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.

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.

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.

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.

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.