Designed by architects in Amsterdam and Beijing, the Lucky Knot Bridge in Changsha, China, combines three bridges in one. Inspired by both the Möbius strip and the Chinese knotting art, the 185-meter pedestrian bridge spans Dragon King Harbor River, connecting multiple levels at varying heights (the river banks, the road, and a park at a higher level) while permitting pedestrians to pass from one route to another using “moon gates.”
“Bridges … have a highly metaphorical quality,” Michel Schreinemachers, a partner at Next Architects, told Wired. “They connect not only in a physical sense, but also people, places, needs, and experiences.”
When you’re driving and see an upcoming traffic light turn yellow, you face an urgent choice: stop quickly or try to run through the intersection before the light turns red. In 1962, Stanford aeronautics professor Howard Seifert worked out that you can choose either alternative if
where your car’s initial speed is v0 ft/sec, its maximum acceleration is a+ ft/sec2, its maximum deceleration is a– ft/sec2, the duration of the yellow light is T seconds, and the intersection is s feet wide and d0 feet away.
“[I]f the left or right inequality is reversed, you will not be able to run through or to stop, respectively,” he concluded. “It can be shown that there are situations where neither alternative will work and hazard and law violation are inevitable, as some palpitating drivers will testify.”
(Howard S. Seifert, “The Stop-Light Dilemma,” American Journal of Physics 30:3 [1962], 216-218.)
In 1817 a young woman appeared in the English village of Almondsbury, speaking a strange language and seeking food and shelter. She revealed herself to be an Eastern princess, kidnapped by pirates from an exotic island. In this week’s episode of the Futility Closet podcast we’ll tell the story of Princess Caraboo, who was both more and less than she seemed.
We’ll also discover a June Christmas and puzzle over some monster soup.
Julian Voss-Andreae studied physics at the University of Vienna before pursuing an art degree in the United States. His sculpture Quantum Man consists of 115 vertical steel sheets spaced by 1,000 short steel rods. The resulting figure looks solid when viewed from the front but almost disappears when viewed from the side, as light passes between the sheets.
“My interest is really nature,” he says. “One way to explore it is through science. Another is through intuitive sense and a search for metaphors.”
In their early studies of time and motion, engineers Frank Bunker Gilbreth and Lillian Moller Gilbreth divided all motions of the hand into 17 varieties:
Magnificently, they called these therbligs, which is roughly Gilbreth spelled backward. “Transport empty” refers to receiving an item with an empty hand, “transport loaded” means moving an object with the hand, and so on. With careful study, a worker’s movements might be optimized to maximize speed and efficiency. (It was the Gilbreths, for example, who suggested that surgeons employ “caddies” to pass their instruments to them.)
This scheme makes an appearance in fiction: In their 1948 novel Cheaper by the Dozen, Frank and Lillian’s children Frank Jr. and Ernestine describe what it’s like to grow up in the home of an efficiency expert:
Suppose a man goes into a bathroom and shave. We’ll assume that his face is all lathered and that he is ready to pick up his razor. He knows where the razor is, but first he must locate it with his eye. That is ‘search’, the first Therblig. His eye finds it and comes to rest — that’s ‘find’, the second Therblig. Third comes ‘select’, the process of sliding the razor prior to the fourth Therblig, ‘grasp’. Fifth is ‘transport loaded’, bringing the razor up to his face, and sixth is ‘position’, getting the razor set on his face.
“There are eleven other Therbligs — the last one is ‘think’!”
Berndnaut Smilde makes clouds. The Dutch artist has devised a way to combine water vapor with smoke to create miniature clouds that hover in enclosed spaces. He’s been deploying it in locations ranging from cathedrals to coal mines.
“I see them as temporary sculptures, made of almost nothing, balancing on the edge of materiality, an image of prospect in an empty space,” he told Rajesh Punj. “For me the work is about the idea of a cloud inside a space and what people project onto it. You can see them as a sign of misfortune or an element from a classical painting. There is something ungraspable about clouds: it might explain why people have been projecting so many meanings and myths upon clouds for centuries.”
Yes. The thing to notice is that we can’t have three routes in the pattern (A,B,C), (A,B,D), (A,C,D), because in that case it’s impossible to fulfill the third condition: If the remaining ports are E and F, then we’ve left ourselves only one permissible route (not two) that visits A and E. That’s (A, E, F). Any other three-port route that includes A and E would “overload” another segment.
This means that if two of the routes are (A,B,C) and (A,B,D), then the second one that covers A,C must be (without loss of generality) (A,C,E). With that in mind the other routes can be worked out uniquely: (A,D,F), (A,E,F), (B,D,E), (B,E,F), (B,C,F), (C,D,E), (C,D,F).