The Mathematics of Relatedness

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Social interactions are beneficial for aging individuals, be they healthy or affected by degenerative disease. Social engagement not only brings support but also acts on brain structure, behavior and cognition to slow aging. The aging process, however, produces multiple changes that compromise people’s ability to interact with others (person too slow or frail to keep to regular outings with family; thought processes and verbal fluency too sluggish, and hearing too feeble, to secure sufficiently frequent turns-at-talk in group conversation with younger individuals; etc.), leading to attrition of numerous and varied social links. The goal of this research program, to be conducted by an interdisciplinary team of socio-cognitive scientists, mathematical physicists and geriatric nursing experts, is to gain understanding on first principles underlying preservation or loss of social interaction in aging. This is accomplished by mathematically modeling the underpinnings of social integration and segregation within heterogeneous groups of older and younger individuals, and by conducting observational studies of group activities involving elderly and younger adults in a memory and wellness center (storytelling, gentle yoga, music making). Our mathematical model of social coordination (empirically validated in young adults) allows to vary each agent’s “coupling” capabilities, (behavioral or cognitive) slowing pace, the memory process of social adaptation and behavioral noise level. Preliminary evidence suggests that pace discrepancy and weak coupling lead to briefer, less frequent periods of coordination, which are fundamentally scale- and context-dependent. Theory also suggests that noise enhances the stability of heterogenous groups, while tending to disrupt that of more homogenous ones. All of those preliminary findings point to systemic effects: interactional opportunities not only depend on individuals, but also nontrivially on the match or mismatch between individuals and their social environment. Therefore, the contribution of this research on methodology and measurement in the behavioral and social sciences lies in a much-needed emphasis on this systemic of social behavior, that is, the effect that the whole exerts on the parts, a key property of complex systems. It leads to an exemplary framework for quantifying individual and collective behavior; provides analysis strategies to characterize their entanglement; and identifies cues to recognize when systemic effects are likely at play. The specific aims of this projects are, first and via models, to quantify the effect that the social environment exerts on elderly social interactions and second, via empirical observations, to develop translational work that connects the model’s first principle with verified outcomes so as to engineer social interactions that maximize connectedness. All of those advances will help to sustain behavioral and cognitive reserve and extend the span of healthy and functional aging. Because of its foundation in a general mathematical model of coordination, the findings and their methodology can also apply in a broad range of translational contexts, including the many facets of communicable health and communicable disease.