  Let $S$ be a Shimura variety with reflex field $E$. We prove that the action
of $\operatorname{Gal}(\overline{\mathbb{Q}}/E)$ on $S$ maps special points to
special points and special subvarieties to special subvarieties. Furthermore,
the Galois conjugates of a special point all have the same complexity (as
defined in the theory of unlikely intersections). These results follow from
Milne and Shih's construction of canonical models of Shimura varieties, based
on a conjecture of Langlands which was proved by Borovoi and Milne.
