"This One" lyrics | Fab Forum

In Indian iconography, the goddess Saraswati is often depicted riding a swan. She is the goddess of learning, wisdom, music, art, and science. More info: http://en.wikipedia.org/wiki/Saraswati

Moreover, Paul seems to associate John with white birds (the peacock in that Anthology photo, Julian said John told him to think of him whenever he saw a white feather, and there's one other example I'm forgetting). The line "fade this swan/one to black" might refer to John's death, especially since Paul has at least twice brought John (and George) up in discussing the meaning of the song itself, as an example of why it's important to say what you want to say to people when you have the chance.