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About 11,000 words on the triviality of finding that positively correlated variables are all correlated with a linear combination of each other, and why this becomes no more profound when the variables are scores on intelligence tests.
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.  This is circular and self-confirming, and the real surprise is that it doesn't work better. ...
My playing around with Thomson's ability-sampling model has taken, all told, about a day, and gotten me at least into back-of-the-envelope, Fermi-problem range. In fact, the biggest problem with Thomson's model is that the appearance of g is too strong, since it easily passes tests for there being only a single factor, when real intelligence tests, such as the Weschler, all fail them. If it wasn't a distraction from my real work, I'd look into whether weakening the assumption that tests are completely independent, uniform samples from the pool of shared abilities couldn't produce something more realistic.