THE EUROPEAN PHYSICAL JOURNAL SPECIAL TOPICS Regular Article Stick balancing, falls and Dragon-Kings

Abstract. The extent to which the occurrence of falls, the dominant feature of human attempts to balance a stick at their fingertip, can be predicted is examined in the context of the “Dragon-King ” hypothe-sis. For skilled stick balancers, fluctuations in the controlled variable, namely the vertical displacement angle θ, exhibit power law behav-iors. When stick balancing is made less stable by either decreasing the length of the stick or by requiring the subject to balance the stick on the surface of a table tennis racket, systematic departures from the power law behaviors are observed in the range of large θ. This ob-servation raises the possibility that the presence of departures from the power law in the large length scale region, possibly Dragon-Kings, may identify situations in which the occurrence of a fall is more im-minent. However, whether or not Dragon-Kings are observed, there is a Weibull-type survival function for stick falling. The possibility that increased risk of falling can, at least to some extent, be predicted fro