Peng Z, Genewein T, Braun DA (2014) Assessing randomness and complexity in human motion trajectories through analysis of symbolic sequences. Front. Hum. Neurosci. 8:168. doi: 10.3389/fnhum.2014.00168
In this paper we analyze the complexity of human motion trajectories and investigate whether humans can generate completely random movements. We also tackle the question of how to measure complexity in human motion trajectories. The difficulty is that many common measures of complexity are simply measures of irregularity that are maximized by completely random trajectories. However, completely random trajectories are not considered very complex to human observers. On the other hand, completely predictable (and thus regular) movements are not complex either. Maximally complex trajectories seem to lie somewhere in-between fully predictable and fully unpredictable movements: complex motions have some regularity but also enough variation to be somewhat unpredictable. In the paper we compare classical complexity measures against the effective measure complexity which is a measure that is maximized for sequences that are neither fully predictable nor completely random.
In our experimental study participants were generating motion trajectories by “drawing” with a virtual stylus in a 3D virtual reality setup. We asked participants to either draw letters or invent their own patterns or perform a movement that is as random as possible. We then analyzed the complexity of their movements using classical measures but also the effective measure complexity (EMC). With the classical measures we find that they are maximized for the random trajectories - however the EMC was maximal for the invented patterns, second largest for drawings of letters and lowest for random movements, which is in line with an intuitive judgment of motion complexity. Additionally we found that the random trajectories generated by humans still contained some regularity, implying that the trajectories were not completely random. In a second experiment we trained humans with a pursuit game where an artificial agent tried to predict where participants would move next while drawing a random trajectory. If the prediction was correct an error sound was played back and participants’ goal was to minimize the errors by being as unpredictable as possible. We found that with this training humans could learn to increase the randomness of their motions.
The results of this paper lead to the question of whether aesthetics and human judgment of aesthetics could be related to the effective measure complexity. The hypothesis is that we find patterns that are either fully predictable or fully unpredictable boring, whereas patterns that contain some regularity but also some surprise (in terms of unpredictability) seem to be interesting. A interesting question would then be whether patterns that have a high EMC would also be judged interesting or aesthetically pleasing. However, this question is subject to future investigations.
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