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## Why does "groove" mean "take pleasure in"?

The original meaning of "groove" is something like a cave, or as a verb, make a groove. Why can "groove" mean "take pleasure in" as a verb?

english-language

## What does "it doesn’t make much of a case for itself" mean?

I have found a phrase here: ... it doesn't make much of a case for itself in ... Obviously, it is some negative remark. Probably, it is a combination of two expressions, but I can't divi

english-language

## Why were even royals in medieval europe living without running water and sewerage?

History books say that after the fall of Rome, 'we' lost our understanding of their technology. But aqueducts, lots of Rome's buildings etc were still standing, monasteries had washing and

history

## Why do antidepressants have a delayed onset of action?

Why do antidepressants take so long to reach efficacy? I've read of theories about it perhaps being due to the strength of negative feedback via serotonergic and adrenergic autoreceptors during th

biology

## Structure Sheaf on Scheme

Given a scheme $X$, its structure sheaf on the elements of the cover by affines is pretty easy to define, say $\mathcal{O}_X(Spec(A))=A$. But how is it then defined on the union of two of these se...

mathematics

## Is the third spin vector of a photon always suppressed?

I like to tell people interested in light polarization that the photon is a vector boson for which the third spin axis, the one in the direction of travel, is suppressed due to photons being massle...

physics

## What's the origin of the saying, "There's no accounting for taste"?

I hear it all the time in arguments over subjective judgements: There's no accounting for taste. Where does this saying come from? Is it a quote or old proverb?

english-language

## Founding Fathers and the American Civil War

I was reading an article and was wondering if there is anything out there to indicate that the Founding Fathers saw the potential for conflict regarding these specific points: Economic and ...

history

## Attempts to return the War to the South's favor after Gettysburg

With regards to the Union victory at Gettysburg being the turning point of the American Civil War: Were there any major Confederate victories after the battle of Gettysburg? Did the Confederacy e...

history

## Change of QM Momentum operator under coordinate transformation

Can any one please let me know what is the general procedure to construct the momentum operator under some coordinate transformation? For example, I understand that if

physics

## Information-theoretic aspects of mathematical systems?

It occured to me that when you perform division in some algebraic system, such as $\frac a b = c$ in $\mathbb R$, the division itself represents a relation of sorts between $a$ and $b$, and once you

mathematics

## How many good words are there?

A “good” word is any seven letter word consisting of letters from $\{A,B,C\}$ (some letters may be absent and some letter can be present more than once), with the restriction that $A$ canno

mathematics

## Why did the southern states secede from the U.S.?

Lincoln's election precipitated the secession, but didn't they have enough congressional power to continue things much as they were? It seems in the preceding two decades the slave states had

history

## What are constraints on a "purity" operator in quantum mechanics?

Consider the normalized state, written in some orthonormal basis as: $$\psi = A |0\rangle + B |1\rangle$$ Let's define a "purity operator" for a basis as any operator whose expectation

physics

mathematics

## Derivative of a Hölder continuous function

Suppose we have a function $u(t,x): A \times B \to R$, where $A$ and $B$ are bounded intervals. We know, the derivative up to order $1$ exists and is continuous, furthermore, the derivative with re...

mathematics

## Equivalence relation question with functions

We'll define on the set: $A=\Bbb R^{[0,1]}$ the relation $R$ by $fRg$ if $f(0)=g(0)$. Make sure it's an equivilence relation. What is $[\cos x]$ ? Describe all the equivalence

mathematics

## How to calculate these integrals about propagator of QFT analytically?

How to get these three analytical solutions? Thanks very much!  G_{ret}(x,y) = \lim_{\epsilon \to 0} \frac{1}{(2 \pi)^4} \int d^4p \, \frac{e^{-ip(x-y)}}{(p_0+i\epsilon)^2 - \vec{p}^2 - m^2} = \...

physics

## What is the difference between /ʃ/ and /ʒ/?

I am trying to understand the difference in pronunciation between the sound /ʃ/ (shell, cash, sure) and /ʒ/ (treasure, pleasure, leisure). I am able to tell these sounds apart when listening; howe.

english-language

## Why aren't there galaxy-sized balls of iron out there?

Since we know that stars burn out, collapse, or blow up when too many of their atoms fuse inti iron, then how come, with all the ancient galaxies we've been observing, there isn't one galaxy w

astronomy

## Neither... nor... nor (more than one "nor")

Is it correct to use more than one "nor" clause in a "neither" expression? For instance: "Neither the question, nor the answers, nor the comments"? Even if it is, is it

english-language

## What is the meaning of "a lot of sleep last night."?

I have read this sentence but can not understand "a lot of sleep last night." I didn't get a lot of sleep last night. Can any one explain about it ?

english-language