Cognitive Dynamics: Additive or Multiplicative?

Abstract

Introduction: Cognition is assumed to rely on distinct and additive substages such as perceptual encoding, memory, and motor control. Nevertheless, questions surrounding the assumptions of modularity and additivity persist. If a stable cognitive architecture exists, then repeatedly executing the same cognitive act should repeatedly engage the self-same structure. If discreet sub-acts behave in a manner consistent with a sum of independent random variables, then the assumption of additive and modular cognitive processes is reasonable. However, if they develop dependencies, then the assumption of additivity and modularity in cognition should be questioned. Methods: The study required participants (N = 180) to successively execute identical elementary cognitive acts in a stacked 1-word, 2-word, and 4-word lexical decision task. Correct response time was the primary dependent measure. Results: Statistical analyses revealed evidence for additivity in mean response time after a logarithmic transformation (r2 = .81, p < .05 & r2 = .74, p < .05). This pattern is consistent with multiplicative dynamics. Conclusions: The results indicate that variance grows multiplicatively as a function of the number of sub-acts. A straightforward way to generate this pattern of variability growth is to assume the sub-acts develop successive dependencies and combine multiplicatively.