Does a donut have a hole topology?

Topology is the branch of mathematics that describes the fundamentals of networks, shapes and the general interconnectedness of things. Topologically speaking, the human body and a ring doughnut have exactly the same shape. The reason why a superficially ridiculous comparison with a sugary comestible is possible is all to do with the gut. The human GI tract, and indeed the GI tract of any creature more phylogenetically advanced than a parasitic flatworm, has both an entrance and an exit and is, at all points, continuous with the surface of the skin. The inside of your GI tract is therefore outside your body. You can test this statement with a thought experiment.

You should be able to touch any part of the outside of your body.

Therefore: anything inside the gut is outside the body. Undigested food has by definition never been inside the body. Your colonic bacteria live outside your body. Excretion is removal of waste products from the body. Defaecation and excretion are therefore not necessarily the same thing [There are one or two things that are secreted into the gut for excretion...]


From Wikipedia Commons
There are many other things that share a topological identity with a doughnut; leaving to one side the obvious tyres and rings etc., How about a coffee mug or even the entire universe.

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