This article offers a critique of the manner in which doctoral supervision is conceptualised in a higher education system dominated by the market order. The authors consider the process of research supervision as an experience held in common, as a way of discovering the world together rather than as the fulfilment of discrete roles within a clearly defined timeframe. They propose an alternative ontology of research supervision, as a process of 'unselfing' informed by the enactment of agape (love) rather than as something that is characterised by conformity to a regulatory framework and informed by the dictates of institutionalised systems of monitoring and surveillance. This approach implies rejection of the relentless focus on choice and action that is characteristic of institutionalised higher education. The authors claim greater scope for consideration of the influence of the more elusive aspects of being human in the process of research supervision. This reappraisal of research supervision calls into question the pre-eminence of the Newtonian order of time as something that flows uniformly, independently of things and their relationships and calls for renewed emphasis on time as lived experience. The authors draw on a musical analogy, namely the differences between classical music and jazz, in order to explore these themes in relation to research supervision.