How many holes do we have?

"If you keep going, you will eventually emerge out my other end. For this reason, the human body has been likened to a doughnut – a bunch of meat packed around a central core. But are humans just a bunch of holes? We do have more than one hole, right? We have nostrils, ears, nipples, pores, and various other openings. But are these holes all the same? Well, not really.

Let's explore the concept of holes on a smaller scale. Imagine cutting a clove of garlic in half and rubbing the fresh, raw end on your foot. After some time, you will start to taste garlic in your mouth. This happens because the molecules that give garlic its taste can permeate your skin cells, enter your bloodstream, and reach your mouth. But the human body is even holier than that. Every second, about 60 billion neutrinos from the Sun pass through just your thumbnail. So, at smaller scales, the question of how many holes a human body has becomes meaningless.

Ultimately, the human body is not a solid entity that can have holes. It is a loose constellation of atoms and molecules. However, if we consider a minimum hole size, let's say about twenty to sixty millionths of a meter (about the width of a human hair), then the answer becomes quite interesting. At this scale, a magic spaceship or string 60 microns wide could fly into your pores like they were giant holes. It could thread through your mouth and come out somewhere else. But it couldn't enter a pore or hair follicle and continue through the vasculature or slip between molecules.

This highlights that not all holes are equal. Pores, urethras, nipples, ears, hair follicles, birth canals, and sinuses are what engineers call blind holes. They can be entered but eventually dead-end, usually at narrow capillaries that are permeable only to substances smaller than a single blood cell. On the other hand, the gastrointestinal (GI) tract is a through-hole. You can enter through your mouth and exit through your anus. The sinuses and the eyeball have their unique characteristics too.

Counting all the pores and hair follicles, there are millions of blind holes all over your body. But are they really holes? That's a complex question because the term "hole" can refer to a range of disparate things. Holes might not even exist as a well-defined concept. Nevertheless, for practical purposes, we can call them holes, and the context will do its work.

Now, let's consider objects with clear arrangements of holes to help us count them. For example, a doughnut and a coffee cup are homeomorphic. You can gently mold a coffee cup into a doughnut shape without cutting or gluing anything. The number of through-holes remains the same. So, a doughnut and a coffee cup have one through-hole. Similarly, a plate does not have a hole, while a bowl and a glass have one through-hole.

Applying these concepts to the human body, we can identify several external openings that do not dead-end, such as the nostrils, mouth, tear ducts, and lacrimal puncta (tiny openings near the eyelids). By considering their connections and passages, we can determine the number of through-holes.

In conclusion, the human body is a fascinating network of holes, both blind and through-holes, depending on their characteristics and connections. Counting these holes can be challenging, but by using concepts from topology and homeomorphisms, we can gain a deeper understanding of the intricate nature of these openings within our bodies."