The complexities of keeping the beat: dynamical structure in the nested behaviors of finger tapping

Abstract

Recent research on fractal scaling in simple human behaviors (e.g., reaction time tasks) has demonstrated that different aspects of the performance (e.g., key presses and key releases) all reveal pink noise signals but yet are uncorrelated with one another in time. These studies have suggested that the independence of these signals might be due to the functional independence of these different sub-actions, given the task constraints. The current experiments investigated whether under a different set of constraints (e.g., finger tapping with and without a metronome) nested sub-actions might show interrelated dynamics, and whether manipulations affecting the fractal scaling of one also might have consequences for the scaling of others. Experiment 1 revealed that the inter-tap intervals and key-press durations of participants' tapping behavior were dynamically related to one another and that the fractal scaling of both changed in the switch from selfpaced to metronome-paced tapping. Consistent with past research, the inter-tap intervals changed toward an antipersistent, blue noise pattern of variation, but the keypress durations became even more persistent. Experiment 2 revealed that this pattern of results could be altered by asking participants to attempt to hold the key down for the entire length of the metronome tone. Specifically, the key-press duration of participants in the Bhold^group became less persistent in the switch across task conditions. Collectively, the results of these experiments suggest that fractal scaling reliably reflects the functional relationships of the processes underlying task performance. Keywords Fractal scaling . Long-range correlation . Finger tappingThere is growing appreciation within the fields of psychology and cognitive science that human behavior is inherently complex. Although there is not yet a consensus scientific definition (Delignières & Marmelat, 2012;Gell-Mann, 1995; Goldberger, Peng, & Lipsitz, 2002;Kelty-Stephen & Dixon, 2012;Kloos & Van Orden, 2010;Mainzer, 2005), Bcomplexity^here is intended to mean not only that behavior involves Ba lot of parts^(neurons, muscles, and bones within an actor, the behavior of other actors, the perpetually changing state of the environment) but also that these parts are interdependently coupled via nonlinear and sometimes nonobvious interactions. Understanding such complexity is no easy task, especially given that even the simplest of behaviors can reveal a surprising degree of complexity.Consider the task of rhythmically tapping one's finger. Although this is a relatively common and easily performed human behavior, scientific investigation has found that this simple act is supported and influenced by a range of complex, interdependent processes. Indeed, a vast literature on Bsensorimotor synchronization^has shown that the ability of humans to time their actions to other events depends on a host of neural

Factorization of Force and Timing in Sensorimotor Performance: Long‐Range Correlation Properties of Two Different Task Goals

“…Evidence from Coey et al. () suggests that it is indeed possible. However, in their study they looked at systematic long‐range variation in two different dependent measures that can be extracted from a time series that could explain performance, namely key‐press durations and response intervals.…”

“…Previous studies in the area such as Coey et al. () and Rigoli, Holman, Spivey, and Kello () have looked at the nested structure of multiple components from the same behavior. The novelty of this study comes from the fact that two sub‐goals of the same behavioral task have not been studied in the context of the independence in their long‐term performance.…”

“…Looking for relations between long‐range correlation properties of simultaneous performance variables has been examined in two recent studies (Coey, Hassebrock, Kloos, & Richardson, ; Rigolli et al., 2014). In the former, dependencies between two different performance variables in the same task were explored: inter‐tap intervals and key press durations in timing.…”

Complexity matching effects in bimanual and interpersonal syncopated finger tapping

“…At the same time, it is important to consider the “emergent” perspective [e.g., 23,27,28], and attempt to develop formal models that demonstrate how CM might spontaneously emerge from continuous coupling between interacting systems. Finally, it is very important to attend to the different task variables (i.e., ITI vs. asynchrony) and to carefully specify the system architecture [e.g., 21]. To this end, it would be advantageous to adopt a “behavioral dynamics” perspective [42] to consider how to understand the CM phenomenon both as a product of two interacting (sub)systems and as a stable dynamic of their operation as a large, unified system.…”

“…If participants tap in synchrony with a metronome stimulus [20], however, the scaling in the inter-tap interval series shifts past white noise toward strongly anti-persistent, “blue noise”, while the asynchrony series continues to display pink noise scaling (H ≈ 0; Fig. 1A and 1B, bottom), indicating a functional re-organization of the behavioral system [10,21]. …”