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Contractible” is topological shorthand for “like a point” or, not to put too fine a point on it, “boring.” A space is contractible if it you can smush it down to a point without tearing the space or gluing any parts of it together.For example, a solid ball is contractible because even though it is three- rather than zero-dimensional like a point, it can be shrunk down all the way to a point without tearing or collapsing any of its interesting features. Hence, for some topological purposes, it’s close enough to being a point that we might as well assume it is. Thanks for reading Scientific American. Create your free account or Sign in to continue. Create Account
EXPLORE THE WORLD OF BING: 4 different room sets to explore and enjoy. Including a fold-out kitchen with opening and closing cupboards. Children's animation. Coco is staying at Bing's house for her first sleepover, but it is not long before the differences in their bedtime routines emerge. More Westwood bing looks very different because it was built by machines. All features of the Westwood works were very different to everything that had come before. Built to fuel Britain’s war machine the designers of Westwood works took full advantage of the technical advances that had taken place since the previous new oil works almost forty years before. This new technology extended to the disposal of the spent shale from the efficient new retorts. This finely graded waste was transported along a conveyor belt to a central bunker from where the spent shale was fed to a large carriage on rails. This was hauled to the top of the bing where the carriage was discharged by gravity.I was skeptical of the house with two rooms for a long time. I just couldn’t see how to squish it up into a point without changing its topology. I took Hatcher’s word for it, but it wasn’t until I made it for myself that I truly believed in its contractibility. The day before spring break last semester, I brought some clay to my topology class, and one of the things we made was the house with two rooms. By the time we were finished, I felt like I truly understood the space. The house with two rooms...and a slightly leaky roof. The house is made of 2-dimensional panels, and has two rooms. The upper room may be entered from the bottom face, while the lower room may be entered from the upper face. There are two small panels attached to the tunnels between the rooms, which make this simplicial complex contractible. If you want to take the easy way out instead, 12-year-old David Hitchman, son of University of Northern Iowa mathematician Theron J. Hitchman, made a fun video about building it in Minecraft, and Ken Baker wrote about it on the blog Sketches of Topology. There, he describes it in a different way:
House with two rooms or Bing's house is a particular contractible, 2-dimensional simplicial complex that is not collapsible. The name was given by R. H. Bing. [1] David Schwimmer's 'Rachel' script slip up accidentally created one of the most awkward lines in Friends
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The Sisters remain in private ownership, and access is discouraged. Without hikers boots or swarms of trail bikes they grow a denser cloak of grass and shrub every year. Athletic cattle sometimes find their way up the lower levels of the bing in search of rare and tasty vegetation, but seem to do little damage ACCESSORIES AND 2 FIGURINES: Includes 9 accessories and 2 Figurines including articulated Bing and Flop! Bing House Playset features popular CBeebies characters – Flop and Bing! Just like the house you see on the hit TV show. Beautifully made from tough, colourful plastic. Includes two posable figures and nine accessories.
Hatcher is asserting that the house with two rooms, like a solid ball, is also equivalent to a point, although less obviously so. The houseis a façade. It looks as though it has holes in it, but they are not really there in a topological sense. A bird's eye view of a house with two rooms while it is under construction. Here, only the first floor has been built. The house with two rooms is sometimes called Bing’s house after R. H. Bing, the mathematician who first described the space. But like many math students, I first encountered it in Allen Hatcher’s algebraic topology book. He gives us the following picture and definition of the space. Since 1995, Westwood Bing (a.k.a the five sisters) has actually been a scheduled monument and is now protected for posterity. They’ve become a symbol of West Lothian, and a memorial to the shale oil industry, yet the famous five-leafed bing is an oddity, a one of a kind.
Scientific American is part of Springer Nature, which owns or has commercial relations with thousands of scientific publications (many of them can be found at www.springernature.com/us). Scientific American maintains a strict policy of editorial independence in reporting developments in science to our readers.We have therefore encouraged every provider to open their ‘online windows and doors’ to help you make an informed choice. The profile score is a measure of how much information has been provided. Here is where I could tell you how I saw that the space was contractible, but I’m not going to do that. I think the best way to see it is to make it out of clay or any pliable material you have on hand. Hatcher’s diagram and description give a good recipe, and I know from personal experience that undergraduates and even postdocs like me can follow the instructions well enough to create a convincing house with two rooms, although I must admit our roof was leaky. We think it’s important you have detailed, comprehensive information so that you can decide which care providers to shortlist. This allowed a huge saving of labour, and created a very different shape of mound to the traditional shale bing. Perhaps because the shale was broken to a smaller size and more bound oil was extracted during retorting process, the Westwood bing supports vegetation more readily and have greened much faster than other shale bings.
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