 We assume that the intervention \(\ido(\bZ = \bz)\) is being performed in the actual world, and hence that we are observing the values that other variables take \((\bX =\bx)\) in the same world where the intervention takes place. In the case of counterfactuals, we observe the value of various variables in the actual world, in which there is no intervention. We then ask what would have happened if an intervention had been performed. The variables whose values we observed may well take on different values in the hypothetical world where the intervention takes place. Here is a simple illustration of the difference. Suppose that we have a causal model in which treatment with a drug causes recovery from a disease. There may be other variables and causal relations among them as well.