Many view the period after the Second Industrial Revolution as a paradigmatic example of a transition to a new economy following a technological revolution and conjecture that this historical experience is useful for understanding other transitions, including that after the Information Technology Revolution. We build a model of diffusion and growth to study transitions. We quantify the learning process in our model using data on the life cycle of U.S. manufacturing plants. This model accounts quantitatively for the productivity paradox, the slow diffusion of new technologies, and the ongoing investment in old technologies after the Second Industrial Revolution. The main lesson from our model for the Information Technology Revolution is that the nature of transition following a technological revolution depends on the historical context: transition and diffusion are slow only if agents have built up through learning a large amount of knowledge about old technologies before the transition begins.