| > Sounds like people mostly living in different bubbles? What do they know about the world? Well, they do know something about math — in particular that it requires a certain "attitude", something that no-one told them about in school and they felt they only discovered by chance. Starting from Descartes and his famous "method", continuing with Newton, Einstein, Grothendieck all these guys insisted that they were special because of this "attitude" and not because of what people call "intelligence". They viewed intelligence as a by-product of their method, not the other way around. They even wrote books as an attempt to share this method (which is quite hard to achieve, for reasons I explain in my book.) Why do you bring "kids who fail in school" and "start selling drugs" into this conversation? What does it have to do with whether math genius is driven by genetics or idiosyncratic cognitive development? And why would a mathematician be disqualified from discussing the specifics of math just because they're not hanging out with lost kids? Are you better qualified? Did you sequence the DNA of those kids and identified the genes responsible for their learning difficulties? >> [they] don't think it's because of their genes > Do you think someone would tell you, if he/she thought it was? Well, an example I know quite well is mine. I was certainly "gifted" in math — something like in the top 1% of my generation, but not much above and definitely nowhere near the IMO gold medallists whom I met early in my studies. A number of random events happened to me, including the chance discovery of certain ways to mentally engage with mathematical objects. This propelled me onto an entirely different trajectory, and I ended up solving tough conjectures & publishing in Inventiones & Annals of Math (an entirely different planet from the top 1% I started from) My relative position wrt my peer group went through a series of well-delineated spikes from 17yo (when I started as an undergrad) to 35yo (when I quit academia), associated with specific methodological & psychological breakthroughs. I'm pretty confident that my genes stayed the same during this entire period. And as to why I was initially "gifted", I do have some very plausible non-genetic factors that might be the explanation. I don't claim this proves anything. But I see no reason why my account should be disqualified on the grounds that I'm good at math. Usually, competency in one domain is presumed to make you a bit more qualified than the random person on the internet when it comes to explaining how this domain operates. Why should math be the exception? |
| > they do know something about math ... that it requires a certain "attitude" Of course. That does not mean that intelligence doesn't play a (big) role. > Starting from Descartes and his famous "method", continuing with Newton, Einstein, Grothendieck all these guys insisted that they were special because of this "attitude" and not because of what people call "intelligence" That doesn't make sense. Back when they were active, intelligence, IQ tests and the heritability of intelligence hadn't been well studied. They didn't have enough information, like we do today: https://en.wikipedia.org/wiki/Heritability_of_IQ#Estimates
"Various studies have estimated the heritability of IQ to be between 0.7 and 0.8 in adults and 0.45 in childhood in the United States." And, evolution and genetics weren't these peolpe's domains. Does it make sense to assume they were authorities in genetics and inheritance, because were good at maths and physics? Sometimes they were wrong about their own domains. Einstein did say "Genius is 1% talent and 99% hard work" (I can understand how it makes sense from his own perspective, although he didn't know enough about this animal species, to say that). But he also said "God does not play dice" and was wrong about his own domain. > Why do you bring "kids who fail in school" and "start selling drugs" into this conversation? It was an example showing that the researchers live in bubbles. That they're forming their believes about humans, based on small skewed samples of people. There's billions of people out there vastly different from themselves, whom they would have left out, if thinking about about others' abilities to learn. In fact, now it seems to me that you too live in a bubble, I hope you don't mind. > Usually, competency in one domain is presumed to make you a bit more qualified than the random person on the internet when it comes to explaining how this domain operates. 1) Maths and 2) evolution, DNA, genetics, intelligence, learning and inheritability are not the same domains. Anyway, best wishes with the book and I hope it'll be helpful to people who want to study mathematics. |
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| ▲ | tptacek 3 days ago | parent | next [-] | | Current estimates of the "heritability" of intelligence are far, far lower than "0.7 or 0.8"; they're probably below 0.1, and that's before digging into what "heritability" means, which is not generally what people think it does. I'd guess the person you're responding to has thought more carefully about this issue than the median HN commenter has. | | |
| ▲ | cutemonster 19 hours ago | parent [-] | | > Current estimates of the "heritability" of intelligence are far, far lower than "0.7 or 0.8"; they're probably below 0.1 Sources please, if you have time? I tried to find something supporting what you wrote, but wasn't able to (this far). Instead I found this from 2015: Thinking positively: The genetics of high intelligence,
https://pmc.ncbi.nlm.nih.gov/articles/PMC4286575/ They've studied men in Sweden during 40 years. From the abstract: "We found that high intelligence is familial, heritable, and caused by the same genetic and environmental factors responsible for the normal distribution of intelligence." "... 360,000 sibling pairs and 9000 twin pairs from 3 million 18-year-old males with cognitive assessments administered as part of conscription to military service in Sweden between 1968 and 2010 ..." Looking at Figure 3, in that pager, about identical twins and non-identical (two-egg) twins -- I think that settles it for me. Seems they arrive at a bit above 0.4 as heritability. Yes that's less than 0.7 - 0.8 but I wouldn't say "far far lower", and more than 0.1. Also, they're 18 years old, not adults. It's been discussed at HN: https://news.ycombinator.com/item?id=10488998 > I'd guess the person you're responding to has thought more carefully about this issue than the median HN commenter has. Well, in his reply to me, he was sort of name dropping and appealing to (the wrong) authorities, didn't make a good impression on me. Plus writing about himself, but he's a single person. -- I would have preferred links to research on large numbers of people. > what "heritability" means, which is not generally what people think it does. That sounds interesting. Can I guess: You mean that people believe that heritability means how likely a trait is to get inherited from parent to child? When in fact it means: (https://en.wikipedia.org/wiki/Heritability)
"What is the proportion of the variation in a given trait within a population that is not explained by the environment or random chance?" | | |
| ▲ | tptacek 13 hours ago | parent [-] | | My sibling comment (unsuprisingly) goes into more depth and with more sourcing. The 0.4 result you've cited is from 2015, which is in the phlogiston era of this science given what we've learned since 2018. As he has aptly demonstrated: his authorities are sound, and he has thought carefully about this matter --- respectfully, far more than you seem to have. That's OK! We're just commenting on a message board. I wouldn't even bring it up, except that you've decided to make his grasp on the subject a topic of debate. | | |
| ▲ | cutemonster 10 hours ago | parent [-] | | > he has thought carefully about this matter --- respectfully, far more than you seem to have He was wrong in his guesses about me and what I've read, and wrong about the quote too (see sibling comment). > is from 2015 ... what we've learned since 2018 You're saying the graph is somehow invalid, because of newer GWAS related research? The blog he links to looks biased to me. Are there two camps that don't get along: looking at DNA (GWAS), vs looking at twin studies etc ... yes seems so. I'll reply to both of you in another comment | | |
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| ▲ | davidbessis 2 days ago | parent | prev [-] | | Dear cutemonster, I know this reply may not suffice to convince you, but unfortunately I won't be able to argue forever. Did you ever consider the possibility that you might be the one living in a bubble? FYI, the concept of innate talent predated IQ tests and twin studies by many millenia. Two of the authors I'm citing in my book (Descartes and Grothendieck) believed that innate talent existed and they both declared they would have loved to be naturally gifted like these or these people they knew. You're declaring that these incredibly smart people were wrong about their own domains, which is a pretty bold claim to make. What do you have in support of this claim? A fake Einstein quote? It's a sad fact of life that most quotes attributed to Einstein are fabricated. Next time, please check "The Ultimate Quotable Einstein", compiled by Alice Calaprice. This may come as a shock to you, but Google page 1 isn't always a reliable resource. Nor is Wikipedia, even though it's quite often correct. As it happens, there's a pretty large "Heritability of IQ" bubble on the internet. It's active and vocal, but it's also quite weak scientifically — the page you're citing is a typical symptom, and it absolutely doesn't reflect the current scientific knowledge. The IQ heritability claims that you're citing are based on twin studies and they have taken in serious beating in the past decade, especially in light of GWAS. It's true that a number of people have been fooled by twin studies, most notably Steven Pinker, in Chapter 19 of the Blank Slate (did you read it?) You see, Pinker is a linguist and apparently he isn't mathematically equipped to fully comprehend the intrinsic limitations of Bouchard's approach. Did you read Bouchard's 1990 paper on twins reared apart? Do you find it convincing? Are you aware that even The Bell Curve's Charles Murray thinks that this approach, abundantly cited by Pinker, is structurally flawed? Are you aware of the fundamental instability of IQ estimates based on twins reared together? Aren't you concerned that even a mild violation of Equal Environment Assumption, plugged into Falconer's equation, would drastically reduce the estimates? If you don't understand what I'm talking about, if you've never read the authors and the primary research I'm citing, then it's quite likely that you're the one living in a social media bubble. If you're interesting in learning more about the actual science of IQ heritability, I recommend using Sasha Gusev's Substack as an entry point:
https://theinfinitesimal.substack.com/p/comments-on-no-intel... Feel free to also subscribe to my own Substack, where I plan to cover these topics in the coming months:
https://davidbessis.substack.com All the best,
David. | | |
| ▲ | cutemonster 10 hours ago | parent | next [-] | | > Did you ever consider the possibility that you might be the one living in a bubble? You're wrong about that, but you couldn't have know. I've lived in far more different places with more different people, than most people you've met. > innate talent predated IQ tests and twin studies by many millenia That's why I wrote it hadn't been well studied, not that it hadn't been studied at all. > You're declaring that Of course not. I'm not the source. > incredibly smart people were wrong about their own domains, which is a pretty bold claim to make. What do you have in support of this claim? A fake Einstein quote? That's from a letter Einstein wrote 1926 to Bohr. He wrote in German, that quote is a paraphrase in English. Look here: https://en.wikipedia.org/wiki/Bohr%E2%80%93Einstein_debates, And, about him being mistaken, quoting that article: "As mentioned above, Einstein's position underwent significant modifications over the course of the years. In the first stage, Einstein refused to accept quantum indeterminism [...]" -- indicating that, at some points, he had the wrong beliefs, right. Here's the quote explained further: https://hsm.stackexchange.com/questions/5937/why-did-einstei... > It's true that a number of people have been fooled by twin studies, most notably Steven Pinker, in Chapter 19 of the Blank Slate (did you read it?) > You see, Pinker ... Bouchard's 1990 ... The Bell Curve's Charles Murray ... thinks ... structurally flawed No, didn't read that book. Continuing in another comment. | | |
| ▲ | davidbessis 7 hours ago | parent [-] | | I was alluding to the quote relevant to the current debate: "Genius is 1% talent and 99% hard work" — which you incorrectly attributed to Einstein. |
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| ▲ | tptacek a day ago | parent | prev [-] | | Some of the stuff on Gusev's substack is pretty startling, and I highly recommend it. Thank you for taking the time to comment here! | | |
| ▲ | cutemonster 10 hours ago | parent [-] | | > > twin studies and they have taken in serious beating in the past decade, especially in light of GWAS. Here's a twin study from 2015, newer than the books (Clean Slate etc) and papers you (David) mentioned. "Thinking positively: The genetics of high intelligence"
https://pmc.ncbi.nlm.nih.gov/articles/PMC4286575/ Figure 3 indicates that intelligence is pretty strongly inherited, and they arrive at 0.44. Now you're saying that that doesn't matter because of GWAS? Sounds a bit hand-wavy to me. > > Sasha Gusev's Substack as an entry point: https://theinfinitesimal.substack.com Blog post looks biased. So there's a controversy: https://en.wikipedia.org/wiki/Missing_heritability_problem And there's two camps: https://www.clearerthinking.org/post/the-missing-heritabilit... (I like that article!) And the two of you (Davind and Thomas) seem to be in the "The DNA Proponents" camp. The other is "The Twin Study Advocates" camp. I guess now I'm in "The middle ground" camp, no longer in the "Twin Study Advocates". Thanks for that. Maybe I'll check back in 10 years later and see what has happened. | | |
| ▲ | tptacek 10 hours ago | parent | next [-] | | The "warring camps" framing is very overstated. Greenberg, who doesn't practice in this space, believes it to be a vital concern, but giants in the twin-study practitioner field freely cite GWAS results, including the EA studies. A 2015 twin study result is basically a citation to the phlogiston era of polygenic population-wide genetic surveys. Heritability estimates of that vintage basically define away indirect genetic effects, which subsequent work appears to have very clearly established; the work now is on characterizing and bounding it, not asking whether it's real. "Blog post looks biased" is not a good way to address this unless you actually practice in the space, like the author does, and are in conversation with other practitioners in the space, like the author is. You find lots of --- let's generally call them pop science writers --- knee-jerk responding to the new rounds of heritability numbers, but those same authors often wrote excitedly about how GWAS results would bolster their priors in the years before the results were published. It's worth paying attention to the backgrounds of the people writing about this stuff! I substantially rewrote this comment, which was sprawling; the original is preserved here: https://gist.github.com/tqbf/b118ec9f9e69e0f3f61003c152d0d44... | |
| ▲ | davidbessis 7 hours ago | parent | prev [-] | | Great to see you're making progress! A few posts ago you were alluding to heritability in the 0.7-0.8 range, as a reason to dismiss the writings of Einstein, Newton, Descartes and Grothendieck. Now you're at 0.44. If you discount for a mild EEA violation correction, you'd easily get to 0.3 or below — a figure which I personally find believable. Just FYI, I don't belong to any "camp". These aren't camps but techniques and models. Intra-family GWAS provide underestimated lower bounds, twin studies provide wildly overestimated upper bounds. I don't care about the exact value, as long at it doesn't serve as a distraction from the (much more interesting!) story of how one can develop one's ability for mathematics. In any case, IQ is a pretty boring construct, especially on the higher end where it's clearly uncalibrated. And it's a deep misunderstanding of mathematics to overestimate the role of "computational ability / short term memory / whatever" vs the particular psychological attitude and mental actions that are key to becoming better at math. Now that the smoke screen has evaporated, can we please return to the main topic? |
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