Here’s a joke: A topologist is a mathematician who can’t tell the difference between a coffee mug and a doughnut. To understand the gag you have to know what topology is: a branch of mathematics concerning spaces that are transformed through bending and stretching (but not severing or intersecting). Klein bottles and Möbius strips are examples of the kinds of subjects a topologist might invest her energies in. To a topologist, both a mug (a volume with a single hole, in its handle) and a doughnut (a volume with a single hole, in its middle) are torithey only appear to be different, while they actually share fundamental similarities in the conditions of their surfaces. At its most mind-bending, topology can point to the interconnectedness of forms, breaking down some assumptions about space and our apprehension of it.
Channing Hansen is interested in such notions. He connects
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