In this paper I use group-analytic, philosophical and psycho-social lenses to explore phenomena associated with the convening of an experiential large group within a two-day conference on the theme of "knowing and not-knowing". Drawing in particular on the work of Earl Hopper, two different models of large group convening--in which the chairs for the group are arranged either in concentric circles or in spirals--are described "topographically" and compared in terms of the tasks which each model might address. I argue that the spiral topography may be more suited to the attempt to construct what the conference organisers posited as "insecure edifices of knowledge" and I borrow from the letters of Keats on "negative capability" to suggest that phenomena of "half-knowledge" may be generated and fleetingly perceived within the dynamic processes in the dilemmatic spaces of experiential large groups thus constituted.