I came across a funny example of problem formation yesterday (cc @Meaningness).
@thilogross, a researcher in Bristol (where I live), showed that Bristol's version of the Königsberg bridge problem (https://en.wikipedia.org/wiki/Seven_Bridges_of_K%C3%B6nigsberg …) *is* soluble, and walked the resulting 33 mile circuit...
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The original walk is here: https://www.bristolcivicsociety.org.uk/bristol-bridges-walk/ … (new version at https://reallygross.de/ops/bridgewalk as there are now more bridges!) Now the interesting bit for me is how much of the work was just defining the problem:pic.twitter.com/2ejPqmLgr9
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Euler's solution involved a creative act of seeing-as, abstracting landmasses as nodes and bridges as lines. But once he'd done that, 18th-century Königsberg maps pretty cleanly onto the problem.pic.twitter.com/A8m3FhyNJo
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Modern Bristol however is a mess. It's roughly two islands in a river, like Königsberg, but there's also two little islets off the west island, and a tributary branching off the river. Also there are a LOT of bridges:pic.twitter.com/nKavotTKPW
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More importantly, there are a bunch of decisions to be made about what counts as a bridge. This is purpose-dependent: rail- and car-only bridges don't count in this solution because the whole point is to be able to walk it.
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Then you have to decide whether bridges like these are two bridges or one bridge. (In this case they all get counted as two.)pic.twitter.com/JudF3BRAvd
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I have a weird memory of trying to decide whether to count this as one bridge or two, but I can’t imagine why I would have wondered that, so I’m probably making it up and have constructed a false memory retrospectively
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