Does anyone know if there is there a name for the idea that new concepts (such as negative numbers, complex numbers or type constructors in a type system) are only ever introduced into a preexisting "system" so that they can be eliminated later, after helping make some progress?
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it sounds like lift in pedestrian fp, we say lift to mean raising A to F[A]. the motivation is for the convenience of F[A1] => F[A2], (F[A1], F[A2]) => F[A3], etc that are complicated in A space, but it could be more general like ℝ => ℍhttps://en.wikipedia.org/wiki/Lift_(mathematics) …
That's reminded me of a stats lecture I had in 2002. I remember nothing except the lecturer's description of a "dual" as like taking the elevator (i.e. "lift") down to the ground floor where you can move around easily, before taking a different lift up a different building...
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I use the term "lift" all the time, and I remember the lecturer's explanation, but for some reason, this was the first time I related the figurative and literal lifts...
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you're not allowed to claim that Englishmen have invented math(s) long before the Babylonians because of literal elevators
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Interesting, for me the dual is _the other side of the mirror_, whereas lifting is moving to a "higher" (more complex, with more properties, etc)
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I think that the idea of a dual *became* a mirror for me, but back then, before I had an intuition, I found this lift explanation useful. The mirror doesn't give quite the same sense of it being "easier to move around" on one side than the other.
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