If you want to take the easy way out instead, 12-year-old David Hitchman, son of University of Northern Iowa mathematician Theron J. Coco is staying at Bing's house for her first sleepover, but it is not long before the differences in their bedtime routines emerge. The views expressed are those of the author(s) and are not necessarily those of Scientific American. Following the closure of Westwood in 1962, the oil works site was sold and new industrial purposes found for many of the buildings. Beginning during World War Two, the two outer bings were first to be formed, set at about 60 degrees to each other and defining the limits of the tip.

Hence, for some topological purposes, it’s close enough to being a point that we might as well assume it is. There are two small panels attached to the tunnels between the rooms, which make this simplicial complex contractible. This allowed a huge saving of labour, and created a very different shape of mound to the traditional shale bing. with Registered Office at Almond Valley Heritage Centre, Millfield, Livingston, West Lothian, EH54 7AR.The house had seen better days by the time it was bought by the Oakbank oil company prior to World War Two and was subdivided into a number of homes. Before we try to understand the space itself, we should figure out why we would bother with it at all.

The upper tunnel is made by punching out a square from the top of the box and another square directly below it from the middle horizontal rectangle, then inserting four vertical rectangles, the walls of the tunnel. This art and archaeology project worked with the Five Sisters shale bings in West Calder and the story of Westwood House buried beneath. The central part of the bing certainly occupies the site of Westwood House, the fine home of Captain Robert Steuart, who had once operated his own oil works in a distant part of his estate. As I was writing this post, I realized that like doubtingThomas, I needed to feel the space with my hands before I would believe it. I took Hatcher’s word for it, but it wasn’t until I made it for myself that I truly believed in its contractibility.

When Westwood oil works closed in 1962, marking the end of the Scottish shale industry, the middle sister still retained space to grow. One letter to the editor described them as “a blight on the landscape and contributing to the reputation of West Lothian as being a dirty, unattractive and industrial county”. When aerial photographs were taken a few years after the war, the house site was already submerged in waste, but the location of the associated estate offices remained exposed. To build this space, start with a box divided into two chambers by a horizontal rectangle, where by a ‘rectangle’ we mean not just the four edges of a rectangle but also its interior.

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. By the early 1950’s the rails had been removed from the outer bings and tipping begun to fill the space between the two outer “sisters”.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.

From here, men pushed and trundled the hutches along rails to the edge of the bing where, with huge effort, they lifted one end of the hutch so that its contents cascaded down the face of the bing in a cloud of dust. ACCESSORIES AND 2 FIGURINES: Includes 9 accessories and 2 Figurines including articulated Bing and Flop! Hatcher is asserting that the house with two rooms, like a solid ball, is also equivalent to a point, although less obviously so. 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.

Blessed are those who have to get out some clay or open Minecraft and create the house with two rooms before they believe in it. Hitchman, made a fun video about building it in Minecraft, and Ken Baker wrote about it on the blog Sketches of Topology.