Inspired by a question that Einstein had asked him, Piaget analyzed the child's conception of time with a series of experiments that were published in book form in 1946. I briefly recapitulate Piaget's analysis as an interpretation of the conception of absolute time in classical physics. Piaget's suggestions as to how the analysis would carry over to a genetic understanding of time in the special theory of relativity are reviewed. In light of Piaget's work, some observations are made about Einstein's 1905 paper on the `Electrodynamics of Moving Bodies.' The specific transformational operations that mediate between the viewpoints of different inertial observers are characterized as a basis for the cognitive restructuring of spatio-temporal c...