Neoclassical economics has only recently considered the problem of sustainability—how to provide for the well-being of future generations given ecological constraints. In general, the neoclassical economist perceives physical and ecological constraints on economy-environment interactions as inconveniences that will inevitably be overcome by substitution—the discovery of new economic resources or technologies allowing the conversion of noneconomic materials to economic goods. Ecologists and ecological economists, however, argue that the constraints will bind. The debate centres on the relevance of entropy to the economics of resource use: irrelevant in the neoclassical view, relevant in the ecological. This paper places entropy, within the context of neoclassical economic thought, as a limit to economic growth. The paper rigorously argues the existence of limits to knowledge and consequently to technology and substitution, undermining a basic assumption of neoclassical economics and establishing the relevance of entropy to economic theories of resource use.