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The task of designing social impact of science (SIS) indicators is an ill-structured or systemic problem involving competing design goals, indeterminate design states, unspecified design rules, and an unbounded design space. These features of the problem are not a result of imperfections of measurement alone; they are due primarily to properties of the knowledge system that make it resemble a tangled river delta (anastomotic reticulum) in which different functional patterns (serial, parallel, assembly, arborescent, segmented, cyclic) coexist. The stunning complexity of knowledge systems makes it difficult but nevertheless possible to develop SIS indicators that are policy relevant by virtue of their being at once relational, causal, and normative (see also Peters, this volume). Any attempt to improve the policy relevance of impact indicators will recognize that systemic problems require nonconventional solutions based on principles of externalization, formalization, and simplification. An initial attempt to externalize the design process yields typologies of science output indicators and social impact indicators that may be conjoined to form social impact of science (SIS) indicators. By formalizing rules for making and challenging causal inferences, we can formulate rival hypotheses about the role of knowledge functions and structures in mediating the impacts of science on the achievement of social goals. By simplifying the design process we can maximize the likelihood that SIS indicators and the basis for their construction are widely comprehended by groups that have a stake in the social performance of science.