Complexity is not equal because the hidden variables of g (I will use it as you do for now) is not equal to the hidden variables of pressure.
The term statistical myth is appropriate because g is a myth. It is not backed by any direct experimental evidence but arises due to manipulations of statistical techniques. The Gas Law you cite was derived from experiments not from muddled manufacturings of statistics. And the tests correleate because they are made to correlate - it is all quite circular. Your post misrepresents Shalizi. Shalizi's argument is not "macroscale variables which abstract away an ensemble of microscale variables are a 'statistical myth'". Rather, it is that the way in which the latent variable g is first arrived at and then subsequently used to drive conclusions is invalid and meaningless:
But now new tests are validated by showing that they are highly correlated with the common factor, and the validity of g is confirmed by pointing to how well intelligence tests correlate with one another and how much of the inter-test correlations g accounts for. (That is, to the extent construct validity is worried about at all, which, as Borsboom explains, is not as much as it should be. There are better ideas about validity, but they drive us back to problems of causal inference.) By this point, I'd guess it's impossible for something to become accepted as an "intelligence test" if it doesn't correlate well with the Weschler and its kin, no matter how much intelligence, in the ordinary sense, it requires, but, as we saw with the first simulated factor analysis example, that makes it inevitable that the leading factor fits well. [13] This is circular and self-confirming, and the real surprise is that it doesn't work better.
As I quoted Shalizi prior: 'I don't want to be mis-understood as being on some positivist-behaviorist crusade against inferences to latent mental variables or structures. As I said, my deepest research interest is, exactly, how to reconstruct hidden causal structures from data.'
I also do not understand how you use g, as explained it is not composed of factors. It is the dominating factor. While I do not know about Intelligence tests I did follow the mathematics he gives and have applied similar in machine learning contexts. And Considering the wide variety of data linear models fail to properly capture my intuition is that yes, linear methods and assumptions of a Gaussian is overly simplistic without a solid backing argument, which has been unable to be given for near on a century now.
p.s. you are right, my original post was orthogonal to what Shalizi had to say. This was just my argument agains't yours in that I don't feel generalizing to one factor for a system as complex as human intelligence will produce as meaningful results as generalizing to a simple law for a collection of atoms/ a gas did.
The term statistical myth is appropriate because g is a myth. It is not backed by any direct experimental evidence but arises due to manipulations of statistical techniques. The Gas Law you cite was derived from experiments not from muddled manufacturings of statistics. And the tests correleate because they are made to correlate - it is all quite circular. Your post misrepresents Shalizi. Shalizi's argument is not "macroscale variables which abstract away an ensemble of microscale variables are a 'statistical myth'". Rather, it is that the way in which the latent variable g is first arrived at and then subsequently used to drive conclusions is invalid and meaningless:
But now new tests are validated by showing that they are highly correlated with the common factor, and the validity of g is confirmed by pointing to how well intelligence tests correlate with one another and how much of the inter-test correlations g accounts for. (That is, to the extent construct validity is worried about at all, which, as Borsboom explains, is not as much as it should be. There are better ideas about validity, but they drive us back to problems of causal inference.) By this point, I'd guess it's impossible for something to become accepted as an "intelligence test" if it doesn't correlate well with the Weschler and its kin, no matter how much intelligence, in the ordinary sense, it requires, but, as we saw with the first simulated factor analysis example, that makes it inevitable that the leading factor fits well. [13] This is circular and self-confirming, and the real surprise is that it doesn't work better.
As I quoted Shalizi prior: 'I don't want to be mis-understood as being on some positivist-behaviorist crusade against inferences to latent mental variables or structures. As I said, my deepest research interest is, exactly, how to reconstruct hidden causal structures from data.'
I also do not understand how you use g, as explained it is not composed of factors. It is the dominating factor. While I do not know about Intelligence tests I did follow the mathematics he gives and have applied similar in machine learning contexts. And Considering the wide variety of data linear models fail to properly capture my intuition is that yes, linear methods and assumptions of a Gaussian is overly simplistic without a solid backing argument, which has been unable to be given for near on a century now.
p.s. you are right, my original post was orthogonal to what Shalizi had to say. This was just my argument agains't yours in that I don't feel generalizing to one factor for a system as complex as human intelligence will produce as meaningful results as generalizing to a simple law for a collection of atoms/ a gas did.