ABSTRACT
Ever since the introduction, over twenty years ago, of a twistor construction for the general anti-self-dual solution of the Einstein vacuum equation, it has been a major problem to see how to extend this in order to incorporate also a self-dual part to the Weyl curvature. Some substantial progress appears to have been made recently towards the solution of not only the gravitational googly problem, but of combining both constructions together so that general solutions of the Einstien field equation are encoded into the structure of a suitably deformed twistor space. According to the conventions, good cuts are actually ruled by dual twistor lines.
