## 4 Discussion
We believe additional research is needed related to reproducing our findings relative to the entropy values using smaller \(r\) values. For this project, we presented the data using smaller \(r\) values, we but are unsure of their clinical interpretation and meaningfulness. Before any measurement tool can be used for clinical purposes, its precision, i.e., reliability or consistency, should be established. Intuition suggests that an amplitude metric like the center of pressure, e.g., the magnitude of postural sway, denotes precision; that is, optimal postural control is evidenced by less movement, or error, about a target position. In the past, based on this assumption, linear modeling and averaging the COP variability, i.e., standard deviation, suggesting that COP variability was a general indicator of error, was practical and justified. However, it has been shown that the COP time series is non-linear and that its variations are neither random nor independent but have deterministic properties [10]. Thus, it appears that the COP is part of a complex of interacting systems, i.e., visual, somatosensory, and vestibular, that must be adaptable and flexible in an unpredictable environment. How might this be explained? Several neurological and biomechanical models of the postural control system have generally evolved from the groundbreaking work of [PERSON] [60], who suggested that coordinated movement in general, and postural control in particular, was a \"problem\" that involved mastering, using a hierarchical central nervous system (CNS) model, the many redundant degrees of freedom (DoF) available to the neuro-musculoskeletal system. [PERSON] suggested that the CNS implemented specific control structures to limit the DoF at four levels, one of which includes muscle synergies. Muscle synergies are groups of muscles that cooperate to produce and/or control movement as part of the somatosensory system. [PERSON] et al. [61], on the other hand, proposed an alternative model guided by a \"principle of abundance\" that suggested that all the elements, i.e., DoF, always participated in all the tasks, which assured both stability and flexibility, i.e., variability, of the performance. [PERSON] et al. triggered a rethinking of how the COP time series might be examined. The successful use of ApEn by clinicians, such as [PERSON], led to the introduction and use of entropic measures in biomechanical posture analysis. Generally, that work demonstrated the following: (1) reduced variability of COP time series is produced by a system under greater constraints and fewer DoF choices associated with poor postural control, and (2) more irregular output, i.e., increased variability, is produced by a less constrained system with more available DoF [10]. This brief review of coordinated movement modeling is relevant to the variability of the ApEn and SampEn values that we observed between trials of individuals, and between individuals. For example, Figure 11 (ApEn) and Figure 12 (SampEn) illustrated several common features related to the medial-lateral excursion of the COP time series among the two entropy methods: (1) reduced ApEn and SampEn average values and inter-trial variability for all participants for the EOFT, i.e., baseline, condition; (2) greater ApEn and SampEn and inter-trial variability for both the eyes-open and eyes-closed tandem stance conditions; and (3) observable differences in the magnitude and variability of ApEn and SampEn between participants #4 and #5 and the other participants. Our data suggest that the reduced average entropy and variability in the baseline condition may be associated with an environment that was more routine and less challenging for each participant, and that reduced adaptability in the use of DoF was necessary. On the other hand, more flexibility and adaptability, i.e., more choices in how patterns of the DoF were solicited and used, were necessary for the more challenging balance tasks.