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鈥檓 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鈥檓 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 鈥渓ovely鈥�. But it is the junction鈥檚 topological properties that ring mathematicians鈥� bell. In the spring issue of The Mathematical Intelligencer, Michael Kleber, a topologist at MIT, waxed enthusiastic about its 鈥渘on-trivial braiding鈥�: 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).
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Baltimoreans aren鈥檛 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 鈥渢he mess鈥�. 鈥淚t鈥檚 a nightmare,鈥� he says. Could the non-trivial braiding have something to do with it?
The design is certainly somewhat unnerving. It has exits on the right and left-hand sides of the road. Enter the I-95/695 interchange from any direction and you can turn right or left in a single elegant arc. Each of the four approaches has a right-hand exit followed by a braiding with the opposite lane of traffic. Then there鈥檚 a left-hand exit, the lanes re-braid, and continue.
Let鈥檚 be honest: it鈥檚 probably known as 鈥渢he mess鈥� because of the sheer number of vehicles trying to get through it. The bloom of suburbia around Baltimore means traffic flow through the interchange swells every morning and evening. Even now, at 2 o鈥檆lock on a Tuesday afternoon, I-95 is uncomfortably crowded. That鈥檚 one of the reasons the Maryland Transportation Authority (MDTA) has plans to alter the interchange. And that, in turn, is why I鈥檓 driving through it now: who knows if the new design will be as mathematically beautiful?
Not wanting to miss any of the beauty, I called Kleber before I left, and asked if he鈥檇 ever actually driven the interchange. His answer confused me. 鈥淚 was going down 95 to Baltimore, and I was going to merge to 695, and I got all excited, and I was like here it is, here it is!鈥� he said. 鈥淎nd then I realised it was the wrong one, the southern intersection. I was so disappointed.鈥�
Looking at the map, I wondered how, driving south on I-95, he could have avoided the intersection. I didn鈥檛 ask 鈥� perhaps topologists navigate in a different way to the rest of us. Instead, I turned to the experience of someone a little closer to the reality of road design: David Lovell, a transportation engineer at the University of Maryland, College Park. He is unimpressed by the idea of aesthetic design: according to Lovell, the elegance of the over and under braiding is most probably an accident related to the lay of the land, and nothing to do with mathematical aesthetics. The main concerns for engineers, he says, are making sure the curvature of a road changes gradually enough to make it easy to drive, without using up excessive amounts of real estate. The only aesthetic consideration is that the interchange does not end up looking like a massive pile of concrete.
鈥淚 was in a web of braided highways. It is a secret topological gem hidden in plain sight鈥�
So maybe the mathematical aesthetics of this interchange is a happy accident. But I鈥檓 here now, and I鈥檓 going to enjoy it anyway. First I drive straight through on I-95 going north. The right lane splits off towards I-695 east. Seconds later the left lane peels off towards I-695 west. I know we must have passed over south-bound traffic moments earlier and are now driving to the left of the oncoming traffic (quite a novelty for drivers in the US) but there are too many trees in-between and all I see are the flame and gold of honey locust in full autumnal splendour. If it wasn鈥檛 so pretty, I would be disappointed.
I turn around, get off, and try it in two other directions, passing from 95 south to 695 west, and 695 east to 95 south. I don鈥檛 notice anything out of the ordinary. If I hadn鈥檛 seen the aerial maps, I wouldn鈥檛 have known I was in a web of braided highways. It鈥檚 a secret topological gem, hidden in plain sight. In some strange, small way, I feel uplifted. How many highway interchanges can do that for you?
Back home, I call the MDTA to ask about their plans for the interchange. They will not tell me anything. I search a copy of their document on the I-95 master plan for clues. Reading it, my heart sinks. I can only hope the writing style is not reflected in the eventual design: 鈥淭ransit is an important transportation option for the transport of people within the study area.鈥� I flick a few pages. Apparently, the section of I-95 directly north of Baltimore operates at 鈥淟evel of Service F鈥� during rush hour. Level F 鈥渄escribes breakdowns in vehicular flow. Such conditions generally occur when the number of vehicles arriving at a freeway section is greater than the number of vehicles that can move through it.鈥� Really.
I can feel my hackles rising. I call them again. Are they planning to do to the intersection what they have done to the English language? No one I talk to knows the answer. Finally, on their website, I find a single depressing sentence: 鈥淎t the I-95/695 interchange, the existing braiding on both I-95 and I-695 would be removed鈥�. A press officer at the MDTA confirms my worst fear; most likely, he says, it will become a multi-tiered interchange with only right-hand exits. I don鈥檛 want to encourage more cars onto the roads, but if topology and beauty mean anything to you, get out there and enjoy I-95/695 now. It may soon be too late.
