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Intrinsic Fluctuations Yield Pervasive 1/f Scaling: Comment on Moscoso del Prado Martín (2011)
Author(s) -
Kello Christopher
Publication year - 2011
Publication title -
cognitive science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.498
H-Index - 114
eISSN - 1551-6709
pISSN - 0364-0213
DOI - 10.1111/j.1551-6709.2011.01185.x
Subject(s) - scaling , yield (engineering) , humanities , psychology , philosophy , physics , mathematics , thermodynamics , geometry
Kello, Beltz, Holden, and Van Orden (2007) reported four experiments in which series of key-presses were elicited so that two parallel series of measurements could be analyzed: reaction times (RTs) and key-contact durations. Spectral analyses showed that both series exhibited 1 ⁄ f (i.e., fractal) scaling, and that scaling in RTs was stronger when cues were predictable, as expressed by steeper slopes (closer to )1) in spectral plots. However, scaling in durations was unaffected by cue predictability, and RTs and durations were mostly uncorrelated. This dissociation was interpreted as evidence that 1 ⁄ f scaling does not have a single, isolable source in human behavior. Given this summary alone, one might think that two isolable sources could explain our results, one for RTs and one for durations. However, the data were found to be inconsistent with the most likely dual-source accounts, that is, those associating RTs with a controlled process of some kind, and durations with an automatic process. Numerous studies have associated controlled processes with cognitive workload, which means that 1 ⁄ f scaling should be associated in a consistent manner with measures of cognitive workload. To the contrary, a survey of 1 ⁄ f scaling findings (including experiments from Kello et al., 2007) showed that estimated scaling exponents sometimes increased and sometimes decreased with cognitive workload. To examine further whether 1 ⁄ f scaling has just one or two isolable sources, Kello, Anderson, Holden, and Van Orden (2008) analyzed fluctuations in acoustic energy over many repetitions of the word ‘‘bucket.’’ A long-term average spectrum covering each syllable was computed, resulting in an estimate of acoustic power for each of 45 frequency bins per syllable. Thus, each bin yielded a series of acoustic power fluctuations, and nearly all series exhibited clear 1 ⁄ f scaling. To test for multiple, linearly isolable sources of 1 ⁄ f scaling, PCA was used to estimate 30 such sources.