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I was thinking intuitionistic math, such as smooth infinitesmal analysis. And yes, they are less developed than classical analysis, and harder to work with. B
by btilly 6y ago
I was thinking intuitionistic math, such as smooth infinitesmal analysis.
And yes, they are less developed than classical analysis, and harder to work with. But should not produce different results.
- Jweb_Guru 6y agoAs someone who does lots of constructive math, intuitionistic math can't reproduce a large number of results on the reals and this is a kind of well-known thing. Even basic notions of continuity can't be reproduced in the same way and as a result there are multiple competing formalisms. It is possible that there are alternative ways to reproduce results of interest to physics but that's far from obvious.
- creata 6y agoThe world of SIA and SDG is a very, very different world to that of classical analysis. If you think that they "should not produce different results", then (a) you're either wrong or incredibly optimistic regarding our ability to carefully rephrase the statements of classical analysis in a way that works constructively. (b) what would be the point of a harder-to-use system that offers exactly the same results, anyway? The whole reason I find SDG interesting is that it will eventually be simpler to use, and because it provides an entirely fresh of the number line.