An ecological approach to modeling human-machine interaction based on extensions of Brunswik's probabilistic functionalism is presented. The general approach is illustrated by a pair of quantitative models in dynamic, interactive task domains. The mathematical techniques used to instantiate the models include genetic algorithms (to describe noncompensatory-logical judgment rules), and multi-dimensional information theory (to describe how a performer generates perceptual information through

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... n, thereby reducing a task's cognitive demands). The models indicate how Brunswik's probabilistic functionalism, previously applied mainly to the analysis of passive judgment, can be extended to the realm of dynamic, interactive tasks. The style of ecological analysis and description portrayed in these models is especially well suited to describing types of, and limits to, adaptation in human-machine interaction.