This talk explores how certain mathematical objects resist decomposition into simpler parts. Starting with classical examples from lattices in simple Lie groups, we extend this phenomenon to dynamical systems, specifically orbit equivalence relations arising from measure preserving actions of lattices on probability spaces. Our main result provides a rigidity theorem describing when orbit equivalence relations from lattice products must be essentially identical. Our approach uniquely combines ergodic theory of algebraic group actions with von Neumann algebras. Joint work with Daniel Drimbe.