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) was determined for different added delays in six sessions of balancing trials performed on different days. The observed relation between L and the overall reaction delay τ reflected the feature of the underlying mathematical models: (i) for the Newtonian dynamics L is proportional to τ²; (ii) for the Aristotelian dynamics L is proportional to τ. Deviation of the measured L(τ) 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.