Assessing randomness in human motion trajectories

Intelligence is often related to the behavioural complexity an agent can generate. For example, when studying human language one typically finds that sequences of letters or words are neither completely random nor totally determinate. This is often assessed quantitatively by studying the conditional entropy of sequences [1]. Similarly, entropy can be used to assess the human ability to generate random numbers. Humans have often been found to be not very good at generating random numbers[2]. Here we test human randomness when generating trajectories and compare entropic measurements of random vs. non-random motion. We designed a motor task where participants controlled a cursor by moving a Phantom manipulandum in a three-dimensional virtual environment. The cursor was constrained to move inside a 10x10 grid. In the first part of the experiment participants were asked to (1) perform a rhythmic movement, (2) write pre-specified letters, and (3) perform a random movement. In the second part of the experiment participants were asked again to perform random movements, but this time they received feedback from an artificial intelligence (based on context-tree weighting algorithm) predicting their next move. We found that the conditional entropy revealed different patterns for different motion types and that participants' motion randomness was only weakly susceptible to feedback