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Nervous systems sense, communicate, compute, and actuate movement, using distributed hardware with tradeoffs in speed and accuracy. The resulting sensorimotor control is nevertheless remarkably fast and accurate due to highly effective layered architectures. However, such architectures have received little attention in neuroscience due to the lack of theory that connects the system and hardware level speed-accuracy tradeoffs. In this paper, we present a theoretical framework that connects the speed-accuracy tradeoffs of sensorimotor control and neurophysiology. We characterize how the component SATs in spiking neuron communication and their sensory and muscle endpoints constrain the system SATs in both stochastic and deterministic models. The results show that appropriate speed -accuracy diversity at the neurons/muscles levels allow nervous systems to improve the speed and accuracy in control performance despite using slow or inaccurate hardware. Then, we characterize the fundamental limits of layered control systems and show that appropriate diversity in planning and reaction layers leads to both fast and accurate system despite being composed of slow or inaccurate layers. We term these phenomena “Diversity Sweet Spots.” The theory presented here is illustrated in a companion paper, which introduces simple demos and a new inexpensive and easy-to-use experimental platform.