This paper models an industrial revolution as a qualitative transition from a world where innovation is infrequent and haphazard to one where it is continuous and systematic. Pre-industrial innovation is treated as a social process where an individual's effectiveness as an innovator depends on the skills of other individuals in his social network. As technology improves, individuals invest more time in learning through social contact. This gradual increase in linkage formation leads to a sudden change in the size of knowledge networks from small, isolated clusters, to a large connected cluster spanning most of the economy, causing a sudden increase in the effectiveness of innovation: an industrial revolution. The predicted sequence of typical innovators - from gifted amateurs, to lucky amateurs, to professionals - is consistent with empirical evidence. This paper is part of the International Trade and Investment Programme of the Geary Institute at UCD.