The Universe of Disco

Mon, 18 Jun 2018

Yesterday I presented as a counterexample the topology induced by the following metric:

A circle, with the
center marked. A shortest-distance path is drawn in blue between two
blue points on the same radius, and in red between two red points on different
radii. The blue path goes straight from one blue point to the other.
The red path goes from one point straight to the origin,
then straight to the other point.

I asked:

It seems like this example could be useful in other circumstances too. Does it have a name?

Several Gentle Readers have written in to tell me that that this metric is variously known as the British Rail metric, French Metro metric, or SNCF metric. (SNCF = Société nationale des chemins de fer français, the French national railway company). In all cases the conceit is the same (up to isomorphism): to travel to a destination on another railway line one must change trains in London / Paris, where all the lines converge.

Wikipedia claims this is called the post office metric, again I suppose because all the mail comes to the central post office for sorting. I have not seen it called the FedEx metric, but it could have been, with the center of the disc in Memphis.

[ Addendum 20180621: Thanks for Brent Yorgey for correcting my claim that the FedEx super hub is in Nashville. It is in Memphis ]

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