Many observers of contemporary economic trends have been perplexed by the contemporary conjuncture of rapid technological innovation with disappointingly slow gains in measured productivity. The purpose of this essay is to show modern economists, and others who share their puzzlement in this matter, the direct relevance to their concerns of historical studies that trace the evolution of techno-economic regimes formed around "general purpose engines". For this purpose an explicit parallel is drawn between two such engines -- the computer and the dynamo. Although the analogy between information technology and electrical technology would have many limitations were it to be interpreted very literally, it nevertheless proves illuminating. Each of the principal empirical phenomena that go to make up modern perceptions of a "productivity paradox", had a striking historical precedent in the conditions that obtained a little less than a century ago in the industrialized West. In 1900 contemporaries might well have said that the electric dynamos were to be seen "everywhere but in the economic statistics". Exploring the reasons for that state of affairs, and the features of commonality between computer and dynamo -- particularly in the dynamics of their diffusion and their incremental improvement, and the problems of capturing their initial effects with conventional productivity measures - provides some clues to help understand our current situation. The paper stresses the importance of keeping an appropriately long time-frame in mind when discussing the connections between the information revolution and productivity growth, as well as appreciating the contingent, path-dependent nature of the process of transition between one techno-economic regime and the next.