
Grasshopper problem yields insight into quantum theory - scentoni
https://phys.org/news/2017-12-grasshopper-problem-yields-insight-quantum.html
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bythemotorway
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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scentoni
Preprint at
[https://arxiv.org/abs/1705.07621](https://arxiv.org/abs/1705.07621)

