Historians generally feel that they possess a historically plausible understanding of the emergence of a new idea when they can account for it as the logical consequence of an existing “state of the art” combined with some principles that the individual innovator has brought to the discussion. But to what extent do we “really understand” the new development when all of these elements have been put together? Two case studies, one from the optical investigations of Ptolemy, another from the mechanical investigations of Galileo, reveal occasions in which a significant step forward has not been taken despite the availability of all the logical preconditions specified above. There must exist, therefore, an additional element or elements, without which innovative moves are not made, and “historically plausible” accounts of scientific progress do not constitute a true understanding of the process of innovation.