We present and formally characterize a novel paradox — hereafter designated The Rodrik Paradox — arising from the application of asymmetric, one-way temporal displacement to a volunteer subject designated Rodrik #1. Beginning at age 30, the subject is transported five years into the past, from which point he observes but cannot interact with his younger self, Rodrik #2. Upon Rodrik #2 reaching age 30, the experiment repeats, spawning Rodrik #3. We demonstrate that this process generates an unbounded, self-sustaining cascade of temporally distinct observer instances, each numerically independent yet biologically and mnemonically convergent. We derive the Accumulation Function N(t), quantify the simultaneous observer population across the subject’s natural lifespan, and identify three irreducible sub-paradoxes: the Identity Collapse Problem, the Bootstrap Causality Loop, and the Infinite Observer Horizon. We further demonstrate that the termination of Rodrik #1 does not — and cannot — terminate the chain. The implications for causal closure, personal identity theory, and the metaphysics of temporal observation are profound and, we argue, unresolved by prior literature.