An algebra which is 'absolutely rigid" from the algebraic point of view (i.e., which has vanishing second cohomology) may nevertheless appear as part of some continuous family when viewed geometrically. This is an old observation rediscovered by Kontsevich, whose example is the algebra C(x, 1/x, 1/(x-1), 1/(x-a)). It was this paradox which led to the definition of a deformation of a 'diagram' of algebras. We will show how this resolves the problem in this and several related examples. In th ehopes of pursueing Hirshfeld's paper for mos tof the semester, let's try to get organized - e.g. look over the paper and decide whihc part you would like to present