I don’t understand what the issue is/could be. “Respectively” is clearly functioning syntactically as an adverb, and the sentence “Bob, Alicia, and Siobhan are a teacher, plumber, and electrician” without the “respectively” is a valid sentence where its two noun phrases happen to be conjunctions of other nouns.
A sentence like “Bob, Alicia, and Siobhan are a teacher, plumber, electrician, and astronaut, respectively” is equally valid syntactically, it’s just invalid semantically.
In many programming languages, phrases are shortened to reduce the time taken to write programs.
I really do not think this is why; the amount of time saved is miniscule, especially with autocomplete. It’s so that more can fit on the screen at one time so you can better comprehend chunks/lines of code. There is also probably a historical aspect where the size of code on disk (or paper!) used to matter more.
Something I see a lot that I think blocks understanding is “the dimensions”, “the 3rd dimension”, “the 4th dimension”, etc. This is wrong.
Dimensionality is a property of something. It is a number which describes some aspect of a thing. As others have said, it corresponds to the number of “independent directions” needed to describe a thing, but these directions need not be uniquely definable in any way, and most certainly you cannot say “this is the first one, this is the second one”, etc.
As a small example, just as you can say North and East are two independent directions on a map, you can also say South and North North East are as well; either of these facts on their own imply that a map is at least two dimensional. The fact that you cannot find a third independent direction means a map is two dimensional.
Uhhhh, what? IMAX is a screen format. It’s the really really big screens.
Lol, yeah. Most of his videos are a couple of minutes, but sometimes he wants a little bit more…
Relevant for anyone who cares about this sort of thing: https://youtu.be/GcjbwkBQeO8
It does indeed scale with r^(n-1), but your factors are not close at all. It involves the gamma function, which in this case can be expanded into various factorials and also a factor of sqrt(pi) when n is odd. According to Wikipedia, the expression is 2pi(n/2)r(n-1)/Gamma(n/2).
Planes can be thought of as spheres of infinite radius, and have infinite surface area. This point of view is very natural in conformal geometry.
I understand that for many people loneliness isn’t a blessing
I think there is a misunderstanding about the word “loneliness” here (which I used to share). I was skimming an academic article about this some time ago, and was very surprised when they gave a definition of loneliness that is apparently standard in academia: something like “your emotional needs are not met by the people around you/in your life”. It has nothing at all to do with whether or not or how many people are present in your life, and whether or not you like the company of other people. By this definition, you are not lonely, and furthermore loneliness is definitionally bad and cannot be a “blessing”.
Maybe I just personally never had a proper definition of “loneliness” in my head to begin with, but I think this rather technical usage of the word “lonely” is an extreme disconnect between researchers/academic writing and how the general populace interprets the word.
Below is just one possible aspect of this, the other answers you’ve received are also valid. Writing systems are complicated!
Your making the mistake that writing systems are supposed to represent speech sounds. They do not (or at least they don’t have to). As an example, in my accent (midwestern American English) there are at least three different sounds I make for “t”:
These are the technical names linguists use for these sounds; you can find them on Wikipedia if you want to know more. English speakers can agree though that they are all “the same thing”; the technical terminology is that they are all allophones of the same phoneme. Different accents will have different allophones, for example some English accents may pronounce this “t” phoneme in “matter” and “mat” the same way as my “touch”. If you think this is splitting hairs, that’s just false; the way languages divide sounds into phonemes varies greatly. For example, Japanese speakers consider my “touch” “t” and my “matter” “t” to be two completely different sounds, i.e. two different phonemes which are not interchangeable.
(Very) roughly speaking, writing systems tend to map better onto phonemes than onto actual sounds. Part of your frustration with Vietnamese writing could partly be from this: Vietnamese possibly has some sounds as allophones which in English are not allophones and belong to different phonemes. In other words, to a Vietnamese speaker they are the same sound. On the flipside, it could be that Vietnamese uses different letters for different phonemes, but those sounds are part of the same phoneme in English and you perceive them as “the same sound” when they are in fact distinct.
One more example is the Cot-Caught merger present in some varieties of English. In my accent, the vowels in these words are two separate sounds for two separate phonemes. In English accents which have the merger, they have become the same phoneme and in fact are pronounced identically, with the exact sound depending on the particular variety of English.
This shows one way you can end up with different spellings for identically-pronounced words.
Funnily enough, yaoi actually is an acronym, I think referring to stereotypical yaoi stories:
Yama nashi, Ochi nashi, Imi nashi
“No climax, no resolution, no meaning”
i,j,k for basis vectors is an interesting one. Historically, Hamilton invented his quaternions before any notion of “vector” existed (as an algebraic object; I believe the geometric notion is older). (So, what, did people just write out everything componentwise? Yes, yes they did. For example, that’s how things like Maxwell’s equations were originally presented.) The reason he chose i,j,k for the unit quaternions is because i was already in use for complex numbers, and i was in use for complex numbers probably to stand for “imaginary”.
The notion of “vector” was invented specifically as a “de-algebraicization” of quaternions. People did not like working with quaternions because they thought it was weird, particurlary because they required 4 numbers but space only required 3, so the likes of Gibbs and Heaviside gutted them and gave us modern 3D vector calculus. The reason we work with the dot product and cross product in 3D is specifically because, given pure imaginary quaternions v, w the product (vw) has real part (-v.w) and imaginary part (v x w).
Also, your last paragraph is somewhat misinformed. Sequences of Greek letters are used all the time, and Hebrew letters are also used in set theory to denote cardinalities (though I can only think of aleph and beth, no sequences of such letters). It is also well-known that some people like to use Japanese よ (yo) for the Yoneda embedding in category theory. But beyond Latin and Greek, there is quite a dearth.
Linguistically, the difference between “he died” and “he’s dead” is called aspect. As for your specific sentences:
“I thought he died” -> There was some event that ocurred which I witnessed or which I was made aware of in someway which I thought had resulted in him dieing.
“I thought he was dead” -> My understanding was that for some time up to now he was a corpse (or in some other such state). I do not necessarily know about the time or event in which he died.
Everything I wrote “is Markdown”, because the program you’re using to view my text assumes that my text is formatted in Markdown. You too are writing in Markdown, which for example is how your comment got displayed in bold. You did not “type boldly” to do that, you typed some text like **this is bold** and that got displayed in bold.
Maybe more examples would help. Here’s something I can do because the program you’re using to view my text assumes it’s Markdown: this is a monospace font and this is not. This desire for my text to be displayed in a monospace font is expressed in Markdown using grave quotes. It’s common to use this to denote literal, unprocessed text, so I would say that what I typed was `this is a monospace font`. If you copy and paste that text into a comment, do nothing else to it, and post it, you will see it displayed as this is a monospace font without the quotes because a Markdown compatible program sees it and knows “this person wants the text between these grave quotes displayed monospace”.
You can also see where I just wrote “without” italicized; in Markdown this is expressed as *without* or _without_.
If I type
* Thing 1
* Thing 2
* Thing 3
You’ll see this displayed with bullets, not asterisks, and proper indenting and vertical spacing for a list:
Thing 1
Thing 2
Thing 3
It also gets displayed in exactly the same way if I write it in these two different ways as well:
* Thing 1
* Thing 2
* Thing 3
* Thing 1
* Thing 2
* Thing 3
Thing 1
Thing 2
Thing 3
Maybe it would be helpful to just skim through a Markdown spec. (There are different flavors of Markdown; this one is called CommonMark, which is usually what people actually mean when they say Markdown. More information on their website.)
You typed some text to make your first comment, and it looked something like this:
Elder Millennial here. All I know about markdown is:
1. To make a hard copy of a thought or conversation. "Mark that down in your notes, so we don't forget."
2. A discount or sale. "Did you see the 30% markdown on three legged jeans?"
The way your comment actually displays is different though, isn’t it? The numbered items are indented and come one after the other without any space inbetween, and the text within each numbered item is properly aligned.
What you entered is just text, and text by itself is inherently meaningless. “Markdown” is the name of a particular standard way of formatting text so that programs can reliably interpret parts of that text as representing the writers desire for their text to be displayed a particular way. You can kind of think of it like a programming language. As another basic example, consider this text:
This is a paragraph.
This is still the same
paragraph.
Here is the second one.
And here is the third one.
I’m going to paste this text right after this sentence; notice how the amount of space doesn’t matter, and how a new paragraph is denoted by at least two line breaks.
This is a paragraph. This is still the same paragraph.
Here is the second one.
And here is the third one.
You made me realize this is actually pretty common in math, e.g. “Let x, y be real numbers” instead of “Let x and y be real numbers”. I imagine this comes from the infuence of notation like “Let x, y ∈ ℝ”.
Well, Con(PA) is a “natural” statement I’d say, and ZFC proves Con(PA).
No one, and I mean absolutely no one, “truly” “thinks in words”, even people who have a constant running narrative in their head. The reason is simple: How can you choose words/form sentences without any prior thought/idea that those words describe? How can you “struggle to find the right words” if your thoughts are originally in words (an experience I assume everyone has had)?
Assuming that 99% of them are hoaxes, clout chasers, or misidentified phenomena, that still leaves 1% of all those videos to be true.
Yes, if you assume something is true then you can conclude that it is true.
You don’t need separate disks like people are saying. You can have two separate EFI System Partitions (ESP) on the same disk, the one Windows makes and one that you make for just Linux so Windows isn’t ever messing with it.
I’ve run Windows 10 & Linux on the same disk through many Windows updates without issue.
And actually, if you’re never going to update Windows, then there would be no reason you can’t have them use the same ESP.