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> Math can't deal with imperfect input and/or side effects without turning into something else. This is just not true. Differential equations certainly deal wi

• sixbrx 7y ago
  It's not called side effects there because there are none, in the modern mathematical formulation at least. The goal is to identify solution functions, and those are just sets of ordered pairs or something similarly inert.
  • pron 7y ago
    Except that even in programming, the name "side-effect" is not too clear. It stems from the fact that subroutines sometimes behave a bit like functions, and when they don't, we call the added behavior a "side effect". If you want to be mathematically precise, subroutines are predicate transformers, and, again, there are no "side effects" (This is a mistake functional programmers make when they speak of referential transparency; most languages are referentially transparent, and that was the whole point of the paper that first introduced the term to programming. They are only not referentially transparent with respect to an incorrect semantic model). The philosophical difference between a subroutine with side effects and a derivative is small.