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Can It Be Wrong To Crystallize Patterns?

In my last post I mentioned my experience of reading over some essays I found really enlightening years ago, finding them on re-examination to be correct but boring, and half doubting that I had ever not-known the things within. In the comments many people said they shared that experience, either with the Less Wrong sequences or something else.

This never happens with other kinds of knowledge. I remember learning the capital of Cuba in my sixth grade Geography class. It is very clear in my memory that before I did this, I didn’t know the capital of Cuba. I can easily conceive of forgetting the capital of Cuba, and indeed if I went long enough without thinking about it I would expect that to happen.

Compare this factual knowledge of the Cuban capital to the idea of mysterious answers to mysterious questions.

The capital of Cuba is a known unknown. Before I learned it was Havana, I knew Cuba must have a capital and that this was a hole in my knowledge. It’s hard to imagine what it would mean for me to understand that I needed a concept like “mysterious answers” without, by that fact itself, having the concept.

Information about Cuba’s capital can be wrong – a vandalized Wikipedia article might tell me it’s Cuba City. I’m not sure what it would mean for the idea of Mysterious Answers to be wrong. The impression I get from that post is that it’s saying “Here is a useful concept, take it or leave it”. If you didn’t like the post, it would be more because you thought very few theories or ideas were really Mysterious Answers, or because Mysterious Answers didn’t have enough extra explanatory power to be worth your time to learn – not because the concept was wrong per se. But I think a more likely reaction is to see the examples and immediately think “Yes, this is a very common failure mode. I can easily think of a lot of times I’ve seen it used. Now I will be able to spot and recognize it more quickly”

Teaching the capital of Cuba imparts new information. Teaching about Mysterious Answers doesn’t, at least for a strict definition of information. Maybe most readers already know all of the particular examples in that post. All they hadn’t done was detect a pattern and give a name to it.

A while ago, a leftist commenter asked me to stop using the term “political correctness”. Without getting into whether or not I should comply, I was struck by the sound strategy behind the request. Without the words “political correctness”, an entire class of things becomes much harder to think about. There are whole debates that would stop happening if the words “political correctness” got removed from the vocabulary. That’s pretty strange. If we removed the word “President” from the vocabulary, people would just start talking about “that guy in the White House” or “the executive branch” or something. But striking out “political correctness” would be a genuine game-changer.

“Political correctness” is also an attempt to detect a pattern (for the purpose of not politicizing this post, I will stay agnostic whether it is real or imagined) and give a name to it. And I think if we stopped using the term, people would stop detecting the pattern and their views about a lot of things would change.

Giving a pattern a name crystallizes it, let people hold it in their minds for a longer period, make it easier to think about and discuss.

This is neat because it lets you formulate a meta-level response to the pattern. If you realize that “God” is sometimes a Mysterious Answer, and “elan vital” is sometimes a Mysterious Answer, then when you’re tempted to use something you like as a Mysterious Answer (“How did the eye form?” “Evolution!”) you’re more likely to recognize it, admit it’s a problem, and apply a general policy of not being satisfied with Mysterious Answers.

And when you encounter it again, it’s much easier to dismiss in a single mental motion. A lot of the problem with debate is time and number-of-mental-steps: the amount of time and energy normal people give to debating things isn’t enough to get past the preliminary outer defenses of bad ideas, and in the rare cases it is, by the time the last defenses have been breached the first ones have already started regenerating. Turning long series of steps into a single convenient package decreases the amount of stuff you need to keep in your mental workspace.

I will now dump a long list of concepts that I think work in more or less this way: “trivial inconveniences”, “Schelling points”, “spoon theory“, “ad hominem fallacy”, “introversion/extraversion”, “social justice”, “ask culture”, “global (versus local) maxima/minima”, “growth mindset”, “logical uncertainty”, “crackpot”, “cult”, “meme”, “self-reference”, “utility”, “warm fuzzies”, “Third World”, “efficient charity”, “entryism”, “witch hunt”, “deontology”, “romantic love”…

…it’s going to be easier to list things that don’t work like this, isn’t it?

“Witch hunt” and “romantic love” seem like especially interesting examples. In olden days, if someone was having a moral panic and decided to unfairly persecute a group of people for something they probably weren’t doing, you would have to come up with some complicated way of explaining this to the public and convincing them that this is a plausible thing that might happen (you can’t borrow my wording; “moral panic” is almost as artificial a crystallized pattern as “witch hunt” is). Good luck getting the public to hold still for that. Now you can just say “They’re holding a witch hunt!” and everyone will understand your objection. I think the existence of the concept “witch hunt” lets everybody coordinate to develop solutions to problems like “How can we best prevent witch hunts from happening?” and really does make witch hunts significantly more difficult.

“Romantic love” shares with the Sequences this pattern of once you’ve got it it’s hard to imagine not having it. We know a lot of our notion of romantic love is Western and modern, but it requires a lot of evidence to prove this to most people because it seems so natural. It’s one possible way of parsing sex and attraction and stuff, and a very natural one for us, but one that was very rarely used in certain circumstances (the crystallization of the pattern “romantic love” probably shouldn’t be confused with semifactual questions like “should we choose partners based on romantic love?”, which already presuppose that we’ve accepted romantic love as a useful concept)

And I’m thinking about these things because of Alexander Stanislaw’s comment on my last post:

Perhaps being immersed in a memeplex such as LW for long enough is sufficient to make the source material seem obvious, whether or not the memes are correct. I’m sure that there are intelligent Christians our age who are re-reading C.S. Lewis and thinking, “wow this is so obvious”.

I admit, I find it very hard to argue with the LW stance on what concepts are for instance, and it drives me nuts when people try to define themselves into being correct, or argue about whether X is really Y, or equivocate between definitions of words. But apparently Gilbert of the Last Conformer disagrees with the LW stance on concepts and he seems knowledgeable.

It’s an interesting question: can crystallizing a pattern be wrong?

First, two kinda trivial examples.

Crystallizing the pattern “ley lines” wouldn’t be super useful if you don’t believe ley lines exist. From one perspective, the crystallization is still nice, because you have an extra concept to toss around and you can do things you couldn’t do before like debate the existence of ley lines (and settle on the negative position). From another perspective, the existence of the pattern makes it too tempting to start believing in ley lines or at least thinking they’re important. So in theory crystallizing the concept “ley lines” is an unalloyed positive (minus the five minutes it takes you to read the definition), but in practice it’s a bad idea.

Crystallizing the pattern “mainstream media” in the sense that some conspiracy theorists use it – ie “this exciting archaeological discovery will never be mentioned in the mainstream media” seems more complicated. There definitely exists a “mainstream media” in the sense of “a media that has much different standards and preferences than the local conspiracy theory rag”. And it’s probably useful to talk about – my reaction to the Siberian discovery was “I’ll believe it once I see it in the mainstream media”. But the way the term is used manages to smuggle in questionable connotations – this is some people’s problem with “political correctness” as well, and with other political terms like “patriarchy”, “the Cathedral”, “international Jewry”, et cetera.

I think the problem here might be that pointing out a pattern suggests an agency fiction? There’s clearly international Jewry in the sense of “Jews in many different countries”. One can even make moderately correct statements about international Jewry, like “international Jewry often puts pressure on different countries to support Israel”, which when stripped of its connotations is more or less correct. But the connotations suggest either that they’re all working together in a conspiracy, or that they’re all doing it in about the same way which is becoming a noteworthy pattern, or that it’s something much more interesting than the way other ethnic groups do other things.

I think this was my interlocutor’s problem with political correctness as well – certainly there are things that fit that category, but once the word starts to be used it’s singling it out as A Unique And Interesting Problem.

But I don’t know how to solve this sort of issue in a way that’s easily distinguishable from trying to ban people from ever talking about political correctness or Jewish support for Israel. Making people use a different term than “international Jewry” (“Jews around the world”?) would work for about ten minutes until it got loaded with exactly the same connotations as the original.

But these two examples seem less interesting than the original question about whether you can crystallize patterns, without falling into any traps or connotations – and still have it be a net loss.

I’m trying to think of something that fits Alexander’s example – something written by C.S. Lewis that provides Christians with much more clarity and afterwards they feel like they’re much more advanced and can’t remember how they lived without the concept – but which from my perspective as a non-Christian is wrong and counterproductive.

(my immediate reaction is “ring theory!”, but that’s not dependent on Christianity and probably correct and useful, so it doesn’t count)

The closest I can come (I am not a Lewis scholar) are his trilemma, his use of the different phases of water (ice, liquid, steam) to explain the Trinity, and his famous saying that “going to church does not make you a Christian any more than going to a garage makes you a car”.

But I like all of these!

Although I don’t agree with his formulation of the trilemma, it puts something that people would otherwise spend interminable hours debating without ever reaching the core of the issue – into sharp relief, so that it can be attacked or defended in its strongest form.

And although I don’t accept the premises of the Trinity or the special necessity of figuring out exactly who is or isn’t a “real Christian”, if I admired the problems I would certainly admire Lewis’ solutions to them.

The worst that can be said about Lewis is that he came up with excessively clever solutions to the wrong problems – that is, maybe if someone was wrestling with the idea of the Trinity, that would convince them to second-guess their religion, but Lewis came up with such an elegant metaphor that it prevents them from having to do that.

And I’m not sure that the garage saying or the Trinity analogy are crystallized patterns per se. The trilemma example might be the purest – but that’s also the one I like most.

So provisionally I’m not sure there’s such a thing as crystallizing a pattern and being wrong to do so. You can crystallize patterns in such a way that it ends out misleading people who were already at risk of being misled – like the “ley lines” and “international Jewry” examples – and in practice this is a HUGE HUGE problem. But it seems to me that if you’re good enough at sorting through connotations to handle it that crystallization is usually a good idea

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117 Responses to Can It Be Wrong To Crystallize Patterns?

  1. Agree denotationally and connotationally, but super disagree with not putting a period at the end of your last sentence and leaving us all hanging as though there’s more stuff you want to say but it just kind of trails off and you’re sitting there waiting for a response but how can I respond when it’s not clear that you’re finished yet AAAAAAHHHHH

    *Runs off clutching at hair and screaming*

    • Scott Alexander says:

      And here I thought when I left eighth grade language arts class I wouldn’t have to deal with people giving me grief over forgetting periods at the end of my sentences any more.

      Here, I’ll end this sentence with two periods to make up for it..

  2. St. Rev says:

    I was excited when you mentioned ring theory and then sad when I clicked the link.

  3. ozymandias says:

    I am less optimistic than you are about crystallizing patterns not being wrong. I can think off the top of my head of half a dozen crystallized patterns I think are non-useful. I think that my big concerns are, in addition to your point about agency:

    (1) Identifying a pattern sets one up for Mysterious Answers: instead of asking why a particular gender inequality exists, a feminist might say “patriarchy.”
    (2) It is easy to identify a pattern that doesn’t actually exist. I feel like “rape culture” is this way, at least in current usage, in which it seems to mean something like “bad things related to rape.” This can make it harder to see the patterns that actually exist and make it easier to make incorrect claims (such as that there is a massive lack of understanding in our culture about what ‘consent’ means).

    In terms of concepts Lewis has that are unhelpful: perhaps some of his writing about sex? Or the idea that every drive has its fulfillment, so the drives that we can’t fulfill on earth must be proof of Heaven?

    • ozymandias says:

      Also, I was highly amused to read your point about international Jewry, go “euphemism treadmill!”, and then go “oooh, I’m matching things Scott is saying to patterns!” Your post has given me a metapattern. 🙂

      • Anonymous says:

        I did the euphemism treadmill thing too!

        Though I was skeptical that a noun-phrase like ‘Jews around the world’ could become as loaded with negative connotations as a dismissive predicate like ‘international jewry.’ I have trouble thinking of any noun phrase of longer than say three words that has negative connotations attached to it (when the words that make it up are neutral).

        I wonder if this is something like Feser’s ‘give it a name’ maneuver. That in order for a crystallized concept to take on connotations it must have a certain short length or otherwise the brain actually ends up parsing the nouns separately and you can’t smuggle in connotations as easily.

        • ozymandias says:

          I have had similar thoughts, and often wondered if that’s the real rationale behind insisting on clunky terminology like “person living with developmental disabilities.”

        • Scott Alexander says:

          I was actually thinking about the same thing recently. Counterexamples I generated were things like “tragedy of the commons” or “right to bear arms” which my brain treats as simple concepts. I agree there are fewer of these than one or two word concepts but I’m not sure if this is just because it’s so simple to give things shorter names so why wouldn’t you?

        • Brian says:

          “Cheese-eating surrender monkey”.

        • Army1987 says:

          I was actually thinking about the same thing recently. Counterexamples I generated were things like “tragedy of the commons” or “right to bear arms” which my brain treats as simple concepts. I agree there are fewer of these than one or two word concepts but I’m not sure if this is just because it’s so simple to give things shorter names so why wouldn’t you?

          I don’t think “tragedy of the commons” is a good counterexample: it’s a several-word name, but one couldn’t figure out its meaning just from knowing the meanings of “tragedy” and “commons”, and explaining it would take much more than four words.

          (On the face of it, this doesn’t apply to “right to bear arms”, which is nothing more than what it sounds like, and I guess the reason why your brain treats it as a simple concept is its prominence in American political discourse and/or the fact that it uses old-fashioned words as opposed to everyday synonyms such as “carry weapons”.)

    • Sniffnoy says:

      (2) It is easy to identify a pattern that doesn’t actually exist. I feel like “rape culture” is this way, at least in current usage, in which it seems to mean something like “bad things related to rape.”

      I like this example! It’s illustrative of a whole other class of examples. Other people having crystallized the pattern, it becomes very hard to argue that there is no pattern — if you try to say the pattern doesn’t exist, people will just point you to the many instances of this supposed pattern. But it’s not that the instances aren’t real, it’s just that they don’t form any coherent pattern that you can predict things from.

    • Doug S. says:

      My working definition of “rape culture” is “those elements of culture which make it more likely for a person to commit rape, more likely for a rapist to get away with rape, or increase the hardships faced by rape victims”. This doesn’t quite cover all the uses (good and bad) of the term, but it does seem to cover the worthwhile ones…

      • I pretty much agree and support that (fairly common) use of the term.

      • Sniffnoy says:

        But then the question is, then, firstly, are these really one intertwined thing, or are they disparate phenomena with similar effects? And, secondly, if they are one intertwined thing, are they one thing that is (to at least some extent) neatly separable from other things to that do not have those effects or may even mitigate them?

        • Sniffnoy says:

          Ugh, grammar got mangled at the end there. Should say, “neatly separable from other things that do not have those effects or may even mitigate them”.

      • suntzuanime says:

        But then things like “the rights of the accused” fall under rape culture. I mean, possibly “rape culture” really is just a way to call classical liberalism nasty names, but…

        • Doug S. says:

          But then things like “the rights of the accused” fall under rape culture.

          They certainly can; the rather ridiculous standard in some forms of Islamic law (of requiring four witnesses, which apparently was a precedent set in a case involving a mistaken accusation; as the saying goes, hard cases make bad law) is a frequent target of “rape culture” criticism.

        • suntzuanime says:

          Anything less than executing every single human being as a suspected rapist makes it more likely for a rapist to get away with rape.

        • blacktrance says:

          This is a highly uncharitable strawman. Feminists generally don’t want to compromise rights of the accused, they just think that rape and the culture around it are an underestimated problem. That doesn’t mean that they think that treating people unfairly is an acceptable solution. Also, feminism and classical liberalism aren’t enemies, in fact, they go together very well, with the common origin of individualism and personal autonomy. Also, “rape culture” cannot be a way to call classical liberalism nasty names because we currently live in a rape culture, but we don’t live in classical liberalism.

          That’s not to say that most feminists are classical liberals – most aren’t. But the parts of feminism that aren’t individualist aren’t essential parts of it. It’s similar to libertarianism – just because too high of a proportion of libertarians are Confederate apologists doesn’t mean that Confederate apologism is an essential part of libertarianism.

        • Sniffnoy says:

          This is a highly uncharitable strawman. Feminists generally don’t want to compromise rights of the accused, they just think that rape and the culture around it are an underestimated problem. That doesn’t mean that they think that treating people unfairly is an acceptable solution.

          It’s not a strawman, exactly — it’s just working from the definition that Doug S stated. It’s only a strawman if we say “this is what feminists do, in fact, mean by rape culture, and therefore the whole concept should be thrown out”. As it is, it’s just pointing out that that definition has bad implications. Thus, an appropriate response on Doug’s part would be “I guess that means my definition was a little overbroad; perhaps a better attempt at a working definition would be…”. And then we could pick holes in that, and so on.

          This sort of iterative refining of working definitions should be a normal part of argument. Unfortunately, the feminist blogosphere seems to have terrible norms of argument that don’t allow for it.

          While I obviously can’t actually get inside their heads, I do have a guess at what mistake they are making: They are assuming common sense. Thus, they say X, and they really mean “X, moderated by (our version of) common sense”. Then someone who either lacks that same common sense or takes things literally points out the problem with X, and instead of saying “Yes, that is a slight hole in what we said, let’s try to pin this down”, they call it a strawman and assume the other person must be being deliberately obtuse.

          But this sort of thing isn’t necessarily trolling, it can just be really trying to pin things down. Especially because not everyone is going to share the same “common sense”. Hell, they even point this out repeatedly — we don’t have the lived experience they do, so we can’t understand it — so they shouldn’t expect us to have the same “common sense” they do! (Not to mention, we’ve been taught that our common sense is misogynist and evil, so we have to disregard it.)

          And I mean jeez what’s the point of saying anything if people are just going to use common sense instead? As Ozy said on the “Five Years and One Week Thread”, ideologies don’t seem to be made for people who won’t compartmentalize them. But they should be, dammit.

          OK, that may have gone off topic a bit. Meanwhile…

          But the parts of feminism that aren’t individualist aren’t essential parts of it.

          It’s not clear to me that that’s true — not because it’s false as such, that the non-individualist parts are essential, but rather because the different schools of thought among feminism are so different from one another that one can’t really make coherent claims about what’s essential and what isn’t. (“Feminism isn’t a monolith!” isn’t just a defense. 😛 )

          That is to say, it seems more to me like a political alliance than anything else — yes, they’ve reached (some of) the same conclusions, but their premises are very different, so there’s no reason you should expect them to continue to agree in the future. It’s like grouping skeptical materialists and hippie spiritualists under “atheists” — useful if you want to get them to unite against forced prayer in schools, useless if you want to talk about just what it is that they think.

          I’ll admit, though, that I’m getting into waters here that I’m not really familiar with. Anyone else care to say whether I’m on track or not?

      • A potential problem with your working definition is that not living in a police state would be part of “rape culture,” since it could make it “more likely for a rapist to get away with rape.”

        • Anthony says:

          An opponent of modern feminism would say that that is precisely the point: using the bludgeon of concepts like “rape culture”, pesky impediments to a police state (run by the right sort of police, naturally) like “the rights of the accused” and “innocent until proven guilty” can be swept away. (Badly, because a bludgeon doesn’t sweep very well.)

          But certainly “rape culture” *is* a crystallized pattern in the sense Scott is talking about. The fact that it is “wrong” does not necessarily show that crystallized patterns *must* be wrong.

        • Tab Atkins says:

          This, like suntzuanime’s “interpretation” of DougS’s definition, seems to be obviously an uncharitable reductio ad absurdum.

          Maybe you and suntzuanime simply have *actually no idea* what DougS is trying to say, but assuming that DougS would agree that “to prevent rape, we must literally execute every single person suspected of being a rapist” or “to prevent rape, we must literally institute a police state” is so absurd as to beggar the imagination.

      • Crimson Wool says:

        It still feels wrong to me because those issues, as far as I’ve ever read, seem far more psychological than cultural. Rapists frequently use the halo effect to their advantage, human beings are unlikely to believe low-status people over high-status ones, ceteris paribus, individuals avoid talking about all kinds of trauma (not just rape) because they don’t want to be a burden to others, it’s easier to believe that your friend is a liar than that your friend is a rapist, etc.

      • Drew Hardies says:

        I agree that your definition matches the common-use pretty well. But I think the term-as-used has some limits.

        In particular, it appears to be a ‘post-hoc’ definition in that it’s based on an knowledge that we can only approximate. I think this use is very much like the way we define ‘health risks’ as ‘the things that make illness more common/worse’.

        On one hand, this provides a really convenient short hand. We can gesture at ‘bad stuff’ without needing to flesh out the entire category.

        On the other hand, these concepts are based on an empirical test. So, they create a very different kind of category than “a simple-boundried region of thing space.”

        I think this creates a dangeous temptatoin to conflate our thing-space ‘map’ (which we have access to) with the ‘bad by definition’ territory (which we don’t) and borrow the ‘bad by definition’ property.

        The image I have in mind is talking to a 1970s doctor about fat-consumption. It would be easy to imagine the doctor saying, “[Based on current science] Fat calories are a health risk. Health risks are bad by definition! How could future scientists ever say that egg-yolks are acceptable?”

        Switch ‘egg yolks’ for ‘porn’ and I think we get a similar problem with rape-culture debates. People inferr (correctly or not) that porn causes risks. So they lump it into rape culture. Then they assert (correctly) that rape culture is bad-by definition and conclude (prematurely) that porn is known to be ojectively harmful.

        I appologize for length, I was just very happy to see someone had found the same definition of ‘rape culture’ that I had and would like to get your take on these sorts of definitions. And do you know if there’s a LW post that I’ve missed that matches this? The ‘hidden queries’ seems close but not quite it.

    • Scott Alexander says:

      I feel like “rape culture” is potentially useful, in the sense that there are an unexpectedly high number of cases where people fail to prosecute rape or are willing to excuse it, and it’s useful to have a convenient way to group together all of these things.

      I feel like it’s not useful in the sense of “let’s say ALL OF SOCIETY IS ONE GIANT RAPE CULTURE”, but this seems more like some people misusing a crystal where it doesn’t belong than like it being wrong to form the crystal in the first place.

      As for Lewis, all the examples you give seem more like theories of his than crystals of his.

  4. Sniffnoy says:

    Oh hey, more Human’s Guide to Words stuff. 😛

    I’m going to say yes, it can be wrong to crystallize certain (false) patterns, unless you’re dealing with people who know how to look out for such things. Basically the problem happens when your false pattern is close enough to a true pattern that it crowds it out or co-opts it. I think your “international Jewry” example is a decent one, though we can do better. But essentially it’s related to the problem of sneaking in connotations. If there’s this pattern where X seems to go together with Y and with Z, and someone makes a word that refers to X and Y and Z and uncorrelated thing W, it’s going to become harder to discuss the X-Y-Z pattern by itself; attempts to think about the X-Y-Z pattern will be overshadowed by the X-Y-Z-W concept. You already have a word for X-Y-Z(-W), so you don’t feel like something’s missing.

    Again, if you’re dealing with LW types, they might notice the problem and insist on splitting off the concepts, or some other similar solution. But most people will not do this. They’ll argue over definitions or fall into The Worst Argument In The World (and it’s awful typical response of “No it isn’t!” instead of “That’s irrelevant”) and similarly unhelpful things.

    Edit: Ah, I notice now that at the end you included “But it seems to me that if you’re good enough at sorting through connotations to handle it”, which addresses a lot of my objection. It’s not enough that you are yourself, though — you also have to be dealing with other people who are. And it’s also a big assumption to make — this sort of thing is easy to screw up even if you think you’re good at it.

  5. St. Rev says:

    I think crystallizing patterns is always necessary and always problematic. Humans are pattern-recognition engines; we have to stop calculating at some point and act on our understanding. It’s good to maintain awareness that one is always engaging in what amounts to lossy and noisy compression. It’s difficult but useful to develop the skills to monitor and interrogate one’s patterns, but it’s not possible to avoid making or using them, unless one wants (for starters) to give up language altogether. There’s no privileged place to stand.

  6. Sid says:

    It is very interesting to me that the word ‘concept’ and the word ‘conceit’ have the etymological derivation: they both come from ‘conceive’—as in, take into the mind—which is derived from the meaning of conceive as in becoming pregnant.

    So in this sense, you’re looking for concepts that are indeed conceits.

  7. Doug S. says:

    You gave an example of a bad one in your Anti-Reactionary FAQ: “demotist”.

    • Andy says:

      Perhaps being immersed in a memeplex such as LW for long enough is sufficient to make the source material seem obvious, whether or not the memes are correct.

      This line from Alexander’s comment reminds me of an encounter I had with a Christian evangelist on my campus. She was this tiny elderly lady who very earnestly told people that God loved everyone, and they needed to get saved before they went to Hell. And the way she talked about Hell wasn’t the way I’d heard fire-and-brimstone preachers describe it, throwing it at people like a threat- she was warning people the way I’d say “hey, be careful on those steps, they’re slippery” – very matter of fact. As if Hell were a fundamental fact of the world, and not a possibly-true or possibly-false spiritual place.
      In my less charitable moments, I suspect this is why many fundamentalist creeds try to minimize contact with the outside world – to prevent memetic contamination that would undermine the crystallized patterns.

    • Scott Alexander says:

      Yes, a concept which tempts the conflation of multiple unlike groups is definitely bad. Although I could imagine situations in which “demotist” might be useful – it just wouldn’t be the investigation of political oppression.

      • I’ve noticed that I very, very often find such crystallized ideas useful in a much less broad form that still feels crystallized (such as Cathedral = “Who taught you critical thinking, anyway?”)

      • Anonymous says:

        If your standard is ‘could imagine situations in which X might be useful’ there will be literally no patterns that are wrong. I have a very vivid imagination; from your writings I think you do as well. I do not think I know of any concept or formation thereof which I cannot find some sort of obscure edge-case or situation of vast improbability where the concept would not have at least a slightly positive value. If that is the standard by which you assess concepts, you will be very unlikely to find one which satisfies your criterion for being a bad pattern. Any classifier or pattern-identifier that classifies all inputs into the same category is not a useful method of classification.

        I personally think that demotist is a fine example of a crystallization of patterns that is only used in ways that are misleading and useless in the real world at past and present, and is sufficiently unlikely to ever make any useful contribution to anything to even begin to show up against the harm it’s already wrought, that I think it is ‘wrong’. I could with sufficient effort imagine a vastly improbably future where the concept had value and meaning and utility, but my ability to imagine that does not actually make the concept more useful in the here-and-now or make that imagined world anything less than staggeringly unlikely.

  8. William Newman says:

    One day I found myself telling a nontechnical person how many math concepts are formalizations or systematizations of things that people tend to develop an intuitive feel for even without math. E.g., orthogonal, derivative, and how easy it is to illustrate some generating ideas of group theory by appealing to what people tend to informally understand about simple symmetry transformations. Until then I hadn’t really thought about the ones that I’ve never heard of people reasoning about informally: e.g., eigenvalue or complex number.

    There seems to be a continuum for ordinary nonmath words, where most of the examples you give at the end where people naturally tend to have the concept already even if they don’t have the word. (Other words like “republic” and “virus” are toward the other extreme, and words like “stampede” and “pregnant” slide from one side of the scale to the other depending on people’s personal experience.) I don’t know a standard name for this property that words have to a variable extent. But I can’t be the only one who’s thought about it: I vaguely remember seeing a comment that not having “schadenfreude” in one’s vocabulary doesn’t mean that one doesn’t have the concept. Having the word can naturally make it a lot easier to talk about it in such cases, but I’m not sure it changes the way people think about it. (If a skier is never told the name for a mogul, does he think about it differently?) I suspect it doesn’t change the connotations all that much either, though perhaps there are important second-order effects of making it harder for connotations to be shared between speakers.

    • ThrustVectoring says:

      Complex numbers are fundamentally an algebra tool – it’s an application of math on math that ensures that an arbitrary polynomial of degree N has exactly N factors.

      I think the closest that complex numbers get to actual usage is in combination with exponential growth. Real exponential growth is straightforward, but what does it mean to extend it to complex exponential growth?

      The short of it is that complex exponential growth has the complex portion somehow perpendicular to what you are growing. For the complex plane it’s straightforward – the real magnitude pushes away from the origin, and the imaginary part spins it around. For a physical spring-mass-damper system, the complex part of the exponential growth corresponds to how energy is passed to the different state variables.

      • peterdjones says:

        Complex numbers are vital to physics. In particular, they stop QM being a classical probability calculus.

      • William Newman says:

        “it’s an application of math on math that ensures that an arbitrary polynomial of degree N has exactly N factors”

        Other things, too. Not just making it easy to express quantum mechanics as peterdjones mentioned, but also many mathematically well-behaved properties besides factoring polynomials, e.g. analytic functions, freedom to slide contour integrals around, and convergence results that are naturally expressed in complex numbers (like the circle of convergence of a power series). And sometimes it is useful that multiple useful things (e.g. Fourier transforms and Laplace transforms) are special cases of the same general idea when expressed in complex numbers.

        From all their nice properties they seem like a very natural abstraction in hindsight, but I don’t think many people ever stumble on them in a informal way.

        • Tab Atkins says:

          Remember that it wasn’t even a century ago that the concept of negative numbers was controversial. We’d of course known about solutions to equations that were less than 0, and had been dealing with mathematical notation for that for quite some time, but accepting them as an ordinary, intuitive type of number, just as “natural” as the natural numbers, was a controversial subject.

          When I learned this I got a lot more comfortable with complex numbers.

          (I also imagined a teaching tool that might be useful, running through a fairly standard complex-number introduction, except with i^2 = 1, then at the very end reveal that you were talking about negative numbers the whole time, and you can get complex numbers just by changing i^2 to -1.

          Since the students already understand negative numbers, bridging them over to the somewhat less convenient methods of manipulating them that complex numbers require makes it easier to feel like actual complex numbers are intuitive, or at least “normal”.)

        • Douglas Knight says:

          Tab, could you provide evidence that negative numbers were controversial a century ago? at least, more controversial than today?

        • Sniffnoy says:

          I’m pretty sure Tab’s chronology is pretty off there. According to WP, negative numbers became well-accepted with the development of calculus, and complex numbers seem to have been well-accepted by the mid-18th century. 100 years ago is far too late; by that time there was already such a subject as complex analysis.

          In addition, I have to say that Tab’s suggestion for an introduction for complex numbers seems ill-advised, and I seriously doubt that it would cause more enlightenment than confusion. (Though it could possibly be rescued; see the bottom.)

          The complex numbers are obtained from the real numbers and formally adjoining a square root of -1 (a root of x^2+1), called i. This yields another field, the complex numbers. Every complex number can be uniquely expressed as x+iy, where x and y are real.

          Trying to introduce complex numbers with an analogue where j^2=1 (I’ll say j rather than i, as I want i to designate the imaginary unit) has several problems. First off — is j a number already in our system (I’m assuming we’re starting from the real numbers here), or not? If so, j could be 1 or -1; either way, it’s already a real number, so why did we introduce it? And we no longer have any sort of uniqueness — any real number can be represented as x+jy in many different ways. (And, of course it can be represented as x; you don’t even need the j.) So, sure, this may help students get used to working with expressions of the form x+jy, with x+iy being analogous, but it seems a pointless step. If they can do algebra, they can work with expressions of the form x+iy as well; the hard part is getting used to the abstract nature of it — having around a mystery symbol, for which the relevant question is not “what is it?” but rather “how does it act?”. And if the former has an answer already in the system (“it’s -1”), then this doesn’t really help with that.

          The other alternative of course is that j is not already in the system — we’re formally adjoining it. Then you’d be introducing students to the split-complex numbers. Suffice it to say that I’m pretty sure that this would be considerably more confusing than the complex numbers, especially if it’s used as a lead-in to the complex numbers. I’m not going to go into detail why here unless people really want; I think it should be pretty clear.

          Now, that said, the proposal’s not totally unrescuable. You could, as an analogy, discuss actually adjoining -1 to the nonnegative real numbers to get the real numbers — i.e. straight up doing negative numbers this way, starting from the nonnegative reals, not introducing things you already have or going to split-complex numbers. But note though that the key property of -1 is not that it satisfies x^2-1=0, it’s that it satisfies x+1=0; that’s the polynomial you’d be formally adjoining a root of. So yes, you absolutely could introduce real numbers as numbers of the form x+jy, where x and y are nonnegative reals, and j+1=0.

          Note, though, that this has the slight complication that such representations are not unique. This might not be too big of a pitfall, but you’re going to have to watch out for it, and stress that the representation is not the number. (I mean, unless you want to talk about equivalence classes, which seems not the best idea.) And then when you get to complex numbers, if they actually understood that point, they may well ask why it is that in the complex numbers we can identify the representation with the number! I mean, this is a good question, but it makes your job a little harder if you have to have an answer ready. 🙂

        • Tab Atkins says:

          I got my information from the pop math book “Negative Math”. It’s possible the book was wrong, of course. ^_^

        • Tab Atkins says:

          @Sniffnoy: The idea is to more or less teach the split-complex numbers, but at the end reveal that j was actually -1 all along (rather than the split unit). The intention would be to teach that the weird structure isn’t something impossibly weird, which is one objection I got from people learning it the first time. It’s an *awkward* way to talk about negative numbers, but it’s understandable.

          The point is to hopefully establish some bridging between “normal” numbers and the complex numbers, since this is usually the first time people have ever encountered number-like things that aren’t the traditional numbers they were taught by parents or elementary school.

        • Douglas Knight says:

          Tab, how about a page number?

        • Sniffnoy says:

          I really don’t think that’s a good idea.

          Problem #1:
          “OK, let’s say we have this number j, which squares to 1–”
          “So, it’s 1 or it’s -1.”
          “Well, OK, but let’s say we don’t know that…”

          Since you want to eventually say j=-1, you can’t say, “Well, suppose that somehow it wasn’t”. The whole time now, they’re going to be thinking of j not as an abstraction but as an unknown — it’s 1 or it’s -1 but you don’t know which. All this talking about j is going to seem pointless; why can’t we just say which it is already? It’s not like you’re introducing any new numbers here!

          Problem #2:
          Let’s suppose you don’t commit so heavily to the j=-1 idea, and allow it to develop more like split-complex numbers. Now you’re in a crazy world where a degree n polynomial can have more than n roots, and where there are things other than zero you can’t divide by. I mean, it’s not that crazy to a mathematician, but to new students? Hoo boy. You may have trouble getting them to accept after this that in the settings they’re familiar with, yes, a degree n polynomial really does have at most n roots.

          Simply put, split-complex numbers are going to mesh even less well with their intuitions for “numbers” than complex numbers will, and may mislead them later. You want them to think of complex numbers as just another sort of number, but you also want them to think of split-complex numbers as just another sort of number, and split-complex numbers I think are just too different from what they’re used to thinking of as “numbers”.

          (And if you go all the way with split-complex numbers — though I realize that’s not your actual suggestion — there’s also the problem that students at this point almost certainly don’t yet know that there’s no real unified notion of “number”, and that there are different systems of numbers, that can be considered on their own, as opposed to there being one big final thing of “all numbers”. So they’re going to be confused about how complex and split-complex numbers fit together. Explaining that they don’t is going to be difficult.)

          Your idea is half one thing, half another thing, and I don’t think it forms anything sensible. And the focus on the polynomial x^2-1 is… why? What is the relevance of it? If you want to introduce j=-1, do it as I suggested — suppose that you only know about nonnegative reals, and want to add this new number j, which has j+1=0, and now you have negative numbers as well. Doing so a.) captures what’s actually important about -1 and negative numbers (that it’s the additive inverse of 1, and that they give you additive inverse more generally; not that it squares to 1, 1 already has that property), b.) doesn’t lead them into settings that will just muddy their intuition, c.) is a situation that is actually analogous in that you are adjoining some new (abstract) thing that has some new property (“squares to 1” is not new if you already have 1 and -1) to solve an actual problem…

          That said, I’m thinking now that my earlier suggestion wasn’t really the best. I think now there is a better solution which matches much better with what you want.

          Namely, instead of saying “pretend we don’t know about negative numbers”, say “pretend we don’t know about irrational numbers”. Then you introduce a j with j^2=2. That’s going to be much closer analogue to the introduction of the complex numbers — you get a field; you’re introducing something new; etc. And unlike my “pretend you don’t know about negative numbers” suggestion above, this one doesn’t have uniqueness problems. And it also has the property that — like what you wanted, with the split-complex-numbers-or-sort-of, the algebraic manipulations involved are very close to what you’d do with complex numbers, it’s just j^2=2 instead of i^2=-1. And then at the end you can say, well, we know that in fact there is such a j, it’s the square root of 2! And now we can do similar formal manipulations with complex numbers, except we have -1 instead of 2 and real numbers instead of rational numbers.

          I think that’s distinctly an improvement over both what you suggested and what I earlier suggested.

        • Tab Atkins says:

          @Douglas Knight: Sorry, I don’t own the book any longer. Cleaned out most of my book shelves when I switched over to ebooks, and didn’t reacquire that book in epub form.

          @Sniffnoy: The focus on “x^2 – 1” is because that’s the definition of imaginary numbers. I’ve always been under the impression that “i^2 = -1” is more canonical/correct to say than “i = sqrt(-1)” (though both are fine to say casually).

          You’re still slightly missing my point – it’s meant to be just a rhetorical trick to help bridging. You pretend you’re teaching the complex numbers, then at the end reveal “Hey, that complicated stuff I just taught you? It’s not complicated at all – it’s just negative numbers, but talked about in a somewhat roundabout way. Now, if we just add a single negative sign, then what you’ve just learned also applies to the complex numbers.”

          The aim, hopefully, is to break down the “why are we learning this useless complicated crap?” barrier that most people throw up when they first learn about complex numbers, by showing that they aren’t complicated by the analogy with negative numbers.

          I’m not a math teacher, though I’ve done small amounts of teaching otherwise. This might not actually work. But if I were put in front of a math class, I’d give it a try.

        • Sniffnoy says:

          The focus on “x^2 – 1″ is because that’s the definition of imaginary numbers.

          Er, complex numbers come from x^2+1, not x^2-1. My point is, just changing the sign from +1 to -1 does not necessarily make a good analogue. Using x^2-2 would be better, if you pretend you don’t know about irrational numbers.

          I’ve always been under the impression that “i^2 = -1″ is more canonical/correct to say than “i = sqrt(-1)” (though both are fine to say casually).

          A true statement, but what’s the relevance here?

          You’re still slightly missing my point – it’s meant to be just a rhetorical trick to help bridging. You pretend you’re teaching the complex numbers, then at the end reveal “Hey, that complicated stuff I just taught you? It’s not complicated at all – it’s just negative numbers, but talked about in a somewhat roundabout way. Now, if we just add a single negative sign, then what you’ve just learned also applies to the complex numbers.”

          Except it isn’t. You are simply wrong about that being “negative numbers talked about in a roundabout way”. Firstly, j^2=1 does not uniquely specify j=-1; as I’ve been saying, j could also be 1. Is 1+2j equal to -1, or is it 3? This isn’t a way of talking about negative numbers at all!

          Secondly, you can’t introduce negative numbers as a more complicated thing if you already have negative numbers. If you want to build up negative numbers from something simpler, great! If you want to build up negative numbers from a system of numbers that already includes them, you are doing something that makes no sense. If you don’t start with “Let’s pretend we don’t know about negative numbers”, then anything you do regarding a “roundabout way of representing negative numbers” is simply pointless.

          (And, once again, the key feature of negative numbers is that they provide additive inverses to the positive numbers, not what they square to. And, as I mentioned above, it doesn’t uniquely specify them.)

          The aim, hopefully, is to break down the “why are we learning this useless complicated crap?” barrier that most people throw up when they first learn about complex numbers, by showing that they aren’t complicated by the analogy with negative numbers.

          You are proposing breaking down the barrier of “Why are we learning things that are complicated and unnecessary?” by introducing something that is more complicated and more unnecessary. Well, OK — it isn’t more complicated (since it’s not like you’re actually talking about split-complex numbers). It’s just more unnecessarily complicated.

          What you are suggesting fails at the introduction. The point of complex numbers is that they do things real numbers cannot. Let’s imagine a (heavily compressed) version of how complex numbers could be introduced…

          “So, complex numbers! In the real numbers, -1 doesn’t have a square root. But suppose it did have a square root! Let’s call it i; it’s some new type of number, not a real number. A complex number will be a number of the form x+iy, where x and y are real numbers.” (Again, obviously this is heavily compressed.)

          Now, let’s analogize that:
          “So, complex numbers! In the real numbers…” — what? What problem are you solving? You are replacing something that may seem unnecessary by something that is very obviously unnecessary.
          “But suppose we did have a number that squared to 1!” — Huh? We already have such numbers. We call them 1 and -1.
          “Let’s call it j. It isn’t some new type of number, it’s a real number.” — Then why are we talking about it? You started off saying you were going to introduce a new type of number. Now you’re not. Which is it? Until you get to this new type of number, you’re wasting my time.
          “A complex number will be a number of the form x+jy, where x and y are real numbers.” — There’s already a name for numbers of that form. They’re called “real numbers”. Any real number can be written in that form. You are not telling me anything substantial and new here, you are just presenting overcomplicated ways to talk about things I already know.”

          This is, start to finish, just a poorly thought-out and ill-informed idea. I say “poorly thought out” because you don’t seem to have considered such basic issues as “Why would students care about this more than they would complex numbers?” (If they have any sense, they’ll care about it less.) Or “How do I get them to go along with the idea that this is a new type of number when it’s plainly not?” I say “ill-informed”, because if you knew more mathematics, you would not only have recognized the problems here, but also thought of a closer analogue; at the least, you’d know how to actually adjoin -1 to a system that doesn’t have it.

          If you want an analogue of C that a.) acts similarly in terms of the algebra they have to do and will help them get used to that, b.) actually builds a new number system on top of an old one, doing something the old one can’t, c.) gets them used to the idea of introducing some new thing and treating it abstractly, while d.) also allowing them to think of that new thing concretely because it’s something they already know exists in the real numbers, thus sparing them for now worries like “What the hell is an imaginary number, really?”, and e.) doesn’t run into problems of “you have to make sure to distinguish the number from the representation” as well as f.) doesn’t run into any craziness like polynomials having more roots than their degree or being unable to divide (which I realize are not actually part of your proposal but are within spitting distance of it), I strongly recommend my example of Q(√2). (At least, if they’re familiar with the notion of “rational number” and that √2 is irrational. Otherwise… maybe go with adjoining -1 as I described it? :-/ I like that one a lot less.)

          Simply put, your proposal sacrifices a lot of essential points just to achieve a.) and d.) above, while not even doing all the things you claim it does (e.g. it will seem more unnecessary, not less). I really don’t think you’ve thought this through and I really don’t think you know what you’re doing here.

        • Sniffnoy says:

          Ugh — my apologies about the bad formatting in the comment above. Since it’s too late to edit it, I’m going to report it and hope that Scott deletes it. Here it is with correct formatting:

          The focus on “x^2 – 1″ is because that’s the definition of imaginary numbers.

          Er, complex numbers come from x^2+1, not x^2-1. My point is, just changing the sign from +1 to -1 does not necessarily make a good analogue. Using x^2-2 would be better, if you pretend you don’t know about irrational numbers.

          I’ve always been under the impression that “i^2 = -1″ is more canonical/correct to say than “i = sqrt(-1)” (though both are fine to say casually).

          A true statement, but what’s the relevance here?

          You’re still slightly missing my point – it’s meant to be just a rhetorical trick to help bridging. You pretend you’re teaching the complex numbers, then at the end reveal “Hey, that complicated stuff I just taught you? It’s not complicated at all – it’s just negative numbers, but talked about in a somewhat roundabout way. Now, if we just add a single negative sign, then what you’ve just learned also applies to the complex numbers.”

          Except it isn’t. You are simply wrong about that being “negative numbers talked about in a roundabout way”. Firstly, j^2=1 does not uniquely specify j=-1; as I’ve been saying, j could also be 1. Is 1+2j equal to -1, or is it 3? This isn’t a way of talking about negative numbers at all!

          Secondly, you can’t introduce negative numbers as a more complicated thing if you already have negative numbers. If you want to build up negative numbers from something simpler, great! If you want to build up negative numbers from a system of numbers that already includes them, you are doing something that makes no sense. If you don’t start with “Let’s pretend we don’t know about negative numbers”, then anything you do regarding a “roundabout way of representing negative numbers” is simply pointless.

          (And, once again, the key feature of negative numbers is that they provide additive inverses to the positive numbers, not what they square to. And, as I mentioned above, it doesn’t uniquely specify them.)

          The aim, hopefully, is to break down the “why are we learning this useless complicated crap?” barrier that most people throw up when they first learn about complex numbers, by showing that they aren’t complicated by the analogy with negative numbers.

          You are proposing breaking down the barrier of “Why are we learning things that are complicated and unnecessary?” by introducing something that is more complicated and more unnecessary. Well, OK — it isn’t more complicated (since it’s not like you’re actually talking about split-complex numbers). It’s just more unnecessarily complicated.

          What you are suggesting fails at the introduction. The point of complex numbers is that they do things real numbers cannot. Let’s imagine a (heavily compressed) version of how complex numbers could be introduced…

          “So, complex numbers! In the real numbers, -1 doesn’t have a square root. But suppose it did have a square root! Let’s call it i; it’s some new type of number, not a real number. A complex number will be a number of the form x+iy, where x and y are real numbers.” (Again, obviously this is heavily compressed.)

          Now, let’s analogize that:
          “So, complex numbers! In the real numbers…” — what? What problem are you solving? You are replacing something that may seem unnecessary by something that is very obviously unnecessary.
          “But suppose we did have a number that squared to 1!” — Huh? We already have such numbers. We call them 1 and -1.
          “Let’s call it j. It isn’t some new type of number, it’s a real number.” — Then why are we talking about it? You started off saying you were going to introduce a new type of number. Now you’re not. Which is it? Until you get to this new type of number, you’re wasting my time.
          “A complex number will be a number of the form x+jy, where x and y are real numbers.” — There’s already a name for numbers of that form. They’re called “real numbers”. Any real number can be written in that form. You are not telling me anything substantial and new here, you are just presenting overcomplicated ways to talk about things I already know.”

          This is, start to finish, just a poorly thought-out and ill-informed idea. I say “poorly thought out” because you don’t seem to have considered such basic issues as “Why would students care about this more than they would complex numbers?” (If they have any sense, they’ll care about it less.) Or “How do I get them to go along with the idea that this is a new type of number when it’s plainly not?” I say “ill-informed”, because if you knew more mathematics, you would not only have recognized the problems here, but also thought of a closer analogue; at the least, you’d know how to actually adjoin -1 to a system that doesn’t have it.

          If you want an analogue of C that a.) acts similarly in terms of the algebra they have to do and will help them get used to that, b.) actually builds a new number system on top of an old one, doing something the old one can’t, c.) gets them used to the idea of introducing some new thing and treating it abstractly, while d.) also allowing them to think of that new thing concretely because it’s something they already know exists in the real numbers, thus sparing them for now worries like “What the hell is an imaginary number, really?”, and e.) doesn’t run into problems of “you have to make sure to distinguish the number from the representation” as well as f.) doesn’t run into any craziness like polynomials having more roots than their degree or being unable to divide (which I realize are not actually part of your proposal but are within spitting distance of it), I strongly recommend my example of Q(√2) (or any other real quadratic field, if you prefer). (At least, if they’re familiar with the notion of “rational number” and that √2 is irrational. Otherwise… maybe go with adjoining -1 as I described it? :-/ I like that one a lot less.)

          Simply put, your proposal sacrifices a lot of essential points just to achieve a.) and d.) above, while not even doing all the things you claim it does (e.g. it will seem more unnecessary, not less). I really don’t think you’ve thought this through and I really don’t think you know what you’re doing here.

        • Tab Atkins says:

          Er, complex numbers come from x^2+1, not x^2-1.

          Sigh, yes. Assume I mistyped.

          A true statement, but what’s the relevance here?

          You specifically asked why I was focusing on that.

          Except it isn’t. You are simply wrong about that being “negative numbers talked about in a roundabout way”. Firstly, j^2=1 does not uniquely specify j=-1; as I’ve been saying, j could also be 1. Is 1+2j equal to -1, or is it 3? This isn’t a way of talking about negative numbers at all!

          i^2 = -1 doesn’t uniquely specify the imaginary unit either. Obviously there are two solutions to any square root.

          There appears to be a fundamental miscommunication between us as to what I’m trying to express, and I don’t think it’s worth the effort to correct it. As I said, I think this would be an interesting experiment to see if it could get kids past the initial “this is stupid and complicated” barrier, by bridging with their existing knowledge of negative numbers. Maybe it wouldn’t work, of course, but who knows?

          Let’s imagine a (heavily compressed) version of how complex numbers could be introduced…

          This is why I’m pretty sure we’re fundamentally miscommunicating – the example that you provide after this quoted section is precisely the thing that I think causes most kids to tune out, because there’s doesn’t seem to be a point to introducing new mathematical baggage.

  9. Brian Potter says:

    I don’t think the risk is sneaking in connotations, I think the risk is that crystallizing a pattern makes people stop thinking about it.

    While it may not apply to the LW set, I’d be willing to bet most people asked to define “witch hunt”, “social justice”, or “political correctness” would have an amazing amount of trouble doing it. People seem to mostly learn concepts by association, and often never learn or think about their actual definitions. This seems to be the whole point of Mysterious Answers to Mysterious Questions, not to mention tabooing words and a whole other host of rationality exercises – it’s simply far too easy to use words without considering their moving parts.

    So, my guess is that situations where crystallizing a pattern is a net negative are where the concept is simple enough that it can be wielded effectively without a proper definition, so that making it easier to communicate is only a somewhat modest gain, but still complex enough that you’re likely to use the word without thinking through the definition if you’re not careful.

    • Sniffnoy says:

      People seem to mostly learn concepts by association, and often never learn or think about their actual definitions.

      Well, outside of technical fields, one typically can’t say there is an “actual definition”! But you do have a point here — seeing the same label applied to the same sets of situations, two people may consider different features to be salient and thus generalize it differently. And then be confused when they try to talk to each other because they don’t mean the same thing.

      As always, reading Eliezer’s “guide to words” can be a helpful inoculation here. But, as always, you really need everyone in the discussion to be able to think like that. And even then it can take a long time to notice the problem, if it’s subtle enough. I’ve certainly had discussions about the notion of “romantic love” where it eventually turned out that me and the person I was talking to seemed to mean rather different things by this; it was very confusing. But it can get much worse when one side refuses to really get into breaking down their terms.

      But I suppose this is straying from the original point — I’m not sure that any of this is so much a reason to avoid crystallizing patterns, so much as a reason to be clear about just what patterns it is that other people are talking about (which may require them to be willing to seriously break down their terms) and just what patterns it is that you are crystallizing.

    • Benquo says:

      I think the risk is that crystallizing a pattern makes people stop thinking about it.

      What makes you think that sort of person ever started?

      Or less flippantly, what’s an example where you’ve observed someone who used to think about something stop prematurely because they formed a crystallized concept?

    • houseboatonstyx says:

      Lewis talked about such risks, at length, in essay #14 BLUSPELS AND FLALANSFERES: A SEMANTIC NIGHTMARE, in
      http://pibbethel.no-ip.org/biblioteca/wp-content/uploads/2013/12/C.S.-Lewis-Collected-Articles-and-Essays-C.S.-Lewis.rtf

    • Ken Arromdee says:

      I’d be willing to bet most people asked to define “witch hunt”, “social justice”, or “political correctness” would have an amazing amount of trouble doing it.

      If you asked someone to define “chair” or worse “apple”, I think they’d have an incredibly difficult time doing it.

  10. Thomas Eliot says:

    The first thing I thought of is if the crystallized idea makes a sort of false dichotomy appear. Or trichotomy, in Lewis’ case. Beyond the liar/lunatic/Lord possibilitys, there is the chance that Jesus never actually said he was the son of God, and that was made up after his death so as to make his message more important. If you think using the trilemma, you won’t conceive of that idea.

    • houseboatonstyx says:

      Some people discuss that idea of Lewis’s by adding terms such as: “Liar, Lunatic, Lord, Lama, or Legend.”

      One could save a lot of time by stating their opinion as “Lunatic, Lama, and Legend” or whatever.

      • Sniffnoy says:

        Lama?

        • Doug S. says:

          The one L lama, he’s a priest
          The two L llama, he’s a beast
          And I will bet my silk pyjama
          There isn’t any three L lllama.

          — O. Nash, to which a fire chief replied that occasionally his department responded to something like a “three L lllama.”

        • Sniffnoy says:

          I should perhaps clarify — I didn’t mean “What is a lama?”, but rather “What exactly is meant by the ‘lama’ fork in this case?”

        • Tab Atkins says:

          The “lama” fork is the “Jesus never claimed to be son of god, just a religious teacher; people made that up later to make him sound more important” thing that Thomas Eliot was talking about at the start of this thread.

  11. Somnicule says:

    Cheers for the link to spoon theory, I hadn’t seen that one before and it is pretty useful

    • Sid says:

      Thanks for cheering for spoon theory. I missed the link when I read the article. After reading your comment I went back. Spoon theory is very valuable.

      • houseboatonstyx says:

        Yes. But like “poltical correctness”, its usage may have changed somewhat from its origin. “Political correctness”, I’ve heard, began as a serious thing in a Communist country. Now it names a group of expressions, words, taboos, etc.

        The essay on “spoon theory” seems to be about a limited amount of energy to be used throughout a day. I’ve seen it used in fora to mean something different and imo more useful: how many projects or responsibilities the speaker feels ready to undertake, how much zie can have ‘on her plate’ this week or this semester.

        • And I’ve seen expansions of spoon theory discouraged because it dilutes the original intent of making it clear that some people have much less energy or physical capacity than most, and even those limited resources may disappear without warning.

        • Brian says:

          The story I heard was that “political correctness” originated as a term of self-criticism in leftist circles, by analogy with the habit in mid-century Communist nations of splitting things between political and temporal circles (i.e. “political officer”) but not after any specific Communist term. Then the right picked up on it and started using it as a straightforward pejorative, and the original use died out soon after.

        • Multiheaded says:

          From what I hear, “political correctness” began as a translation of the Chinese expression with Maoist groups in the US, and had a very literal, emotionally neutral meaning in internal criticism: how correct something is at adhering to or extrapolating the party line. But it did begin to be mocked in leftist circles early on, as a symbol of rigidity and left-authoritarianism.

          The modern “anti-authoritarian” Right generally adopted a whole lot of things from the 1960s New Left, and that’s how political correctness ended up over there, I guess.

        • houseboatonstyx says:

          @Nancy Lebovitz

          Apparently ‘spoons’ has already taken on a life of its own, at least on LJ. What you call the ‘diluted’ meaning has been spreading, communicated by context, much wider than the original story has. I see an internal linguistic factor here, and an external.

          Internally, the metaphor does not actually fit the originator’s point. Spoons are countable, but the originator’s meaning was an uncountable: energy, strength, endurance.

          Externally, we already had plenty of words for the uncountables: energy, endurance, strength, functionality, etc. We lacked any crystallizing term for “Having the physical energy, time, resources — and mental energy to take on and complete an additional task or project.” How many different projects a person can keep track of, is countable, at least in theory. Even here I’m having to say ‘projects’ because there is no word to crystallize the sort of … mental actions … that “enough spoons” implies.

  12. St. Rev says:

    A crystallized pattern can go bad if it identifies, glues together, things that are importantly different, or identifies coherent things with incoherent things. An good example of the latter would be ‘qualia’, per Dennett’s exegesis.

    • Scott Alexander says:

      Can you explain the last part further? (“No” is an acceptable answer)

      • St. Rev says:

        I strongly recommend reading Dennett’s “alternative neurosurgery” discussion; the summary at Wikipedia isn’t too bad.

        To summarize the summary, or at least my gloss on Dennett’s argument: the qualia of redness, ‘what it’s like to experience redness’, is a broken concept, because it sneaks in an extra variable that can’t ever be accessed–and thus can be argued in circles forever. There is no meaningful quasi-Platonic ‘experience of redness’ that goes beyond comparisons between ‘this experience I have now’ and other experiences–either my own memories (this looks like other things I have called red in the past), or of others (Bob also calls this thing red).

        Because the concept of qualia conflates universally accessible sensory experiences with a fundamentally incoherent abstract construction, it is bad and should go away.

        • Said Achmiz says:

          “Qualia Disqualified”, which is chapter 12 in Dennett’s Consciousness Explained, is imo, the best thing to read to get his position on this.

        • St. Rev says:

          Can’t give an HTML link to a whole book! Or maybe you can nowadays, dunno. Obviously everybody should read the original Dennett, but that doesn’t mean everybody will.

      • johnw says:

        Your description of the neo-reactionary term “demotism” ting together unrelated political systems, in a similar way to tying together mice and elephants, sounds like the sort of thing they mean.

        Tying together things into a false category leads to making false, but potentially persuasive claims about the shared features of that category.

  13. suntzuanime says:

    A “crystalized pattern” seems more like an instinctive mental response to a particular pattern. I haven’t actually read Thinking Fast and Slow, but presumably it comes about when you’ve solved a particular interpretation problem enough times that future interpretation can be handled Fast instead of Slow. So once you’ve seen enough witch hunts, you aren’t surprised when people bring out the kindling, and you don’t have to puzzle out what they’re doing with those scales and that duck, you just say, “aha! a witch hunt! I know those!”

    The problem comes when you get bad data in your cache. This can come about accidentally, but it seems like it tends to happen maliciously or quasi-maliciously more often. Your cache ends up bad because someone poisoned it. This is what is at work with “International Jewry” – probably you did not come to the conclusion of a massive international Jewish conspiracy to dominate world affairs on your own, by direct observation of many world affairs that Jews conspired to dominate. Rather, someone made persuasive arguments and got you to accept “International Jewry” as a meaningful lens through which to perceive the world.

    So I would say that you will know crystallized patterns by their fruits. How much more sense does the world make given an understanding of “Schelling Points”, “countersignalling”, “political correctness”, “entryism”, “romantic love”, “patriarchy”, etc.? You can judge them by the same standards you’d judge a scientific theory: does the crystallized pattern “gravity” make the motions of the planets make more sense?

    • Scott Alexander says:

      Doesn’t work. To a Nazi, “international Jewry” explains everything. I mean, otherwise the German defeat in the First World War wouldn’t make any sense!

      • suntzuanime says:

        When you say “doesn’t work” what you mean is “doesn’t instantly solve all your epistemic problems”. If you’ve got a bad interpretation of WWI, yes, anything that relies on that interpretation is going to end up poisoned too. Believing correct things is, like, really hard? I’m sorry to be the one to break it to you.

        The question is, given a bunch of false data pointing to an international Jewish conspiracy, is it incorrect to infer the existence of an international Jewish conspiracy? And the answer seems to me to be, of course not.

  14. a person says:

    This is a weird article coming from you because I feel like you argued sort of the opposite position in the past. Diseased thinking? The meditation against conceptual superweapons? Like, don’t pattern-match too much, once you give something a name it means you can stop thinking about it, words contain hidden inferences?

  15. Scott says:

    Crystallizing a pattern is bad if you give the crystal to someone who hasn’t noticed or understood the pattern. They tend to then use that crystal-word to talk about non-pattern things, or even worse, fail to understand the use of the pattern to begin with. A certain type of very effective probabilistic reasoning using conditionals got crystallized as Bayesian, and then some learn the crystal ‘Bayesian’ without realising it is useful because when an uncertain belief encounters new evidence, the ‘Bayesian’ crystal reminds us to investigate prior and posterior probabilities (among other things, of course). So our ignorant crystal-bearer encounters a rare situation they would have been able to fumble through with their existing tools, but they instead happily say ‘Bayes!’ and hold up their pretty crystal.

    This is technically already covered by your disclaimer, but I think it’s a genuine risk, since patterns are usually taught crystal-first.

    (Can you tell how in love I am with the imagery?)

  16. Alejandro says:

    How about “original sin” as a pattern that Christians crystallize wrongly? It is inarguable that humans are often wrong and bad in different ways, and persist in their bad ways even knowing at some level that they are bad, et cetera; but crystallizing these and other facts into the concept “original sin” feels like great progress for a convert to Christianity, while being actually (we atheists would say) a step back in terms of progressing towards explaining and solving them.

    • Scott Alexander says:

      Hmmmm…this is the best example I’ve seen so far and I’m not sure what to do with it.

      Original sin is a really powerful metaphor and does seem to capture something important about the human condition. I can see what you might mean about it prematurely crystallizing something that could fit better somewhere else, but I’m not sure atheism has a great replacement for it; it mostly just acknowledges some of the component concepts but doesn’t bring up the pattern as much.

      I think a big part of the problem is that the name “original sin” is closely linked to the whole Garden of Eden story, so it might not be just a concept, but rather a concept + explanation package where I disagree with the explanation.

      This is especially true insofar as original sin interlocks with pieces like “and you need Jesus so you can be cleansed from it” or “and it can send you to Hell”.

      Insofar as it’s just crystallizing that humans have some really really hard to surmount possibly insurmountable flaws, it’s hard for me to find objection to it.

      But now we might just be playing some game where I’m interpreting the problems with it as external to the crystallization process and you’re interpreting the problems with it as internal to that process.

      • Alejandro says:

        I think one could summarize the situation thusly. Whenever there is a pattern crystallization (that many intelligent people adopt–clause to avoid crackpot counterexamples) then this is at least potentially useful in that there is a “real pattern in the world” we can talk about now succinctly. However, in many cases it is also true that:

        a) the pattern is only superficial and has no interesting deep explanation, to find an explanation one would have to break it down in components and analyze each separately, and having a single word for it might make that more difficult to realize (cf. your article on “diseased thinking”),

        b) the specific way the pattern is crystallized may smuggle in extra assumptions about its causes, explanations and solutions, that go beyond the mere recognition of the pattern and might very well be false (like the ones you point out about original sin).

        Because of these two reasons, one may be justifiably be skeptical about “crystallizations” which seem great and useful to others.

        Another good historical example might be Aristotelian philosophy. Reading it without any modern scientific knowledge, it seems like an impressive crystallization of hugely general and useful patterns. We can now analyze and explain any occurrence in terms of its formal, material, efficient and final cause! We can now describe everything as form and matter coming together in substance! Act and potency! Essential and accidental properties! No wonder the Scholastics were fascinated when Aristotle was rediscovered in Europe in the 1100s and started building more and more philosophy and theology on top of it, culminating in St. Thomas’ Summae.

        And yet, from the point of view of modern science and philosophy (with the exception of Feser and a handful of other diehards), Aristotle’s philosophy is just a crystallization of patterns of speech used in common sense descriptions of nature, that actively harms scientific and philosophical progress in the many, many cases where our common sense descriptions have mistaken hidden assumptions.

      • Nornagest says:

        I was raised mostly secular (though my family’s historically Catholic), but I found the Fall of Man/Original Sin memeplex absolutely fascinating for a long while. I think I was thinking of it in vague evopsych terms (though I wouldn’t have used that label), with the garden as the ancestral environment and the fruit of knowledge representing the agricultural transition and related memes; I still find that analogy pretty compelling, although the holes in it are a little more apparent to me now.

  17. “he 1%” strikes me as a concept which has crystalized recently, and has some problems. Are all the people at the top 1% (of income or of property ownership) making things worse by owning what they’ve got? Is 1% the right cut-off?

    I thought at least some people had a concept for romantic love long before it was idealized– it’s just that people used to think it was a madness.

    • Scott Alexander says:

      I don’t get what “the 1%” has over just saying “the rich”. It must have something or people wouldn’t use it so much, but I don’t get what it is (especially since it’s very vulnerable to criticism where someone holds up some upper middle class individual who has worked very hard to get where they are and doesn’t seem to be living extravagantly and points out that they are technically part of “the 1%”).

      My best guess is that people got immune to hearing stuff about “the rich” and built up filters to tone it out, and this is an attempt to make it sound new again.

      • stubydoo says:

        I think part of the reason why they chose to use “the 1%” crystal is that it gets an extra persuasive kick by pretending to be based on math. You see that also with its right-wing doppelganger “the 47%”. In both cases the people wielding the crystal are woefully misinformed about who it targets, but even if you point that out to them, and get them to understand it, they still prefer to keep using the crystal.

      • ozymandias says:

        Americans generally underestimate the amount of income inequality in our society. “The rich” is pretty susceptible to that– people might assume they are ten percent of society and own some reasonable percentage of the wealth. “The top one percent earned 20% of the income!” is clearer and more outrageous.

      • Andrew G. says:

        “The 0.1%” would have been more accurate but much less catchy.

        Thing is, if you just say “the rich”, people will do things like make counterarguments comparing, say, the top and bottom quintiles of the income or wealth distribution, and then you have to go back and say “hey, being in the top quintile doesn’t make you rich enough to matter”. “The 1%” at least establishes a lower bound.

        In the sense usually used, “The 1%” really refers to something more like, “The people in the top of the wealth distribution starting somewhere from 0.5% to 0.1%, who have the kind of money that you cannot generally accumulate via a top-end professional income outside the financial sector”.

      • Max says:

        I think it is an implicit reference to income inequality – the top 1% earning 20% of income and holding 35% of wealth. Pretty useful reminder (in both “crystalling” and political senses of the world).

        • houseboatonstyx says:

          The term must have spread far from its origin, if its plain meaning has been reduced to an implicit reference.

        • moridinamael says:

          This is it. This is the whole basis of how crystallizing works and why we do it – “chunking” in the learning literature. Taking complex information and automatically compressing it, and manipulating the compressed version, a mental paintbrush handle. It’s a pointer to this concept. I’m running out of metaphors here.

          Anyway, it’s not like somebody spontaneously decided to start using “the 1%” one day for no reason.

      • Anthony says:

        As political propaganda, “The 1%” has the added kick not just of being mathematical as stubydoo points out, but of automatically setting up the opponents of “The 1%” as representing The Will of The People, since they claim to represent 99% of the people.

        I think this discussion shows two different failure modes for crystallized concepts: one of just being factually wrong – the pattern doesn’t actually exist, like some uses of “rape culture” or “institutional racism”, or the person who crystallized the concept has snuck in a connotation which is not true, and uses the term to propagate the connotation, like “The 1%” or “International Jewry”.

      • Tab Atkins says:

        That one person is also technically part of “the rich”, so I’m not sure why “the 1%” is any worse by that argument.

        1% isn’t any precise mathematical cut-off, but it’s a good round number, and somewhere around the right point that separate “really well-off” from “actually rich”. There is a very substantial difference there, because wealth distribution follows a pretty harsh power law, and 1% is roughly the point where the graph “goes vertical”. The top 5% (excluding the 1%) have average incomes that are small-integer multiples of the national average, or even the lower 20%, but at around 1% the multiplier reaches 100x and higher.

        Regarding “are the 1% making things worse by owning what they’ve got”, it depends on exactly what you’re asking. In a sense, yes – there is only a finite amount of money at any given time, and by concentrating more of it at the top, there’s less to go around at the bottom. There’s also the fact that in real-money terms the poor have either stagnated or gotten poorer in the last few decades, while the rich have definitely gotten richer, and the “unfairness” of this difference is frustrating to many. There’s also also the fact that some of the most notorious “1%ers” are those who got rich specifically by exploiting the poor, such as encouraging much riskier loans, and by generally being douchebags, such as knowingly packaging those loans together into even riskier vehicles and lying about the risk, so the moral outrage adds to the general sense of anger at the class.

  18. houseboatonstyx says:

    A good crystallization from Lewis is “chronological snobbery”: an assumption that the modern version of something is always better than a version from a past century. “Believ[ing] this, not because it is true, but for some other reason” can be argued with, but it describes an attitude worth describing. I’ll probably remember more by tomorrow.

  19. suntzuanime says:

    The correct way to approach this problem seems to me to be, what are some crystallized patterns that you formerly used but which you had to abandon because they led you into error? And what was the source of that error, what was the problem with the pattern? This will give us examples of how crystallization goes wrong from the inside, instead of pointing to nazis and feminazis and saying “well they obviously must be doing something wrong.”

    • malpollyon says:

      Feminazi is a terrible crystal, it’s pretty much a metastasized form of the Worst Argument it the Universe.

      • suntzuanime says:

        You mean they’re technically National Socialists but they lack the negative properties we ordinarily associate with Nazis? Somehow I think you are mistaken.

  20. Eli says:

    The question is whether your “crystallized patterns” that you’ve turned into words actually cleave reality at its joints and constrain your expectations.

    For example: “international Jewry”. It’s easy to be a naif and notice that, hey, there are quite a lot of organizations that self-identify as Jewish organizations and seem to exert some political pressure on what they identify as the interests of Israel. Oh Lord, we say, the antisemites were right! However, if you instead ask, what events are ruled out by the idea that “international Jewry exerts pressure for Israel”, and ask the people talking about that idea, you find out that the answer is: plumb nothing. Everything somehow winds up sounding to them like a Jewish plot, up to and including violent attacks on Jews or Israel.

    And then they tell you about the “kosher tax”, notice you’re trying not to giggle, and rightfully resolve that “international Jewry exerts pressure on behalf of Israel” is an incoherent idea.

  21. Nate Gabriel says:

    When I was growing up, I was taught that any time someone argues against Christianity, their stated arguments aren’t the real reason they’re not Christians. They’re just refusing to accept it. I don’t think there was a neat two-word name for “all non-Christian interlocutors are using motivated cognition,” (Maybe the God-shaped vacuum?) but it’s a concept that we’d pattern-match people into. And it would often be “obvious in retrospect” because of course nobody could be convinced by those arguments. Close enough to count as a crystallized pattern?

    (It also might be from Lewis. I know he said that it used to be true of him, but I don’t know if the claim that it’s true of all non-Christians is his fault or not.)

    • houseboatonstyx says:

      Lewis said there are quite reasonable grounds for not being a Christian; it is a legitimate difference of opinion, to be respected and met on its own grounds. Not that his own material always did that; much of it was meeting different audiences on different grounds.

      I don’t think there was a neat two-word name for “all non-Christian interlocutors are using motivated cognition,” [….]

      Actually Lewis did have a crystallization that covers that and many other instances: “Bulverism”. Wikipedia has an entry for it, with the relevant quotes.

    • Roman Davis says:

      There is really only one reason I don’t believe in God (requirement of extraordinary evidence, consult your local FSM, RTP or IPU) and many, many arguments against God’s existence. As a probabilistic heuristic, it ain’t so bad.

      It’s easy to find out that people’s arguments don’t always match their real objections. This is largely because people’s real objections are naked emotional reactions, but this isn’t always the case.

    • Gilbert says:

      There are, of course, also atheist versions of that kind of theory, cristallized even, with very similar plausibility.

  22. Nathan Cook says:

    Crystallized patterns form the building blocks of the explicit parts of one’s ideology. The danger is that ideology can be performed quite effectively without an actual mapping between the patterns and physical reality, or even any particular mental referent – it becomes a word-game. I believe this is in essence the same phenomena Orwell referred to as duckspeak in Nineteen Eighty-Four; it appears, as a mental faculty, to be a human universal, no doubt highly adaptive. Nevertheless, it’s not a truth-producing process, whatever building blocks one uses.

    Does this mean that adopting a term induces duckspeak? For Less Wrong derived terms, one would hope the opposite to be the case – that a sentence including the phrase “fully general counterargument” would be less likely to be false than one without. On the other hand “international Jewry” pattern-matches almost of its own accord to a statement acceptable in antisemitic ideology. As for “political correctness”, I find it hard to conceive of anyone using it who did not want to claim, from the position of being non-ideological, that a certain stance was a) fashioned by left-wing ideology, b) corrosive to freedom and c) objectively incorrect. As I do not think that any of these criteria imply the others, and disavowing one’s own ideology is about as far from epistemic honesty as it gets, I see no reason for a phrase which makes me sound like a political naïf and encapsulates three disparate accusations. Plus, on the pattern-matching side, I grew up in Britain. For me, the only words which could ever follow “political correctness” are “gone mad”.

    • Roman Davis says:

      That’s true now, but I don’t think it always was. Whenever I try to think of instances of things that are PC verses not PC, it basically comes down to good manners, and making fun of PC basically amounts to saying that strict observance of good manners isn’t very fun.

  23. Bruno Coelho says:

    A (bad)crystallized pattern seems like a term for debunked statistics.

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  25. moridinamael says:

    Hey, this reminds me quite a bit of my bad concepts repository.

  26. Drew Hardies says:

    I think you raise excellent points. But, I think there is a danger (or at least a potential blindspot). I’d worry about ‘crystals’ in thing space that look like this: (worksafe, pyrite cubes sharing corners)

    ‘Political Correctness’ is a single crystal. Roughly, it’s shifts in language that are adopted to recognize (or avoid criticism by) a newly-vocal subgroup. At the same time, it’s the sort of concept that lends itself to a number of natural sub-divisions.

    For instance, groups can demand changes as a simple show of power. Demands for certain ‘Trigger Warning’ come off as exercises in tribal-marking.

    In other cases, groups can ask people to stop using their identity as an insult. Take ‘fruit’ when used as an insult.

    I suspect we can all thing of examples that fall into the overlapping region.

    Concept crystilization could do something similar. If someone learned the term ‘political correctness’ they could mentally emphasize the connecteness of the clusters.

    This could lead to problems like the ones described in your article on BINGO. The fact that Political Correctness seems like A Single Thing makes it tempting to over-generalize.

  27. Shmi Nux says:

    Is there a reason you used “crystallized patterns” instead of the more standard “abstraction”?

  28. Here’s a concept I’ve crystallized for myself: motivation-mongering. It’s the claim that you know the disreputable reasons people have for disagreeing with you.

  29. Xzibit says:

    Yo dawg, I’d really like you to stop using the term “Crystallized Patterns”. It only serves to dismiss ideas you don’t agree with as some catagorized phenomenon, rather than judging the idea on its own merits. The idea of a crystallized pattern maps a large set of of real life ideas onto a single signle pattern, and it is a-priori entirely unclear if an idea is a crystallized pattern or not. Labeling, or not labeling the idea like this serves no purpose.

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