The Physical Limits of Finite Observation: Seven Bounds on Sensing, Inference, and Control

Engineering practice often treats the error of a sensing-and-control system as a quantity that may, in principle, be driven to zero. We argue that this target is unreachable under finite resources, and we make the obstruction precise. We assemble seven established bounds — from information theory, statistical estimation, thermodynamics, the relativistic limits of computation, computability, and learning theory — and show how they constrain any finite observer that senses, infers, and acts. We are explicit that these are limits of three different kinds — physical, statistical, and logical — assembled, not derived from a single principle. Taken together they imply that no finite observer can at once represent a continuous environment without loss, estimate a continuous quantity exactly, retain its full history, be optimal across all environments, and certify its own consistency. We then adopt one modest criterion of correctness — bounded error on every input the system acts upon — and show that, under it, the bounds force a definite operating discipline: a declared error budget, an explicit representation of the boundary of competence, and the capacity to abstain on inputs that fall outside it. The result is substrate-independent, applying alike to a structural monitor, a quantum estimator, and an autonomous agent. We give the necessary properties of such a system, not a construction. The bounds are established results; their assembly, and the conditional architecture they imply, are the contribution.