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by giomasce
2988 days ago
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The author itself admits in the postscript that he has embellished a bit the article, but allow me to take it at its face value: to me, it seems that the article confuses mathematics with its notation (and the same for computer science, but at this level CS is just a branch of mathematics). All the funny stuff he goes on describing follow from this confusion. When a mathematician does mathematics, they have very well defined concepts for "equality", "equality up to some equivalent relation" (my preferred: "equality up to diffeomorphisms that are isotopic to the identity") and so on. However notation is chosen saving on clarity and conciseness, sometimes at the expense of the direct mapping with underlying mathematical concepts. Thus in some case the sign "=" is meant to mean equality (in a certain sense), in some other cases it is not. Computer languages make no exception: they are nothing else than formalisms to express computations. As for every other formalism, the meaning of signs is chosen to be what appears most comfortable in that context by the formalism designer. The statement "x = x+1" has very different interpretations depending on whether you consider it written in C or in standard polynomial equation theory; but in both cases there is a well known meaning for it. In exactly the same way the word "case" has different meaning depending on whether your are reading in English or in Italian. |
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