Abstract
Time series of human performances present fluctuations around a mean value. These fluctuations are typically considered as insignificant, and attributable to random noise. Over recent decades, it became clear that temporal fluctuations possess interesting properties, however, one of which the property of fractal 1/f scaling. 1/f scaling indicates that a measured process extends over a wide range of timescales, suggesting an assembly over multiple scales simultaneously. This paper reviews neurological, physiological, and cognitive studies that corroborate the claim that 1/f scaling is most clearly present in healthy, well-coordinated activities. Prominent hypotheses about the origins of 1/f scaling are confronted with these reviewed studies. It is concluded that 1/f scaling in living systems appears to reflect their genuine complex nature, rather than constituting a coincidental side-effect. The consequences of fractal dynamics extending from the small spatial and temporal scales (e.g., neurons) to the larger scales of human behavior and cognition, are vast, and impact the way in which relevant research questions may be approached. Rather than focusing on specialized isolable subsystems, using additive linear methodologies, nonlinear dynamics, more elegantly so, imply a complex systems methodology, thereby exploiting, rather than rejecting, mathematical concepts that enable describing large sets of natural phenomena.
Highlights
The presence of 1/f scaling in human performances is arguably one of the most puzzling, yet lawful phenomena in cognitive science. 1/f scaling represents fractal, self-similar processes nested across multiple scales of measurement
Deviations from 1/f scaling are observed in asthma patients, out of which those with more pronounced 1/f signatures in breathing rhythm showed better recovery after treatment [73]. These findings indicate together that fractal dynamics increase the overall efficiency of the respiratory system
From this perspective, 1/f scaling represents a functional aspect of human performance related to cognitive timekeeping, but the different source of 1/f scaling in each domainspecific application has the form of a fractal generator that and together with nonfractal components, makes up the dynamics of repeated responses
Summary
The presence of 1/f scaling in human performances is arguably one of the most puzzling, yet lawful phenomena in cognitive science (see [1,2,3,4,5,6,7]). 1/f scaling represents fractal, self-similar processes nested across multiple scales of measurement. Its occurrence implies that the rescaling of a time series leaves the distributional properties of the time series unaffected From both a statistical and theoretical point of view, fractal scaling is widespread across the central nervous system, motor behavior, cognitive performances, and well beyond. The associated serial correlations from trial to trial decay very slowly as the number of intervening trials increases, indicating persistent serial correlations, in contrast with the traditional view that they are transient (see e.g., [2]) This sets 1/f scaling apart from random noise, which lacks this serial dependence. 1/f scaling, in contrast, is expressed as an inversely proportional relation between log power and log frequency (see Figure 1(d)) This implies a nested sequence effect spanning over the entire time course of a measurement and even beyond, encompassing undulating “waves” of relatively longer and shorter response times travelling across the series. Each distinct account will have to deal with this broad linkage
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