The article moves from a theorisation of the global scale in higher education and knowledge to a critical review of actual global imaginings and practices. Geo-cognitive scales such 'the global' or 'the national' are constituted by three elements: pre-given material structures, the imaginings and interpretations of agents, and the social practices of agents. Synchronous networks, time/space compression and travel have materially expanded the scope for relationality, including world-spanning systems such as science, cross-border connections, and global diffusion of ideas and models. Potentials for multi-scalar understanding and 'thinking through the world' have been enhanced. However, these imaginaries are not dominant. More prevalent are methodological globalism, in which the global displaces the national, or methodological nationalism, which blocks one-world potentials from view. In a Hobbesian global space without relational ethics, global higher education is ordered by an Anglo-American hegemony, manifest in neo-liberal economics, cultural and linguistic homogeneity, and White Supremacy in continuity with colonialism. Methodological globalism facilitates the neo-imperial claim to intervene anywhere, while methodological nationalism justifies claims to cultural superiority without obligation to engage with the other. However, no relations of power are fixed or wholly homogeneous and in global higher education there is continuing potential for multiple positionality, mutual respect and unity-in-diversity.