Virtual stick balancing: skill development in Newtonian and Aristotelian dynamics

Human reaction delay significantly limits manual control of unstable systems. It is more difficult to balance a short stick on a fingertip than a long one, because a shorter stick falls faster and therefore requires faster reactions. In this study, a virtual stick balancing environment was developed where the reaction delay can be artificially modulated and the law of motion can be changed between second-order (Newtonian) and first-order (Aristotelian) dynamics. Twenty-four subjects were separated into two groups and asked to perform virtual stick balancing programmed according to either Newtonian or Aristotelian dynamics. The shortest stick length (critical length, L-c) was determined for different added delays in six sessions of balancing trials performed on different days. The observed relation between L-c and the overall reaction delay tau reflected the feature of the underlying mathematical models: (i) for the Newtonian dynamics L-c is proportional to tau(2); (ii) for the Aristotelian dynamics L-c is proportional to tau. Deviation of the measured L-c(tau) function from the theoretical one was larger for the Newtonian dynamics for all sessions, which suggests that, at least in virtually controlled tasks, it is more difficult to adopt second-order dynamics than first-order dynamics.