Some comments on intelligence
After reading another article on IQ, there are a few things that I wish would become common knowledge to increase the quality of the debate. Posting them here:
1)
There is a difference between an abstract definition of intelligence such that it could also apply to aliens or AIs (something like “an agent able to optimize for outcomes in various environments”) and the specific way the intelligence is implemented in human brains. Because of the implementation details, things can be true about human intelligence even if they are not necessarily true about intelligence in general.
For example, we might empirically find that humans better at X are usually also better at Y, even if we could imagine a hypothetical AI (or even take an already existing one) whose skills at X and Y are unrelated. The fact that X and Y are unrelated in principle doesn’t disprove the hypothesis that they are related in human brains.
2)
Saying “the important thing is not intelligence (or rationality), but domain knowledge or experience or something else” is...
...on one hand, true; and the fans of intelligence (or rationality) should probably be reminded of it quite often. Yes, your Mensa membership card or LessWrong account doesn’t mean that you no longer have to study things because you can solve relativity in five minutes of armchair reasoning...
...on the other hand, it’s not like these things are completely unrelated. Yes, you acquire knowledge by studying, but your intelligence probably has a huge impact on how fast you can do that, or even whether you can do that at all.
So we need to distinguish between short term and long term. In short term, yes, domain knowledge and experience matter a lot, and intelligence is probably not going to save you if the inferential distances are large. But in long term, intelligence may be necessary for acquiring the domain knowledge and experience.
In other words, there is a huge difference between “can use intelligence instead of X, Y, Z” and “can use intelligence to acquire X, Y, Z”. The argument about intelligence being less important that X, Y, Z is irrelevant as an objection to the latter.
3)
An article that led me to writing this all proposed that we do not need separate education for gifted children; instead we should simply say that some children are further ahead in certain topics (this part is not going to trigger anyone’s political instincts) and therefore we should have separate classes for… those who already know something, and those who don’t know it yet. This would nicely avoid the controversy around intelligence and heredity etc., while still allowing the more intelligent kids (assuming that there is such a thing) to study at their own speed. A win/win solution for both those who believe in intelligence and those who don’t?
Unfortunately, I think this is not going to work. I approve of the idea of disentangling “intelligence” from “previously gained experience”. But the entire point of IQ is that previously gained experience does not screen off intelligence. Your starting point is one thing; the speed at which you progress is another thing.
Yes, it makes sense in the classroom to separate the children who already know X (“advanced”) from the children who don’t know X yet (“beginners”). No need for the advanced to listen again to the things they already know. But if you keep teaching both groups at the speed optimal for their average members, both the gifted beginners and the gifted advanced will be bored, each one in their own group.
A system that allows everyone to achieve their full potential would be the one where the gifted beginner is allowed to catch up on the average advanced, and where the gifted advanced is allowed to leave the average advanced behind. But if the gifted beginner is in the classroom full of average beginners, that is not going to happen, because their lessons will always stay behind the advanced group. Even if the advanced group only progresses at the speed of the average advanced, the only way for the gifted beginner to get to that group would be to get some knowledge outside their classroom.
It might actually be better for the gifted beginner to be incorrectly sorted into the advanced group—at the beginning, they would feel lost because they wouldn’t know what their classmates already do, but there is a chance they might sooner or later catch up on them. But if we tried to make such accidents happen on purpose, then we are kinda reinventing sorting by intelligence.
Thus from certain perspective, sorting children by their initial experience could be even worse for the gifted beginners than not being sorted at all—not being sorted at all at least allows them to progress at the average speed, while being sorted to the beginner group reduces them to the average-beginner speed. And if there is a(n imperfect) correlation between intelligence and initial experience, then we have effectively sorted the gifted beginner into the lower-intelligence classroom. (And if children from disadvantaged groups are likely to have lower initial experience than would be expected for their intelligence, then we have designed a system to sort gifted children from disadvantaged groups into lower-intelligence classrooms.) Ouch!
(However, allowing each child to individually progress at their own speed, that would be good for everyone. Also, very expensive, or would require AI tutors. So perhaps the AI tutors will finally solve this problem without anyone having to make an official statement on the intelligence and its possible relevance for education.)
I’ll give a citation on learning speed to show the extent of the problem, at least in early years (bold added):
Note that this is above what the mere “intelligence quotient” seems to predict—i.e. at a given chronological age, IQ 140 children have 1.4x the mental age of those at IQ 100, and IQ 170 have 1.7x that mental age. So why would you get 2x and 4x learning speeds respectively?
One guess is that, at least within this elementary-school age range, higher mental age also means they’ve figured out better strategies for paying attention, noticing when you’ve understood something vs when you need to go back and re-read, etc.—which other kids may eventually figure out too. Another guess is that, for at least some kids, it seems that one of the things that manifests as higher intelligence is an increased need for intellectual stimulation; so in general, it may be that the higher-IQ kids are more naturally inclined to pay attention when the teacher is saying new things, and more inclined to read the textbook and think back to it, so there’s less need for self-control, and so they’re less handicapped by the lack of it in early years.
I don’t know how far up in age the above extends. I do expect the lower-IQ learning rate to catch up somewhat in later years, perhaps bringing the difference down to the IQ ratio. (The learning-rate difference certainly doesn’t disappear, though; I believe it’s common that if an exceptionally gifted kid gets accelerated into college classes with adults of equal knowledge—several of whom are probably moderately gifted—she’ll still finish at the top of her class.)
Yes, that (what the citation says) is exactly the problem. Maybe with the objection that the time coefficient can be different for different school subjects, because some of them are more focused on understanding things, and others are more focused on memorizing things—the intelligence speed impact on understanding is greater than on memorizing. So you could get e.g. ×4 on math, but only ×1.5 on languages.
Among the various ways to take up the extra time of the rapid learners, probably the best one is “don’t go faster, go wider”. (Note: I am not saying that this is optimal for the rapid learner. The optimal thing for the rapid learner would be to… learn faster, obviously. I am just saying that if the constraint “you can’t learn faster” is absolute, this is probably the best you can do.) For example, if you have to learn a foreign language slowly, maybe you could learn two foreign languages simultaneously? So that after you learned lesson 1 in 50% of time, and now you need to wait for your classmates before proceeding to lesson 2, you can study lesson 1 from the other language. It’s not optimal, but you are not wasting time, and you end up with some extra knowledge as a result (so it’s not just meaningless busywork).
A more realistic example would be a math textbook, where each chapter is followed by exercises, some of them marked as “optional, too difficult”, where the average kids are supposed to only do the standard exercises, and the gifted kid can do the extra exercises. That also is: not optimal, but not entirely useless. I guess the missing part is getting some extra reward for the extra work. (In the case of learning an extra language, the reward is knowing the extra language. In the case of doing extra math exercises, maybe you get a deeper knowledge as a result… but maybe you don’t, who knows.) So maybe you should also get some “golden star” on your report card, for completing all the extra exercises? Not sure; different things motivate different people. Problem is, it’s not always easy to design the extra exercises.
It is difficult to predict how the speed bonus of intelligence evolves with age; arguments can be made on both sides. On one hand you get the “Matthew effect”—even a small advantage over your classmates can result in rewards, greater motivation, having more solid fundamentals, etc. On the other hand, being artificially slowed down by the school system teaches laziness; and the gifted people are more likely to be interested in many different things, which divides their effort. (Though you never know whether the divided effort today will result in some useful synergy tomorrow. Like, maybe studying math and biology at the same time is less efficient for your career than focusing fully on one; but maybe one you make an important discovery by applying some advanced math technique on some biological data. Similarly, programming skills or better English—for those who are not native speakers—can turn out to be useful at whatever is your work, because you can automate something or talk to someone you otherwise couldn’t.)
But if I had to guess, I would guess that the gifted kids who stay within the confines of school will probably lose most of their advantage, and the ones who focus on something else (competitions, books, online courses, personal projects) will probably keep it.
Possibly. It’s also the case that IQ is an aggregated measure of a set of cognitive subtests, and the underlying capabilities they measure can probably be factored out into things like working memory, spatial reasoning, etc., which are probably all correlated but imperfectly so; then if some of those are more useful for some subjects than others, you’ll expect some variance in progression between subjects. And you certainly observe that the ultra-gifted kids, while generally above average at everything, are often significantly more ahead in math than in language, or vice versa (some of this is probably due to where they choose to spend their time, but I think a nonzero amount is innate advantage).
The term of art, for doing this within a single subject, is “enrichment”. And yeah, if you can do it, it fits nicely into schedules. “Taking more classes” is a more general approach. There are administrative obstacles to the latter: K-12 schools seem unlikely to permit a kid to skip half the sessions of one class so he can attend half the sessions of another class (and make up any gaps by reading the textbooks). Colleges are more likely to permit this by default, due to often not having attendance requirements, though one must beware of double-booking exams.
I think the best setup—can’t find the citation—is believed to be “taking a class with equally gifted children of the same age, paced for them”. If you don’t have that, then skipping grades (ideally per-subject) would address knowledge gaps; taking a class paced for at least somewhat gifted kids (possibly called an “advanced” class, or a class at a high-tier college) would partly address the learning speed gap, and enrichment would also address the learning speed gap, to a variable extent depending on the details.
A specific way of doing this, which I think would be good for education to move towards, is to have a programming component: have some of those optional exercises be “Write programs to implement the concepts from this chapter”.
Oh yup:
Versus:
Though one could say this is more of an attitude and habit and “ever bothered to figure out study skills” thing, than a “you’ve permanently lost your advantage” thing. If you took one of those jaded dropouts (of 160+ IQ) and, at age 30, threw them into a job where they had to do some serious and challenging scientific work… There’s a chance that their attitude and habits would make them fail and get fired within the first few months, that chance depending on how severe and how ingrained they are. But if they did ok enough to not get fired, then I expect that, within a year, they would be pulling ahead of a hypothetical 120 IQ counterpart for whom everything had gone great and who started with slightly more knowledge.
Yet another reason for different speeds in different subjects is that gifted kids often read about their interests in their free time—which can also increase the speed in given subject.
Yeah, learning by reading at home definitely has a huge effect in many cases. In Terence Tao’s education, he was allowed to progress through multiple years of a subject per year (and to do so at different rates in different subjects), and since the classes he attended were normal ones, I think his academic progression must have been essentially determined by his ability to teach himself at home via textbooks. Unless perhaps they let him e.g. attend 7th grade science 2 days a week and 6th grade science the rest? I should learn more about his life.
The educational setup can also feed into the reading aspect. During my childhood, on a few occasions, I did explicitly think, “Well, I would like to read more of this math stuff (at home), but on the other hand, each thing I learn by reading at home is another thing I’ll have to sit through the teacher telling me, being bored because I already know it”, and actually decided to not read certain advanced math stuff because of that. (Years later, I changed my mind and chose to learn calculus from my sister’s textbook around 8th grade—which did, in fact, cause me to be bored sitting through BC Calculus eventually.) This could, of course, be solved by letting kids easily skip past stuff by taking a test to prove they’ve already learned it.