The complex Fourier series provides two independent images, a real image and an imaginary image. This means there should be two independent proj lines in probabilistic proj geometry. However, these two images are linked, and modifications in one (for example the real part of the Fourier series) impact the other image (i.e. the imaginary part). These two images together form a complete image.
This is another mechanism for developing evolution mechanism. In the immigration plan, I work on, I said that any plan on this issue should consist of arguments from both sides. If the right develops a plan that pleases right-wing voters, once the right loses the election left will discard that and will develop an entirely different plan. The evolution of plans is not possible in this situation. But if two independent images are developing at the same time that form one entity then these two images will interact with each other to form one coherent entity.