I spent about a month in the UK earlier this summer, and that meant I took a lot of train trips. I love riding trains: the feeling of endless possibility I get when I look at the departure boards, the countryside rolling by, the fantastic people-watching, the two-hour delay between Edinburgh and Manchester because a train got stuck on the tracks in front of us, and of course, the mathematical properties of train routes. I spend a lot of time on trains, or really on any mode of transit, thinking about metrics.
Somewhat scandalously, British rail prices fail to satisfy the triangle inequality, one of the basic rules that metrics must follow. Read the full post to find out why.
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