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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 hom... | 0 |
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 l... | 0 |
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 c... | 0 |
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 ins... | 0 |
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 ... | 0 |
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 vi... | 0 |
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... | 0 |
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 ... | 0 |
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 languag... | 0 |
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 post... | 0 |
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, a... | 0 |
I hope this question hasn't already been asked, but I looked and couldn't find a question with a similar title. It is my understanding that Maxwell's equations and the Lorentz force law form the foundation of classical electromagnetism. These are fundamental because (in the classical limit) they are always obeyed, in c... | 0 |
I am currently reading "No-Nonsense Quantum Field Theory" by Jakob Schwichtenberg and in several derivations in the book it'll pull a partial derivative operator out of an integral, or change the order of full and partial derivatives on a function, etc. without explanation. So my question is: Are the differential and i... | 0 |
I would like to learn Mathematics for understanding GR, Differential Geometry, Riemannian Geometry and related research papers rigorously. I would like to carve out a clear path to understand these topics by listing out all the necessary prerequisites. I have undergrad Math under my belt such as: Real Analysis, Algebra... | 0 |
I was explaining the tidal locking phenomenon to a friend. First I started with the formation of solar system and how at the beginning the planets were actually like balls of magma-esque rocks. And then how the force of gravity would eventually affect their shape and mass distribution and consequently, moment of inerti... | 0 |
I've recently started using Texmaker to edit on my LaTeX documents (up to now, I mostly used Overleaf or TeXworks), so I am still new to this program's shortcuts. I have been looking for a shortcut in specific that I can't seem to find, and I would like to know whether this is something this specific LaTeX editor has. ... | 0 |
This is a question that a high school student asked me and I couldn't give him a satisfactory answer. He started by saying that An object appears red because the energy corresponding to a "red" (don't take it literally) photon isn't equal to that of the energy gap of the elctronic energy levels of the object. And now i... | 0 |
I would like to find the distance function for a curve comprised of all points within a lune that are of equal perpendicular distance to both circular arcs. In other words, what's the minimum distance by which a given point inside of the lune would need to move in order to become equidistant to both arcs? My use case w... | 0 |
I am searching for a book on group theory that follows in the style of textbooks written for math students (since I was one), but that covers all (or at least most) topics that would be needed in physics, such as in QFT for example (Think of the topics in Zee's Group theory in a nutshell). My problem with Zee is that i... | 0 |
Please correct me if I am wrong. Electron is fundamental and is zero dimensional (probably made up of strings). Electron is bound to the nucleus. Electron in an atom has velocity and position which are statistically distributed. Electron mainly interacts electromagnetically. Temperature is the measure of statistical ki... | 0 |
I am a veteran of the wars in Iraq and Afghanistan. When talking about the people opposing us, I have always referred to them as the "enemy." Now, as I get a little older, and a little more aware (specifically, as I became a determinist), I have lost any hostility I feel towards them, and I feel that calling them the "... | 0 |
I recently received a newsletter from an entity I previously thought to be credible which is embarking on a brand/campaign around the concept of ambition which makes me wonder if my understanding of the word is "off". Can the following be examples of Ambition? Starting a new hobby. Getting out for a walk on the beach. ... | 0 |
I got a bit confused about independent clauses,so I decided to ask ChatGpt, which has given me three different answers for the same sentence I think he is getting too old, suffering from Alzheimer's disease. The sentence is: I bring a natural positivity and a can-do attitude, allowing me to effectively solve challengin... | 0 |
I was reading a paper on black-hole information loss and it mentioned backreaction. I had never heard the word before so I googled it and was surprised to find no cohesive definition that I could understand. The best I found was this wikipedia article which gives a definition akin to "a backreaction is a field that is ... | 0 |
I am currently studying Linear Algebra Done Right (LADR) by Sheldon Axler and also How to prove it by Daniel Velleman. Currently I am in the chapter of Bases in LADR and I already read the chapter on equivalence relations in How to prove it. I tend to be somebody who looks for analogous things and something that I want... | 0 |
A common construct for comparison (making parallels) is "the X of A is similar to that of B". Quoting an example here ... the animals' situation is similar to that of the plants. which is equivalent to the situation of the animals is similar to that (i.e. the situation) of the plants. I often wondered whether this cons... | 0 |
I have the following diffraction pattern produced by a fabry-perot etalon The red represents the center of that pattern. Taking the mean intensity of the pattern as a function of the radius from the red dot and applying a cut-off radius results in This clearly shows a superposition of at least two diffraction patterns.... | 0 |
Two up quarks in a proton lead to an imbalance, which results in the proton having the ability to attract electrons. Two down quarks in a neutron lead to balance in the electromagnetic force, leading to no interactions happening with electrons. The strong force and electromagnetic force appear to be directly related. U... | 0 |
I am trying to simulate the reflection of a sound ray, that goes from a sound source, bounces off a wall, and is received by a microphone. The wall has a an absorption coefficient, and a specular reflection coefficient, both of which vary by frequency. Thus, the sound reflected by the wall specularly can be characteriz... | 0 |
I have a couple questions on the mechanism for how solar projection through a telescope works: I recently took a small telescope focused at infinity, aimed it at the sun, and held a sheet of paper behind the eyepiece. It projected a focused image of the sun onto the paper. When I changed the focus away from infinity in... | 0 |
Suppose we have two bodies at different temperatures, and we let them interact thermally in such a way that the process is not quasistatic (e.g. two different metal spheres touching). Do we arrive at the same final temperature as if the same spheres had equilibrated via a quasistatic process? If so then, rigorously, wh... | 0 |
Clarification: the word "important" is ambiguous. Here, I use "important" to mean that we want to know the value of a quantity accurately. For many optimisation problems, it looks as if we are more interested in finding the minimum value, rather than finding the argmin. For instance, in machine learning models, we care... | 0 |
Some English nouns are identical to their verbs (and their adjectives) both in spelling and pronunciation, for example: "This is fake"; "to fake"; "this is a fake" "To tear"; "a tear" "To parody"; "a parody" "A misfire"; "to misfire" There are some examples where the (disyllabic) noun is spelt exactly like its verb but... | 0 |
Imagine a situation where I'm moving at the same velocity as the electrons in a conducting wire. In this scenario, from my frame of reference, the electrons appear to be stationary and thus there is no current from my POV. Now, for a brief moment, these "stationary" electrons come into contact with (or pass right next ... | 0 |
I am trying to check if my understanding is correct. This is not really a question but a request for validation. I hope this is allowed. When painting with a heat reflective paint there are two options A- The room does not contain a significant heat source. This will always lead to a reduction in ambient temperature as... | 0 |
In algebraic number theory, we would like to study rings of algebraic integers but sometimes they are not PIDs and thus they don't possess good properties. Because of this, we have introduced the notion of Dedekind domains, in which rings of algebraic integer are included and one can study the nice properties of Dedeki... | 0 |
I came across a question a while back. It stated that a oil droplet was suspended vertically within an electric field. The man who suspended it had left to eat a very LONG lunch, and came back to see that it was splattered on the top plate (nothing with the setup had changed), and the question asked us to state a physi... | 0 |
I have learned some basic measure theory as covered in the first chapter of Durrett's Probability: Theory and Examples, which includes the construction of Lebesgue integral (from simple functions to bounded to positive to integrable ones), as well as some basic properties such as Fatou's Lemma, monotone convergence the... | 0 |
Google dictionary (based on Oxford dictionary) has an entry for the verb "reveal" as follows: make (something) known to humans by divine or supernatural means. And it includes one example: "the truth revealed at the Incarnation" Based on the definition, I find it hard to understand the role of "the truth" in this examp... | 0 |
If I have a stick that has a spinning disc on the end of it, and I try to rotate the stick, I will feel more inertia the faster the disc is spinning because I have to transform its rotational energy into a different axis. It seems intuitive to me that this would apply to electromagnetic fields as well, since you have t... | 0 |
Often we define a quantum phase of matter as a set of ground states of a gapped family of Hamiltonians, where the gap does not close anywhere in the family. Equivalently, we can define it as a set of states which are related by constant depth quantum circuits with local gates (equivalence of these two definitions is sh... | 0 |
This question might be very silly, but I am really confused about it from several days. Look transverse waves on a string propagate along the string due to the electromagnetic (EM) forces between adjacent particles of the string. So when one of the particles is displaced, it will drag nearby particles and thus the dist... | 0 |
I am working on automated templates, and I want to use latexmake with luaLaTeX, as suggested in a comment on this question, where I attempted a similar setup with XeLaTeX. However, I am facing challenges with the configuration. My goal is to automate the process of typesetting my documents with luaLaTeX using latexmake... | 0 |
For context, I watched PBS Spacetime's video on virtual particles (link goes to relevant timestamp) where they say that virtual particles aren't mathematically necessary, because the lattice version of nonperturbative QFT doesn't use them, and yet still makes all the same predictions as perturbative QFT. I was satisfie... | 0 |
Let S be a compact orientable surface and U an open connected subset of S with finitely many ideal boundary points (or ends). U has a prime ends compactification which is a surface with boundary (following Mather). Let b be one of these ideal boundary points and Z(b) its impression in S. If Z(b) has more than one point... | 0 |
In the situation above, we have a power line which uses an alternating current. This alternating current causes a change in magnetic flux through the loop below the power line, which induces a current according to Lenz's law/Faraday's law, which eventually goes to the farmer's equipment. This is classed as power theft.... | 0 |
I have a hard time understanding time dilation and special relativity; each explanation seems to contradict the other, and don't explain the apparent paradoxes they cause. Say clock A orbits clock B at a very high speed. According to the explanations I've heard, B would perceive A as ticking slower than B, because of t... | 0 |
Usually when we introduce postulates it is so they are of some use to us. I do not see the reason for these two. The Line Separation Postulate: Each point on a given line divides the line into three disjoint sets: the set containing the point, and the two half lines on either side of the point. The Plane Separation Pos... | 0 |
Suppose that, as a manager, I am creating a campign to evaluate employees based on the NPS (Net Promoter Score) of their sales - the objective is to reward high perfoming employees. However, due to the different nature of each role, some employees have a lot more sales than others. What is the best way to create a rank... | 0 |
I've noticed while playing Minesweeper that when I have too few bombs, I get very easy to play games. In other words, I get games that can be solved with very simple algorithms. When I play games with too many bombs, I get unsolvable games or games that can't be solved without guessing. There seems to be a region in th... | 0 |
In an office, there are typically various different kinds of environments in which each employee carries out their work. Some have their own rooms, some have cubicles, some only have a desk in an open landscape etc. I'm looking for a word for the place where an individual employee carries out their work, regardless of ... | 0 |
There are Two different defintions for the event horizon of a black hole. The Absolute horizon and the Apparent horizon. An apparent horizon is a surface that is the boundary between light rays that are directed outwards and moving outwards and those directed outward but moving inward. While and Absolute Horiozn is a b... | 0 |
I interpret the expression 'If P then Q' as asserting that if P is true Q is automatically true. So, we would say 'If P then Q' is true only when it indeed is the case that P being true implies Q is true. However, in logic, the truth of 'If P then Q' is determined solely on the basis of the truth values of P and Q indi... | 0 |
One possible formulation of the second law of thermodynamics is that the work extracted during the change of a thermodynamic system between two thermodynamic states is at most equal to the free energy difference between those two states. One possible derivation of this empirical result from statistical mechanics is the... | 0 |
I'd like to prove: Given two points A and B and a straight line connecting them AB, any smooth curve passing through A and B will, at some point, have a derivative that exceeds the slope of AB. My proof uses the Mean Value Theorem. So, any curve passing through A and B has, at some point, a derivative equal to slope of... | 0 |
I'm trying to understand where heat energy goes in a substance. I've seen that mainly it's translation at lower temperatures, rotation at mid range, and vibration at high range, but I'm not sure of that. Someone made the claim that an atom can expand as it is heated, which I don't think is right, but in a way, this is ... | 0 |
Recently I saw a video talking about the Yoneda lemma from category theory being used in neuroscience. It was my first introduction to category theory. In category theory we have objects and maps between the same objects called morphisms. For example we have one type of object called set and its morphism would be the f... | 0 |
My first name is "Jean-Baptiste". "Baptiste" is not a second or middle name, however I noticed that it's not unusual for native English speakers to address me just as "Jean". I don't mind it at all, I'm not offended and find it actually charming, but it would be quite unusual for a speaker of my native language (France... | 0 |
An event horizon appears in the Schwarzschild metric when considering a positive point mass in General Relativity. But for a negative point mass in the negative mass Schwarzschild metric, which repulses test particles, no matter how big the negative mass is, no repulsive event horizon forms. Intuitively, a big negative... | 0 |
I am interested in calculating the power received by an object near a black body radiator. Say, for example, I had a piece of paper perpendicular to the earth's surface normal. If I make assumptions about the earth's temperature, I can calculate its black body radiation. If I had a range of wavelengths I was interested... | 0 |
I would like to ask correspondence between Euclidean and non-Euclidean geometries. In the science and hypothesis, Poincare says that non-Euclidean geometry can be translated into Euclidean geometry with the following correspondence. ref)https://mathshistory.st-andrews.ac.uk/Extras/Poincare_non-Euclidean/ Space -> The p... | 0 |
When it comes to topologies, my understanding is that we designate elements of that topology as 'open.' In the context of a metric space, a topology is formed by selecting open sets, as defined with respect to a given metric. Moreover, a normed vector space is equipped with an induced metric derived from its norm. This... | 0 |
My wife, a native Spanish speaker, today asked me about why a youtuber would call themselves 'craftypants'. I explained that -pants was added to something as synecdoche, so for example an intelligent person might be called a 'smarty-pants', a poor-humored person a 'grumpy-pants', etc. However, I then realized that whil... | 0 |
I've studied in my physics class, absorption and emission spectra for gases or more "spread out" molecules like what is done in atomic absorption spectroscopy (learnt that one in chemistry). As in what discrete wavelengths of light a singular atom absorbs and why it only absorbs those specific wavelengths because of wh... | 0 |
I have been reading into X-ray and gamma spectroscopy. I have found that they can both be done with scintillation detectors and work off similar principles. That is to say that when a sample is bombarded with high amounts of radiation, electrons will be excited, and electrons from other shells will fill the spot of the... | 0 |
Now this might be a very dumb question but this has been bothering me from some days. Imagine I want to create the real number line and for that I start with the rational numbers. So I start to put the numbers on the line (like toppings on a pizza). Now I know that between any two rational numbers I can add another rat... | 0 |
In accordance with special relativity, if we take into account length contraction then ideally the Planck length which is the smallest possible length possible should be frame dependent. Well we know that the number of particles are invariant in different frames. So, a frame travelling with some relative velocity will ... | 0 |
I am a Canadian, but I study in Edinburgh, Scotland. I have discovered a peculiar feature of my speach that seems to surprise most people from here. When ill befalls others, I use the phrase "that's too bad" to express my honest heartfelt sympathy with the victim. I have been surprised to find that most people here int... | 0 |
What is the simple relationship expressed verbally between flux, circulation, div, and curl, as captured by Green's, Stokes', and Gauss' Theorems? Below is what I've been able to assemble: Can you confirm or improve it? Given a vector field, we can measure its instantaneous rate of change in multiple ways, the two most... | 0 |
I have been frequently stuck on this question since first realizing it in the shower. While watching the hot water drop from the above shower head, and then watching cold water drop, I realize they both appear to be moving at the same speed. This puzzles me, because I know that when an object is hot, its atoms are movi... | 0 |
The title might be a bit misleading, but basically I've been self studying differential equations so I could apply them in electronic circuit design. I was wondering what books could be recommended on differential equations, the Fourier, Laplace, and Z transforms, PDEs up to solving the wave equation, convolutions, fil... | 0 |
I'm looking for an existing word that roughly means "the process or idea of replacing bad/negative elements/deeds with good/positive elements/deeds, such as when a negative thing is eliminated at the same time that a positive thing is added". In terms of words that would not fit this goal are words that could (to some ... | 0 |
I am trying to do ray tracing for an endoscope, but I don't see how it could form a sharp image that could be viewed at the eyepiece. In the diagram the box in the middle is the "fiber", but the light from the object (the dot on the left) comes out of the fiber as if they originate from two locations (top and bottom), ... | 0 |
I've been struggling with this one... I'm trying to figure out whether it's okay to use the expression "call of the blood" to describe the phenomenon of doing something naturally (or coming to like it naturally) because it's in your blood, because your ancestors did it/were skillful at it, etc. For example, my ancestor... | 0 |
It is said that most of what we call "mass" of nucleons are in fact from the kinetic and binding energies of quarks, and that the rest mass of quarks, from the higgs mechanism is much smaller compared to the nucleon. There are other examples, like the binding energy of a nucleus, that show how energy contributes to the... | 0 |
I've been playing around with the concept of entropy and how it can be manipulated when I came onto the complex workings of quantum waves. To my understanding, everything we know as a particle is a wave on a quantum field. Those waves are the result of energy being introduced to, and then propagated through, the field-... | 0 |
I just watched a rather unreliable (or so I think) Physics YouTuber who asserted that absolute acceleration is impossible to measure, because it is impossible to ever calibrate an accelerometer accordingly, and I'm rather stumped by this argument. My understanding for all these years has been that acceleration can be a... | 0 |
In a recent conversation with my professor, he explained to me a misconception I had, in that given how physicists says that the Higgs "gives" the mass of all other particles, I was under the impression that a particle's interaction with the Higgs field is what gives it the property of mass. However, my professor expla... | 0 |
We know that a static charge only produces an electric field and a charge in motion (be it constant velocity or accelerated) creates both magnetic and electric field. But recently I came across that "changing electric field changing magnetic field, and a charge moving with uniform velocity doesn't create a changing mag... | 0 |
The diffusion coefficient is known in the traditional physical literature as an empirical parameter of Fick's law. Here the observation is that spatial gradients of densities are suppressed by a rate proportional to the gradient of the density, and the diffusion constant is identified as the constant of proportionality... | 0 |
According to my environmental science textbook and various sources on the web, the thermosphere has the second highest density of any part of the atmosphere. It falls only behind the troposphere which can be explained as the most dense because the force of gravity holds gas particles there. But here is where I get lost... | 0 |
Consider a simple chemical reaction, such as the association of two hydrogen atoms within the gas phase to form one hydrogen molecule. It is known that this reaction is related with energy release in the form of heat because the hydrogen molecule is more stable than the two hydrogen atoms. Within a gas containing hydro... | 0 |
I have been reading this article about the quantum vacuum state, and in the section that I linked to, there is a video showing an experiment that shows visibly that quantum fluctuations are actually happening (see the video in the link). The quantum fluctuations are visible because they amplified them using Spontaneous... | 0 |
I'm trying to figure out if a hexagonal grid can embed rectangular coordinates in whole numbers of "Y-steps". In the image below, one "Y-step" is the spacing between red hexagon centers in the Y dimension. For some arbitrary hexagonal grid size, how many hexagons do I need to produce some whole-valued number of "Y-step... | 0 |
I would like to perform something that resembles a curve fitting optimization but for which i could not find much info. Lets say i have a function that yields a time series. What i would like to do is tune the parameters of this function so that the time series it yields has a specific shape. For instance i want it to ... | 0 |
Classical mechanical systems observable on a dynamical scale are subject to Newton's laws. In this case, knowledge of the Hamiltonian allows us to minimize energy taking into account inertia. This allows us to calculate trajectories, find equilibria and derive many properties. Classical mechanical systems consisting of... | 0 |
I have observed that when an insect is electrocuted in a bug zapper, there are typically a few sparks or flashes of light. Sometimes the insect will catch on flame in a tiny fire, and the body will burn for a few seconds before stopping burning. The lights and flames stop after a few seconds, but the insect body often,... | 0 |
Is it okay (in terms of usage) to use present participle clause for an action that follows another action as a result? For instance, the following sentence seems correct to me: The bomb will explode, sending shrapnel everywhere. Yet the following sentence does not correct at all to me: I will run one mile to reach my t... | 0 |
The following problem has bugged me for a while, ever since I noticed it. On the Visible Spectrum Wikipedia, the following is the visible spectrum: Now, in Photoshop, or really any colour picker, the hue slider looks something like this: Or sometimes this: I noticed that in both of these, the colour loops back to red. ... | 0 |
I understand why the temperature of the hot reservoir has to be minimally higher than the temperature of the hot working fluid during the isothermal expansion phase of the Carnot cycle (to limit new entropy being produced in the working fluid that we have to get rid of). But during the isothermal compression phase why ... | 0 |
So, as I was browsing a bunch of the tachyon questions throughout the years in this forum, and an oddity of these hypothetical faster-than-light particles came to mind. Ordinary particles with mass always have an inertial frame of reference where they are at rest, thus their rest mass can be measured. Lightspeed partic... | 0 |
Electricity is used for many things. One of the biggest uses is transporting energy, almost instantly, from a power plant to the machines in my home and many others'. I was wondering if a similar energy transport grid could be created using a fluid under pressure. The power plant would use its energy to pump a fluid in... | 0 |
I hope this isn't the completely wrong community for my question, please let me know. I did search for 'varifocal' and got some hits, it seems (still getting used to these glasses, so it is a bit hard to use my PC) So, it seems that when you get these glasses - we call them varifocal in UK, not sure if that is the inte... | 0 |
Even though a black hole has a Scwarzschild radius that indicates a finite small distance to the center of the hole, the distance traveled by an infalling particle seems a lot bigger than the Schwarzschild radius due to the extreme curvature of spacetime. An infinite curvature even seems to imply an infinite distance. ... | 0 |
Short introduction to my understanding: As far as i understand, virtual particles are usually defined to be the internal lines in Feynman Diagrams. But we know that those are just useful tools to calculate amplitudes in interacting quantum field theories. In a free theory I have no interactions, hence no internal lines... | 0 |
I was reading about effective field theories and wondering how much an EFT can tell you about the ''underlying'' theory which is then reflected in the EFT. Can one extrapolate back from what one sees in the EFT to derive features of the theory for the high energy degrees of freedom? As an example, general relativity is... | 0 |
So, just to expand on the question in the title, I know group representation theory, and especially character theory, are quintessential tools for anyone hoping to study finite groups. That said, from what I've seen and read, some people study characters in and of themselves (say, density of zeroes, Brauer characters, ... | 0 |
(Honestly I fear this is borderline off-topic... be gentle with the downvotes ;-)) Most of the packages I've written are for personal use but a couple of them are used by some other people. These packages change relatively often as I'm constantly implementing requested features. Right now I tend to ship out the most re... | 0 |
It seems correct to write "A host of tools exists..." or "A range of tools exists...", i.e. the verb reflects the fact that you are referring to one collective noun. But, if I want to continue to talk about that collection of things, it often seems natural to say ". They aim to solve..." or ", which attempt to model...... | 0 |
It is currently understood that gravity is not actually a force, and a fact that is often used to show this is that an object in free fall doesn't "feel" that it is accelerating and is thus an inertial frame. However, it seems to me that Newtonian mechanics can already predict that this will be the case. Since all the ... | 0 |
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