[ Question ]

Why so much variance in human intelligence?

by Ben Pace3 min read22nd Aug 201928 comments


IQ and g-factor

Epistemic status: Practising thinking aloud. There might be an important question here, but I might be making a simple error.

There is a lot of variance in general competence between species. Here is the standard Bostrom/Yudkowsky graph to display this notion.

There's a sense that while some mice are more genetically fit than others, they're broadly all just mice, bound within a relatively narrow range of competence. Chimps should not be worried about most mice, in the short or long term, but they also shouldn't worry especially so about peak mice - there's no incredibly strong or cunning mouse they ought to look out for.

However, my intuition is very different for humans. While I understand that humans are all broadly similar, that a single human cannot have a complex adaptation that is not universal [1], I also have many beliefs that humans differ massively in cognitive capacities in ways that can lead to major disparities in general competence. The difference between someone who does understand calculus and someone who does not, is the difference between someone who can build a rocket and someone who cannot. And I think I've tried to teach people that kind of math, and sometimes succeeded, and sometimes failed to even teach basic fractions.

I can try to operationalise my hypothesis: if the average human intelligence was lowered to be equal to an IQ of 75 in present day society, that society could not have built rockets or do a lot of other engineering and science.

(Sidenote: I think the hope of iterated amplification is that this is false. That if I have enough humans with hard limits to how much thinking they can do, stacking lots of them can still produce all the intellectual progress we're going to need. My initial thought is that this doesn't make sense, because there are many intellectual feats like writing a book or coming up with special relativity that I generally expect individuals (situated within a conducive culture and institutions) to be much better at than groups of individuals (e.g. companies).

This is also my understanding of Eliezer's critique, that while it's possible to get humans with hard limits on cognition to make mathematical progress, it's by running an algorithm on them that they don't understand, not running an algorithm that they do understand, and only if they understand it do you get nice properties about them being aligned in the same way you might feel many humans are today.

It's likely I'm wrong about the motivation behind Iterated Amplification though.)

This hypothesis doesn't imply that someone who can do successful abstract reasoning is strictly more competent than a whole society of people who cannot. The Secret of our Success talks about how smart modern individuals stranded in forests fail to develop basic food preparation techniques that other, primitive cultures were able to build.

I'm saying that a culture with no people who can do calculus will in the long run score basically zero against the accomplishments of a culture with people who can.

One question is why we're in a culture so precariously balanced on this split between "can take off to the stars" and "mostly cannot". An idea I've heard is that if a culture is easily able to reach technologically maturity, it will come later than a culture who is barely able to become technologically maturity, because evolution works over much longer time scales than culture + technological innovation. As such, if you observe yourself to be in a culture that is able to reach technologically maturity, you're probably "the stupidest such culture that could get there, because if it could be done at a stupider level then it would've happened there first."

As such, we're a species whereby if we try as hard as we can, if we take brains optimised for social coordination and make them do math, then we can just about reach technical maturity (i.e. build nanotech, AI, etc).

That may be true, but the question I want to ask about is what is it about humans, culture and brains that allows for such high variance within the species, that isn't true about mice and chimps? Something about this is still confusing to me. Like, if it is the case that some humans are able to do great feats of engineering like build rockets that land, and some aren't, what's the difference between these humans that causes such massive changes in outcome? Because, as above, it's not some big complex genetic adaptation some have and some don't. I think we're all running pretty similar genetic code.

Is there some simple amount of working memory that's required to do complex recursion? Like, 6 working memory slots makes things way harder than 7?

I can imagine that there are many hacks, and not a single thing. I'm reminded of the story of Richard Feynman learning to count time, where he'd practice being able to count a whole minute. He'd do it while doing the laundry, while cooking breakfast, and so on. He later met the mathematician John Tukey, who could do the same, but they had some fierce disagreements. Tukey said you couldn't do it while reading the newspaper, and Feynman said he could. Feynman said you couldn't do it while having a conversation, and Tukey said they could. They then both surprised each other by doing exactly what they said they could.

It turned out Feynman was hearing numbers being spoken, whereas Tukey was visualising the numbers ticking over. So Feynman could still read at the same time, and his friend could still listen and talk.

The idea here is that if you're unable to use one type of cognitive resource, you may make up for it with another. This is probably the same situation as when you make trade-offs between space and time in computational complexity.

So I can imagine different humans finding different hacky ways to build up the skill to do very abstract truth-tracking thinking. Perhaps you have a little less working memory than average, but you have a great capacity for visualisation, and primarily work in areas that lend themselves to geometric / spacial thinking. Or perhaps your culture can be very conducive to abstract thought in some way.

But even if this is right I'm interested in the details of what the key variables actually are.

What are your thoughts?

[1] Note: humans can lack important pieces of machinery.


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A mouse brain has ~75 million neurons, a human brain ~85 billion neurons. The standard deviation of human brain size is ~10%. If we think of that as a proportional increase rather than an absolute increase in the # of neurons, that's ~74 standard deviations of difference. The correlation between # of neurons and IQ in humans is ~0.3, but that's still a massive difference. Total neurons/computational capacity does show a pattern somewhat like that in the figure. Chimps' brains are a factor of ~3x smaller than humans, ~12 standard deviations.

Selection can cumulatively produce gaps that are large relative to intraspecific variation (one can see the same relationships even more blatantly considering total body mass). Mice do show substantial variation in maze performance, etc.

And the cumulative cognitive work that has gone into optimizing the language, technical toolkit, norms, and other factors involved in human culture and training into are immensely beyond those of mice (and note that human training of animals can greatly expand the set of tasks they can perform, especially with some breeding to adjust their personalities to be more enthusiastic about training). Humans with their language abilities can properly interface with that culture, dwarfing the capabilities both of small animals and people in smaller earlier human cultures with less accumulated technology or economies of scale.

Hominid culture took off enabled by human capabilities [so we are not incredibly far from the minimum need for strongly accumulating culture, the selection effect you reference in the post], and kept rising over hundreds of thousands and millions of years, at accelerating pace as the population grew with new tech, expediting further technical advance. Different regions advanced at different rates (generally larger connected regions grew faster, with more innovators to accumulate innovations), but all but the smallest advanced. So if humans overall had lower cognitive abilities there would be slack for technological advance to have happened anyway, just at slower rates (perhaps manyfold), accumulating more by trial and error.

Human individual differences are also amplified by individual control over environments, e.g. people who find studying more congenial or fruitful study more and learn more.

Four factors of some relevance:

First, humans aren't at equilibrium; as you point out, our environment has shifted much more quickly than evolution has time to catch up with. So we should expect that many analyses that make sense at equilibrium aren't correctly describing what's happening now.

Second, while it seems like "humans are very different yet mice are all the same," this is often because it's easy to track the differences in humans but difficult to track the differences in mice. What fraction of mice become parents (a decent proxy for the primary measure of success, according to evolution)? Would it look like the core skills of being a mouse (finding food, evading predators, sociability, or so on) have variance comparable to the human variation in intelligence? What fraction of humans become parents?

Third, while we have some evidence that humans are selected for intelligence (like the whole skull/birth canal business), intelligence is just one of many traits that are useful for humans, and we don't have reason to believe this is the equilibrium that would result if intelligence were the only determinant of fitness. Consider Cochran et al on evidence for selection for intelligence for Ashkenazi Jews; they estimate that parents had perhaps a 1 IQ point edge over non-parents for the last ~500 years (with lower estimates on the heritability of intelligence having to only slightly increase that number).

Fourth, rapid population growth generally amplifies variance along dimensions that aren't heavily selected for if the population growth is accomplished in part by increasing the number of parents.

Half formed thoughts towards how I think about this:

Something like Turing completeness is at work, where our intelligence gains the ability to loop in on itself, and build on its former products (eg definitions) to reach new insights. We are at the threshold of the transition to this capability, half god and half beast, so even a small change in the distance we are across that threshold makes a big difference.

Content warning: taboo topics

From "complex adaptations require a sequence of simpler adaptations", we cannot conclude "that a single human cannot have a complex adaptation that is not universal"! What you are missing is physical barriers that existed for large parts of human history and prehistory, such as the Sahara Desert, that largely prevented any significant amount of gene flow. While individual early European explorers could cross the Sahara Desert and might even have survived for a short while, they would face considerable dangers on the other side: tropical diseases such as malaria to which their bodies and immune systems in particular were poorly adapted, no modern science-based medicine to treat them with and no easy way to communicate with locals, unfamiliar wild animals such as the very dangerous hippopotamus, and hostile African tribes.

And yes, African tribes would probably have been highly suspicious of, and hostile towards, white outsiders - not least because of their "strange-coloured" skin, strange clothes, and incomprehensible language. Even today, Albino Africans are discriminated against in Africa, and sometimes even killed for their flesh to be used by witch-doctors. The modern notion that we should care about all humans equally, because racial and national differences are superficial at most, is quite a modern phenomenon. There is little sign of these kinds of ideas in most of human history, although Islam approaches this idea with the idea of the Ummah (brotherhood of all Muslim men and sisterhood of all Muslim women) and Christianity gets even closer with the idea of people of other races (the Good Samaritan, for example) being "your neighbour" who should be treated "as yourself". Both were quite radical breaks from the more tribal pasts that had preceded them - and we can see that in evidence in the Old Testament. The God of the Old Testament is portrayed as snuffing out entire rival tribes - or in one case, the Great Flood story, the entire outside world. But of course, the period I am referring to was before European imperialism spread Christianity in Africa. (And in practice, Christian ideals of treating others as neighbours were not in evidence in the Crusades, or in the many expulsions of Jews from European countries.)

One cause of variation in intelligence is injuries, such as head injuries. (It is a little-known fact that this can also cause personality changes, such as increased risk-taking - so there is an intriguing hypothesis that the prevalence of both diagnosed and undiagnosed blunt-force head trauma caused by male students playing American Football may have led to some men randomly obtaining the "gift" of risk-taking, leading to greater US entrepreneurship, and thus contributed to America's impressive economic performance. My confidence in this hypothesis is very low, however, because I have only seen it mentioned on Twitter.)

However, it is noteworthy that while injuries, such as brain injuries caused by temporary loss of oxygen during a badly-managed birth, or caused by blunt-force trauma, can cause a reduction in IQ, the "moron level" or "idiot level" - the IQ level at which someone is considered developmentally disabled - can differ by population group. It is an unpalatable fact that a white European with an IQ of 60 and the typical impairments going along with that would probably be considered developmentally disabled, while a pygmy hunter-gatherer with an IQ of 60 - normalised to the same scale as the European - might not. Although the pygmy, in line with other traditional hunter-gatherer peoples that survive today, perhaps does not read or write or count above ten in their native language, and spends a lot of time hunting, gathering, or trying to sell what they have hunted, and thus the cognitive demands upon them in their daily lives would arguably be a bit lower, this difference in assessments is mainly because the IQ averages of the two groups are significantly different. Why might we expect this to be so? Well, as already noted, different population groups were semi-completely separated by physical barriers, such as the Sahara Desert and the ocean around Australia, for long periods of time. They also faced different selection pressures - another factor making substantial group differences plausible from an evolutionary perspective. Recall that the majority of experts believe that homo sapiens originated in Africa, so if that's true, all races have ancestors there - so white and Asian people must have had ancestors who lived in Africa, some of whom must have migrated out of Africa at some point. (And by the way, we have research on how each population group on earth got where they reside today, including Native Americans and Australian Aborigines.) The development of farming - obviously a technological factor, but one that was sort of necessitated by migrating into harsher environments with harsher winters - may have exacerbated these selection pressures.

Hunter-gathering requires a certain amount of intelligence, clearly, but perhaps less so than farming. Farming, particularly in challenging environments with long, heavy winters with snow on the ground, requires more long-term thinking and values, and rewards intelligence that produces innovations that yield more food more reliably - in the Malthusian era that comprised most of human history and prehistory, those who were able to have and feed and protect more children because of their superior food-obtaining abilities, would often have passed on more copies of their genes, and those that had less success at doing so would have passed on fewer copies of their genes, or even none at all. This is so even though such technological innovations will have spread out over time, thanks to the one intelligence characteristic that dramatically differs between humans and all other species - the ability to learn from and teach each other. (Note that many humans throughout Malthusian times never had any surviving children - whether due to infertility, extreme poverty or injuries acquired from war or other violence.)

But the group differences don't stop there. Certain specific population groups, such as Ashkenazi Jews in Europe, the Igbo tribes in Nigeria, and - as recent indirect findings by Gregory Clark have indicated - in modern times, the Southern English (which includes Northern English individuals who migrated, or whose ancestors migrated, to the South of England), seem to have higher average intelligence than the average of the broader groups they live next to, despite not having been physically separated from other groups in quite the same way. On the other end of the intelligence spectrum, though this is doubtless somewhat embarrassing for at least some people with such ancestry, there seems to be correlations in humans between brain size and IQ, between height and IQ, and between height and brain size, and the observed intelligence of certain population groups with shorter average height seems to bear this correlation out. (However, it is important to note that women are not substantially less intelligent than men on average, despite being significantly shorter on average. I would speculate that perhaps women have a similar total number of neurons to men, but packed in more densely on average - in line with how certain other parts of their bodies are often genetically programmed to be smaller than, larger than or structurally different to men's. Animal research has established that an underlying factor influencing intelligence on an inter-species level is number of neurons, rather than brain size per se - which explains why whales and elephants are not more intelligent than humans.)

Why might this be so? For Ashkenazi Jews - that is, Jews of proximate European ancestry - we don't know for sure. However, one plausible hypothesis holds that that the regulatory environment over the course of hundreds of years of living in European nations, where Jewish people were frequently the only people allowed to levy interest-bearing loans due to the then-in-force Christian prohibition on usury, together with high-pressure sexual selection and notably arranged marriages, would have selected for successful and intelligent people and their genes.

Note that this probably seems very implausible from the perspective of the idea, common among non-scientists in the West, that evolution takes a very, very long time to do anything, especially to produce complex traits, a conception of evolution which has probably been influenced by the highly influential essaying of the anti-hereditarian (i.e. opposed to the idea that there are genetically-caused differences in average IQ between groups) Steven Jay Gould. But actually we have an existence proof that selection doesn't have to take a long time to produce changes from the human development of dog breeds using artificial selection, and of cows bred to have unnaturally large udders to maximise milk production and so on, and scientific research on species with much shorter generation lengths than our own bears this out as well. And even Gould himself was a proponent of the theory of punctuated equilibrium, which literally means slow periods where nothing much happened punctuated by periods of comparatively rapid change. And if you think about it, there are an incredibly large number of adaptations required to turn simple microorganisms into modern humans, both ones currently known to science and presumably a large number not known to science yet, because of our comparative lack of understanding of the human brain, so it's not the case that each and every one of those changes would have taken millions of years - there simply wouldn't have been enough time.

In addition, being able to memorise and interpret large portions of the scriptures was highly valued, which would plausibly have selected for verbal abilities, which is anecdotally extraordinarily high among Ashkenazi Jews (I know an Ashkenazi Jewish man who speaks several languages fluently - including English, which is not his first language, with flawless pronunciation). Indeed, not only would more successful Jewish financiers, religious scholars and rabbis on average have had more children - less successful Jewish men, if they had reproduced at all, might have simply out-married from the group and therefore their heirs would not have been considered Jewish. This would be despite having the same proportion of Jewish blood - 50% - as a child of a Jewish female and a Christian convert, who would be considered Jewish under traditional Jewish law, and would of course be raised as part of the Jewish community. So the whole traditional demarcation between Jewish and non-Jewish people, defined by "mother is Jewish", technically makes little sense from a modern scientific perspective with the benefit of our knowledge of how genetics works, but it could help to form part of the story of how the average intelligence of Jewish people living in Europe apparently rose more than their non-Jewish peers despite not-inconsiderable intermarriage in both directions over the centuries (which is probably why Jewish and non-Jewish people of European ancestry are often difficult to distinguish visually, in the absence of clothing or grooming cues in the case of Orthodox Jewish men).

Less is known about the history of the Igbo tribes, who were historically farmers, and even less about the past of individual hunter-gatherer tribes.

In England, the South is more prosperous due to the very economically-important city of London, in modern times one of the world's top financial centres, but which has also been a key global city for centuries. So there would have been strong economic incentives to migrate for work, or a better or more reliable income, over the course of a number of centuries - especially in centuries past when the equivalents of "welfare" (in British English, "benefits"), were slim or inadequate compared to today, or when there was no year-round work available in the local village, with its relatively simple economy. I don't know how open to migration the English are on average, but Americans are unusually prone to migrate for a better job (another possible reason for unusually high salaries in America, I would speculate), and many Americans have English ancestry, of course. So perhaps selection effects alone could explain the apparent average IQ differences within England.

I have my own (unoriginal) answer, outlined in this post.

In short, I think it's important to distinguish learning ability and competence. The reason why Magnus Carlsen towers above me in chess is because he has more practice, not because he's superintelligent.

However, I also think that even putting this distinction aside, we shouldn't be surprised by large variation. If we think of the brain like a machine, and cognitive deficits as parts being broken parts in the machine, then it is easy to see how distributed cognitive deficits can lead to wide variation.

I think there's a lot of variance in the intelligence of animals too. (I was a veterinary surgeon and am definitely an "animal person".)

Variance in human intelligence, (but how are you judging that? - ability to learn and repeat, ability to problem solve?) but anyway a quick list ...

Genetics. Roll a multi-faced (Humans have about 20,000 to 23,000 genes. - Merck manual) dice, roll another one. That's your randomly selected DNA.

Interactions with others. - positive influences on your life. People that teach and explain. (when kids are at that "why" stage they should be answered with quality information).

Opportunity and Stimulation. - exposure to knowledge/education/new experiences.

Environmental factors. - Nutrition. Exposures to negative influences (disease, pollution)

Attitude - personality, desire to learn/interest in a subject.

Just a few thoughts.

Is there some simple amount of working memory that's required to do complex recursion? Like, 6 working memory slots makes things way harder than 7?

My theory is that 4 is enough, and the extra that many people have is just there because it's useful overkill that's there because it doesn't hurt anything and extra memory makes things easier faster.

So, first, note that for computing pairwise operations, you only need a stack as high as 3 (so long as additional future inputs can come from somewhere else). If you've ever worked with a stack-based calculator, like one that supports reverse polish notation (RPN), or a stack-based computer language, you probably found this out empirically, but you might have also known it from the fact that early stack-based calculators had only 3 registers and that was good enough.

Well, almost. With 3 registers you can only carry forward a single term between operations and only perform scalar operations. With 4 registers to construct the stack you can do pairwise operations of two variables or carry forward an additional term. But more importantly in practice having only 3 registers is annoying and although you can theoretically do whatever you want it requires careful ordering of operations to avoid a stack overflow. With 4 you rarely have to think ahead, which is nice: you just perform the operations and having the extra register lets you get into and out of near overflows without actually running out of space and having to start over.

More registers are nice, but registers cost money, and for a long time stack-based calculators settled on using 4 registers because it was the best balance of cost, functionality, and flexibility. Again, 3 was enough, but annoying enough to work with that everyone was happy to pay for 4, but few were willing to pay for more.

Now, does this mean 4 is enough for complex recursion? I mean, sure, so long as you are tail call optimizing. More just makes life easier and means you don't have to recurse. Why wouldn't you want to do that, though?

Well, doing all this assumes you can perform the complex mental operations you want as pairwise operations. And maybe you can do that, but also maybe you don't know how, so you end up needing more working memory to deal with trying to perform operations you can't perform "natively", yet.

And why think of the mind as performing mental operations over working memory at all or that you can develop access to more powerful operations that let you do more with the same memory? That's a long topic, but I'd recommend this paper as a starting point that melds well with the viewpoint I've expressed here.

I'd say that intelligence variations are more visible in (modern) humans, not that they're necessarily larger.

Let's go back to the tribal environment. In that situation, humans want to mate, to dominate/be admired, to have food and shelter, and so on. Apart from a few people with mental defects, the variability in outcome is actually quite small - most humans won't get ostracised, many will have children, only very few will rise to the top of the hierarchy (and even there, tribal environments are more egalitarian that most, so the leader is not that much different from the others). So we might say that the variation in human intelligence (or social intelligence) is low.

Fast forward to an agricultural empire, or to the modern world. Now the top minds can become god emperor, invading and sacking other civilizations, or can be part of projects that produce atom bombs and lunar rockets. The variability of outcomes is huge, and so the variability in intelligence appears to be much higher.

the question I want to ask about is what is it about humans, culture and brains that allows for such high variance within the species, that isn't true about mice and chimps?

Some points to consider:

1. Has it been demonstrated that variations in intelligence is that much greater for humans than for mice or chimps? This may be true, but you didn't indicate any references.

Whereas I could imagine a test for chimp intelligence, and even timed maze experiments on mice, the concept of what we mean by intelligence becomes increasingly attenuated as we deal with ever simpler life forms; so that, at some point, and maybe even quite early, experts will begin disagreeing on what they are trying to measure.

2. Modern day humans have a big advantage not only over other animals, but also over our cognitively equivalent ancestors of 12+ thousand years ago. Thanks to the invention of culture, we pass knowledge to our offspring, meaning that knowledge can be accumulated from generation to generation. Variations in cognitive performance isn't only a consequence in variations in intelligence, but also reflects large differences in the quality of acculturation.

3. I wonder if your decision to compare interspecies variations in intelligence follows from a mistaken analogy. Consider, that intelligence is a human specialty. Other species have their own specialities. For instance, maybe we should be comparing variations in human intelligence with variations in the maximum speed of healthy, adult cheetahs. (I wonder, whether anyone has ever done this?)

4. The idea that we can assign a number to the variation in human intelligence is suspect. True, we can claim that the standard deviation in IQ is 15% of average IQ value. But it doesn't follow that a +1 sigma individual is 15% smarter than an average individual, because the IQ scale itself is arbitrary and intelligence has never been defined apart from performance on the test. To make the point in another way, 1-sigma variations in intelligence was arbitrarily set to 15 IQ points purely for convenience. We might just as well have set the mark at 900 IQ points. But that wouldn't mean that the +1-sigma individual was then ten times as intelligent as average.

Compare the situation with the cheetahs, where a statement like: "the ratio between the standard deviation in maximum running speeds and the average individual's maximum running speed is .15", really means something in terms of performance that can be measured with a metre and stopwatch.

What would be wanted to put IQ and maximum speed on par, would be credible results showing that a certain superiority in IQ is closely connected with a certain improved ability in raising fertile offspring to maturity, which is the definition of evolutionary success.

How are measuring intelligence? Most of the WAIS puts machines far, far ahead of humans. This includes block design, arithmetic, digit symbol, anything that tests memory, etc.

Why do we care about intelligence? We actually care about "mental skills humans have that machines can't yet replace". Measuring this doesn't seem easy, especially if the WAIS favors machines so much.

This just makes me think if you can see such different output using essentially the same hardware, what kind of difference would make an improved one

I think intelligence is much like homosexuality ...

... in that, it mostly benefits the tribe/gene-pool, but not the individual.

Being of average intelligence you are more intelligent than a good portion of the population and that helps you, just as being sub-average might be a hindrance in some situations. But being that much more intelligent does not help that individual much.

One does not have to be intelligent to profit from the intelligence of others. "We flew to the moon." No, *we* did not. We did not find Antibiotics, but we have much more breeding success because of it.

The fact that someone does not understand calculus, does not imply that they are incapable of understanding calculus. They could simply be unwilling. There are many good reasons not to learn calculus. For one, it takes years of work. Some people may have better things to do. So I suggest that your entire premise is dubious - the variance may not be as large as you imagine.