The Digestive Tract from a Topological Perspective
In topology, the exact length, thickness, or curvature of an object is less important than its connectivity and the number of holes it has—properties that remain unchanged as long as the object is not cut apart or newly joined together. From this perspective, the digestive tract is a particularly interesting structure.
The human digestive tract is a single continuous passage that begins at the mouth and continues through the esophagus → stomach → small intestine → large intestine → anus. Because the space inside the digestive tract is connected to the outside through both the mouth and the anus, topologically speaking, it can be regarded as a long tunnel passing through the body from one end to the other.
Therefore, we can imagine continuously deforming the complex shape of the human body as follows:
Human body → mass surrounding the digestive tract → long hollow cylinder → short, thick cylinder → doughnut shape(torus)
If, during this process, we are allowed only to stretch, shrink, and bend the object without tearing it or joining separate parts together, the single hole passing through the middle remains unchanged. Thus, if the human body is greatly simplified by considering only the digestive tract, it can be regarded as having the same kind of topological structure as a doughnut with one hole.
To be more precise, however, this does not mean that the digestive tract itself is a doughnut. The digestive tract itself is more like a long tube with two open ends: the mouth and the anus. What is topologically comparable to a doughnut is the entire body containing the digestive tract as a passage running through it. In three-dimensional topology, this can be idealized as a structure similar to a solid torus.
The actual human body also contains the nasal passages, airways, ear canals, various ducts, and many microscopic structures. Therefore, it is not mathematically rigorous to describe the topology of the entire human body simply as “one doughnut.” It is more appropriate to regard this as an educational model in which only the digestive tract is retained and other structures are ignored.