Gaze fluctuations are not additively decomposable: reply to Bogartz and Staub

Our previous work interpreted single-lognormal fits to inter-gaze distance (i.e., "gaze steps") histograms as evidence of multiplicativity and hence interactions across scales in visual cognition. Bogartz and Staub (2012) proposed that gaze steps are additively decomposable into fixations and saccades, matching the histograms better and illustrating how additive processes can generate tailed histograms. In this reply, we consider the validity of fixation-versus-saccade distinctions, reviewing eye-movement literature and re-analyzing our original data. Careful examination of empirical literature undermines rigid fixation-versus-saccade distinctions. By comparing original gaze-step series with surrogate data, we present new evidence that temporal clustering in gaze-step data reflects interactive rather than additive processes. We conclude by discussing the relation between traditional notions of interactivity between components and complex-systems notions of interactivity across scales.