There's a common misconception that after seeing atomic bombs tested, Robert Oppenheimer quoted the following passage from a Hindu epic poem, the Bhagavad Gita: Now I am become Death, the destroyer of worlds. Does he ever say this in the movie?

I was reading a book by Amy Karofsky where she puts forward the case for necessitarianism: the idea that what happens is the only possible way that it could have happened. She talks about how very few philosophers consider this view since almost everyone takes contingency for granted, especially ...

How to compute the rational approximation of square root of a fraction, i.e. I'd like to find $ \frac{a}{b} \approx \sqrt{\frac{m}{n}}$, where $a$, $b$, $m$ and $n$ are integers. Ideally, the approximation should only use additions, subtractions and multiplications. Thanks.

I was watching a debate here where the idealist says that on a physicalist perspective, consciousness is a brute fact. But if one posits that consciousness is a fundamental part of reality, the hard problem can be explained since consciousness is not arising from physical stuff anymore: it simply...

Based on the information given, what would be the color of the planet's sky? Here is the composition of the planet's atmosphere: Nitrogen: 64% Ammonia: 19.7% Methane: 7% Neon: 5% Argon: 1.1% Ethylene: 1% Ethane: 1% Hydrogen: 0.9% Propylene: 0.2% Others: 0.1% The planet has a mass of 4 Earths an...

From the post, the array is better than alignedat for aligning the equation. However, it seems that alignedat would adjust the line space but array won't. For example \documentclass{article} \usepackage{amsmath} \usepackage{array} \begin{document} \begin{equation} \left. \begin{alignedat...

Is a supernova explosion an essential condition for the formation of a neutron stars?

I have decided to leave industry and pursue a PhD in geology. I studied physics (bach) and mechanical engineering (masters) but have been working in ML/software for 4 years. Due to my situation I wasn't ready to apply to programs in Dec 2023, but now am daunted at another year+ at my job if I wai...

Looked around online for a bit and could not find an answer - most resources are about making a cell fracture + rigid body explosion. But I don't want an explosion/destruction animation. I just want to animate cracks appearing on a solid block, but nothing explodes or gets pushed out (please see ...

Let $\mathrm{G}$ be a complex reductive group and let $\mathrm{O}_g$ be the adjoint orbit of $g\in \mathrm{G}$. I wonder is the centralizer $\mathrm{C}_{\mathrm{G}}(\mathrm{O}_g)$ still a reductive group in general? If not, how about the identity component of $\mathrm{C}_{\mathrm{G}}(\mathrm{O}_g...

Is there any example of a locally conformally flat manifold that is neither a space form nor a product of space forms?

As title states, I'm interested in figuring out how to construct a model of $\mathsf{ZFC} + \neg\mathsf{Reg}$, preferably off any regular model $\langle M, \in_M \rangle$ of $\mathsf{ZFC}$ without any forcing shenanigans involved. As I'm still working on the problem and don't want to spoil myself...

I have written a research article in the field of mathematics. This article has been put by me at https://arxiv.org/, which means now it is accessible by anyone, and also this article has been communicated to an SCIE journal (Science Citation Index Expanded journal). I want to present this articl...

"The very rich man never walks; he always goes in a carriage. But in the course of years, he wakes up one day paralyzed all over. Then he begins to feel that the way he had lived was not good after all. No man can walk for me." why did the speaker use the past perfect tense when the story is in t...

I'm tracking the configuration of some system in JSON format in a revision control system. Unfortunately that configuration is retrieved using some closed-source proprietary command, and the output changes from one run to the next as the order in objects and arrays is more or less random. One tim...

Is there a term for the relationship between two integers that have the same prime factors? For example, $6=(2)(3)$ and $12=(2)(2)(3)$. Can one describe this with something along the lines of "$6$ and $12$ are <term>" or "$6$ is <term> to $12$"? ETA: "Multiples" is indeed not what I'm after. $...

What is Tapscript? How is it different from script? Is it the same thing as "Leaf script"? How does it relate to Witness Script, miniscript and any other type of script used in Bitcoin transactions? How and when was it implemented? What can it be used for?

I understand that one way to know is if an English translation like the NKJV or NASB has words in italics. Then I can know that the English word is implied rather than actually stated in the original Hebrew or Greek. But, let's take an example like Genesis 15:6, which I have been studying. In the...

It's a well known result that the Gaussian integral $$\int_0^\infty e^{-x^2} dx = \frac{\sqrt{\pi}}{2}$$ evaluates to $\frac{\sqrt{\pi}}{2}$. This result can be obtained using double integrals with polar coordinates, among other things, but I'm particularly interested in evaluating this integral ...

When I was having a conversation with someone and they looked at me and said "Man, You're a trip" was it referring to when I tripped over a word? Or didn't use the word right?

I have got a lot of errors in there just posting 2 of them atm 2024-04-27T09:00:03.860270+02:00 Desktop gnome-shell[1659]: Extension ubuntu-dock@ubuntu.com: Error: No signal connection 10 found#012#012Stack trace:#012 _disconnect@resource:///org/gnome/gjs/modules/core/_signals.js:58:15#012 disa...

below is my current PS string in .bashrc PS1='${debian_chroot:+($debian_chroot)}\[\033[00;37m\]\u@\h\[\033[01;32m\]:\[\033[01;34m\]\w\[\033[01;31m\] $(parse_git_branch)\[\033[00m\]\$ which works fine but it is very difficult to write single color code while colors are also limited ; so create ...

I am working on a story set on a world where cars (or in a broader sense road based vehicles) are the main transport mode (aircraft have never been invented here and most bodies of water are so small that water travel is mostly used for pleasure craft) and thus liked the idea that every even slig...

Suppose two variables X1 and X2 are correlated and we know that X1 causes X2 and X2 causes X1. For example, leg strength and an interest in cycling interest might be correlated. And (suppose) we know that having stronger legs makes you more likely to take up cycling and cycling causes your legs t...

In the discussion on defining and distinguishing between naturalism and supernaturalism, is it coherent to entertain the notion of a supernatural realm governed by rules or laws, and if so, would it make sense to explore the potential for a testable predictive theory of the supernatural? In short...

I have two implementations of the crc calculation. The crc_classic is based on the typical implementation you can find for example on Wikipedia The second one might be found in D.3.2 here IO-Link I'm looking for an explanation why the second one does the same as the first one. The second one is t...

Find the basis of the image of a matrix: $$ A = \begin{pmatrix} 1 & 0 & 1\\ -1 & 1 & -2 \\ 2 & -1 & 4 \end{pmatrix} $$ I'm somewhat confused about the concept of the basis of the image, and I find it perplexing. I find the row-reduced echelon form of the matrix: $$ \begin{pmatrix} 1 & 0 & 1\\ 0 &...

Consider this simple 5th order polynomial: pol=x^5+x^4+1 Factor[pol] (* (1+x+x^2)(1-x+x^3) *) root=FindInstance[pol==0, x] (* -1/2 -I/2 Sqrt[3] *) Suppose we would like to see the 4th order polynomial with this root removed. This does not immediately seem to be easy... For instance: F...

I came across multiple research papers where they have mentioned that two 1-generic reals $x,y$ can be constructed such that $x \oplus y \equiv_{T} \textbf{0'}$ where $\textbf{0'}$ is the degree containing the halting set. I was wondering how to prove this fact. I know some basic computability th...

I have a hosted OS project that uses the MIT license attributed to my user name. I also provide packaged releases of the software for convenience (so users don't need to build and package locally). The license file is included in the packaged application. I want to add a link to the repository so...

Is it acceptable in formal American English to pronounce the first vowel in "regret", "realize", and "return" as an open-mid front unrounded vowel as opposed to a close front unrounded vowel? Also, how were these words pronounced in Middle English?

I am trying to understand why chemical potential $= U/2$ is considered to be at half-filling in the case of the Hubbard Model Hamiltonian. So when I substitute this in its Hamiltonian, this is the equation I am getting $$ H = K.E-\frac{U}{2}\Sigma [n_{j,up}n_{j,down} + (n_{j,up} - n_{j,down})^{...

Abraham went to Mitsrayim c. 2000 BCE. At that time the Egyptians knew themselves as Kemet, not Misr. The earliest reference to the name Misr to my knowledge is from the Amarna Letters c. 1350 BCE. This is after the Hebrews reached Israel. How do we explain this?

The probabilistic method uses arguments from probability to prove deterministic statements. This has been applied to diverse fields such as combinatorics, topology and number theory. In this method, you constructs a random variable based on the theorem that you want to prove. Using probabilistic ...

I've been recapping an Amstrad PCW 9256 computer. All the electrotyics are bad on the analogue board - I've replaced the electrolytics I have in stock and the CRT is now working almost perfectly but there is still a bit of 'jittering'. There are some high voltage, low capacitance capacitors that ...

I was just wondering if PEMDAS is realy needed in Math. I think that instead of trying to interpret math by using conventions, we just need to write math in the right order of operation from left to right. PEMDAS does not reflect the real life order of doing things. I am no Math expert, but if I ...

I am trying to construct a bifurcation diagram of the system $$dx/dt=yz+a,\quad dy/dt=x^2-y, \quad dz/dt=1-4x.$$ I've scoured the internet for pre-made bifurcation diagrams and found many (mostly of the logistic map). However, as the code is quite complicated I am not sure how to edit the code so...

I'll be DMing for a party in an adventure where a lot of enemies will have resistance or immunity to the most common damage types, like Fire, Cold or Poison. In the previous adventure my Sorcerer dealt with it using Transmuted Spell with a Thunder option. Of course I won't put a DMPC in the campa...

I understand that English people generally want to delete paragraph indentation everywhere... This is not the french custom, and I there is very few tips on how to add indentation in LaTeX. Hence my question ^^ For now, every time I write a formula between \[ , \], I write \par juste after that s...

I've been learning graphics engine recently and I come across a term - conservative: The CPU-GPU sync point problem Unreal solves like any other engine that uses queries, by deferring reading the query data for a number of frames. This approach works, although it might introduce props popping in...

Common wisdom dictates that bikes, especially those used in the rain or in the winter, should be washed frequently to prolong component life, but I honestly cannot see how. I am aware of the following: drivetrain cleaning and chain rotation is obviously necessary cleaning braking surfaces used t...

The question is to show that the function $ f(x) = 2x + |\cos x|$ is both one-one and onto. I have managed to show that it is onto but got stuck at proving that it is also one-to-one. To prove this I thought of using the first derivative and showing that the function is always increasing. For bo...

I have come across an expression as below $d\left({W_t}^4\right) = 4 {W_t}^3 d\left({W_t}\right) + 6{W_t}^2 dt$ where $W_t$ is standard Wiener process. While I understand the first part of the RHS, I fail to understand the second part. Could you please help to explain it? What is the expression f...

It is known that if $X$ is the sum of $n$ independent and identical Bernoulli random variables, $X$ follows a Binomial distribution. How about the reverse, can a sum of dependent and/or non-identical Bernoulli random variables still follow a Binomial Distribution?

I want to install a new stereo for my car which requires 12V. I tested the battery first it and shows 12.29V but when I started the car the battery became 6V. Is this normal? What am i doing wrong?

All Fresh install Ubuntu 24.04 - all work fine - but 'ubuntu-drivers list' - show me only 535 driver udevadm hwdb is deprecated. Use systemd-hwdb instead. udevadm hwdb is deprecated. Use systemd-hwdb instead. udevadm hwdb is deprecated. Use systemd-hwdb instead. udevadm hwdb is deprecated. Use s...

I am trying to understand a statement about symmetries of a triangle. The set of lecture notes I am working through assert that (1) every permutation corresponds to a symmetry and (2) every symmetry corresponds to exactly one permutation. As there are only six symmetries, I can write out each of ...

"He says he remembers that." would be, if I am not mistaken, "Is dicit se illius meminisse.". But how would you say "He says he used to remember that."?

I have a 10 year old Suntour suspension fork where some of the material on the dropout has started to chip and fall off. I think it has happened because of some harsh winters with lots of road salt. Is it still safe to ride though, based on the attached picture?

This came to me as a generalization of another question: What does the algorithm matter, if the input-output game plus performance is the same? And lead me to a rabbit hole of following philosophical conclusions: (I go top-down. So, don't stop just after the first statements. Explanation follows....

In Chapter $5$, Section $4$ of the book Continuum theory by Sam B. Nadler, Jr., the auther defines $\sigma$-connectedness (Definition $5.15$) to be the property of not being a disjoint union of countably many (including finitely many) and more than one nonempty closed subsets. It is well known (f...

To begin with, the bureaucratic process was extremely time-consuming, and when I inquired about the status of my documents, they gave me the runaround. After incessantly contacting them regarding my documents, I eventually discovered the reason for the delay: they had misplaced my documents. When...

I am doing spin-orbit coupling (SOC) calculations using VASP. I had done a magnetic anisotropy calculation, but I do not know how to check whether the SOC is weak or strong. Any help would be highly appreciated.

I'm planning a multi-destination trip (TLS -> AKL -> YUL -> TLS). Flight finders are showing me prices around €2-3000 for EACH of these legs, total up to €9000, whereas the (geographically similar) TLS -> AKL -> TLS round trip is reasonably priced (€1400). It seems that I'd save loads of money if...

Modern physics defines fundamental forces and particles as particular “fields”. I have read some things like “gauge symmetry” play an important role in these theories. I have looked up a good reference material on axiomatic quantum field theory, which has sections on the ontological interpretatio...

Consider the following expression (x-y+a)^2 + (x-z+b)^2 // Expand The result is a^2 + b^2 + 2 a x + 2 b x + 2 x^2 - 2 a y - 2 x y + y^2 - 2 b z - 2 x z + z^2 I want now to write a code that extracts the coefficients into a matrix and a vector so that I can rewrite the original expression as {x,...

Kait rolls a fair 6-sided die until she rolls a 6. if she rolls a 6 on the nth roll, she then rolls the die n more times. what is the probability that she rolls a 6 during these next $n$ times? This can be treated as two events, event $A_n$ she rolls a 6 on the $n$th roll and event $B_n$ she roll...

I am learning complex analysis and currently reading Ahlfors’ Complex Analysis. I feel like I need to do more exercises than the five problems provided in each section. Therefore, I am seeking recommendations for complex analysis books with more exercises than Ahlfors’, but still at the same leve...