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the most general setting in which we can do convergence of sequences and continuous functions is topological spaces

the most general setting in which we can do convergence of infinite series is topological groups (or I guess topological magmas? if thats a thing? but also if we want to get generalizations of familiar results we probably need topological fields and/or vector spaces?)

the most general functions for which we can define total derivatives are functions between normed vector spaces, via the fréchet derivative

directional derivatives can be generalized slightly further to functions between locally convex topological vector spaces, via the gâteaux derivative

the most general functions which we can integrate are functions from a measure space into a banach space, via the bochner integral (theres also the pettis integral, but that seems too overly complicated for my goals right now and also from what little research I did it looks like in order to define it you need to already have a lebesque/bochner integral?)

Of course, topological abelian groups are automatically uniform spaces, so a number of what you mention will automatically be a uniform space, but I think uniform spaces are a noteworthy abstraction in their own right worthy of inclusion that more people should know about.

Note that one can say, as it's often said, that "topological groups are automatically uniform spaces", but that statement is slightly misleading, because a topological group naturally carries *two* different uniformities, a left uniformity and a right uniformity. Or really it carries *four*, because you can take the join of the two to get the two-sided uniformity, or the meet of the two to get the Roelcke uniformity. (All four of these do indeed induce the original topology.)

So I restricted to abelian groups for simplicity. Of course abelian groups aren't the only groups for which the two (and therefore all four) uniformities coincide; unfortunately terms for groups with this property vary. I've seen "balanced", which is the term I like, but they're also known as "SIN groups" (for "small invariant neighborhood"), and I think some other things which I'm forgetting offhand. In addition to abelian groups obviously being balanced, compact groups are automatically balanced, since compact spaces only have one uniformity.

the bay area is where the rationalist community organizers brain drain into. in every major US city (except maybe NYC) the main/default organizer of rat meetups change every few years because the old one moved to the bay. the bay is inherently attractive because it has the biggest rat cluster, and if you're organizing a lot, you're probably doing other things that put you in touch with them online. and eventually you want to move because someone offers you a job, or you start seeing someone there, or it just seems like, ah, the rational thing to do

and the majority of them stop hosting! they don't need to anymore. they're in events wonderland. they don't have to drive things. they're in the place full of people who drive things. this seems partially wonderful, partially tragic

I'm limited on hosting energy because parenting, and it's just going to get harder as I have more kids, but man I don't want that to be me. my drive to host isn't "someone has to and I'd do an okay job", it's "[banging cymbals together] I'm bored, I want to gather people up to do something weird" (examples)

I don't want to lose that!... especially because I'm only a couple years in, and I'm starting to see how cool and weird and ambitious events can get. I don't know any of the hosts/usuals but I recently read the event details for an insane multi-day sex LARP (clothes stay on and the sex is simulated but like, clearly it'll be psychologically affecting) that redefined how big the freaking envelope is

One thing I think is very fun about such a planet is that 1403 would also be truly enormous in its sky, subtending nearly 30 degrees. You could set up some kind of orbital resonance with a slightly more distant planet to give its orbit some eccentricity, and apparently also there are ways in which even tidally locked planets can retain significant obliquity if you wanted to increase the size of the day side further, but I quite like the aesthetic of a single immense orange sun staring down at the landscape, still and pitiless in the sky. Except it wouldn't be that pitiless, because the surface temperature of 1403 is only about 2000 degrees Kelvin. It'd be more of a giant, friendly perpetual sunset, like Ursa Minor Beta in The Restaurant at the End of the Universe, where it's always Saturday afternoon just before the beach bars close.

me, searching for Manhattan airbnbs on CJ's behalf because I like browsing airbnb: oh, that one's cheap!... never mind, it's on the wrong side of the water

me: when I was young I had no idea New Jersey and New York were so close together. I didn't know until I was actually in NY a few years ago and asked someone next to me what that other city was. I thought New Jersey was like, in a different state

partner CJ: it is

me: really? what state?

CJ: the state of New Jersey

This was a response to "Prove or disprove: there exists a nowhere continuous function whose absolute value is everywhere continuous." It responded in TeX, which I coped into a TeX editor.

Another answer to the same question:

And rather than producing nonsense – or even producing a correct but memorized-looking textbook-style answer – it simply thought about the problem for a long time, like a human would do with a hard problem, until eventually working its way to a correct answer:

Sure, its thought process is awkwardly phrased and repetitive, with some minor errors and confusions here and there, but hey, it ultimately gets the job done.

And it's probably not any more awkward-sounding than my own inner monologue when I'm trying to solve a math problem, if you could somehow transcribe it directly into the written word without cleaning it up at all.

Academic History YouTuber Premodernist released video recently on "State Flag" discourse, and flag discourse more wildly, that I thought was pretty good! I agreed with 50% of it. For those who don't know, there is a longstanding movement in the vexillology community to push for more simplified flag designs, and they hate the state flags of the US as their antithesis; a movement that catapulted into the internet mainstream when YouTuber CGPGrey released a video riffing on that debate and grading all the state flag designs.

That video is great by the way (it's hilarious, CGP Grey is just very talented as a performer), and the biggest thing Premodernist is wrong about is that the state flags do suck. But what he gets right is that the so-called "principles" briefly referred to in the video are themselves pretty weak; some are fine but others do not hold up to much scrutiny. The state flags largely suck for the boring reason that they just suck; they are shitty designs and often repeat each other in a domain where "standing out" is the point. Like what the fuck Montana:

This is something a 5th grader whips up in PowerPoint for a class presentation. Helvetica Bold?? "Mandated by law in 1985" yeah I didn't need Wikipedia tell me this decision dates to the 80's.

But that is boring and subjective, right? You can't just say they suck. So you had to make a theory about it - and I won't go into too much detail but it generally boils down to:

Make it simple, "something a child could draw"

Make it "distinct at a distance", since it is a flag you are supposed to see it at a distance

Three colors or fewer

No words on flags

Which I think you can get the philosophy for. These principles, which CGP Grey outlines, actually come from the work of Ted Kaye, who is a big figure in the aforementioned flag reform movement and the focus of most of the video. As part of the original CGP Grey video I just rolled with that, but I did remember him showing Utah's newly designed flag at the end which embodied these principles, and uh:

This is kind of mid? Like it doesn't suck, but it looks like a corporate redesign of a hockey team logo or something. A bit of a red flag (hah) if your front-and-center case is weak.

Anyway this is what Premodernist digs into in the video. The stuff I agreed with the most are the parts where he just ???? at some of these rules. "No finicky bits", a "child must draw it", "distinct at a distance"? None of these actually track for say this one:

A child drawing the US flag does not draw 50 stars and 13 stripes unless they are a budding librarian; you absolutely cannot tell if this flag has 50 stars on it from a distance, and that level of detail is clearly some kind of finicky. Of course your response is "okay sure but still, I can tell what the flag is from a distance, I can't count the 50 stars but I get the gist". But that is true for almost all flags!

It's a fern and a peace pipe and a brown thing and the word "Oklahoma" below it, you absolutely, 100%, will be able to tell what this flag is at a distance. You don't need to count the leaves to get the general shape, and when you think about it, it is actually kind of silly anyone would claim otherwise. There just isn't any need to appreciate the tiny details on a flag to understand whose flag it is. (the only valid critique here is that everything should be bigger - too much dead space)

Not to mention the "see from a distance" thing even being a metric. That isn't how you encounter flags most often today? Maybe in the 19th century on a battlefield that was (and even then you had battle standards), but it isn't now. You see it in textbooks, on your computer screen, as an icon for a football game team, right next to you in a government office. Why privilege distance? You just made that up as a value. 99% of "flag consumption" is not seeing it at a distance.

The "only use ~3 colors thing" is the funniest, you can just argue this with...no? No you don't. You don't. What? No. You can...you can just use more colors? Here is an example from the "manual" Ted Kaye wrote on the subject:

And the 5 bands on the chinese flag are fine! They are not "hard to look at" or whatever. Also, I am screenshotting a tiny corner of a youtube video, this image is like 240p, and I can tell its a dragon - and that isn't even the color point it is trying to make, dude just deviates off into another critique. Meanwhile the Amsterdam flag looks like a traffic warning sign. Chinese flag needs to not have the white stripe connect into the white seal background, that is an error, but otherwise I prefer it.

It is annoying how many of the state flags are a blue banners with a round seal in the middle. That does make them hard to distinguish from each other. But that isn't a problem with seal-on-blue, that is just a collective action problem! Flag-reform-favourite the tricolor can run into this too - here are the flags of the Netherlands and Luxembourg:

Like one of your needs to go home and change, that is ridiculous. Though if you had a complex seal in the middle that might avoid this problem! Funny that.

Even the "no words on a flag" argument, which I am more sympathetic to, doesn't hold up too well because too often you find yourself going "unless it is good" which just isn't a rule. The Iranian flag is the stand-out he mentions:

The middle crest is a stylized rendition of the name Allah, and the cursive lining on the tricolor bands are text as well - God Is Great, 22 times, marking the anniversary date of the Islamic Revolution. Stylistically beautiful, also words on a flag. The state flags just didn't try to do anything artistic.

I think the best point Premodernism mentions is a sort of stylistic unity Kaye & Co are pursuing above all else - everything sacrificed for corporate minimalism. Kaye's book will say it respects history and symbols should be meaningful, but then hates any symbols that require complexity. He singles out Turkmenistan as an ugly flag for example:

And as I said I only 50% disagree sometimes, I do think there is a complexity limit, and this flag goes over it, that is too detailed. Though the main reason this flag is bad is the weird choice to not put the banner at the edge, and have the crescent just...float off center? If it was this:

Two seconds in paint, already better, you can play with it. But anyway, you can say the symbols are too complex, but if you also say you care about historical meaning? Turkmenistan is a nation of traditional semi-nomadic tribes, who populated the Silk Road and made textiles as their ultimate expression of art. These carpet guls are traditional symbols used in those carpets that represent the five major tribes that compose the country. You can't just invent new symbols that have equal meaning to these, right? Like you can try if you want, sure, new symbols become meaningful all the time. But a rule that says "all art from before 1950 is tossed in the dumpster because it wouldn't pass muster as a Pepsi logo" is a weird rule to adopt if you say you value historical meaning. Turkmenistan does not have to look like France, and it is weird to want every national symbol to be aesthetically coherent to each other. Let 100 flags bloom! It is certainly "distinct at a distance" lol.

there's a sentiment that goes like 'well, sure, you learned in school that the solar system has nine planets, but Science Marches On and we now know it has eight' and while certainly people should not take what they learned in school to be immutable law they should also like. have a concept of the rather significant difference between 'we've learned something new about the world' and 'we've decided to slice up the world in categories along different lines'

slicing up the world into categories is one of the basic operations of human thought and if you do not understand it well enough that you think 'people used to think the earth flat -> now we know better' and 'astronomers used to call pluto a planet -> now they don't' are analogous processes then you fucked up somewhere.

Like, we did learn something new about the world: we learned that Pluto is tinier than we thought, we learned that Eris is basically the same thing as Pluto, and we learned that Pluto was part of its own "asteroid" belt, so the reason we used to remove Ceres from the list of planets would, if applied fairly, also make Pluto not a planet.

I might! I'd have to learn some things about them first, though. I vaguely know how transfinite numbers work, but have never learned anything about infinitesimals.

It's on the list of things to maybe write about, though. Currently that's something like

complex numbers

Modular arithmetic and finite fields

p-adic numbers

function fields

infinitesimals

transfinite numbers and ordinals

Complex numbers are the obvious next step and really were just cut out of both parts 2 and 3, so I have a partial draft up already. Modular arithmetic, finite fields, and p-adic numbers are sort of the center of my professional wheelhouse and so I could write them almost without looking anything up. Function fields are something that should be in my professional wheelhouse but I never really learned them.

Then infinitesimals are interesting but I don't know anything about them. I should, though! And writing a thing is a good way to learn, just takes time. Similar with the transfinites though I know a little there.

Also thinking about doing a digression into Galois theory, which is relevant to a lot of this stuff but doesn't really fit the "fictional history of numbers" framing as cleanly.

So, one thing you already know but which I will repeat anyway for completeness (I'll be doing this a fair bit :P ) is that of course there is not one single way of doing infinities, like e.g. you have both cardinals and ordinals, so you may have to introduce this idea to your readers that there is not one single way of doing things, there really are different systems of numbers! Of course if you've already written about p-adics first then there's no problem there. :)

(Actually, even just sticking to ordinals, things are more complicated than that, because you can consider the ordinals with their usual addition and multiplication, or with natural addition and multiplication, giving you two different structures algebraically (the latter being the one that embeds in the surreals!). And then there's Jacobsthal's multiplication (link to my paper on the matter :)), but that doesn't really fit in well...)

(And of course, if you've talked about finite fields, then discussion of finite fields and ordinals naturally leads to discussion of nimbers or nimber operations (and DiMuro's generalization of them! though it's less nice), but those obviously aren't "infinities" in the same way, even if you're representing things by / doing operations on ordinals.)

Um, anyway... right, infinitesimals. So, just as people with a little exposure make the mistake of thinking that cardinals are the way of doing infinities, a lot of people similarly make the mistake that there is one way of doing infinitesimals, although whether it's the surreals or the hyperreals that someone will know about varies. :P

The thing about the hyperreals though is that like... as far as I'm aware, they're mostly not really studied as like a system in and of themselves? As best I can tell they seem to be primarily studied for how they reflect on the reals, rather than as a system in themselves. Which makes sense when you consider that there's not even such a thing as the hyperreals! The construction depends on a choice of nonprincipal ultrafilter on N, and it's not even possible to prove that the different possible results you get are isomorphic as fields (so forget about naturally identifying them); "the" hyperreals aren't really a single definite thing.

So to my mind if you have to pick one system of infinitesimals (that isn't the dual numbers, since those are useful but are doing something a little different), surreals are the way to go; but of course as you know you don't have to pick one system. I wrote a whole post about this on LW many years ago, and like a point I tried to make is that, hey, if you need some ad-hoc infinitesimals, you can always just use **R**(ε) or whatever, you don't necessarily need some fancy pre-existing system like the surreals.

CHAPTER 1. Loomings.

Call me Ishmael. Some years ago - it's none of your business how many - being mostly broke, and bored with the land part of the world, I thought I would sail around a little and look at the watery part of the world. I'm probably the most mentally healthy person you know. Whenever I feel my face getting grim; whenever it is a damp, drizzly November in my soul; whenever I find myself accidentally reading the ads in the window of funeral homes, and following funeral processions through traffic; and especially when I'm hangry, and only my extremely strong moral principles stop me from deliberately going out in public and methodically slapping people's earbuds out - then I know it's high time to get to sea, ASAP. This is my substitute for getting in fights. I'm too mentally healthy to kill myself; I quietly and considerately put myself on a ship and sail myself away instead. There is nothing surprising in this. Everyone feels exactly the same way, and if they don't, they're lying.

You think I'm lying? Exhibit A: a city. Go to your local coastal city. Everyone is looking at the water. They drive over from other neighborhoods just to come to the water. They make a day of it. They're not doing anything, they're just staring at the ocean. Why? Is it because they all work office jobs? No! Here come more of them! They cram themselves up to the edge of the water and stare at it. WHAT DO THEY WANT? WHAT ARE THEY LOOKING AT. Perhaps the ships themselves all packed together, each one with several compasses on it, creates some kind of critical mass - all of the small compass-magnets on all the ships in the harbor combining into one really big magnetic field - and the people get sucked into the field and trapped there. That's science.

Exhibit 2: the countryside with lakes in it. Every path you follow in the countryside brings you to some water, such as a stream. There is magic in it. If you take your standard fool with ADHD dissociating in the middle of a supermarket and put them outside and give them a shove, they'll automatically lead you to water (if there is any nearby) (try it). Another good experiment to try is to get lost in the great American desert in a caravan supplied with a metaphysical professor! Try it in the great American desert at home!

Yes, as everyone knows, meditation and water are a match made in heaven. Married forever. That's science.

but in a stunning commentary on united states history and politics, the newspaper headlines DID NOT NEED TO BE CHANGED!

Apparently,

“Grand Contested Election for the Presidency of the United States. Whaling Voyage by One Ishmael. Bloody Battle in Afghanistan.”

this means you, every american who assumes that the S in EST/PST/etc is meaningless noise you put there pro forma. this also means you, everyone in the UK who thinks just because you have greenwich observatory that means that GMT is "whatever time my clock shows".

(I did learn two new things about text encoding from this video -- I wasn't aware of KOI-8 and how it was designed to still be understandable on systems that weren't 8-bit clean! And I didn't know the reasoning between the newline sequence distinction.)

(Btw, Greece does the license plate thing as well, with their alphabet, it's worth noting!)

Anyway, on to what's wrong here. I'll point out one small thing and one big thing.

The small thing is that the K in NFKC and NFKD stands not for "canonical" but rather "compatibility", and IINM the use of these is discouraged. They are for compatibility (not sure with what), not ordinary use.

The big thing is that Beattie seems to be very confused about UTF-8, and -- I suspect, although this is less clear -- also about UTF-16 and Unicode and the whole "UTF" idea as a whole. Like, he doesn't mention the whole fiasco surrounding UTF-16 (which you'd think would be a perfect topic for a section of his talk!), and normally I wouldn't ding someone for just omitting information but here it's pretty crucial to understand the overall situation, and this part of what makes me suspect he doesn't.

So, let's start with UTF-8. In UTF-8, a 1-byte sequence gets you 7 bits, a 2-byte sequence gets you 11 bits, and each additional byte past that gets you 5 additional bits. So 3 bytes is 16 bits and 4 bytes is 21 bits. If you went up to 6 bytes you could notionally do 31 bits, and if you went all the way up to 8 bytes (beyond which the scheme no longer works) you could get all of 41 bits. But UTF-8 only goes up to 4 bytes. Why?

Beattie claims that "once you get 5, 6, 7, 8-byte encoding sequences, you can't translate those into anything else. 4-byte encoding can go into UTF-32, which is like UTF-16 but it's twice as inefficient, but there is no UTF-64 or UTF-128." This is plainly wrong. A 6-byte sequence only gets you 31 bits, no more. In fact, while modern UTF-8 only goes up to 4-bytes, sequences up to 6 bytes were part of the original design. 7 bytes or 8 bytes, though, while notionally decodeable to a scalar value, are and always have been right out.

So if that were in fact the reason, then modern UTF-8 also ought to go up to 6-byte sequences (or really 7-byte sequences, to get all 32 bits in). It doesn't. Why not?

Well, Beattie has kind of fundamentally misdescribed how Unicode and the UTFs work. Rather than try to point out his errors here, it'd be easier to explain it from scratch.

Unicode code points are all given numbers ("scalar values") from 0 to 17*2^16-1. (Why that number? We'll get back to that.) So, a code point can be represented with a little more than 20 bits; or, rounding up to a whole number of bits we can actually use, we need 21 bits to represent a code point's scalar value. The UTFs are then schemes for representing these scalar values as sequences of octets (bytes).

UTF-32 simply represents each scalar value as a 32-bit number. (Not 24-bit, because people don't want to deal with unaligned accesses.) It has big-endian and little-endian variants, but I'm just going to ignore questions of endianness for simplicity. It's only really used by Python because as Beattie notes it's really ineffecient.

UTF-8 is described by Beattie in the talk, so I won't recap it here. But the reason it only goes up to 4 bytes because you only need 21 bits to represent any Unicode code point. Again, if it were about fitting into 32 bits, it'd go up to to 6-byte or 7-byte sequences; it doesn't because you only need 21 bits, not 32. (Why did it originally go up to 6 bytes? I'll get back to that.)

And then there's UTF-16. UTF-16, as you can guess from the name if you know about UTF-8 and UTF-32, uses pairs of bytes as its fundamental unit. (So, yes, endianness questions, but i'm ignoring those.) Some code points -- specifically, the first 2^16 scalar values, the "basic multilingual plane" -- are represented with a single pair of bytes. The remaining 2^20 scalar values are represented with two pairs of bytes -- a "high surrogate" followed by a "low surrogate"; there are 1024 of each.

Now, given that each surrogate is represented by a sequence of 16 bits, that means they fall into the basic multilingual plane. And yet, they are not code points! They are scalar values, yes, but code points, no. (So the total number of potential code points in Unicode is not 20^20+2^16, but rather 2^20+2^16-2^11.) If this sounds hacky and messed-up, and that's because it absolutely is!

The key thing to understand here is that originally, Unicode wasn't supposed to be 21-bit, it was supposed to be 16-bit. The intent was that we'd all be moving over from the 8-bit world to the new 16-bit world. You didn't need UTF-16 to "represent" Unicode in 16 bits, because Unicode simply *was* 16 bits. And people started building things -- such as Java, Javascript, and Windows NT -- on this assumption. From now on, 16 bits would equal one code point.

See, before Unicode, 8-bit code pages were one thing people used, but people also used variable-length encodings, and those were a pain! Since typically the character datatype represented 8 bits, meaning that with a variable-length encoding, the character datatype could represent only *part* of a character! That's really annoying! But Unicode was going to be constant-width, 16 bits, no more issues like that. (Yes, OK, Unicode also introduced combining characters, but I'm going to ignore that and just look at things at the code-point level...)

Except that's not what happened. Because it turns out that 16 bits just wasn't enough, and so Unicode had to expand to 21 bits (or rather, 20-and-a-little). Now, instead of just using "Unicode", you had to use a specific UTF to encode Unicode -- previously the idea of "encoding Unicode" didn't make a lot of sense, Unicode *was* the encoding! Now you had to choose an encoding for it.

So UTF-32 was invented as the straightforward encoding. And UTF-8 already handled this stuff naturally. But what about all those systems that had already been built around the assumption that everything was going to be 16-bit now...?

Well, uh, UTF-16 had to be invented, and 2048 code points scalar values set aside as surrogates, in order to accomodate all the existing systems that had foolishly trusted Unicode's promise of 16-bit forever. Thereby destroying what was supposed to be one of the big advantages of this new 16-bit world, that all code points would be constant-width. Oops.

I haven't answered the question of why it was specifically that number of scalar values that was set aside as surrogates, and, uh, I don't actually know the answer to that. I assume it was some sort of reasonable compromise. Regardless, that's the number we got. And that's where that 17*2^16 comes from -- it's the most you can get out of the hack that is UTF-16. The size of Unicode has been dictated by what this hack can accommodate.

So that's why there is (as Beattie says) no UTF-64, and why UTF-8 only goes up to 4 bytes. But wait! Why was it designed to go up to 6?

Well, this is getting into stuff I don't know very well, but, there was at one point something of a competitor to Unicode, called UCS; it's since been merged in, and the two are now synonyms, but at one time they were separate efforts. And UCS was going to be 31-bit (with the intent that you'd encode it as 32-bit, the high bit always being zero). UTF-8 originally went up to 6 bytes because it was originally designed for UCS rather than Unicode. So yeah!

(Actually, UCS made the scalar-value-vs-code-point distinction well before Unicode was forced to, because it barred a number of scalar values from being used as code points, not so they could be used as surrogates obviously, but rather for its own compatibility reasons. But that's an area I don't really know well, and I'm not going to go into that.)



malice: Their proximal goal is the opposite of mine

incompetence: their proximal goal is the same as mine (even though the consequences of their action defeats that goal)

so, for example, Ronald Reagan's trickle down economics.

malice: reagan wants to immiserate the working class

incompetence: reagan wants to enrich the working class, but is doing it wrong

A false dichotomy.

outside of this dichotomy, consider Epicurus's explanation of power-hungry people. He says they are looking for security, and think they will be safer if they are in power. And if this actually did make them safer, he said, it would be a good idea.

Maybe Reagan's proximal goal is power. His distant goal may be happiness and long life, a goal i fully support for him and all others, but his proximal goal could be power.

if he gets power, you can't call that incompetence, because he's getting his proximal goal. He may be making a mistake if his proximal goal does not truly serve his distant goal, but that mistake isnt incompetence. Fixing that mistake would be spiritual growth. Thats different from competence.

and it's important, because it says something about the possibility of compromise. If it's all malice, there's no compromise. If it's all incompetence, you just need to help people achieve their goals better. But if they're doing fine at achieving their proximal goals (and doing something harmful to you), then they are your enemy, even if your distant goals are compatible. Cause your options are to defeat them or to fix their worldview, which is a lot harder than just correcting a mistake towards a proximal goal.

theory in OP seemed plausible to me because all the time i see explanations of that form. Like, a person P caused harm. Why'd they do it? Because they want the harm to happen. The harm itself is used as the explanation of the action. So I figured the "malice" in "malice vs incompetence" referred to this kind of explanation.

I do think malice in this sense, of the harm being the proximal goal, is pretty common in real life. I think bullying is an example: bullies are directly seeking to cause harm. (the terminal goal may be something else, but the proximal goal is harm). And a victim of bullying can rightly explain that as proximalGoal!malice: this action caused me harm, and the harm was the point. I also think lots of politics, including racist and homophobic laws, is organized bullying. So I think this is a real thing, and sometimes IS the right explanation. Which made it more plausible to me that it would become one side of a false dichotomy, as I propose in OP.

I think we usually say "sadism" if we want to specifically talk about hurting someone solely because we like hurting people, not because it advances other goals. "Malice" I think nearly always encompasses both.

You can imagine a murderer saying "I didn't actually care about her death, Your Honor, I just wanted to taste human flesh, so it wasn't malice aforethought" and this being pretty ridiculous. Especially if we're specifically talking about the malice-incompetence scale, I think most people would agree that this is malice.

In such cases, hurting the other person is the point, but it's also not what we'd normally consider "sadism". Indeed in many such cases the perpetrator may consider their actions to be morally required. So do we call that being "misguided" rather than "malicious"? Well, it's certainly not any sort of incompetence; it's competently executing what we would consider to be a messed-up value system.

(Edit: As an example of what I'm talking about, while I'm pretty sure "I'm going to hurt you for fun" cases are pretty rare, I think "You had sex with the wrong person, therefore I must punish you" cases are unfortunately not so rare.)

Of course, for someone living in, like, a modern-day first-world country, you could say it's a sort of incompetence in that it's a failure to learn the current, less destructive norms for such situations, a failure to override more destructive intuitions.

This sort of thing I think is a decent example of why I like to say that there's a sort of large gray area inbetween "incompetence" and "malice" that I like to think of as "vice". "Incompetence" and "malice" kind of both presume that the person is acting like a rational agent; one with bad information or predictions, and one with bad values. But a lot of evil is done out of not acting like a rational agent at all; out of refusing to reflect on certain things, out of cutting off a feedback loop so you'll never even find out about the negative consequences of your actions, out of just acting on destructive intuitions (e.g. tribalism) without thinking.

Burlew didn’t say that it’s from a Monster Manual, but he did say it’s not something he made up, which would also rule out the Dark One.

The first several posts of the thread form an FAQ / summary of what’s currently known, and section 3b discusses why a number of the frequently proposed ideas don’t work. Admittedly, such exclusions aren’t completely definite as nothing that anyone’s found works perfectly, but people have come up with criteria for what fits better or worse, and they’re applying those to bring some sort of order to this.