A group action is transitive iff it has one orbit. Intuitively, this seems to say $G$ shuffles around all the elements of the $G$-set.
A group action is primitive iff it has no nontrivial blocks, which intuitively seems to say that no nontrivial subsets can move around as blocks without interacting with the rest of the "particles" of the $G$-set.
Now if I think about dynamical systems, the transitivity of an action tells me I can look at my $G$-set as one system because the dynamics apply to all of it. Along the same train of thought, the primitiveness of an action tells me the system is irreducible in the sense that there is no nontrivial subsystem whose composition, or size, being invariant under the dynamics. The analogy with ergodicity is obvious.
I'm pretty sure someone has already thought of this, but I haven't found anything about it, so I'm asking here: Is my intuition misguided or just plain wrong? What's the connection?