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Not impossible, but it would have been harder. If you did succeed in thinking about them, it seems likely that along the way you would invent a language that su
by philh 17y ago
Not impossible, but it would have been harder. If you did succeed in thinking about them, it seems likely that along the way you would invent a language that supported them. By that I mean you would have developed notation to write your thoughts down compactly. You wouldn't need to implement the language.
There was nothing to stop people from doing calculus pre-Newton. But doing calculus without the language (theorems and definitions) of calculus would be hard. Once Newton had provided the language, it became something high school students could learn.
(Historical accuracy not guaranteed, but I hope it illustrates my point.)
- btilly 17y agoHistorical note. Newton invented Calculus then carefully found other ways to regenerate the results he got that way. The language of Calculus that we have was separately invented by Leibniz. The subject of the first big priority dispute was whether Leibniz' invention of Calculus was independent, or was obtained from the traces of it left in the Principia.
- brlewis 17y agoThat fits my experience. In the 1980s as a teenager I programmed in BASIC. I read a magazine article about generating mazes. I couldn't wrap my head around the algorithm. Later I learned Forth. After that, the algorithm made sense, because I finally had a language in my head suitable for recursion.