The theory of a flat earth is a thing that keeps popping up in history. If you are not familiar with this theory: It basically states that the Earth is not a globe, but rather a disc, because … reasons.
Taking a closer look at this theory, at first it may seem reasonable to deduce that earth is flat from empiric observations. Because of earth’s size, it appears locally flat which means that the curvature is not directly perceivable. Directly refers here to everyday experience. If an experiment is set up to look out for the curvature, it is measurable. Eratosthenes, for example, did this to get an estimate for earth’s circumference.
However, what if flat earthers are not as crazy as they seem to be? Consider the following: In topology a 3-ball is a three dimensional object which is enclosed by a 2-sphere, i.e. a compact topological manifold without a boundary which surface has two dimensions. This is the object that is normally used to approximate earth’s shape. However, in topology certain objects are considered equivalent (homeomorphic) if they share the same properties. In this case, a homeomorphism can be used to transform these objects into one another. It turns out that a 3-ball and a disc with thickness ε > 0 indeed can be transformed into each other. That’s kind of the same as a cup and a donut are homeomorphic to each other, because both represent a 2-torus with genus 1.
So, what tells that about the theory of flat earth? Basically, it says that flat earthers can be transformed into scientifically thinking human beings by applying a certain homeomorphism to them. If that homeomorphism is somehow related to homeopathy is beyond my limits, but I think that might be something interesting for further investigations.