Topology is a field of mathematics concerned with the properties of spaces and their invariants. One of these invariants is the number of ways you can cut out slices of an object without it falling apart, known as the “genus”. You can cut a donut and it becomes an open ring, yet it is still one piece, and you can cut the handle of a mug and it won’t fall off. Thus, they’re topologically the same.The genus counts essentially the number of holes though that can be slightly misleading. A representative survey among our household members for example revealed that the majority of people count four holes in a T-shirt, while its genus is actually 3. (Make it a tank top, cut open shoulders and down the front. If you cut any more, it will fall apart.)
Every now and then I read that humans are topologically donuts, with anus, excuse me, genus one. Yes, that is obviously wrong, and I know you’ve all been waiting for me to count the holes in your body.
To begin with the surface of the human body, as any other non-mathematical surface, is not impenetrable, and how many holes it has is a matter of resolution. For a neutrino for example you’re pretty much all holes.
Leaving aside subatomic physics and marching on to the molecular level, the human body possesses an intricate network of transport routes for essential nutrients, proteins, bacteria and cells, and what went in one location can leave pretty much anywhere else. You can for example absorb some things through your lungs and get rid of them in your sweat, and you can absorb some medications through your skin. Not to mention that the fluid you ingest passes through some cellular layers and eventually leaves though yet another hole.
But even above the molecular level, the human body has more than one hole. One of the most unfortunate evolutionary heritage we have is that our airways are conjoined with the foodways. As you might have figured out when you were 4 years old, you can drink through your nose, and since you have two nostrils that brings you up to genus three.
Next, the human eyes sit pretty loosely in their sockets and the nasal cavities are connected to the eye sockets in various ways. I can blow out air through my eyes, so I count up to genus 5 then. Alas, people tend to find this a rather strange skill, so I’ll leave it to you whether you want to count your eyes to uppen your holyness. And while we are speaking of personal oddities, should you have any body piercings, these will pimp up your genus further. I have piercings in my ears, so that brings my counting to genus 7.
Finally, for the ladies, the fallopian tubes are not sealed off by the ovaries. The egg that is released during ovulation has to first make it to the tube. It is known to happen occasionally that an egg travels to the fallopian tube on the other side, meaning the tubes are connected through the abdominal cavity, forming a loop that adds one to the genus.
This brings my counting to 5 for the guys, 6 for the ladies, plus any piercings that you may have.
And if you have trouble imagining a genus 6 surface, below some visual aid.