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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 cours
by earthicus 8y ago
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 (finite) iteratively defined function - the fixed point returned is the full recursive function. Lastly when talking about programming languages, and interpreter computes a fixed point. The scheme language is the fixed point of the scheme meta-circular evaluator.
- emmelaich 8y agoOK, 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.
- earthicus 8y agoThe first genralization is in section 1.3.3 and 1.3.4 https://mitpress.mit.edu/sites/default/files/sicp/full-text/book/book-Z-H-12.html#%_sec_1.3.3 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.