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pressures that are going on in hominids is in terms of essentially outsmarting the other apes for the sake of having a larger genetic load for the next generation. So chimpanzees undoubtedly spend so much of their time trying to model each other and outsmart each other so that they can form coalitions and ultimately make more babies, which is very disheartening, but that seems to be agree with experience to a large extent. And yeah, I mean, I think that has quite a bit of explanatory power. But then finally, the theory that I actually find the most compelling as kind of explaining most of what we consider to be kind of like general intelligence is actually intelligence as kind of a peacock's tail display. Essentially is less having to do with manipulating the physical world around it and more as a way of signaling genetic fitness. So that would be kind of this book I would recommend by Jeffrey Miller, The Mating Mind, where, yeah, I think it's very compelling. He talks about how language and math and visualization ability, all sorts of things can be ultimately explained to a large extent as costly displays of genetic fitness. And as an aside, a funny thing is that across the species, you will see that to a large extent, actually the things that are prized as kind of, oh, wow, this is very attractive, you know, very sexually desirable, are things that are like very wasteful, that they don't immediately actually contribute to genetic fitness, it's more kind of like showing that you're so fit that you can afford to waste all those resources. So a lot of adaptations are in a sense like tinkering with different kinds of waste, which is crazy. I mean, like there's some birds, yeah, they form these huge nests, most of it is waste and it gets appreciated. And yeah, the most wasteful is the one that gets selected. Is it an insane? But yeah, I mean, that happens across the evolutionary kingdom. And to show you kind of like a display of waste, not only do I have one of these books, I have two of these books, I have three of these books, I also have the original book of all of these mating ones. I used to have more, but I gave some of them away. But yeah, anyway, that's just a practical joke. Don't take it too seriously. Anyway, that's kind of like some evolutionary background for like, why are we smart? And yeah, I mean, Jeffrey Miller would say that there's a lot of empirical evidence that, for example, vocabulary size is considered sexually attractive. You can do studies on this and it's true. It actually is the case. And also you will find that people are more incentivized to kind of display their intelligence when there is mating opportunities available. And that's another fascinating kind of empirical research. I do believe it. I do think there's something

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text:
to that. Okay, so now let's get on to intelligence and its quantification, operationalization. And yeah, I mean, to a first approximation, a lot of people will say that intelligence comes down to something like IQ or what, in a more politically correct environment, you might describe as general mental ability, GMA. And I think there's definitely something to this. I mean, it is very much the case, I believe that, you know, in order to advance a scientific field, you probably do require a threshold amount of kind of, you know, general mental ability in these, you know, very classical sense. And I don't believe it is the case that you can get away without it. In my experience, great conversations, especially kind of like the more technical stuff of, you know, whatever it may be like data science, you know, math, or, for example, even philosophy, to get there, you don't really need kind of like a super, super, you know, savant, you know, who scores like 180 in IQ tests, but probably scoring 120, 130 is kind of a prerequisite for a lot of conversations to make sense of a lot of conversations. And, yeah, I mean, frankly, I do think that communities of people who, on average, have like a much higher IQ than other communities, they inhabit other worlds, because their mental representations have a level of complexity that is just qualitatively different. And I mean, that's just something to kind of like be aware of. And I don't want to say, actually, you know, that, you know, IQ is the most important trait at all. You know, that's definitely not the case. But it is essential, and also it is quite correlated with health. I mean, like one way of tracking your overall health is to actually conduct IQ tests on yourself over time, because those skills, you know, will be correlated with things such as your cardiovascular health, or your respiratory health. Like those things are all entangled. So I would not, you know, dismiss them. And now, what is kind of like the theory behind this? Well, to our first approximation, I would say, intelligence, classical intelligence studies. I have like a couple books here. Okay, so this would be kind of archetypical, kind of like this kind of research on general mental ability and things like that. I don't necessarily, you know, endorse reading all the... It's not that insightful, actually, because it's very repetitive. Like, there's only a few key insights you actually need to know. But yeah, the first approximation, we're talking about statistical techniques that are called principal component analysis and factor analysis. And here's the thing. So, you may be very skeptical at first, that there is kind of like a unifying trait or unifying dimension that brings together all these disparate cognitive abilities. But if you essentially get a lot of people, like a ton of people to kind of like answer kind of like puzzles,

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text:
verbal puzzles, you know, visual, spatial puzzles, math puzzles, and so on. And you kind of like have... Let's see. You kind of have like the items here and the people here, you know, person A, person B, person C, and so on. You will have kind of this matrix. You see, you will have like matrix of item relative to person. And essentially, this is going to be kind of like a scatterplot in a high dimensional space, you know, where the dimensions are essentially, yeah, the items and, you know, the dots might represent the individuals. So if you take this and you apply what's called a principal component analysis, you will see that by a large extent, a lot of the variance in that space can be accounted for by a few set of dimensions. Now, it's not going to account for everything. I mean, like, for example, if one of the questions is, you know, what was in the TV last night? You know, okay, that's not going to really measure anything interesting because that is kind of like, okay, you either know it or you don't. And it's not correlated with, you know, a cognitive ability or something like that. So that, you know, piece of, you know, that particular item will show up as having just no loadings on the main dimensions that are identified by principal component analysis. And if you do this, I mean, to a first approximation, you will find that even if, you know, it is you who create the items, like you may be very skeptical, you know, something like this is real, but like, come on, you make a test, you know, make an interesting test with puzzles and such, don't like make them as culture fair as you want or whatever, then do a principal component analysis or factor analysis on it. And you will find these core dimensions. And if you do just one factor, which is like, you know, something that you can set on statistical analysis software, it will be this factor that is called a G, which is often described as general mental ability. If you ask for more factors, by and large, you will start to get things such as, oh, there's a general factor for mathematical ability. Oh, and there's another general factor that kind of includes all of the verbal items. And there's another factor that includes all of the kind of visual reasoning and pattern finding patterns. And you know, all of these are actually correlated, which is, yeah, I mean, ideally you would use this technique, which is called oblique factor analysis, which doesn't assume that the factors are completely uncorrelated with one another. So that's kind of a, just a technical aside. Now, I must admit though, factor analysis does have a lot of caveats. And if you're really clever about how you design the test, you could probably in a sense, like make it look like

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text:
one factor is much more prevalent than another. So if your test, for example, is like, you know, 999 questions about the movie Shrek and one question about like, you know, some like mathematical puzzle, yeah, if you do like, you know, factor analysis on that, you will have like the factor of like, you know, knowledge about the Shrek movie and you know, the mathematical ability factor will just not even show up. Okay. So that's like one caveat. The other thing is that you may in a sense find like a lot of like statistical artifacts, depending on how the question, what is the similarity between the questions. So you can kind of like create an artificial factor as well by adding a bunch of questions that are actually kind of the same question, just like phrased differently. And so how do you get out of this conundrum? Well, so if you just focus on that, if you don't kind of like do the test very, you know, cleverly, you might have those artifacts. And there's where essentially these other techniques, which are called structural equation modeling, which are essentially predictive in nature, it's kind of like, okay, like, I don't know if those factors matter. Let's say you did a, yeah, you did a test, 500 questions of Shrek the movie and 500 questions of, you know, math or something like that. Okay. You will have like those two factors up here. But if you then use those factors to predict, let's say your GPA at your college, you know, like what is your GPA in your, you know, physics major or something like that. Yeah, the Shrek movie may actually show us like zero correlation or like zero predictive capacity. And maybe the math one would show up as like, yeah, very highly predictive. So the really cool thing with like structural equation modeling is essentially it allows you to identify how these factors are related to one another in a causal fashion. All of these also is very related to what's called probabilistic graphical models. Look up the work of Judea Peril. There's ways of kind of inferring causality in networks of statistical correlations. It's actually super tricky. And you know, honestly, you probably need to, you know, invest, you know, five years in a PhD to like really know what this is doing and how to do it properly. But the beautiful thing is that you can, you know, in Python or in R you can import, you know, structural equation modeling or probabilistic graphical models and just, you know, play with it without like deeply understanding, okay, the message passing algorithms and you know, the, anyway, the mark of chains, all the ways in which all of these things are actually implemented. It doesn't matter. You can just use them. And in a sense, when you do that, yes, it does appear that a lot of like problem solving does come down to

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text:
kind of these core factors of, okay, math ability, visual ability, and verbal ability, and there's like sub factors, you know. Now there are kind of like further caveats here. And here actually I'm going to get into hopefully, I mean, it's like slightly polemical, but it's hopefully fun to think about this. So which is the recent meme. Well it's not recent, it's been like a year, but recent, you know, it broke out into kind of mainstream discourse, which is shape rotators versus, well, something that I consider kind of like a slur. So I'm going to say shape rotators versus wordsmiths, essentially people who are like very loaded in math ability or visual spatial ability, people who are very loaded on verbal ability. Now, intuitively you may say, Hey, but like, aren't you saying that all of these things are correlated? So, okay. Like if you kind of like do a scatterplot, you know, okay. Like this is a math and this is verbal. Okay. You see like for the most part, there's going to be a high correlation between the two and G factor as it were, is going to be, okay. Like what is the projection that you have into the line that goes through them? But it turns out, well, actually a couple of things. So first of all, yes, that is the correlation in the general population. Okay. But if you have a selection criteria where, for example, you take the sum of verbal and math and that is the thing you're selecting for, then all of a sudden the population of interest is going to be way over here. And therefore the, you know, the actual line, the correlation line will become negative. I hope you see what I mean. So this is related to what's called the Simpson's paradox in statistics. So essentially once you add a selection criteria, the correlation may turn from positive to negative. Is this relevant? The answer is yes. So if you go to like, for example, a very selective college, you know, let's say Stanford, MIT, whatever it may be, Harvard. Yeah. If there you learn that somebody is an extraordinarily brilliant, you know, novelist or writer, like a journalist, incredible writing, like, you know, nationally recognized poet or something like that, that will actually be evidence that they're probably not very good at math because for them to be so extreme in that distribution, once you have kind of like used this cutoff, it means that, yeah, they will probably be way over here, meaning that their math is probably not going to be that good. The other, so that's one reason why actually kind of a share rotators versus wordsmiths actually does kind of show up in real life. The other reason is as follow, which is to a large extent, if you go to a place that is even more extreme in kind of its selection of specialization for cognitive tasks, let's

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text:
say like a Silicon Valley startup where you have kind of a data science team over here, the managers, marketing, and let's say they're all incredibly competent. You know, you have like the person who's actually writing the white papers and things like that. All of a sudden the selection criteria is not going to be aligned like this. The selection criteria is going to be something even more skewed. It's going to be something like this, right? Because if that person is kind of like a machine learning researcher or something like that, you know, it might be that all you actually care about is that they are like way over here in kind of like the super advanced like math ability. And like maybe their verbal skills don't matter very much as, you know, Rune from Twitter says like they can, you know, make an incredible, you know, AutoCAD model in a couple of minutes, but you know, they confuse the two there in their emails and the responding to short sentences and things like that. So yeah, you will have that. And then you will have people who might be like extremely good at kind of like verbal ability and their quote unquote bullshitting capacities, extraordinary, but they might not necessarily have kind of the mathematical understanding to back it up. So all of a sudden you will have a, yeah, you will have a communication problem between these two. And you will need to some extent what I call soap molecules, which is okay, the verbal, you know, it's kind of like the super ultra nerdy, like mathy kids, you know, very, very incapable of kind of like typical normal social cognition. You know, you've got to have a manager that can interface with them successfully while also being able to translate what, you know, their skills and abilities and advantages are in a language that, yeah, the other clusters can understand. So ideally you will also have some kind of like connecting tissue here, which to some extent this might be the most rare people and harder to find and test for. Because yeah, I mean like they might not like excel at like either of the two, but you know, they're good enough to actually form a bridge. Okay. The other thing too is like, I mean, legitimately I do think that, you know, very highly intelligent mathy people sometimes, I mean, sometimes they're actually kind of oppressed. Why? Because they're not good at selling themselves. So actually what you may end up having is kind of like, yeah, I mean like the very verbal, you know, managers might be able to capture all of the value that these kids are generating without necessarily giving them the proper credit because they're able to frame the circumstance, frame what's going on in favorable terms, favorable terms, and they may not be able to do that. So that's something to watch out for. But there's a

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text:
further reason why this divide actually happens and why let's say humanities and STEM and you know, hard sciences, they don't, you know, why there are two cultures, why this is actually two clusters. There's another reason which is this thing that is called the Spearman law of diminishing returns, which is that essentially, yes, all of these different skills will be correlated highly, but they are like especially well correlated within kind of like normal ranges, let's say like between minus two and plus two standard deviations. When you get out of those normal ranges, they become less and less correlated. And that's kind of like a tricky thing because all of a sudden you have to understand that, yeah, there will be people who have kind of like very specialized hardware. They're like extremely brilliant in one particular cognitive domain, but they're not be like that brilliant in others. And like for a lot of people, that's kind of surprising, like if you don't know enough about kind of like classical intelligence research, you may leave under the impression that all of these things are just positively correlated and just kind of expect, yeah, this person is going to be like an overall well-rounded person because they're brilliant at math or something like that, which is absolutely not the case. Like when you go to the extremes of the distribution, you find, I don't want to be, it's not demeaning. I'm just saying like from a normal perspective, you're going to find very weird, atypical people who think and feel very different. Their cognitive style is highly specialized. Just a fact of life. Okay. Now an important criticism of all of these kind of like classical intelligence test theory and so on is something that I remember finding out early on, which was a lot of these tests, actually the way in which they analyze them, and I would say like factor analysis and principal component analysis have these assumptions inbuilt into them is that they assume that to a first approximation, the items are roughly of equal difficulty and that the underlying latent trait, which would be kind of like this latent trait of like overall intelligence or something like that, follows a Gaussian distribution. But that is not true at all. I mean, like that's one of the crazy things. So like, okay, like if you take, for example, the height of people in a classroom, if the classroom is not very large, let's say if it's like 50 people, yes, you will actually see to a first approximation, you know, that they will follow kind of like a Gaussian distribution. And you know, that is kind of like a good first approximation. Sorry. A good first approximation. But the truth though, is that if you kind of like go towards the extremes of the distribution, you will find people who are way taller than it would be possible if this was actually a Gaussian distribution.

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text:
The reason is that Gaussian distributions fall very rapidly, like very rapidly. I mean, this is, you know, if you look at the equation of a Gaussian distribution is, you know, e to the minus, like, like the standard deviation squared. So like, is like actually falling faster, you know, than an exponential is like falling super fast. And for that reason, like after a certain standard deviation, things in principle should be extremely rare, like just incredibly difficult to find. I don't think that's the case for actual biological phenomena. This is definitely not the case for height, definitely not the case for other traits like strength. And it's definitely not the case for like cognitive abilities. Essentially the first approximation, there are people, there are way more super smart people than you would expect if there are, if this was a Gaussian distribution. So how do you, how do you actually kind of like solve this problem? Well, so I used to be very into this stuff, especially when I was like early teenagers. I think I mentioned a different video because I was very keen on finding the others, finding other kids with whom I could have like meaningful, you know, non-trivial conversations about philosophy and the universe and stuff like that. And I mean, I did have like a really wonderful friend. I was able to do that, but the gap with other kids was just so large. And even with teachers, yeah, just kind of like I felt in a completely different world. So I was like very incentivized to like, okay, where can I find like other kids with whom I could actually have kind of like a peer relationship? And which is, yeah, why I got interested in things like, you know, high IQ societies. And I was kind of, I used to romanticize them, you know, when I was 12 or 13. Now I'm not so hot on them. I don't think they're that interesting, but I did discover this one high IQ society, which is called Sigma Society founded by Hindenburg Melau Jr. in Brazil, which actually did significantly update my understanding of the distribution of cognitive abilities. So even though everything was in Portuguese and there was no Google translate, I read, you know, everything they had on the website, which was in Portuguese. I mean, thankfully I know Spanish and I was able to make sense of it. So the first thing to say is that something that is very laudable, something very admirable about Hindenburg Melau Jr. is that, yeah, precisely he realized that standard IQ tests, standard kind of general mental ability tests, they assume an underlying Gaussian distribution doesn't seem to be true because there's people like Einstein, there's people like Newton, et cetera. So what kind of statistical technique can you use that in a sense, try to actually ground these cognitive abilities? So he actually tried to ground it by kind of this idea

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of how many people of a certain ability do you need to put together so that they have the same probability of solving a problem as somebody of a higher mental ability. And I think the equation that arrived, you know, approximately from essentially all of this work was, I believe it was something like for every 18 points of IQ, you need kind of like five times the number of people. So essentially if there's a problem that like somebody with an IQ of 118 solves with a 50% chance, you will need maybe like five people of like an IQ of a hundred in order to be able to solve with the same probability. Which yeah, I mean like it doesn't sound like much, but obviously it's an exponential, so it grows pretty high pretty quickly. And the other thing is that he used this paradigm called item response theory, which does not assume underlying Gaussian distribution. And I actually really love this paradigm. I mean, you should check it out if you're into statistics, psychometrics, or even if you're into analyzing surveys, independently of, you know, it having anything to do with psychometrics. Yeah. Analyzing surveys, like for example, what are the drivers of people at your company leaving or staying? Yeah. Probably analyzing the survey with an item response theory paradigm, I think will give you like a much better model than if you just use kind of like standard methods that assume Gaussian distributions like yeah, linear regression or classical test theory, because by and large, these distributions are not actually going to be Gaussian. And yeah, that's an important insight. So with all of these, essentially he reanalyzed, for example, the performance of people in these like high end IQ tests, it's called high range IQ tests, where essentially you have all the time you want to try to solve them. And he found out that essentially people's IQ should go much higher than what these tests are actually saying. So for example, there's this test called the Mega test. I believe, what is his name? Christopher Langan, supposedly one of the smartest person. I mean, he's really smart, no doubt. And you know, he performed really well on like one of these like super difficult tests. And he has interesting metaphysics and things like that. Yeah, I mean, as I'll explain, he might not have like the full range of intelligence that I'm concerned about, but clearly he's a brilliant, brilliant guy. And yeah, I mean, if you score very high on the Mega test, you probably have something going for you. And within this paradigm, he actually was arriving at the conclusion that there are actually lots of people who have IQs above 200, which is crazy. I mean, he was estimating based on a number of indicators that people like Newton and Einstein actually had IQs of 130. Like that's kind of the upper range of human ability. And you know,

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text:
now I will also say that I actually think that not in every case, but in many cases like tests such as the IMO, the International Math Olympiad, if you just kind of like look at it from the point of view of kind of like rarity, if you want to grade it under the curve or something like that, you will say like, yeah, this is kind of like testing people's IQ at the level of like 160 or something like that. But I know if you use like atom response theory and you compare it with the general population, no, I mean, like to score like a perfect score on an IMO test, like 42 points, the magic number, you probably need something like in the 190 range of IQ, which again is insane. But I think there's something to that. Again, this is kind of like testing, yeah, kind of like these narrow cognitive abilities, not necessarily the full generality. Now, okay, let's kind of like ground it a little bit with kind of like important personalities that we know that are like extraordinary in one way or another. So I would say Terence Tao and John von Neumann both exemplify these things. A, they exemplify that intelligence goes way higher in the distribution that you would expect with a Gaussian distribution. And they also exemplify Spearman's law of diminishing returns. That yes, I mean like Terence Tao, for example, his math ability is just so, so, so far superior than his verbal ability that like obviously a kind of like correlation of like 0.7 or something like that as happens in the general range of minus two to plus two standard deviations, yeah, that would be impossible. It's statistically impossible. So obviously something else is going on. And yeah, I mean, I do think somebody like Terence Tao definitely has a math IQ definitely higher than 200, especially if you put any stock in kind of this paradigm. One other thing I was going to say is that I actually, I remember spent a weekend like downloading all of the data of IMO participants. And then rather than analyzing it with a classical test theory, I remember, yeah, analyzing with a item response theory. And it actually ended up being like roughly as predictive. So like your performance in one IMO in terms of like just the raw score is approximately as predictive for your performance in the next IMO. Well, sorry, the percentile, your percentile in the IMO is roughly as predictive for your performance in the next IMO as your latent trait item response theory, inferred latent trait. But there's a really good reason why. And that is that IMO tests are actually really well constructed. So essentially, yeah, I mean, people who construct these studies, these tests, they were participants themselves. They're like super brilliant mathematicians. And they have a really good sense of like what is the difficulty of these test items.

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text:
And the test items are actually really clever. I mean, like IMO test items are not things that you kind of just get out of luck. Like the luck component is going to be fairly minor. It is like mostly ability. And because there's like six items and they're like approximately equally spaced in their difficulty, it is actually the sort of test where both item response theory and classical test theory gives you more or less the same results. Where you will find a completely different kind of analysis is when the test is poorly constructed such that you have, for example, a lot of like very simple items and maybe a few very hard items. So what will often happen, for example, with gifted children is that they might be able to solve the hard items and nobody else will be able to solve them, but they will make silly mistakes on the simple items and they will be penalized for that. So like they might be penalized for like, you know, like mistaking a number, an arithmetic mistake, things like that, that, yeah, they kind of are correlated with general mental ability. But no, I mean, when you go to kind of the extremes of distribution, it's much more interesting to look at, okay, what is the hardest item that this person is capable of solving? Not are you able to, you know, solve 200 items that are trivial with like no arithmetic mistakes. And this is also actually the reason why I do, you know, would criticize something like the SAT for, you know, estimating your math ability, the SAT math component. Why? Because the items are actually very simple, very easy. Like anybody who's been to a math Olympiad and like performed at like national levels and so on, every item in the math SAT is super trivial. And the only reason why they might not get like a perfect score is because of like a silly mistake or like they just forgot of the formula in that one moment or something. I would advocate for like the SAT having kind of like an extra kind of like bonus component or something with actually difficult questions to actually, yeah, be able to separate the, the, yeah, the brilliant from, from, yeah, the really brilliant. Okay. But John von Neumann though, somebody might say is kind of a counter example and I would disagree. Why? Okay. So John von Neumann, I'll also add a link in the description. You know, he's mathematical abilities probably unparalleled. Like not only was he like incredibly good at kind of like proving theorems, he also was extremely good at arithmetic. Like you could give him like a huge number and tell him, find the square root in your head and he would do it super fast. So he also had kind of like this savant like abilities. He also was extremely creative in the context of like, yeah, these technical

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fields. He was able to also write it out in a way that others would understand. Like he also had like tremendous verbal ability. And there's like these crazy anecdotes of like somebody, for example, like opening a book you know, a book that von Neumann read once in his childhood and starting to read a random paragraph and von Neumann would be able to complete that paragraph. And in addition say like, oh yeah, that happened in, you know, page 120 and this was the context. So he also had kind of like perfect verbal memory and like perfect writing skills. Like it needs a stunning kind of personality, but okay. You know, he thought that exercise was nonsense. You know, he was very unhealthy in the way he ate, but you know, at the time, like I wouldn't necessarily, you know, say that's kind of like failing some kind of intelligence test, but I would say he did have like a huge blunder and you know, I would, I would die on this heel as it were that he was kind of an idiot in this way, which is he was advocating for nuking Russia actually, when Russia didn't have nukes yet and the US did after the second world war, he was very belligerent. He was very, he was a warmonger. I mean, he was saying, if people say, let's nuke Russia tomorrow, I will say, let's do it this afternoon. And if people say, let's do it this afternoon, I would say, let's do it today in the morning. So crazy. I mean, like I would say that's insane. Now somebody might argue, well, I mean, he's the smartest person in the, in the earth. Clearly he foresaw kind of like the social forces moving and like the Cold War and how it would be like risking everybody's life and so on and so forth. Well, no, here's my counter. I think that actually he lacked some aspects of a more general broad intelligence where rather than just looking at the situation from kind of a strict game theoretical point of view that assumes an adversarial escalatory ego driven mindset, he could have, you know, actually explored how adversarial mindsets get constructed to begin with and how they get reinforced. And in that way, I think if he actually had been kind of a super intelligence in a more broad sense, he wouldn't have advocated for nuking Russia. He would have become a super diplomat. He would have used all of his incredible intelligence. And rather than pointing them towards how can we make my country win without valuing the lives of other countries instead of to how can I find an ideology and a system of thought that will unite the different nations. Okay, maybe it sounds unrealistic to hippie, but no, I think that's the case. So Von Neumann, you get a lot of points deducted for that one blunder. Okay, so there are

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