In My Childhood Role Model, Eliezer Yudkowsky argues that people often think about intelligence like this, with village idiot and chimps on the left, and Einstein on the right.

However, he says, this view is too narrow. All humans have nearly identical hardware. Therefore, the true range of variation looks something like this instead:

This alternative view has implications for an AI takeoff duration. If you imagine that AI will slowly crawl from village idiot to Einstein, then presumably we will have ample time to see powerful AI coming in advance. On the other hand, if the second view is correct, then the intelligence of computers is more likely to swoosh right past human level once it reaches the village idiot stage. Or as Nick Bostrom put it, "The train doesn't stop at Humanville Station."

Katja Grace disagrees, finding that there isn't much reason to believe in a small variation in human abilities. Her evidence comes from measuring human performance on various strategically relevant indicators: chess, go, checkers, physical manipulation, and Jeopardy.

In this post, I argue that the debate is partly based on a misunderstanding: in particular, a conflation of learning ability and competence. I further posit that when this distinction is unraveled, the remaining variation we observe isn't that surprising. Similar machines regularly demonstrate large variation in performance if some parts are broken, despite having nearly identical components.

These ideas are not original to me (see the Appendix). I have simply put two explanations together, which in my opinion, explain a large fraction of the observed variation.

Explanation 1: Distinguish learning from competence

Humans, despite our great differences in other regards, still mostly learn things the same way. We listen to lectures at roughly the same pace, we read at mostly the same speeds, and we process thoughts in similar sized chunks. To the extent that people do speed up lectures by 2x on Youtube, or speed read, they lose retention.

And putting aside tall tales of people learning quantum mechanics over a weekend, it turns out to be surprisingly difficult for humans to beat the strategy of long-term focused practice for becoming an expert at some task.

From this, we have an important insight: the range of learning abilities in humans is relatively small. There don't really seem to be humans who tower above us in terms of their ability to soak up new information and process it.

This prompts the following hypothetical objection,

Are you sure? If I walk into a graduate-level mathematics course without taking the prerequisites seriously, then I'm going to be seriously behind the other students. While they learn the material, I will be struggling to understand even the most basic of concepts in the course.

Yes, but that's because you haven't taken the prerequisites. Doing well in a course is a product of learning ability * competence at connecting it to prior knowledge. If you separate learning ability and competence, you will see that your learning ability is still quite similar to the other students.

Eric Drexler makes this distinction in Reframing Superintelligence,

Since Good (1966), superhuman intelligence has been equated with superhuman intellectual competence, yet this definition misses what we mean by human intelligence. A child is considered intelligent because of learning capacity, not competence, while an expert is considered intelligent because of competence, not learning capacity. Learning capacity and competent performance are distinct characteristics in human beings, and are routinely separated in AI development. Distinguishing learning from competence is crucial to understanding both prospects for AI development and potential mechanisms for controlling superintelligent-level AI systems.

Let's consider this distinction in light of one of the cases that Katja pointed to above: chess. I find it easy to believe that Magnus Carlsen would beat me handily in chess, even while playing upside-down and blindfolded. But does this mean that Magnus Carlsen is vastly more intelligent than me?

Well, no, because Magnus Carlsen has spent several hours a day playing chess ever since he was 5, and I've spent roughly 0 hours a day. A fairer comparison is other human experts who have spent the same amount of practicing chess. And there, you might still see a lot of variation (see the next theory), but not nearly as much as between Magnus Carlson and me.

This theory can also be empirically tested. In my mind there are (at least) two formulations of the theory:

One version roughly states that, background knowledge and motivation levels being equal, humans will learn how to perform new tasks at roughly equal rates.

Another version of this theory roughly states that everything that top-humans can learn, most humans can too if they actually tried. That is, there is psychological unity of humankind in what we can learn, but not necessarily what we have learned. By contrast, a mouse really couldn't learn chess, even if they tried. And in turn, no human can learn to play 90-dimensional chess, unlike the hypothetical superintelligences that can.

You can also use this framework to cast the intelligence of machine learning systems in a new light. AlphaGo took a hundred million games to grow to the competence of Lee Sedol. But Lee Sedol has only played about 50,000 games in his life.

Point being, when we talk about AI getting more advanced, we're really mostly talking about what type of tasks computers can now learn, and how quickly. Hence the name machine learning...

Explanation 2: Similar architecture does not imply similar performance

Someone reading the above discussion might object, saying

That seems right... but I still feel like there are some people who can't learn calculus, or learn to code no matter how hard they try. And I don't feel like this is just them not taking prerequisites seriously or lack of motivation. I feel like it's a fundamental limitation in their brain, and this produces a large amount of variation in learning ability.

I agree with this to an extent. $^{1}$ However, I think that there is a rather simple explanation for this phenomenon -- the same one in fact that Katja Grace pointed to in her article,

Why should we not be surprised? [...] You can often make a machine worse by breaking a random piece, but this does not mean that the machine was easy to design or that you can make the machine better by adding a random piece. Similarly, levels of variation of cognitive performance in humans may tell us very little about the difficulty of making a human-level intelligence smarter.

In the extreme case, we can observe that brain-dead humans often have very similar cognitive architectures. But this does not mean that it is easy to start from an AI at the level of a dead human and reach one at the level of a living human.

Imagine lining up 100 identical machines that produce widgets. At the beginning they all produce widgets at the same pace. But if I go to each machine and break a random part -- a different one for each machine -- some will stop working completely. Others will continue working, but will sometimes spontaneously fail. Others will slow down their performance, and produce fewer widgets. Others still will continue unimpeded since the broken part was unimportant. This is all despite the fact that the machines are nearly identical in design space!

If a human cannot learn calculus, even after trying their hardest, and putting in the hours, I would attribute this fact to a learning deficit. In other words, they have a 'broken part.' Learning deficits can be small things: I often procrastinate on Reddit rather than doing tasks that I should be doing. People's minds drift off when they're listening to lectures, finding the material to be boring.

The brightest people are the ones who can use the full capacity of their brains to learn the task. In other words, the baseline of human performance is set by people who have no 'broken parts.' Among those people, the people with no harmful mutations or cognitive deficits, I expect human learning ability to be extremely similar. Unfortunately there aren't really any humans who fit this description, and thus we see some variation, even for humans near the top.

Appendix

What about other theories?

There have been numerous proposed theories that I have seen. Here are a few posts:

Why so much variance in human intelligence? by Ben Pace. This question prompted the community to find reasons for the above phenomenon. None of the answers quite match my response, hence why I created this post. Still, I think a few of the replies were onto something and worth reading.

Where the Falling Einstein Meets the Rising Mouse, a post on SlateStarCodex. Scott Alexander introduces a few of his own theories, such as the idea that humans are simply lightyears above animals in abilities. While this theory seems plausible in some domains, I did not ultimately find it compelling. In light of the learning ability distinction, however, I do think we are lightyears above many animals in learning.

The range of human intelligence by Katja Grace. Her post prompted me to write this one. I agree that there is a large variation in human abilities but I felt that the lack of a coherent distinction between learning and competence ultimately made the argument rest on a confusion. As for whether this alters our perception of a more continuous takeoff, I am not so sure. I think the implications are non-obvious.

Where did the learning/competence distinction come from?

To the best of my knowledge, Eric Drexler kindled the idea. However, I do know that many people have made the distinction in the past; I just haven't really seen it applied to this debate in particular.

$^{1}$ However, I do think that most people are probably able to learn calculus, and how to code. I agree with Sal Khan who says,

If we were to go 400 years into the past to Western Europe, which even then, was one of the more literate parts of the planet, you would see that about 15 percent of the population knew how to read. And I suspect that if you asked someone who did know how to read, say a member of the clergy, "What percentage of the population do you think is even capable of reading?" They might say, "Well, with a great education system, maybe 20 or 30 percent." But if you fast forward to today, we know that that prediction would have been wildly pessimistic, that pretty close to 100 percent of the population is capable of reading. But if I were to ask you a similar question: "What percentage of the population do you think is capable of truly mastering calculus, or understanding organic chemistry, or being able to contribute to cancer research?" A lot of you might say, "Well, with a great education system, maybe 20, 30 percent."

Edit: I want to point out that this optimism is not a crux for my main argument.