement, do we have an exponential decay at all? I just do not understand at what point in the unitary evolution of the unstable system the tunnelling effect is spontaneously happening. The polling process I imagined is just a way to ask "why does the tunnelling effect manifest iself ?" because I cannot see how it can manifest without a measurement. Please do not infer that I am making up my pet theory here. I am only looking for a way to picture the situation, which at this time I don't get at all.
We have statements, and we have questions. A request made in the form of a statement has a question equivalent. But is that question equivalent implicit, or is it simply a rewording of the statement form? Take the following: "Please tell me why I sound like a sissy." This has the question form of: "Why do I sound like a sissy?" Is that question form implied within the statement form? I would argue it is not. http://www.merriam-webster.com/ defines imply as: "to express (something) in an indirect way : to suggest (something) without saying or showing it plainly" This definition can be interpreted to mean: Something implied must be identified with knowledge outside of what is only directly stated but based on what is stated - one must add context to what is stated. That may be stretching it a bit, but if one does not use any logic or outside knowledge to examine the meaning of provided information, other than that needed to identify the direct meaning directly present, one cannot identify anything that is implied. Here's an example: in the statement form of the quote I provided, one could say that it is implied that the individual requesting the information wants to know said information. It is implied because it is not directly stated in any of the words that the individual requesting actually wants to know; it is suggested, but not directly stated. For all we know, the individual is requesting for someone else. The reason I say that the question form is not implied is because we need no more information (other than the "why do", but that is simply part of forming a question) than what is presented in the statement. We have all the information needed to form a question out of what is provided, but we do not have enough information to state with absolute certainty that the individual requesting the information is the one who actually wants to know said information. Based on this, I would say that the question form of a statement is not implicit. Am I correct?