There is an intimate connection between algebraic K-theory and the space of pseudo-isotopies P(M) of a compact d-manifold M (that is, diffeomorphisms of a cylinder M x I that are the identity on M x 0 and ?M x I). Classically, the pseudo-isotopy space P(M) is studied in two steps: there is a stabilisation map P(M) -> P(M x I) which is approximately d/3-connected by a deep result of Igusa, and the colimit has a description in terms of Waldhausen?s algebraic K-theory of spaces due to Waldhausen--Jahren--Rognes' stable parametrised h-cobordism theorem. In this talk, I will focus on the case of an even-dimensional disc and explain a new method to relate its space of pseudo-isotopies to the algebraic K-theory of the integers, independent of the usual route. When combined with work of Goodwillie and of Randal-Williams, one consequence of this approach is that the stabilisation map P(M) -> P(M x I) for 2-connected d-manifolds M is rationally about d-connected, which is essentially optimal.