Virtual stick balancing: skill development in Newtonian and Aristotelian dynamics.

Abstract

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, <i>L</i>_<i>c</i>) was determined for different added delays in six sessions of balancing trials performed on different days. The observed relation between <i>L</i>_<i>c</i> and the overall reaction delay <i>τ</i> reflected the feature of the underlying mathematical models: (i) for the Newtonian dynamics <i>L</i>_<i>c</i> is proportional to <i>τ</i>²; (ii) for the Aristotelian dynamics <i>L</i>_<i>c</i> is proportional to <i>τ</i>. Deviation of the measured <i>L</i>_<i>c</i>(<i>τ</i>) 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.