Towards assessing randomness and complexity 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 measures can also be used to assess the human ability to generate random numbers — a task that humans often find difficult [2]. Previous studies in motor control have found, for example, that humans cannot significantly increase the level of trajectory randomness in single-joint movements [3]. 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) predicting their next move. We found that participants can change the randomness of their behaviour through feedback and that excess entropy can be used as a complexity measure of motion trajectories. [1] Rao, R. P. N., Yadav, N., Vahia, M. N., Joglekar, H., Adhikari, R., and Mahadevan, I. (2009). Entropic evidence for linguistic structure in the Indus script. Science, 324(5931):1165. [2] Figurska, M., Stanczyk, M., and Kulesza, K. (2008). Humans cannot consciously generate random numbers sequences: Polemic study. Medical hypotheses