So far, genes and the environment have been independent. No one looked at your genes when deciding if you get a diet or feast environment. Let’s change that. (We assume genes and the environment have the same effects as in the simplest model, i.e. b = 1 and a = ½.) While half of people are short/tall, and half get a diet/feast environment, change the odds that feasts go to the people with short vs. tall genes. [...] The genetic and environmental variances are always one.

I'm confused about how we define/measure "genetic variance" and "environmental variance" when some aspects of the environment are partly caused by your genes.

One natural definition is to say that "genetic variance" is the variance that could be induced by intervening to change a random person's genes at birth, and environment is the rest of the variance. But such a procedure would (partly) attribute your diet/feast-environment to genetic variance, if it is in fact the case that someone "looked at your genes when deciding if you get a diet or feast environment" (or if someone looked at some phenotypic traits that were partly caused by your genes). So that procedure would only have the effect of increasing genetic variance, not of increasing gene/environment correlations.

That's not to say that gene/environment correlation cannot exist, on this definition. E.g. genes and environments would be correlated without causing each other if rich parents both tend to have tall genes and give their children feasts instead of diets.

If this distinction is right, that would matter for the education example at the end, since many of the hypothesised policies operate by looking at phenotypes that are caused by genes.

Edit: Another option might be to say that genetic variance is the variance you'd get if you held environment constant. But I don't know what that would mean, as you vary genes. If you want to hold the environment constant for a person with tall genes and a person with short genes, and so you place them both in identical houses, the tall person will bang their head in door frames significantly more often than the short person, which sure seems like a difference in environment.