Complex Dynamics of Human Activity: Language, Cities, Collaboration, and Baseball

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A few areas of human activity are examined here, using a number of different types of mathematical and computational models. First, we examine networks of five languages of the world, with their connectivity derived from the sounds of the words in these languages. We explore the graph-theoretic properties of these networks, finding that these phonological language networks have common properties, and are in turn topologically distinct from other types of complex networks observed in the literature. In addition, we discuss what these common properties imply for how we process language and why natural language is structured the way it is. In addition, by examining the networks of English and Spanish, we explain a surprising difference in processing that was uncovered in some recent experiments, and discuss some more general implications of competition or facilitation between different modes of cognition.

We next explore a more macro-scale area of human activity: cities. Superlinear scaling in cities, which appears in sociological quantities such as economic productivity and creative output relative to urban population size, has been observed but not been given a satisfactory theoretical explanation. We provide a model for the superlinear relationship between population size and innovation found in cities, with a reasonable range for the exponent.

Next, we examine collaboration and innovation in the scientific world. We attempt to understand how variations in 'scientific distance' among collaborators affect the degree to which that collaboration is a productive one. Using both mathematical models and empirical data, we explore the relationship between the scientific or social distance of collaborators and the fruitfulness of their output.

Last, we examine Joe DiMaggio's 56-game hitting streak and look at its probability, using a number of simple models. And it turns out that, contrary to many people's expectations, an extreme streak, while unlikely, is not unlikely to have occurred about once within the history of baseball. Surprisingly, however, such a record should have occurred far earlier in baseball history: back in the late 1800's or early 1900's. But not in 1941, when it actually happened.

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NSF DMS 0412757

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Complexity; Complex systems; Computational social science; social networks; networks


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