I know how the game works, I’ve paged through the Pearl book. But here, in this case, I don’t care much about causality. I can observe the existence of stupid people and smart people (and somewhat-stupid, and middle-of-the-road, and a bit smart, etc.). I can roughly rank them on the smart—stupid axis. That axis won’t capture all the diversity and the variation, but it will capture some. Whether what it captures is sufficient depends, of course. It depends on the purpose of the exercise and in some cases that’s all you need and in some cases it’s entirely inadequate. However in my experience that axis is pretty relevant to a lot of things. It’s useful.
Note that here no prediction is involved. I’m not talking about whether estimates of g (IQ, basically) can/will predict your success in life or any similar stuff. That’s a different discussion.
To the extent that you view g as what it is, I have no problem. But people think g is (a) a real thing and (b) causal. It’s not at all clear it is either. “Real things” involved in human intelligence are super complicated and have to do with brain architecture (stuff we really don’t understand well). We are miles and miles and miles away from “real things” in this setting.
The game I was describing was how PCA works, not stuff in Pearl’s book. The point was PCA is just relying on a model of a joint distribution, and you have to be super careful with assumptions to extract causality from that.
I think of g as, basically, a projection from the high-dimensional space of, let’s say, mind capabilities into low dimensions, in this case just a single one. Of course it’s an “artifact”, and of course you lose information when you do that.
However what I mean by g pointing a finger at the real thing is that this high-dimensional cloud has some structure. Things are correlated (or, more generally, dependent on each other). One way—a rough, simple way—to get an estimate of one feature of this structure is to do IQ testing. Because it’s so simple and because it’s robust and because it can be shown to be correlated to a variety of real-life useful things, IQ scores became popular. They are not the Ultimate Explanation for Everything, but they are better than nothing.
With respect to causality, I would say that the high-dimensional cloud of mind capabilities is the “cause”. But it’s hard to get a handle on it, for obvious reasons, and our one-scalar simplification of the whole thing might or might not be relevant to the causal relationship we are interested in.
P.S.
The point was PCA is just relying on a model of a joint distribution, and you have to be super careful with assumptions to extract causality from that.
PCA actually has deeper problems because it’s entirely linear and while that makes it easily tractable, real life, especially its biological bits, is rarely that convenient.
Also in practical informal talk, people overemphasize IQ because it is so fun for hierarchy-minded primates to arrange people from best to worst.
edit re: PCA: Yes, PCA is a super-parametric method, with the usual super-parametric method problems. However, the issue I have with PCA in this context is different, and also occurs in very flexible, fully non-parametric methods. Basically the issue is, no matter how you massage it, the joint distribution simply does not have the causal information you want in it, in general.
I know how the game works, I’ve paged through the Pearl book. But here, in this case, I don’t care much about causality. I can observe the existence of stupid people and smart people (and somewhat-stupid, and middle-of-the-road, and a bit smart, etc.). I can roughly rank them on the smart—stupid axis. That axis won’t capture all the diversity and the variation, but it will capture some. Whether what it captures is sufficient depends, of course. It depends on the purpose of the exercise and in some cases that’s all you need and in some cases it’s entirely inadequate. However in my experience that axis is pretty relevant to a lot of things. It’s useful.
Note that here no prediction is involved. I’m not talking about whether estimates of g (IQ, basically) can/will predict your success in life or any similar stuff. That’s a different discussion.
???
To the extent that you view g as what it is, I have no problem. But people think g is (a) a real thing and (b) causal. It’s not at all clear it is either. “Real things” involved in human intelligence are super complicated and have to do with brain architecture (stuff we really don’t understand well). We are miles and miles and miles away from “real things” in this setting.
The game I was describing was how PCA works, not stuff in Pearl’s book. The point was PCA is just relying on a model of a joint distribution, and you have to be super careful with assumptions to extract causality from that.
I think of g as, basically, a projection from the high-dimensional space of, let’s say, mind capabilities into low dimensions, in this case just a single one. Of course it’s an “artifact”, and of course you lose information when you do that.
However what I mean by g pointing a finger at the real thing is that this high-dimensional cloud has some structure. Things are correlated (or, more generally, dependent on each other). One way—a rough, simple way—to get an estimate of one feature of this structure is to do IQ testing. Because it’s so simple and because it’s robust and because it can be shown to be correlated to a variety of real-life useful things, IQ scores became popular. They are not the Ultimate Explanation for Everything, but they are better than nothing.
With respect to causality, I would say that the high-dimensional cloud of mind capabilities is the “cause”. But it’s hard to get a handle on it, for obvious reasons, and our one-scalar simplification of the whole thing might or might not be relevant to the causal relationship we are interested in.
P.S.
PCA actually has deeper problems because it’s entirely linear and while that makes it easily tractable, real life, especially its biological bits, is rarely that convenient.
I don’t think we disagree (?anymore?).
Also in practical informal talk, people overemphasize IQ because it is so fun for hierarchy-minded primates to arrange people from best to worst.
edit re: PCA: Yes, PCA is a super-parametric method, with the usual super-parametric method problems. However, the issue I have with PCA in this context is different, and also occurs in very flexible, fully non-parametric methods. Basically the issue is, no matter how you massage it, the joint distribution simply does not have the causal information you want in it, in general.
Yep. You just have to pick the correct metric: the one where you come out on top ;-)