We would like to examine the direct effect of $X$ on $Y$ without allowing $M$ to change. In the context of the Berkeley example, X represents the gender, Y represents the admission result, M represents the mediator(department candidates apply to). We force everybody to apply to the history department by setting $do(M = 0)$. People are randomly asked to report their sex as male ($do(X = 1)$) or as female ($do(X = 0)$), regardless of their actual genders. We obtain CDE through the difference in admission rates between the two groups. In symbols, $CDE(0)$ indicates that we forced the mediator to take on the value zero, i.e. the history department. We could also force everybody to apply to the engineering department: $do(M = 1)$. We would then denote the resulting controlled direct effect as $CDE(1)$.