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@2rt49
"are you a girl or a boy?"
"you've just assumed the law of the excluded middle"

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average first sentence of a math wikipedia page:
A snorkle basis is a particular sort of set that has some properties and is generally "nice" (in a rigorous sense) and can do many things and is very practical.
average first sentence of an nlab page:
A snorkle complex generalizes the geometric notion of a snorkle basis to a context where there are not only internal morphisms, but pseudomonic ∞-morphisms on higher modalities.
The stable (∞,1)-category of snorkle complexes is anti-equivalent to the stable (∞,1)-category of (connective) bumblical complexes, by a celebrated theorem of Goncharov.
N LAB!
2 + 2 = ????
it's 2 + 2 because addition is commutative
{∅, {∅}, {∅,{∅}}, {∅,{∅}, {∅,{∅}}}, {∅,{∅}, {∅,{∅}}, {∅,{∅}, {∅,{∅}}}}}, by definition of 2 and the + operation.
and that is the long way of saying 3
Oh wait I wrote 5, another monument to my failures. I shall not edit it, as a reminder of my hubris
if I counted correctly, you actually wrote 6
It's 5 :/
{∅, {∅}, {∅,{∅}}, {∅,{∅}, {∅,{∅}}}, {∅,{∅}, {∅,{∅}}, {∅,{∅}, {∅,{∅}}}}}
{0, 1, 2, 3, 4}
indeed it seems i missed brackets
you know what since i'm pissed i define funtion composition to be
g∘f = ((x)g)f where f and g are functions AND for funtion g : A(x) ---> B(y) (x)F = y
oh this looks like this notation that some category theory people use
(screenshot is from the book "Seven Sketches in Compositionality")
I wrote this after ranting about how some people use g∘f = f(g(x)) and others use g∘f = g(f(x))
addendum
g∘f is NOW EQUAL to mean ((x)g)f where f and g are functions AND for funtion F : A(x) ---> B(y) (x)F = y

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Discord ranting upload:
basically some people use f∘g to mean g(f(x) where f and g are functions
some people use g∘f to mean g(f(x) where f and g are functions
it's like if someone were to say that like 3-5 is 2, because the minuser is on the left on their notation, and it's TRUE
interpreted this way
like think if you were to read a collection of papers, formal and 50% of the papers use 3 - 5 = 2 and the others use 5 - 3 = 2
but like
For a important consept like function composition
Y'know if the inconsistency were some loopyfuck symbol used in tabloidal ilogic would cause a 5 year scism
it's tempting to think of numbers as little points on a line or in some kind of space but they're more like little computers aren't they, "3" is really a little machine that you put something in and it makes three of it or it moves you three steps forwards, you can't go and find "3" somewhere as a point in space, nor you can describe it to someone else without giving them a machine to take them there, and that machine is 3.
every number is a computer! except for all the numbers (if you can even call them numbers) that aren't computers.
this is indeed how they work in the lambda calculus
and how they do it in category theory too
Oh my god
this will change math forever
Who tf thought it was a good idea to give the "golden ratio" a special symbol.
e has a special symbol because it shows up in anything to do with derivatives and exponentiation (and it's transcendental, so you need a special symbol to represent it).
π has a symbol because it shows up in anything related to rotation and circles (and it's also transcendental).
i has a special symbol because it is what expands real numbers so into the complex plane, thus creating an algebraically complete system of math.
𝛄 has a special symbol because it shows up in a bunch of really complex stuff related to the harmonic series, the factorial function, and the 1/x function, and we don't even know it's rational or not.
What the fuck is so special about (1+√5)/2 that gives it the right to have its own symbol φ. Who though that this random polynomial root was so important that we give it names like "the golden ratio" and "the divine ratio". Get real.
Though i understood moniods
Im reading

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Some games on Steam use the "Female Protagonist" tag the same way live-action Disney films get promoted for gay representation. I once bumped into a game that was tagged "Female Protagonist" because there's an interactive cutscene where a female NPC is briefly controllable. You walk across a room.
The tag search doesn't look too bad if you go with "sort by relevance" because that tends to make the ones with actual female protagonists float to the top, but under literally any other sorting it's like:
First-person open world RPG that lets you pick "she/her" at chargen (note: you are never referred to in the third person)
Visual novel where the all-but-faceless viewpoint character is explicitly male, but the plot centres on the woman he's dating
Party-based game where the male lead does all the talking, but your party has girls in it
Plotless puzzle game where the game board has a picture of a woman next to it
Street Fighter 6, for some reason
I've had a couple of people ask for a digestible version of the whole "the real problem with Dungeons & Dragons is false advertising, not anything that's present in its text" thing I keep alluding to, so here's the bullet point version of that argument:
Dungeons & Dragons is owned by Hasbro. Yes, the same Hasbro that owns Monopoly and My Little Pony.
Hasbro wants D&D to be the only tabletop RPG that anyone plays.
In order to accomplish this, Hasbro needs D&D to be a universal entry-level game.
D&D is not a universal entry-level game.
All game rules are opinionated about how the game ought to be played, and as tabletop RPGs go, D&D's rules are more opinionated than most. This is not a flaw, but it's not what Hasbro needs.
D&D is also on the high end of complexity as far as tabletop RPGs go, and it's complex in a way that strongly rewards system mastery, so it's pretty far from "entry level".
Hasbro could produce a version of D&D that's at the very least less opinionated and more entry-level than it presently is, but they don't want to, because they've determined that certain rules features which run counter to both of those goals are critical to D&D's brand identity.
They also don't want to produce multiple versions of D&D tailored for different audiences, because they want every single D&D group to be a potential purchaser of every single D&D product; they'd be effectively competing with themselves for their own customer base if the published game was actually modular in any meaningful way.
So how does Hasbro square that circle?
Simple: they lie. They insist that D&D is in fact a universal entry-level game in spite of all evidence to the contrary, and back their advertising up with sponsored thinkpieces and podcasts and such to "prove" it.
Further, they've spent decades fostering a culture of play which conceals the gap between the game they're advertising and the game they're selling by ascribing any appearance that D&D isn't a universal entry-level game to the incompetence or malice of individual GMs.
The game the rules want to produce disagrees with the game the group wants to play? Nonsense – even the rankest beginner should be able to produce any experience of play using any set of rules, and if your GM can't, they're a Bad GM.
The game is hard to learn? No, it isn't – your GM is merely gatekeeping you. This wouldn't be a problem with a Good GM.
The upshot is that the published rules are more or less irrelevant with respect to achieving the desired experience of play, because they're operating within a culture of play which dumps 100% of the work of making that desired experience of play happen on the GM.
Indeed, much of what modern D&D presents as GMing best practices are really methods of working around the fact that the rules you're using disagree with you about what kind of game you're playing.
(It's not a coincidence that D&D's entrenched culture of play also insists that it's normal for GMs to be miserably overworked and treats GM burnout as a big funny joke, then turns around and loudly wonders why there's a constant GM shortage.)
The trick is, because you're still at least notionally using the rules of D&D, the fruits of all that GM labour are perceived as the product of "playing D&D", not of the GM's hard work.
In essence, Hasbro's business model for Dungeons & Dragons is selling you your own GM's labour with a D&D sticker on it.
It's a very neat trick, if you can pull it off.
Now, at this point some readers may be asking: well, sure, but not all GMs are doormats. What about "killer" GMs who do gatekeep and railroad their players and otherwise act like complete tyrants? I hear horror stories about them all the time.
That's the second trick: these are not opposites. The GM as human Xbox and the GM as tyrant of the table both represent the GM doing all the actual work of making the game happen. The latter isn't the outcome that Hasbro wants, but it's a logical conclusion of the position they want the GM to be in.
I've seen a few folks in the notes respond "okay, but if that's true, why is D&D so much more flexible than most indie RPGs?", and the answer is that it's not. That's part of the sleight of hand I've talked about where the GM's labour is framed as part of the product. To break it down:
As noted above, all game rules are opinionated about what kind of game they wanted to produce. This isn't just a matter of setting (though setting-neutral games are often misleadingly called "universal" games), but also a matter of the basic structure of the narrative which emerges when you follow the rules.
The rules of Dungeons & Dragons are not less opinionated than those of your average indie RPG, and in fact are more opinionated than most. (Again, having strongly opinionated rules is not something that's wrong with D&D; it's merely something that's inconvenient for Hasbro's marketing goals in a way they're unwilling to address.)
In brief, D&D really, really wants your game to be a sword and sorcery dungeon crawl. If the GM is using the framework of play furnished by the rules at all, or if the players are responding to the rules' player-facing incentives even a little bit, it's going to squish your game into something dungeon-crawl-shaped.
(This should not be surprising; it's literally in the name!)
The rules of D&D being opinionated in this way tends to fly under the radar for a couple of reasons, one less problematic and one more so.
The relatively benign reason is that many popular RPG premises are not done any great violence by being squished into the shape of a sword and sorcery dungeon crawl.
A cyberpunk smash and grab caper? Basically a dungeon crawl already.
A special forces op in a modern military game? That doesn't need to be shaped like a sword and sorcery dungeon crawl, but it can be shaped like one and remain intelligible as what it's supposed to be.
Gritty logistics-driven survival horror? Not inherently dungeon crawl shaped, but the two genres are compatible – a game can be both at the same time, as video games like Fear & Hunger and Look Outside demonstrate. (Indeed, Look Outside's apartment building follows the structure of an old school D&D megadungeon nearly beat for beat!)
Thanks to D&D's pervasive cultural influence informing what people expect a tabletop RPG to be, as long as this kind of compatibility is present, many folks won't even notice their intended premise is being squished into the shape of a sword and sorcery dungeon crawl.
If your chosen premise isn't compatible in this way, or if the group notices what's happening and decides to push back against it, though? That's where the sleight of hand I alluded to above starts to come into play.
Remember: a Good GM™, even a total novice, ought to be able to use any set of rules to produce any desired experience of play, right?
So get to work!
i.e., just as much of the game's putative approachability is the product of Hasbro selling the players their GM's labour in a D&D-shaped box, much of D&D's putative flexibility is the product of the GM being sold their own labour in a D&D-shaped box.
To be clear, this is not militating against homebrew content or rules. Homebrew is perfectly cromulent, and certainly, some games are more or less structurally amenable to it (though modern D&D tends to fall on the "less" side).
The problem is that what we've got on our hands is a culture of play that wants to have its cake and eat it too: when doing extensive homebrew is treated as part of the GM's basic, entry-level responsibilities, it's easy to fall into the trap of thinking of the product of that labour as merely being a feature of the game.
Which is, of course, exactly what Hasbro's marketing ghouls want.
They found the NAND gate for mathematics! Now we need a no-holds-barred bare-knuckle drag-out fight between this and Binary Lambda Calculus
A single two-input gate suffices for all of Boolean logic in digital hardware. No comparable primitive has been known for continuous mathema
Not sure
I did some myself, it works as long as you allow ln(0)
but the reason why i said not sure was because i got introduced to this though a agi bullshit video on linking math and consciousness
kinda a shame i got introduced thisay
They found the NAND gate for mathematics! Now we need a no-holds-barred bare-knuckle drag-out fight between this and Binary Lambda Calculus
A single two-input gate suffices for all of Boolean logic in digital hardware. No comparable primitive has been known for continuous mathema
Not sure

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Let's start a thread where we collect papers with funny titles. I'll start.
We prove that the groups associated with the Revenge Cube and the Professor's Cube can be realized as Galois groups over the rationals.
Following a remark of Lawvere, we explicitly exhibit a particularly elementary bijection between the set T of finite binary trees and the se
Batman... My homology is my cohomology backwards, Batman.........
The well known Joker $\mathcal{A}(1)$-module of Adams and Priddy is known to be realisable as the cohomology of a $1$-connected space. By at