The knot driver
Northern Baltimore's I-95/695 highway interchange is a "topological masterpiece," and its superb "mathematical aesthetics" might just save it from being destroyed.
[Image: “I was in a web of braided highways." New Scientist].
"In the spring issue of The Mathematical Intelligencer, Michael Kleber, a topologist at MIT, waxed enthusiastic about [the interchange's] '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."
However, those simultaneous right/left exits don't seem to be helping with traffic flow, and the system's moving circular symmetry may soon be traded-in for something far simpler.
"I don't want to encourage more cars onto the roads," the New Scientist writes, "but if topology and beauty mean anything to you, get out there and enjoy I-95/695 now. It may soon be too late."
This leads me to wonder, of course, if you could take-over the U.S. Department of Transportation, and rebuild the nation's highway infrastructure as a massive textbook in driveable knot theory.
Seattle to Chicago, you drive achiral knots; Los Angeles to Phoenix, trefoils; New York to Miami, Brunnian links; while the most complicated ones are saved for a private highway system built between Washington DC and Denver.
All the tunnels of Manhattan, recurved and cross-torqued through themselves, with some so maddening only postgraduate researchers can find their way out of the city.
A new Olympic sport: driving the New York knots.
(Earlier: BLDGBLOG's Wormholes).
[Image: “I was in a web of braided highways." New Scientist]."In the spring issue of The Mathematical Intelligencer, Michael Kleber, a topologist at MIT, waxed enthusiastic about [the interchange's] '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."
However, those simultaneous right/left exits don't seem to be helping with traffic flow, and the system's moving circular symmetry may soon be traded-in for something far simpler. "I don't want to encourage more cars onto the roads," the New Scientist writes, "but if topology and beauty mean anything to you, get out there and enjoy I-95/695 now. It may soon be too late."
This leads me to wonder, of course, if you could take-over the U.S. Department of Transportation, and rebuild the nation's highway infrastructure as a massive textbook in driveable knot theory. Seattle to Chicago, you drive achiral knots; Los Angeles to Phoenix, trefoils; New York to Miami, Brunnian links; while the most complicated ones are saved for a private highway system built between Washington DC and Denver.
All the tunnels of Manhattan, recurved and cross-torqued through themselves, with some so maddening only postgraduate researchers can find their way out of the city.
A new Olympic sport: driving the New York knots.
(Earlier: BLDGBLOG's Wormholes).
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I've driven through this thing dozens of times, I was headed north on 95 out of town this evening after reading this post so I paid special attention to it. The surprising thing is that all this intricacy isn't apparent at all from the ground. The slope of the land around it, the trees, and the heavy traffic make the complexity imperceptible.
We're indifferent to the shape of highway interchanges, I think, because all that's important are the signs. When we're looping around on these things, we don't care which way true north is, we only care which branch is labeled north, in this case the northeast one.
Hi,
i'm no expert in road architecture, but loved your "artistic" way of thinking. great post!
"Driving the New York knots"--well, New York drives ME knots...
Just saw this again on delicious, are you coming to Baltimore in '08, Geoff?
Seems so! I should have a more official sense of that soon - stay tuned. I'll put up a post to announce the talk once I have all the details. But it will be springing from this post.
Say goodbye to your masterpiece. As of 7/4/09 it is no more. DOT must've found your blog and decided to mess with you. Blame it on future express toll lanes or "Lexus Lanes".
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