Highway heaven or highway hell?

 作者:裴蚊馓     |      日期:2019-03-15 07:17:01
By Kim Krieger (Image: US Geological Survey) THE smell of cooking asphalt wafts across the queues of cars on Interstate-95. Seagulls screech overhead, cutting through the bass rumble of the trucks pulling out of the toll plaza as they make for the freeway. I hit the brakes as a Cadillac Escalade veers in front of me. A truck looms in my rear-view mirror, too close for comfort, but I escape into the middle lane as the toll booths disappear behind me. I’m aiming for an intersection, north-east of Baltimore, where I-95 crosses I-695, the beltway that encircles the city. Other drivers may not realise it but this intersection is a mathematical masterpiece. I’m here to pay homage. Dror Bar-Natan of the University of Toronto, Canada, was the first to point out its beauty. His website describes its symmetrical layout as “lovely”. But it is the junction’s topological properties that ring mathematicians’ bell. In the spring issue of The Mathematical Intelligencer, Michael Kleber, a topologist at MIT, waxed enthusiastic about its “non-trivial braiding”: while it is possible to just lift I-95 up and away from I-695, the northbound lane of I-95 braids both over, and then under, the southbound lane, making it impossible to pull them apart without cutting one of the lanes (see Diagram). Baltimoreans aren’t as affectionate towards the I-95/695 north-east interchange as mathematicians, however. A friend of mine who traverses the roadways regularly refers to it as “the mess”. “It’s a nightmare,” he says. Could the non-trivial braiding have something to do with it?