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dynomight's avatar

P.S. Please no one say anything mean about PendingKetchup. (The original comment was in a quiet forum that it seemed rude to link to.)

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Nick Bailey's avatar

An irony here is I did take some small social subtext from your article, regardless of whether I should have or not, which was just that the concept of heritability is so abstract and difficult to measure it couldn’t possibly give credence to any social ideology using it.

Next is for some people’s point ITT that you should’ve mentioned the eugenic origins of the concept. There’s no denying the history of genetics/statistics/eugenics are initimately tied up. I’ve been reading a lot of Fisher and stuff about him recently and seen arguments in published papers and lectures about whether Fisher was firstly interested in “the science” or “the eugenics”. As far as I can tell, Fisher was a dude with multiple interests, many connected. Fisher thought up stat stuff, and he thought up eugenic stuff, and he knowingly applied stat stuff to eugenic stuff. I still think it’d be a simplification to say “Fisher invented X model for X eugenic purpose”, that’s like expecting a novelist to give a singular reason why they wrote a novel. Apply across the board for any idea and it should be clear that that idea that heritability was created solely for eugenics (saying it was part is more reasonable) becomes nonsense, and isn’t worth pointing out in every context the concept is raised (though certainly some contexts!).

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Nick Bailey's avatar

Yeah I’ve definitely given it a few looks; never with full comprehension yet but step by step improvement! Definitely runs the stats -> genetics -> eugenics gamut. The last just cause it discusses human height, not in the ideological sense we’d say today.

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dynomight's avatar

My impression is that eugenics in the modern sense isn't really a significant part of this paper, so I don't think it's correct to say variance was invented "for" eugenics.

Though the words "eugenics" does appear in that paper twice, and Fisher himself did indeed support policies that would be called eugenics in the modern sense. So there are adjacent statements that are probably true. For example, I guess "variance was invented by a eugenicist" is correct.

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Nick Bailey's avatar

I agree that a statement like “variance was invented for eugenics” isn’t meaningful, maybe I didn’t convey that well in my first comment. Even in the extreme hypothetical scenario that he immediately applied variance for some eugenic purpose in the first sentence variance is introduced we’d still have to consider that a final paper is a product of editing where people deliberately make connections they didn’t when starting their work. He almost certainly did not consciously think something like “Boy, if I had a formula describing variation around the mean, I’d be able to apply it to human traits I personally want the government to incentivize!” lol.

But I’d also be slow to say “variance was invented by a eugenicist” is the only connection we could make. I recently finished The Genetical Theory of Natural Selection, which is no easy read but a lot easier than the 1918 paper overal. He clearly considered there to be a throughline from Mendelian genetics and natural selection, to his concept of fitness and the Fundamental Theorem of Natural Selection, to what we’d now call the fertility crisis, to his policy suggestions, which are ironically really tame compared to a lot of what you can find on the internet these days. The book is a product of years of work spread over multiple papers, I don’t think he began his career thinking “one day I’ll create stats concepts for eugenics!” but he certainly felt it all was connected by the time the book was out.

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dynomight's avatar

Very well said!

Personally, I find the question of how one we should mention Fisher's sins quite difficult. (Wait a second—I wrote a whole post about that. https://dynomight.net/bad/) When I take someone like, say, Heidegger, I feel fine about people always mentioning that he was a Nazi every time he appears. But it seems impossible to do this with Fisher, even if you thought his sins were equally bad, because his ideas are simply everywhere. (What parts of science don't use variance or p-values or heritability or the modern synthesis?)

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Nick Bailey's avatar

I’ll definitely give that post a read! Yeah, for sure it’s not necessary to criticize Fisher every time a p-value is used or whatever. And, not trying to pick excessively on specific people, but I’ve seen an example of

something like that in the wild that stuck with me (https://www.pinkerite.com/2025/04/what-happened-to-adam-rutherford-part-3.html?m=1). In that post she criticizes a paper for citing multiple hereditarians and racists and Fisher’s on her list. A quick look-see at the paper in question and it’s just citing Fisher 1918 to make a point about how increasing sample size affects effect size.

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dynomight's avatar

Have you ever looked at the paper where variance was actually defined? It's extremely dense reading, but I think you can get a picture of the kind of context you're talking about: http://digamoo.free.fr/fisher1919.pdf

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Cameron Sours's avatar

Eugenics is Definitely Evil.

If I keep talking after this ... that probably feels bad.

Because if something is Evil, you don't need to think about it anymore, and you probably Should Not think about it anymore.

Anyway ... something like eugenics will keep coming around because it SEEMS like it might make sense, or at least it SEEMS like something like it might make sense.

Even "Definitely Evil" topics deserve some discussion, but that type of discussion is frankly impossible on the internet because of the Heckler's Veto/Troll's Veto.

Most of the people involved can participate in a discussion with a certain shared understanding - like "eugenics is evil, but it's probably worth discussing why so many otherwise smart people bought into it, because world events seem to take place on a 80 year cycle and it's been about 80 years ... " - but it only takes one troll to blow you up on social media.

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Mark Neyer's avatar

Love the example you’re setting here.

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Michael's avatar

Great stuff, tbh. Some scattered thoughts on your overall ouevre:

1. (on heritability) Since the definition of heritability is bad and unintuitive, have you considered new definitions? My friend suggests using mutual information with I(X; Y) / H(Y) or something to that effect. We didn't think about this much. It has a lot more of the properties you want + I think in the taylor expansion it might reduce to the usual definition

2. This feels like a classic case of what you called a 'heat mirage' argument

2. (a potential point to consider) There's this tendency to assume moral arguments work in an entirely logical way (the 'entirely' is load-bearing), but they don't. In particular, I think transitivity often gets tricky because most moral statements are pretty fuzzy so 'doing logic' becomes a fraught affair. The more transitivity steps, the less seriously I take a moral argument, because every time you go from A -> B you're really going from 80% A -> 60% B, saying 'A implies B', and then treating B as if it's 100%. Just slapping the 'B' label on something that's only mostly B is a pretty major approximation. KendingPetchup made some really reasonable logical steps, but every time he adds a label, they're basically rounding their moral statement. E.g. You discuss heritability, which was invented by a sketchy guy, so you are sketchy. College is attained -> people can attain college -> you're ignoring people who can't. Etc, etc. I see lots of people do stuff like this, and once I saw it, it was hard to unsee. The case most people are familiar with is the classic 'is this person evil or not because they talked to a guy who platformed an evil person', but in fact this occurs in almost any moral debate I see online.

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Douglas Knight's avatar

Most of the original article applies just as much to mutual information as covariance.

Maybe broad sense heritability is arbitrary, but narrow sense heritability is fundamental because it appears in the breeder's equation. If you're an animal breeder or eugenicist, you need variance. Also, it is relevant to natural selection. It gives a quantitative description of natural selection relevant to questions like what trade-offs lead to schizophrenia because we can measure the fitness cost of schizophrenia and the narrow sense heritability. Also, the breeder's equation says that recessive alleles cannot evolve. Since blue eyes exist (and came after brown eyes), they must have been selected for some advantage in the heterozygous state, which cannot be the visible eye color.

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dynomight's avatar

I think what what we usually want from heritability is to know what impact different potential interventions might have. I thiiiiink the best way to formalize "trait X is heritable" would be something like "trait is highly predictable from genes and there are no known interventions that would have significant impact on that trait". I'm doubtful that information-theoretic quantities like mutual information (I guess I(trait; genes)) would capture that, because those are still observational statistics.

I think I'd argue that PendingKetchup is innocent of heat-miraging. Whatever our disagreements, they were fair in that they never said I was "wrong", but rather that they got a bad vibe and that they felt I should have stressed Fisher's history with eugenics, etc. Then they said they suspected various motivations from me. Those weren't true, but they stated them as suspicions, and they were concrete! (This is why I like their comment—it follows many of the patterns for the ideal ways of arguing.)

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Michael's avatar

Statistics aren't magic, of course, and don't replace good experiments :) But I would counter with, clearly, 'the people' want a metric for heritability -- why not improve the one that exists? At the very least, a metric like the one I suggest it would make heritability <= 1 always and give us a vague idea of where to look based on extant datasets. Certainly better than calculating covariances! It's not going to replace actually testing hypotheses in the field, but no statistic will, or should try do so. In fact, in many situations, I suspect that "trait is highly predictable from genes and there are no known interventions that would have significant impact on that trait" will best be quantified in exactly this way.

Maybe I'm just making shit up, though...

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dynomight's avatar

At first glance, I(TRAIT; GENES) / H(TRAIT) seems like quite a nice measure. That's basically "what fraction of the randomness in TRAIT is explained by GENES". The main issue I see is that estimating it from small datasets (e.g. twin studies) would be really hard due to the curse of dimensionality. H(TRAIT) might not be *too* bad, but the mutual information seems very difficult. You could assume everything is Gaussian, but then you're basically back to covariances.

(A more minor issue is that these kinds of information theoretic measures just care about "information" rather than "magnitudes".)

In principle, I'd be quite interested to see those numbers, but I think getting them would be really hard. At the end of the day, I think the reason the original definition has endured so long is that it's very hard to estimate almost anything else more interesting. This might still be a useful exercise for the sake of thinking about the limitations of the definition, though.

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Fang's avatar
Sep 11Edited

So, I read the whole of the original blogpost and was fully convinced that your motivations for making the post actually *was* entirely to point out out how weird, convoluted, and unintuitive the math of heritability was. It was clear from how you talked about it in the post, and was totally in line with the rest of your blog (which I would describe as "delightfully autistic", if you would take that as a complement).

I'll be honest. After reading this lengthy, meandering comment response, I came away *less* convinced that the original post was just about the math, and that you have no ulterior motives. (Perhaps because this post uses some of the same rhetorical tricks as another blogger I like - whose blog "is a ten" - but intentionally talks *around* the poorly-kept secret of his positive opinion of eugenics). Presumably, hearing that this post has had the exact opposite effect of its intent for at least some of your audience is useful information for you (to cheekily quote, "I imagine you’ll be interested to learn that you were incorrect").

Also, the fact(?) that variance *and* heritability were invented by card-carrying eugenicists is interesting information that I wish had been included in the sidebar of the original post. It really contextualizes the whole thing, and obscuring it reduces my model of reality: there's a huge difference between "heritability is weird, convoluted, and unintuitive, and eugenicists use it to justify their ideas, but sometimes science uses weird math/measurements and that's value neutral" and "heritability is weird, convoluted, and unintuitive, and eugenicists *invented* it to justify their ideas, which maybe explains the former".

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dynomight's avatar

> I'll be honest. After reading this lengthy, meandering comment response, I came away *less* convinced that the original post was just about the math, and that you have no ulterior motives.

I appreciate your honesty, but to be clear... this is exactly what I expect! That's sort of the point I was trying to make. Even if you truly just want to explain heritability, SAYING "I just want to explain heritability" just makes people question your motivations.

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Sol Hando's avatar

Now that the dynomight.net/ketchup URL has finally been occupied, does this mean the long awaited dynomight ketchup review has been canceled?

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dynomight's avatar

My favorite ketchup is plain american mustard.

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Sol Hando's avatar

I’ll hold out hope for dynomight.net/mustard then.

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dynomight's avatar

> dear internet

>

> listen up

> the best mustard

> is regular plain american mustard

> all other mustard

> is worse

> whole grain mustard

> worse

> honey mustard

> worse

> dijon mustard

> worse

> strong irish mustard

> worst-est

> don't forget to like and subscribe

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Alexander Kaplan's avatar

Have you tried squeezing the different mustards from varying heights to see how prolonged exposure to air during the drop affects taste? This will probably be messier than the tea experiment; still, I eagerly await the results.

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Ben's avatar

I didn't read the initial heritability post until now because at the time I was bored by the discourse on the topic, but after reading *this* post, I went back and read the original article. And wow, I'm actually impressed by how much I misunderstood heritability, and how much I learned about the concept (metric?) in a single blog post.

Perhaps this is spoiling your future post on the missing heritability debate, but I think your whole discussion of how heritability is limited to "typical" environments, and isn't as useful as a metric outside of that domain, probably serves as a really compelling explanation for the gap between twin and GWAS studies? My uneducated impression is that the "perfect" genetic concordance between twins would kind of break down assumptions around "typical" genetic similarities, which have to engage with some randomness, inter-gene interactions, and feedback loops thereof.

On a tangent, I think you interacted with (and perhaps blocked?) Isaac King in a previous comment section, but it reminded me a lot of his blog post on p-values: https://outsidetheasylum.blog/an-actually-correct-explanation-of-p-values/

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dynomight's avatar

Thanks. Not sure I will actually write that future post on missing heritability, though! I looked into it a bit and there's all sorts of weirdness with GWAS and with twin studies and I don't know what to think. The three basic possibilities are:

(1) Narrow heritability (GWAS) and broad heritability (twin studies) just are very different

(2) GWAS studies are underestimating narrow heritability

(3) Twin studies are overestimating broad heritability.

All of these seem possible to me.

(Regarding Isaac, I *temporarily* banned him, but it was either for a week or a month and he's welcome back. (My beef count remains at one.) I only skimmed the post, but I like the quiz format to test things at the end.)

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Mr T.'s avatar

FWIW I will greatly appreciate a post on missing heritability

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Doctor Hammer's avatar

As a former educator and current trainer, it always has bothered me that educate is a transitive verb, something that is done to people as opposed to something they participate in. Every time someone says “I wasn’t trained on that” I have to ask whether the training was unavailable or they just didn’t take it (or didn’t t pay attention). You can’t make someone become educated, they have to put in effort as well, a two sided effort.

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dynomight's avatar

Interesting. What do you make of the theory that a big part of the role of educators is to provide a sort of "supportive environment" with structures that make it easier for people to educate themselves? (Personally, this is my best guess as for why MOOCS haven't had more impact.)

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Doctor Hammer's avatar

I would say off the cuff, never having fully formalized this, that there is sort of a triangle between supportive environment / active instruction/ student effort, with motivation being important. Motivation can come from the teacher, either by being genuinely interesting or through “learn or fail”, but mostly needs to come from the student. Enough motivation in the student and you can get away with just a good environment (eg YouTube), but a co plate lack of motivation and the best teacher and environment won’t help.

What the teacher really helps with is often telling people what they should be motivated to learn. What is important to understand, what matters vs what is trivia, etc. Especially with kids that is critical because many important things are not obviously interesting or require a lot of start up energy before they get useful.

The other important thing is feedback, testing whether you actually understand something or not. I think often the teacher is needed to provide that, as even if you can try stuff and see whether it worked you often won’t be able to fully understand why you failed, or how much better it could be. MOOC kind of fail there I think because outside of technical stuff you can do yourself there is no good feedback.

So. I guess all that is to say that the supportive environment is just a part. It needs to be sufficient, but students need direction and motivation, and often both come from the teacher to a fair extent. Motivation and effort are necessary on the part of the student as well. I think attainment is a good way (or at least not a bad way) to think of education as after a certain level at least it really is a question of what the student puts in. You can’t teach someone something they don’t want to know to the level of understanding.

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lin's avatar

I’ve always thought this was just obvious. Like, I think I’m a relatively motivated and intellectually curious person—I have the PhD and everything to prove it—and I’ve never managed to learn a damned thing outside a social environment explicitly designed for learning, featuring at least a human mentor or supportive human peers, if not both. Like that’s what sends the signal to my brain that the thing is worth being intellectually curious about; otherwise why should it bother? So the stuff people say about MOOCs—that their lack of uptake proves that nobody cares about learning or education is all signaling or whatever—is insane and offensive to me. Being an intrinsically social creature isn’t a goddamn character flaw.

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Greg G's avatar

I'm not sure I understand. Are you literally saying you never learned anything without a mentor or supportive peers? What about making a recipe or how to use an app or whether a product you're considering buying should meet your needs? We're all learning stuff all the time, and in my experience I don't need a social setting for every instance of that.

I'm worried that this puts too little accountability on an individual's agency and too much on society. In my opinion, if someone puts a course they have invested massive amounts of time into in front of you, and all you have to do is complete it, then failing to complete it does provide some information on your motivation to do so. Maybe the social setting isn't ideal, but some people complete the course and others don't. Everything else being equal, I'm comfortable saying the people who completed it were more motivated / cared more.

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lin's avatar

Sure, I’m exaggerating; there’s a difference between a recipe and the contents of an advanced math course. My point is that the fact that I had to pay tuition for a real school in order to learn math, and could not have done the same sitting alone in the library, is not because I didn’t care about learning and only wanted the degree on my resume, or something.

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Doctor Hammer's avatar

I would phrase it as having a group to do the thing with and an instructor to guide you creates a lot of motivation. I am a lot better about exercising if it is a class or group that I go to routinely and I will feel guilty for missing, for example. For a lot of people social activities are inherently motivating.

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