CHAPTER 6 Gauging the Fractal Dimension of Response Times from Cognitive Tasks John G. Holden Department of Psychology California State University, Northridge Northridge, CA 91330-8255 U. S. A. E-mail:
[email protected] Holden An unexpected and exotic brand of variability resides in the trial-by-trial fluctuations of human judgments of passing time. The pattern, called 1/ƒ or pink noise, is a construct from fractal geometry. Pink noise is associated with complex systems whose components interact on multiple time scales to self-organize their behavior (Bassingthwaighte, Liebovitch, & West, 1994; Jensen, 1998; Van Orden, Holden, & Turvey, 2003; see also Aks, Chapter 7). This chapter describes the phenomenon of pink noise, and explains how to conduct statistical analyses that identify it in response time data from elementary cognitive tasks. It was Gilden, Thorton, and Mallon (1995) who first reported pink noise in response time variability during the fundamentally cognitive task of estimating fixed intervals of time. Gilden et al.’s temporal estimation task required participants to repeatedly estimate fixed intervals of time—in essence to “become a clock”—by pressing a button at each instant they believed a specific time interval had elapsed. Separate laboratory sessions were administered for each of several fixed target time-interval conditions. In each session 1000 time- interval judgments were collected in succession. The time-interval conditions ranged from 1/3 s up to 10 s. Of course, no participant’s succession of time-interval judgments was exactly the same on every trial. Instead they varied from trial to trial. Lining up the series of successive time estimates in the strict order in which they were collected (i.e., trial 1, 2, … 1000) yielded a trial series of response times, which was treated very much like a standard time series in Gilden et al.’s statistical analyses.