Cartographers’ nightmare, Digital print on plain paper with tape, 2012.
Process of transformation of structures
Discussions with a work colleague, prompted us to explore how visualisations of globes are represented. Finding a different template each online, we constructed a globe under time constraints. As with Doughnut the hope was to gain a physical understanding of the process of transformation of structures. The globe itself is crudely assembled, further illustrating the idea of approximations.
To turn a flat square into a Torus, first, form a cylinder by joining the top edge of the square to the bottom edge, then bend that cylinder into a circle and join its two open ends. There is just one problem: for the two ends to meet, the torus must be stretched in a way that distorts the original shape of the square. Any horizontal lines on the original square will be stretched on the torus, while vertical lines will remain the same. Cartographers encounter a similar problem when unwrapping a globe of the Earth to create flat maps. They are forced then to make compromises such as inflating the size of Greenland, which can appear similar in size to Africa on standard maps but is actually one-fourteenth as big. The earth was believed to be flat; what we see on small scales does however, appear flat. In general any object that is nearly “flat” on small scales is a manifold, and so manifolds constitute a generalisation of objects we could live on in which we would encounter the round / flat earth problem, as codified by Poincare. (New Scientist Magazine)