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Register a new userFitts Law for speed-accuracy trade-off describes a diversity-enabled sweet spot in sensorimotor control
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Human sensorimotor control exhibits remarkable speed and accuracy, and the tradeoff between them is encapsulated in Fitts Law for reaching and pointing. While Fitts related this to Shannons channel capacity theorem, despite widespread study of Fitts Law, a theory that connects implementation of sensorimotor control at the system and hardware level has not emerged. Here we describe a theory that connects hardware (neurons and muscles with inherent severe speed-accuracy tradeoffs) with system level control to explain Fitts Law for reaching and related laws. The results supporting the theory show that diversity between hardware components is exploited to achieve both fast and accurate control performance despite slow or inaccurate hardware. Such diversity-enabled sweet spots (DESSs) are ubiquitous in biology and technology, and explain why large heterogeneities exist in biological and technical components and how both engineers and natural selection routinely evolve fast and accurate systems using imperfect hardware.
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Nervous systems sense, communicate, compute and actuate movement using distributed components with severe trade-offs in speed, accuracy, sparsity, noise and saturation. Nevertheless, brains achieve remarkably fast, accurate, and robust control performance due to a highly effective layered control architecture. Here we introduce a driving task to study how a mountain biker mitigates the immediate disturbance of trail bumps and responds to changes in trail direction. We manipulated the time delays and accuracy of the control input from the wheel as a surrogate for manipulating the characteristics of neurons in the control loop. The observed speed-accuracy trade-offs (SATs) motivated a theoretical framework consisting of layers of control loops with components having diverse speeds and accuracies within each physical level, such as nerve bundles containing axons with a wide range of sizes. Our model explains why the errors from two control loops -- one fast but inaccurate reflexive layer that corrects for bumps, and a planning layer that is slow but accurate -- are additive, and show how the errors in each control loop can be decomposed into the errors caused by the limited speeds and accuracies of the components. These results demonstrate that an appropriate diversity in the properties of neurons across layers helps to create diversity-enabled sweet spots (DESSs) so that both fast and accurate control is achieved using slow or inaccurate components.
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