Dynamical incompatibilities in paced finger tapping experiments
Paced finger-tapping tasks are used to probe the error correction mechanism underlying sensorimotor synchronization. Despite their century-long history, fundamental contradictions persist in the literature. One such contradiction arises when comparing the two most common types of period perturbation: step change and phase shift. The stimulus sequence is exactly the same up to and including the (unexpected) perturbed stimulus. Why then would the timing of the next response be different between perturbation types, as observed? We show, both experimentally and theoretically, that responses to both types of perturbation are dynamically incompatible when recorded in separate experiments; that is, they cannot be described by a single underlying dynamical system due to the build-up of different temporal contexts. In contrast, when both types of perturbation are presented randomly within the same experiment, the responses become compatible and can be explained by a single mechanism. We conclude that a single underlying dynamical system can represent the response to all perturbation types, signs, and sizes, which is nevertheless calibrated by temporal context. Our results challenge the established idea of phase and period correction processes that are separately activated for different perturbation types.