How can imagination, which normally serves us to break free from reality, endow our social imaginaries with powers that can regulate actual social interactions? How can we imagine, properly speaking, together in the first place? And are those forms of imagining together in which we imagine something pertaining to 'us' more 'real' than others? Or do all collective imaginaries exert the same normative pressures on their members as to what and how they ought to imagine? In this paper, we propose to address these issues by going beyond the standard literature on social imaginary. We argue that what allows imagination to impact our social reality, is, first, the way in which beliefs and desires intersect with our imaginings, and secondly, those normative features of imagination that make collective imagination possible and regulate what we can and ought to imagine together. Moreover, we suggest that different types of collective imagination need to be distinguished according to the different degrees and scope to which norms penetrate our shared imaginaries, as well as to the recognition of those norms. Finally, by critically drawing on research on population genomics, we argue that social imaginaries are those collective imaginations in which imagination is most likely to intermesh with what we wish to be real or in which we imagine communities we wish to belong to.