We observe that approaches to intersubjectivity, involving mirror neurons and involving emulation and prediction, have eclipsed discussion of those same mechanisms for achieving coordination between the two hemispheres of the human brain. We explore some of the implications of the suggestion that the mutual modelling of the two situated hemispheres (each hemisphere 'second guessing' the other) is a productive place to start in understanding the phylogenetic and ontogenetic development of cognition and of intersubjectivity.