The incidence relation is preserved under an overall re-scaling of the twistor, so usually one works in projective twistor space formula_25 which is isomorphic as a complex manifold to formula_2. A point formula_27 thereby determines a line formula_28 in formula_1 parametrised by formula_30 A twistor formula_31 is easiest understood in space-time for complex values of the coordinates where it defines a totally null two-plane that is self-dual. Take formula_32 to be real, then if formula_33 vanishes, then formula_32 lies on a light ray, whereas if formula_33 is non-vanishing, there are no solutions, and indeed then formula_36 corresponds to a massless particle with spin that are not localised in real space-time.