I asked Véra Nabokov was the fish image in Pale Fire a homage to Hokusai? With a smile, she said Yes. So I think that settles the matter.
I have loved Hokusai's work for over forty years. He's incomparably the greatest Japanese artist. I had three Hokusai prints in my part of the On the Origin of Art exhibition at the Museum of Old and New Art in Hobart, Tasmania, 2016-17, including the Great Wave (the last and culminating piece in the show).
Here's the better known of his carp in waterfall (two fish--one could imagine that the lower one is not going to make it; but we can suspect that Nabokov knew only the image, not the legend) and a Hokusai carp image I like even more, almost monochrome, with
two turtles also enjoying the water and its ripples.
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
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