To describe the complex projective space in an analogous manner requires a generalization of the idea of vector, line, and direction. Imagine that instead of standing in a real Euclidean space, the artist is standing in a complex Euclidean space C"n"+1 (which has real dimension 2"n"+2) and the landscape is a "complex" hyperplane (of real dimension 2"n"). Unlike the case of real Euclidean space, in the complex case there are directions in which the artist can look which do not see the landscape (because it does not have high enough dimension). However, in a complex space, there is an additional "phase" associated with the directions through a point, and by adjusting this phase the artist can guarantee that he typically sees the landscape. The "horizon" is then the space of directions, but such that two directions are regarded as "the same" if they differ only by a phase. The complex projective space is then the landscape (C"n") with the horizon attached "at infinity". Just like the real case, the complex projective space is the space of directions through the origin of C"n"+1, where two directions are regarded as the same if they differ by a phase.