Causality, Criticality, and Reading Words: Distinct Sources of Fractal Scaling in Behavioral Sequences

Cognitive Science 35 (5):785-837 (2011)
The finding of fractal scaling (FS) in behavioral sequences has raised a debate on whether FS is a pervasive property of the cognitive system or is the result of specific processes. Inferences about the origins of properties in time sequences are causal. That is, as opposed to correlational inferences reflecting instantaneous symmetrical relations, causal inferences concern asymmetric relations lagged in time. Here, I integrate Granger-causality with inferences about FS. Four simulations illustrate that causal analyses can isolate distinct FS sources, whereas correlational techniques cannot. I then analyze three simultaneous sequences of responses from a database of word-naming trials. I find that two, or perhaps three, distinct sources account for the presence of FS in these sequences, but FS is not a general property of the system. This suggests that FS arises due to the properties of a limited number of identifiable psychological and/or neural processes. Finally, I reanalyze a previously published dataset of acoustic frequency spectra using the new tools. The causality/criticality combination introduced here offers a new important perspective in the study of cognition
Keywords Word naming  Bayesian assessment of scaling  Transfer entropy  Reaction time  Fractal scaling  Granger causality
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DOI 10.1111/j.1551-6709.2011.01184.x
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Claude Shannon (1948). A Mathematical Theory of Communication. Bell System Technical Journal 27:379–423.

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