Yes, it’s part of defeating Gannon in multiple games. Ocarina of Time, Wind Waker, maybe Twilight Princess and Breath of the Wild if I remember correctly. There are definitely more. I always thought it was a core part of her iconography…
Read the actual actual article: https://arxiv.org/abs/2502.14367
The authors prove that given any sequence of rotations W “almost always” there is a sequence of rotations W’ formed by scaling every rotation angle in W by the same positive factor, such that the sequence W’W’ is the identity (that is, apply all the rotations in W’ and then apply all of them again).
The issue isn’t the result, it’s popsci writing.
No, the original paper is saying something like: given the sequence say 12 -> 3 -> 7, there is a sequence 12 -> 3x -> 7x -> 7x + 3x -> 7x + 3x + 4x where 7x+3x+4x = 12. Obviously here x=6/7, but doing something like this with arbitrary rotations in 3D isn’t so simple.
If you’re referring to doing moves on a Rubik’s cube, no that’s irrelevant to the theorem. If you’re referring to applying a sequence of rotations to a whole solid cube, then yes.
The example given in the OP is incorrect. /u/gameryamen is implying something like: given a sequence of rotations W there is a scale factor a>0 such that W(a)W(a)W = 1, with W(a) the same sequence of rotations as W but with all rotation angles scaled by a.
This is not what the paper does. The paper finds an a such that W(a)W(a) = 1.
His whole post seems bunk, honestly. Example:
Having one more shot in your follow up acts as kind of a hinge, opening up more possibilities.
This seems completely irrelevant. It seems that maybe they’re referring to the probabilistic argument the authors give to justify why their theorem should be true (before giving a complete proof), but this argument involves repeating the same exact rotation two times, not two different rotations in sequence.
They use continuity and the fact that F(0) = 1 to conclude that, since it also takes on a negative value (what they put effort into arguing), it must also attain 0. So no, they don’t find it directly, but it is technically possible to express F explicitly and then numerically find a root.
Should be Steam/logs, with Steam your Steam folder where e.g. steamapps is.
I’ve had an issue with controllers before because Steam’s udev rules straight up give the wrong permissions to the device files they create. Check Steam logs, there’s one specifically for controllers if I remember correctly (or maybe it was a generic “console” log) and it should be very clear if this is the issue because there will be a permission error recorded.
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”
Yes, “quantum teleportation” just means transfering a quantum state from one location to another without knowing what that state is, in the same sense that you can copy a file from one place to another without knowing its contents. So it’s just a particular kind of information being transfered, not anything about how quickly it’s transfered. There is a lot of awful terminology in quantum mechanics.
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.
This sentence is shit, but I want to point out at least that “magic” is jargon for “well-behaved” or “particularly well-suited (for our application)”. It’s essentially “magic” like in the phrase “it works like magic”.
Have you read the authors current series, Dai Dark? I’ve only read a couple of chapters so I can’t say too much about how it compares to Dorohedoro, but…
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”.
China tariffs have only been slashed temporarily, for now and many other countries are still awaiting negotiations on where their tariff levels will end up, after that other 90-day pause, on Trump’s “reciprocal” levies, due to end in July.
Commas how, do they work?
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.