Near the end of Kinbote’s note to line 691 (“the attack”), he pictures JS “squirming up the college hall stairs as a Japanese fish up a cataract” (250). Kinbote seems to think we will understand the image, and indeed it turns out that the carp ascending a waterfall is a common image in Japanese art. There is even a story to go with the image, as told here by M. McLean from his 1889 book, Echoes of Japan:
The Carp Ascending The Waterfall.
It is a common sight to see, on Japanese works of art, and in picture-books, a carp trying to swim against a strong current or waterfall. This allegorical picture has a very interesting history, and is derived from a Chinese story. In some part of China there is a strong current, called Rio-mon, or Dragon's Gate. This stream is looked upon as sacred; so that, if any fish succeeds in scaling it, it becomes a dragon. The passage is very difficult, it being rocky and steep, and every fish except the carp fails in the attempt.
Other versions make clear that only one of a thousand carp ascends to the top and is transformed. The others remain mere fish in the pool below. I see at least three connections to PF in this story. First, it is a story of animal metamorphosis—a theme associated with Hazel (wood duck, trying on furs, Vanessa). It is also a story of the passage into immortality—certainly a theme of the novel, played out in myriad ways. Thirdly, we might see a transmuted version of the Gradus ad Parnassum, as Shade ascends the academic stairs. Did he make it to the top? I think he did. Perhaps others can do more with the image/allusion.
PS. I have attached a representative image of the koi’s ascent