Sol, having also strayed close to the mythical number, calls his fish Icarus in relation to Max. It may just be another link to the theme of flying too close to something posited as greater than the human capacity. Max flies close to Sol's old work that he believes gave him a stroke.
Just as the machines (both Sol's and Max's) spat the number out before they burned, so too did Sol (the second stroke) and Max (the drill).
I reckon you're right about the staring at the sun having a link with it. It all ties in nicely.
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