Classifying clothing: the quest for the non-orientable tank top.

 January 22, 2007 personal

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When I walk down the street, I create patterns in how I walk, often by controlling my stride length so I will step on cracks every third sidewalk square, or whatnot. If I were a true master, my stride length would be incommensurable with respect to the sidewalk length–surely this was the problem that forced irrationalities upon the Greeks…

Anyway, I was also happy to realize (at a recent retreat) that clothing is nicely categorized by how many disks must be removed from a sphere to produce the particular clothing item. For some examples, consider:

  • A sock or a hat is a sphere minus a disk.
  • A headband (or tube top) is a sphere minus two disks.
  • Jeans are a sphere minus three disks (the fabled “pair of pants”).
  • A shirt is a sphere minus four disks (the “lantern”).
  • A bathing suit is a sphere minus five disks.
  • A fingerless glove might be a sphere minus six disks.
  • Two fingerless gloves connected by a band is a sphere minus 11 disks.

Another lovely example is that of some scarves, which are a projective plane minus a disk (i.e., a Mobius strip), and therefore sit flat against one’s neck. I would be very interested in owning more non-orientable clothing (someone, somewhere, must own a non-orientable tank top–though perhaps that mythical object would be too annoying to be allowed to exist).