The study of quantitative risk in security systems is often based around complex and subtle mathematical ideas involving probabilities. The notations for these ideas can pose a communication barrier between collaborating researchers even when those researchers are working within a similar framework.

This paper describes the use of geometrical representation and reasoning as a way to share ideas using the minimum of notation so as to build intuition about what kinds of properties might or might not be true. We describe a faithful geometrical setting for the channel model of quantitative information flow (QIF) and demonstrate how it can facilitate "proofs without words" for problems in the QIF setting.