The human body is extraordinarily complicated, possessing several openings and a few exits. But the question is: how many holes does a person have? Maybe it sounds like a simple enough question to answer, but it’s not quite that easy if one starts considering questions like: “What is a hole?”
Defining a “Hole” in Mathematical Terms
According to Katie Steckles, a lecturer in mathematics at Manchester Metropolitan University in the U.K., mathematicians use the term “hole” to mean something like the hole in a donut: one that goes all the way through a shape and out the other side. Similarly, James Arthur, a mathematical communicator, stated that “in topology, a ‘hole’ is a through-hole, that is, one you can pass your finger through the object.”
Returning to the Topic of the Body
If we go back to the question “how many holes does the human body have?”, we might initially try to count all the openings. The common ones are probably our mouth, our urethra (the one we pee out of), our anus, as well as the openings in our nostrils and our ears. For women, there are also milk ducts in the nipples and the vagina. Besides these, there are also four less-obvious openings that we all have in the corners of the eyelids closest to our nose—the four lacrimal puncta, which drain tears from our eyes into our nasal cavities.
On an even smaller scale, there are pores that enable sweat to escape our bodies and sebum to lubricate our skin. In total, there are potentially millions of these openings in our bodies. But the question is, do they all count as holes?
Applying the Topological Definition
If we think about whether we could pass a very thin string into one opening and out of another, then we have to set a fixed string size. If we set the size of this string to be about 60 microns (60 millionths of a meter), then it’s possible that the string could enter an opening as small as a pore. However, the fact is, it wouldn’t be able to come out the other end. It would be blocked by the cells at the bottom of the pore because the barrier is too thick to pass through into the vasculature that supplies the pore.
According to Steckles, these are not actually holes in the topological sense, as they don’t go all the way through; they are simply blind pits. By this definition, we can rule out all the pores, milk ducts, and urethras. We couldn’t thread a string in one of these openings and out of another. Even the ear canals have to go (be excluded), as they are separated from the rest of the sinuses by the eardrums.
The Main Contenders for “Through-Holes”
It was said by Arthur that we have our mouth, our anus, and our nostrils, which are the four openings that form a hole. However, it was also stated that we actually have eight. The remaining four were said to come from the tear ducts, with two in each eye—an upper and a lower.
However, it was pointed out by Steckles that this does not necessarily mean eight holes. It was explained that when holes pass through a shape, counting how many there are becomes more difficult.
The Topological Perspective
In the end, the question is not just about counting openings but about understanding connections. Topologically speaking, our bodies are less like Swiss cheese and more like a carefully constructed onesie for an octopus.
The digestive tract (mouth to anus) forms one continuous tunnel. The nostrils connect to the nasal cavity and eventually to the throat (which links back to the digestive tract), while the tear ducts drain into the nasal cavity as well. This interconnected system means the body is often considered to have just one single through-hole in strict topological terms—much like a donut has one hole—even though we intuitively feel there are multiple separate openings.
