Earlier quoted context omitted.
The motivation for using that example in particular is, I believe, that it's computing a fixed point - which is an idea that came up several times in the course in increasingly general settings. First you do the concrete example of newton's method, then do a more general fixed-point (higher order) function, and a more general newton's method. Later on the Y-combinator is presented as computing the fixed point of an (…
OK, that's interesting. I should go back to it. But it would be good to hint about it's relationship to later material. Perhaps it's the timing/context; I had an very odd lecturer for numerical methods.
https://mitpress.mit.edu/sites/default/files/sicp/full-text/...
Unfortunately I couldn't find the material about interpreters - my memory of it is them discussing it in the lectures so perhaps it never actually made it in the book, or was only in the 1st edition. Those lectures are available on youtube if you want to find it.