darklight03/StackMIAsub huggingface dataset:
Whenever I get into a disagreement with an individual I notice that this phenomenon always occurs. (I either notice it during the argument or afterward.) Allow me to provide you with an instance to help describe exactly what I am talking about: I am having a disagreement with an individual regarding bottled water VS tap water. I am supporting the consumption of tap water and simultaneously attacking bottled water. At one point, it seems like I have won the argument as my points outweigh his. However, he then starts bringing up additional points and he now feels that he has won that argument. I tell him, "Any argument could be supported with the English language, due to its vast vocabulary, but my points are logical and outweigh yours". Therefore, here is a summary of what I am asking for help with: What is this phenomenon called when someone uses the vast vocabulary of the English language and all associated knowledge to formulate points to support their argument? What is a good word for this phrase/How could this phrase be reworded to a simpler form without out sounding cruel? - "any argument could be supported with the English language, due to its vast vocabulary, but that my points are logical and outweigh yours"
I'm trying to understand how Newton's third law works with springs. If we hang a block on an ideal spring mounted to the ceiling, in equilibrium, the block is affected by gravity downwards and the spring force upwards. So according to Newton's third law the spring itself is affected by the spring force downwards. This makes sense in my brain, but what would be the force upwards, since the spring is also in equilibrium, right? Is this the reaction force to the gravitational force on the block? That wouldn't work if the block was accelerating e.g. downwards, since then the spring would be accelerating upwards which is not what's happening? There also has to be some force from the spring on the ceiling, does the reaction force to that just always cancel out the reaction force to the spring force so the spring stays in rest? But shouldn't that force depend on the weight of the block somehow?
My question may be simple but I'm curious, let's say I start bouncing a ball like a footballer with my foot on an elevator, and it starts moving upwards (with acceleration) and then it stabilises itself moving upwards with no acceleration at a constant velocity. My question is if the ball will or not start bouncing less due to the upward motion of the elevator. My thoughts are that it depends, if the elevator is accelerating upwards then the ball will get a force pointing downwards so that it will start reaching less height than if we would be bouncing it on a stationary case. And if the elevator is not accelerating but moving upwards with constant velocity, it doesn't feel any difference with the stationary case since there is no acceleration, but I don't know
I am wondering how this sentence is to be paraphrased: At weekends they prefer to stay home and visit some friends. I am not sure which ones are close to the original: They like to remain in their house at weekends and they also like to go and see their friends. They like to remain in their house at weekends and to go and see their friends. They like to remain in their house for a while at weekends and then go and see their friends. They go and see their friends on weekdays but would rather remain in their house at weekends. They generally go and see their friends but would rather remain in their house at weekends. They like to remain in their house at weekends or else to go and see their friends.
The task is: The farmer has several sheep, each responding to one or more names, and several sheep may respond to the same name. Each sheep answers to at least one of the names, the farmer knows which sheep respond to which names. The farmer has two paddocks for food and a haircut. A farmer can say a name, and then all the sheep who answer that name go to another paddock. Prove that farmer can say names several times, so that at least half of all the sheep will be in the haircut paddock. I really want to solve this problem using probabilistic method - I need to show that probability of this event is more than zero, then the task will be solved. But I can't come up with a strict solution how to do it. (I am new to probabilistic method) Please, help me out!
I was talking to a colleague professor the other day and he said something that got me curious. The way I remember it, he said basically that in experiments a Bose-Einstein condensation is usually trapped by some external potential, which I imagine to be an electric or magnetic field. Then, the temperature is considerably lowered, the trap is turned off and one studies the evolution of this state. Can someone further elaborate this kind of experiment? For instance, it was not clear to me what exactly one tries to measure with it; as far as I understood, the temperature is cooled down so to form a condensate in the first place and the release of the external field is intended to study its evolution. What one wants to understand with the evolution of such a condensate? Moreover, what material is used in such experiments? (I am thinking about liquid Hellium?)
If all matrices can represent a linear transformation, can I refer to some general notion of the transformation associated with the matrix to make conclusions about the matrix? For example, I want to prove a simple true/false statement, "If A and B are square matrices such that AB is invertible, then both A and B must be invertible." I believe that the statement is true for the following reason: Assuming AB is well-defined and A and B are square, A and B have the same dimension. The product, AB is square as well then. AB is invertible and square, so the transformation AB represents is an isomorphism, thus the transformation associated with AB is a bijection. The transformation associated with AB is a bijection, so the transformation B represents is surjective and the transformation A represents is injective. Since both A and B have square matrices representing their linear transformations, injective and surjective respectively, the transformations must also be isomorphisms. Hence the transformation associated with A and B has an inverse, and thus A and B (the matrices) are invertible. This feels convoluted and likely isn't the simplest solution. I am just wondering if it is OK to bring in the notion of the transformations the matrices could represent like this? Am I missing some subtlety?
I do not understand at all why, if an object is sitting on a spinning platform, the friction force is towards the center. I understand the need for a centripetal force during circular motion, but friction is only in opposition to a force being applied to an object / system, why does it act as centripetal? I understand for a car, for example, the wheels providing the forces needed, but, for example, a penny sitting on a rotating disc, why would the friction be towards the center, would it not be in opposition to the impending motion of the tangential velocity? I have seen a lot of explanations on why there would obviously be a centripetal force, the need for one because there is a change in velocity, etc, but none of these explain why friction acts as this force, or how.
A flat spiral in immersed in a homogeneous magnetic field. An electric current is flowing in the spiral. The directions of the B field, the spiral and the current can be seen in the picture. As the result of the electric current and the B field, Lorentz Force appears acting on the electrons, aka the Hall Effect. The electrons are flowing from the edge to the center of the spiral, the Lorentz Force F also points to the center. Seemingly the Lorentz Force is helping the electrons to move to the center of the spiral. If that reasoning is correct, can we say that e.m.f. (electromotive force) is created because of the Lorentz Force? The bigger is the current, the bigger the emf gets, as opposed to the Ohm Law. Voltage is created out of nothing. How would you justify the energy conservation? If you think I am wrong, please point out my mistake concretely.
It is stated that an object in motion acquires "kinetic energy" while an object under the influence of gravity when raised to a height acquires "potential energy" but I have a doubt that what leads to the object acquiring the energy in actual sense? What special is happening that an object in motion or an object at a height acquires the ability to do some work(i.e. energy)? If I start thinking about it more energy is just an "abstract thing" so is it just that we assign this value to an object under a specific condition and we say that it "gains" this energy? Also, isn't this energy just a "numerical value" with no real meaning so what is it even representing under a specific condition of motion or change in height? P.S. I tried searching for similar questions on the internet and Physics S.E but couldn't find a satisfactory answer yet.
I am doing an experiment with the overall research question of: To what extent does the amount of fluid within a hollow cylindrical can affect its dynamics while rolling down an inclined plane I was able to derive an equation for acceleration for the case of a fully solid cylindrical shell and then used law of conservation of energy to determine equations for the velocity of a solid and hollow cylinder and I understand that the moment of inertia's of the aforementioned cans can also be found easily using the radius. However, I am finding difficulty in finding a method to determine the moment of inertia for cans that are partially filled other than the parallel axis theorem which I am not sure can be applied to this scenario. Furthermore, I am also unsure about the actual experiment that I am doing to answer the initial research question (I have access to a motion sensor and photogate sensor) and was wondering if I should simply measure the final velocities and relate it to varying moment of inertias if it is possible to calculate but would appreciate any alternatives to this experiment. Finally, I am not sure if I should treat the water as an inviscid fluid as that would mean there would be no effects on the moment of inertias but the mass would still change so that would affect it in that regard, right? For now I have been treating it as an inviscid fluid for the purpose of the derivations that I have made.
Also, how do different sets of principles affect the results we can get in our meta-theory? The more concrete questions that lead me to ask the above two questions are stated below. If we are studying intuitionistic logic, should we also drop the excluded middle rule in our meta-theory? Besides, in classic logic, I seem to notice that a proof of the compactness theorem must utilise the axiom of choice, be it directly or indirectly. The proofs I ever saw so far all implicitly assumed the axiom of choice in its meta-theory. (Actually, so are the proofs of the completeness theorem.) Does that mean, if we are to drop the AC, we can't even have the compactness theorem? What if we are studying a set theory without the AC? Should we assume the AC in our meta-theory when studying a set theory with the axiom of determinacy instead of AC? Or maybe we should adopt the AD instead of AC? Are we supposed to use the same rules in meta-theory as those in our formal theory?
I've been exploring the concept of gravitational wave (G-wave) emission from symmetrically accelerating systems and have encountered a puzzling question. Standard sources typically state that symmetrical systems, such as a perfectly rotating sphere, do not emit G waves. As they require a changing quadrupole moment, which such systems do not exhibit. However, this leads me to draw parallels with concepts like standing waves and the Fourier transform of a static field, where individual waves can cancel each other out, resulting in what appears to be a static field. My question, therefore: Is it that each part of a symmetrically accelerating system never actually emits any gravitational waves, or is it more accurate to say that any potential gravitational waves are effectively cancelled out due to the system's symmetry? To illustrate this, consider a hypothetical scenario: If a rotating spherical mass were to suddenly appear in an ideal space-time, would an observer detect non-zero gravitational waves during the initial moments when the gravitational effects from different parts of the sphere begin to propagate at the speed of light (c)?
Is the essential argument that these systems are microscopically chaotic enough that we can approximate their evolution as random (vastly simplifying calculations) and still make accurate experimental predictions? Or are there deeper physical/mathematical foundations? A related question: how does one interpret the distributions we end up using (e.g. over particle velocities)? E.g. when we calculate expectation values are we (A) implicitly averaging over an ensemble of universes with different microscopic system configurations? If so, why is it "okay" to make predictions about measurements in one universe from an average over universes? Does one have to invoke some kind of further self-averaging argument? Or (B) are we taking a more Bayesian perspective, where there is only one universe, with the distribution representing our uncertainty over the system state? If this is the case what other assumptions are made? Should we think of the distributions we manipulate as posteriors, given some prior? If so, what is that prior? Or are (A) and (B) equivalent in some sense? Or am I thinking about this the wrong way entirely?
So, I have been studying thermodynamics, in it I read that state functions are those functions which depend only on one state of the system and are independent of the path taken, which is pretty easy to understand. And this clears why properties like enthalpy, pressure, volume etc are state functions. Then there was the statement, Change in a state function is not a state function. which took me some time to understand, but I got it once I referred to the original definition of a state function. But now when I read about Hess law, which basically states that change in a state function is independent of the path taken, I'm confused as doesn't this imply that change in state function is infact a state function. Can someone please clarify this.
I often come across materials discussing convergence spaces and their relevance in various contexts. It's commonly mentioned that the existence of a natural convergence on the space of continuous functions (turning them into exponential objects) makes the category of these spaces a suitable environment for studying homotopy. However, I've found only a limited number of resources that actually delve into this idea (mainly this and this). As someone who doesn't engage with algebraic topology on a daily basis, this leaves me with a few questions. Are there any works that effectively highlight the significance of these spaces for the typical algebraic topologist? If not, could the issue possibly be attributed to an "excessive" use of filter-related terminology? I would greatly appreciate any insights or references that could shed light on this matter.
Say we're drawing marbles from a box. The marbles can be labeled X, Y, or Z and can be either black, brown, or white. The probability of drawing a marble with each letter label is unknown but fixed and marbles are replaced after each draw. A marble labeled X is half as likely to be brown as the other colors. A marble labeled Y is half as likely to be black as the other colors. A marble labeled Z is half as likely to be white as the other colors. Say on our twentieth draw from the box you see a black Y for the first time. Question I came up with: What is the best estimate for the probability of drawing a marble labeled Y from the box?
In the "talk" tab for Wikipedia Heat Engine article, someone is questioning whether an internal combustion engine can be modeled as a heat engine - and therefore is limited or is not limited by Carnot efficiency. The arguments are that the input is chemical energy, not heat. And also that IC engines dont operate on a closed cycle. Fresh air enters and is expelled each cycle. There are some answers there as well, but I'd like to get input from you guys to settle this matter once and for all! Is it ok to model IC engines as heat engines? And in a wider sence; can you model a solar cell as a heat engine and calculate carnot efficiency with T_c being the air temperature, and T_h being temperature of the sun. (I saw this in a textbook once, I believe.) https://en.wikipedia.org/wiki/Talk:Heat_engine (section headline: "Internal combustion engines can't be considered heat engines")
If I were sorting, for example, audio recordings based upon the performer, then "Vince Guaraldi" and "Bob Seger" would be sorted as "Guaraldi, Vince" and "Seger, Bob" On the other hand it's not immediately clear to me how I should sort a recording by "Vince Guaraldi Trio" or "Bob Seger & The Silver Bullet Band." My instinct is that this is now an entire proper name for a group and shouldn't be split up (just like I wouldn't sort things under "Zeppelin, Led"), but in both cases the group name is created to highlight the most famous member. Both of my print style-guides are silent on this; the MusicBrainz style guide, is clear that e.g. "Guaraldi, Vince, Trio" is correct, but I'm not sure if that's just a quirk of a single site, or if it is something more universally done.
I am thinking about the following question: when I look at the atomic emission spectrum of a specific element and I am only interested in the visible section of this spectrum and the method of retrieving it is via putting the element inside a flame, does the type of the flame in any significant way impact the observed spectrum? For example, does it matter wheter I excite lithium with a standard propane flame or instead a hydrogen or acetylene flame? I am trying to find ressources on this online but so far I haven't found any spectrum of any element that was measured using anything else than "the flame method" which I suspect refers to using propane gas (or other falmes with less known composition) as the exciting medium. I was tasked to find such spectra measured using different types of flames but since I couldn't find anything on this I am wondering if this question makes sense in the first place.
Suppose we have a loop of copper wire moving perpendicularly through a constant finite rectangular magnetic field directed into the screen . When the loop enters the field, the induced current would be counter-clockwise and when it leaves the field the induced current would be clockwise according to Lenz's law if we view the loop moving through the field from above. But the question here is that when the loop is moving through the middle of the field where it is neither entering nor leaving the field, can we say that the magnetic flux is changing and thus producing an induced current in the loop? The field is constant throughout, so will the change in flux be zero? But if not, how can we tell in which direction the current will be flowing? How could Lenz's law be applied to such a case?
I'm studying about electric field and referring to an article about electric field in wikipedia And in here, there are some doubtful sentences: The electric field is defined as a vector field that associates to each point in space the electrostatic (Coulomb) force per unit of charge exerted on an infinitesimal positive test charge at rest at that point First, in this sentence, i'm doubtful about 'electrostatic force'. As i know, moving charges also make electric field. This implies there are two kinds of electric fields: electrostatic fields and fields arising from time-varying magnetic fields. And i think, in here, there is electric field which is not belonging to 'electrostatic field and field time-varying magnetic fields'. For example, steady current, not in wire, makes electric field but don't make time varying magnetic field.. Is there something I'm thinking wrong? I think above sentences are uncomplete
In the vacuum state, particles and antiparticles can spontaneously emerge as virtual pairs due to the uncertainty principle. These virtual particles have a brief existence before they annihilate each other. This process is a manifestation of vacuum fluctuations. Similarly, in particle interactions, intermediate states involve virtual particles that can exist for a short time before contributing to the overall interaction process. These virtual particles mediate the exchange of momentum and energy between the initial and final states of the particles involved. If the intermediate state is represented by virtual particles, should we distinguish the actual physical process of the in-between, intermediate state from the vacuum state? Are intermediate states just mathematical constructs only useful for calculating; or they have a physical significance within the framework of quantum field theory? We cannot think of the intermediate state as the vacuum state despite having the same description involving virtual particles that cannot be observed due to their brief existence?
I am what most of the world considers a "non-native" speaker of English. I, however, consider myself a "native" speaker of English because: I grew up speaking English since birth, English is the language that I am most fluent at, I have never formally studied English, I just picked it up as a child as the first language that I acquired. Recently, a "non-native" friend of mine asked me whether it is "a helicopter" or , "an helicopter", and I realised that I would personally say "a helicopter" when the stress in the sentence was on the noun helicopter, but when the stress was elsewhere, I would say "an helicopter". Is this correct in the main standard dialects of English or is this some bad habit I have picked up?
In all of the treatments of elementary Euclidean geometry which I've seen so far, the section about triangle congruences introduces S.A.S. criterion as the basic postulate from which A.S.A. and S.S.S. criteria are deduced. I remember reading somewhere that one could choose any one of these three as "the congruence postulate" and deduce others from it. I am able to produce proofs for S.A.S. by taking A.S.A. as an axiom and vice versa, but S.S.S. seems to be the "odd" one since I cannot reach either S.A.S. or A.S.A. by taking it as the axiom. I was unable to find anything online that shows such a proof so my question is whether the premise that any one of these three criteria can be picked as the axiom is true or not. If it is, how can we prove, for example, S.A.S. through S.S.S.?
How would little, native English speaking kids say "Tell me a story about the bear!"? In my language, they might say something like "Tell me the bear!". Does "Tell me the bear!" sounds like a valid "little English" question from a little kid who is catching up the language? Context: Each language has different logic, and the kids build up the logic differently. I am very much curious about how young kids in native English environment build up the logic of the English language. For example, in my language, they might say something like "Tell me the bear!" instead of "Tell me the story about the bear!" Do English-speaking kids make similar mistakes, like saying "Tell me the bear"? What are the common mistakes they make in this context?