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Grasshopper problem yields insight into quantum theory (phys.org)
21 points by scentoni 11 months ago | hide | past | web | favorite | 2 comments



A useful if comparatively unsophisticated application might be in urban spatial and transport network analysis/planning.

Typically, spatial models use a basic circular catchment geometry to approximate random travel patterns across a city or suburb or neighborhood. That invariably influences a network's or neighborhood's real-world shape when it gets built/modified.

For example, consider the area of influence ("walkshed") of a bus stop or train station, and how perhaps walkability improvements across surrounding streets might be prioritized as a result of modelled demand distribution. A grasshopper solution could apply if the bus/train trip is the first hop and the last-mile walk is the second hop and the street grid or neighborhood is the lawn.

A more refined initial catchment geometry based on these grasshopper solutions could ultimately make a difference in how scarce resources for urban/transport infrastructure get allocated, lifting net benefits on average. It should at least make for more realistic predictions as well as more accurate explanations of real-world observable travel/development patterns.

The paper mentions the "ant problem" as an extension of the grasshopper problem, i.e. excluding disconnected shapes. That would be even more useful for the application above.

Of course, as a first order approximation, a simple circle catchment geometry isn't necessarily terrible (being not that far from a cogwheel), but there's probably a category of analogous distances in urban life where non-circle-like shapes would make a marked difference.





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