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The paper explores "systems-theoretic" approaches to the interdependent policy issues arising from the dynamics of science, technology and innovation in their relationship to economic growth. Considering the current economics literature's treatment of technology and growth policies, we consider the critical question: what kind of "systems paradigm" is likely to prove particularly fruitful in this problem-domain? Neo-Schumpeterian "new growth theory" models of macroeconomic processes driven by R&D-based innovation, and more radical "evolutionary" approaches that emphasize complex system dynamics, are examined from this angle. While each has its conceptually attractive features, both are seen to have rather problematic short-comings as guides in micro-level resource allocations that are entailed by the practical implementation of public policy-decisions affecting scientific and technological research and educational investments. Not content to have pointed out a number of imposing obstructions encountered on the path toward harnessing "knowledge for growth," the concluding discussion suggest that greater use be made of stochastic simulation modeling as means of integrating findings from partial policy-experiments and empirical research, and assessing their implications within a complex adaptive systems framework.