Cognitive and Neural Representations of Fractals in Vision, Music, and Action.

The concept of fractal was popularized by Mandelbrot as a tool to tame the geometrical structure of objects with infinite hierarchical depth. The key aspect of fractals is the use of simple parsimonious rules and initial conditions, which when applied recursively can generate unbounded complexity. Fractals are structures ubiquitous in nature, being present in coast lines, bacteria colonies, trees, and physiological time series. However, within the field of cognitive science, the core question is not which phenomena can generate fractal structures, but whether human or animal minds can represent recursive processes, and if so in which domains. In this chapter, we will explore the cognitive and neural mechanisms underlying the representation of recursive hierarchical embedding. Language is the domain in which this capacity is best studied. Humans can generate an infinite array of hierarchically structured sentences, and this capacity distinguishes us from other species. However, recent research suggests that humans can represent similar structures in the domains of music, vision, and action and has provided additional cues as to how these capacities are cognitively implemented. Using a comparative approach, we will map the commonalities and differences across domains and offer a roadmap to understand the neurobiological implementation of fractal cognition.

Hierarchical Structure in Sequence Processing: How to Measure It and Determine Its Neural Implementation.

In many domains of human cognition, hierarchically structured representations are thought to play a key role. In this paper, we start with some foundational definitions of key phenomena like "sequence" and "hierarchy," and then outline potential signatures of hierarchical structure that can be observed in behavioral and neuroimaging data. Appropriate behavioral methods include classic ones from psycholinguistics along with some from the more recent artificial grammar learning and sentence processing literature. We then turn to neuroimaging evidence for hierarchical structure with a focus on the functional MRI literature. We conclude that, although a broad consensus exists about a role for a neural circuit incorporating the inferior frontal gyrus, the superior temporal sulcus, and the arcuate fasciculus, considerable uncertainty remains about the precise computational function(s) of this circuitry. An explicit theoretical framework, combined with an empirical approach focusing on distinguishing between plausible alternative hypotheses, will be necessary for further progress.

Hierarchy, multidomain modules, and the evolution of intelligence.

In this commentary, we support a complex, mosaic, and multimodal approach to the evolution of intelligence. Using the arcuate fasciculus as an example of discontinuity in the evolution of neurobiological architectures, we argue that the strict dichotomy of modules versus G, adopted by Burkart et al. in the target article, is insufficient to interpret the available statistical and experimental evidence.