This paper draws attention to the tendency of a range of technologies to reduce pedagogical interactions to a series of datafied transactions of information. This is problematic because such transactions are always by definition reducible to finite possibilities. As the ability to gather and analyse data becomes increasingly fine-grained, the threat that these datafied approaches over-determine the pedagogical space increases. Drawing on the work of Hegel, as interpreted by twentieth century French radical philosopher Alexandre Kojève, this paper develops a model of relational pedagogy which highlights three points of incompatibility with a datafied learning environment reduced to finite measures. Firstly: Kojève's account of authority in Hegel posits two aspects to the mimetic relation between teacher and student: recognition and realisation, which belong to the ipseity or about-selfness of the subject, and are incompatible with a general definition of data. Secondly, the Hegelian approach to human historical time, in particular the assertion that time and desire are begun in the future, not the past, renders it incompatible with mathematical time as used in data processing. Finally, from these it is possible to derive a distinctive notion of the work of pedagogy, grounded in Kojève's realist reading of Hegel, irreducible to information processing. In consequence of this threefold irreducibility, the paper draws attention to a need for relations of human pedagogical work to be inherent in the design of educational technologies and highlights the dangers of presuming a machine intelligence model in the design of learning environments.