I was listening to the WNYC Radiolab podcast “Guts” in which one of the hosts likened the human body to a torus (a donut) in that we have a hole going through our body.
For some reason, that really hit me when I heard it. I mean, it’s technically true, we do have a hole going through us, though there are various doorways/valves in the way.
Hearing that was one of those weird moments when you realize we humans really aren’t all that special (or that’s how I felt).
Being pedantic, I’ll note that the GI tract connects with your two nostrils, so the human body is not exactly like a torus unless you’re willing to ignore the nose (I will if you will).
I once saw a video of a guy who ate a bunch of dental floss, but deliberately kept one end hanging out of his mouth. A couple of days later he shat out the other end of the floss, and so managed to have a piece of dental floss running the through his entire GI tract. Coulda tied it in a loop, just like you could tie a string onto a brass ring. (as peculiar as it was, that stunt struck me as a bad idea; seems like it would be easy for the floss to saw through tender portions of your innards.)
The human body is more complicated than a torus because there are a bunch of holes–not only for the two ends of the digestive tract, but for our ears, nostrils, and all the pores on our skin. Still, if you don’t really care about that, you can go around telling your friends that the human body is not simply connected.
I don’t know why, but this example always irritates me. Probably because it sounds really cool without actually conveying any useful information to someone who hasn’t studied topology.
I first learned this back when Enron was formed. At the time I actively collected advertising cheap tricks and “goofs.”
Their first choice of name was “Enteron” I remember laughing myself silly with a friend when we read about the multi-million dollar marketing study that had gone into choosing the name. Bwaaahahaha!
Since then it has vastly changed the way I respond to my appetite and any stomach upset. I can’t think why, but my stomach seized to be an entity unto itself - it’s really just a portion of this long tube with specialized glands in it’s walls. In some way this knowledge allowed me to divorce hunger from emotion and treat it just like any other message my body sent.
So true! There was a neat Time-Life book on Mathematics that was well illustrated and easy to read where I picked up all sorts of trivia. In fact, that whole series had some great stuff in it.
What was the one about in order to cover a sphere with hair it would have to have a “crown” like human hair has?
And there was something about having a piece of paper with a grid of numbered squares on it and if you crumpled an exact copy up and dropped it anywhere on the original there would have to be a matchup between a numbered square on the crumpled one directly above its counterpart on the uncrumpled one.
Going through my father’s books recently, I was disappointed that that book had disappeared (probably years ago). So, I no longer have a copy, but I can still remember much of it. (Not to give away too much, but it must be at least 35 years since I last saw it.)
Those are illustrations of two well-known, relatively simple, but at-first surprising results in topology. The first one is often stated as “you can’t comb the hair on a bowling ball.” Wikipedia calls it the Hairy Ball Theorem. There are several ways of stating it: If, at every point of a ball you have a strand of hair, and all the strands are of the same length, then there’s no way to comb them all flat and have the directions vary continuously. Or: You can do it if you allow the lengths to vary, but at at least one point the length of the strand has to be 0.
The other is Brouwer’s Fixed-Point Theorem. It says that, if f is a continuous function from a disc (or something equivalent to one) to itself, then f must have a fixed-point, that is, a point that f takes to itself. The piece of paper with a grid on it is the disc, and crumpling the paper (no tearing, please!) and placing it on top of a copy illustrates a continuous function from it to itself. As such, Brouwer’s theorem says that there must be a point on the crumpled paper sitting exactly over the corresponding point on the uncrumpled copy.
I remember Dr. Drew (from Loveline fame) kept badgering Adam Corrola on the point that the contents of the stomach were outside of your body. The basic point being that from the starting point of your mouth (ignoring the aforementioned nostril detail) all the way through your anus, your alimentary canal is basically an open tube to the outside world, and (ducts not withstanding) everything contained therein is technically outside of your body. As opposed to things like blood, lymph, various organs and the like which are enclosed by your skin.
Here’s a fact that caused a similar feeling for me. We all know the normal states of matter; gas, liquid, and solid. And in high school we learned about a fourth state of matter, plasma. Plasma was treated as this exotic and rare state.
Except it isn’t exotic or rare. Almost all of the matter in the universe is in a plasma state. It’s the three “normal” states that are exotic and rare. Most of the matter in the universe is in stars. Things like liquids and gases and solids only exist on “unusual” places like a planet.
