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Yep. The Flynn Effect is essentially this, scaled up to the level of entire populations.

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When it comes to the effect of education on intelligence, mostly I feel confused, and this post doesn't fully solve my confusion. Here's my understanding:

I'll start with the basics; what is cognition and the g factor, and why is it important? As a simplified model, we might say that people face various tasks in their life; for instance maybe they need to go buy some food, or they need to solve some sort of issue at work, or whatever. Some of these tasks are cognitive tasks, in the sense that performing them is significantly dependent on intelligence; e.g. "abstraction, logic, understanding, self-awareness, learning, emotional knowledge, reasoning, planning, creativity, critical thinking, and problem-solving".

For any given cognitive task, people vary in their ability to solve it. This can happen for a lot of reasons, e.g. task familiarity or domain-specific knowledge, or more generally applicable skills and biological (especially brain) factors that are useful for the task. But there are a lot of cognitive tasks, and so that naturally raises the question of, what are the usual patterns in individual differences in task solving ability?

And the overwhelmingly important and dominant finding here is then the g factor: There is variation in a cognitive process or set of processes which is useful for just about any task you can think of. This variation appears to be mostly biological in origin. Why is this important? Because the modern world is so heavily dependent on cognitive abilities, and because the g factor is so broad, it becomes one of the biggest influences on outcomes of interest, in particular on "broad" outcomes. Whenever there is some outcome we want to study, there are likely some cognitive challenges that people need to face in order to achieve it, and those cognitive challenges will always depend fairly strongly on the g factor, so g automatically becomes important for the outcome.

I believe the above is pretty standard, and pretty compatible with your post? Now the parts that confuse me or which I think are less compatible with your post:

According to the above argument, g is primarily important because it improves your cognitive performance in a variety of real-world scenarios. But this seems like it implies that if there is any other factor, which also improves your cognitive performance in a similar variety of real-world scenarios, then it should also similarly improve your outcomes. It doesn't have to have the exact same pattern of associations as g has, or have the exact same mechanisms as g has, presumably the main thing that matters is that it improves your performance sufficiently broadly and sufficiently much.

Now suppose we take the first study you looked at in this post. It claims that education improves scores across all of the test types they tested, and that it does so in a persistent way. If it is right, then I think whether it is "on g" shouldn't matter for whether it has knock-on effects on things like economic productivity, because per the above argument even non-g factors which have broad effects should still be useful in practice. (That doesn't mean that it doesn't matter at all whether it is "on g". After all, whether the factor is "on g" can be useful for understanding other topics, such as the nature of race differences in intelligence; if education is off g but race differences are on g, then differences in education cannot be the cause of differences in intelligence.)

After analyzing this study, in the rest of your post, you argue that education doesn't improve real-world outcomes. This would be weird according to my theory, except you also argue that education doesn't improve test scores on all tests, which makes it make sense. Maybe education improves some abilities that are not useful, while there are other abilities that are useful that don't get improved by education. I'm not sure I buy the idea though, since the claims that there are such tests seem kind of sketch in some ways (e.g. reliant on multiple comparisons). But supposing we grant it, it seems like that should make it a huge priority to gather a battery of such tests, since they can presumably be more valid, and causally cleaner.

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Physics nitpicking here: having an absolute zero doesn't imply a meaningful or well-defined multiplication operation. In fact, the example of the Kelvin scale is good for illustrating this: as it is a little-known fact that negative Kelvin degrees are not only theoretically possible but have also been obtainable in the lab for several decades now - and negative Kelvin degrees are actually hotter than any finite positive-Kelvin temperature. So clearly -10K is not -1 hotter than 10K. As it happens, temperature just isn't a concept with a natural preferred scale - e.g., there is no objective advantage of using Kelvin over Rankine.

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Just the blanket term education implies a "good" education which is a joke. How many bad teachers have people had who were pretty much worthless or even destructive to teaching anything worthwhile? On the other hand I believe that constantly reading on one's own, especially good books actually does increase IQ. A person who reads constantly will undoubtedly be quicker on the draw mentally to his peers who do not. I mean think about it. No brainer. Reading is to the mind what exercise is to the body. Case and point is the life story of Dr. Ben Carson the famous brain surgeon turned Department Of Housing Secretary. Carson hailed from the poorest of slums of Detroit with no father. How did he succeed? His mother made him take out any two books from the library he wanted every week and do a book report on them. Engendering a life long love of reading early is the hugest factor in increasing mental acuity.

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