# What kind of topological object is the human body? **URL:** \ **Category:** Factual Questions\ **Created:** [December 8, 2012, 5:54pm UTC](https://boards.straightdope.com/t/what-kind-of-topological-object-is-the-human-body/643432 "2012-12-08T17:54:49Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![Leo\_Bloom](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/leo_bloom/32/10377_2.png) [@Leo\_Bloom](https://boards.straightdope.com/u/Leo_Bloom)\ **Post date:** [December 8, 2012, 5:54pm UTC](https://boards.straightdope.com/t/what-kind-of-topological-object-is-the-human-body/643432/1 "2012-12-08T17:54:49Z")
I was counting up the holes in a male and female body, and came to the conclusion that it had two real holes/tracks–obviously I don’t know how topologists term things, but I’d like to know. I’ve seen some “a coffee cup is not a sphere”-type classifications. I see two holes: mouth-to anus and nose-sinus-to-mouth. 1: True? 2. Description in mathematical language? ---
**Author:** ![Leo\_Bloom](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/leo_bloom/32/10377_2.png) [@Leo\_Bloom](https://boards.straightdope.com/u/Leo_Bloom)\ **Post date:** [December 8, 2012, 5:59pm UTC](https://boards.straightdope.com/t/what-kind-of-topological-object-is-the-human-body/643432/2 "2012-12-08T17:59:12Z")
ETA: clarification: nose-sinus-mouth ---
**Author:** ![Ludovic](https://avatars.discourse-cdn.com/v4/letter/l/7ab992/32.png) [@Ludovic](https://boards.straightdope.com/u/Ludovic)\ **Post date:** [December 8, 2012, 6:01pm UTC](https://boards.straightdope.com/t/what-kind-of-topological-object-is-the-human-body/643432/3 "2012-12-08T18:01:22Z")
The nostrils and the mouth and the anus and also, I believe, the ears, are connected to each other but use different openings. Is this different topologically than a simple mouth-anus connection? someday, we’ll find it ---
**Author:** ![Leo\_Bloom](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/leo_bloom/32/10377_2.png) [@Leo\_Bloom](https://boards.straightdope.com/u/Leo_Bloom)\ **Post date:** [December 8, 2012, 6:06pm UTC](https://boards.straightdope.com/t/what-kind-of-topological-object-is-the-human-body/643432/4 "2012-12-08T18:06:57Z")
Add ears-mouth? Also, mouth-urethra. ---
**Author:** ![Leo\_Bloom](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/leo_bloom/32/10377_2.png) [@Leo\_Bloom](https://boards.straightdope.com/u/Leo_Bloom)\ **Post date:** [December 8, 2012, 6:08pm UTC](https://boards.straightdope.com/t/what-kind-of-topological-object-is-the-human-body/643432/5 "2012-12-08T18:08:03Z")
Missed the wire. 🙂 ---
**Author:** ![Xema](https://avatars.discourse-cdn.com/v4/letter/x/9de053/32.png) [@Xema](https://boards.straightdope.com/u/Xema)\ **Post date:** [December 8, 2012, 6:14pm UTC](https://boards.straightdope.com/t/what-kind-of-topological-object-is-the-human-body/643432/6 "2012-12-08T18:14:15Z")
> [@Leo\_Bloom](#): > > Add ears-mouth? Eardrum doesn’t matter? > [@](#): > > mouth-urethra. No direct passageway there at all. ---
**Author:** ![leahcim](https://avatars.discourse-cdn.com/v4/letter/l/b4bc9f/32.png) [@leahcim](https://boards.straightdope.com/u/leahcim)\ **Post date:** [December 8, 2012, 6:20pm UTC](https://boards.straightdope.com/t/what-kind-of-topological-object-is-the-human-body/643432/7 "2012-12-08T18:20:22Z")
If you count the digestive tract as only one hole (which is what I’ve usually seen done), then “the surface of a human” is an orientable manifold of genus 1. Counting the nostrils, it’s an orientable manifold of genus 3. ---
**Author:** ![njtt](https://avatars.discourse-cdn.com/v4/letter/n/ecd19e/32.png) [@njtt](https://boards.straightdope.com/u/njtt)\ **Post date:** [December 8, 2012, 6:20pm UTC](https://boards.straightdope.com/t/what-kind-of-topological-object-is-the-human-body/643432/8 "2012-12-08T18:20:24Z")
> [@Leo\_Bloom](#): > > Add ears-mouth? > Also, mouth-urethra. No. The ears are not open, and the mouth is not connected to the urethra. Either way there are membranes in the way. The eardrum in the one case, and lots of membranes through which liquids permeate in the other. (If you are going to count permeable membranes as holes, it will get absurd. We are just one big hole that way.) ---
**Author:** ![Iggy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/iggy/32/3364_2.png) [@Iggy](https://boards.straightdope.com/u/Iggy)\ **Post date:** [December 8, 2012, 6:24pm UTC](https://boards.straightdope.com/t/what-kind-of-topological-object-is-the-human-body/643432/9 "2012-12-08T18:24:21Z")
Middle ear space connects to the mouth-sinus-nose pathway via the eustachian tube. Outer ear to the eardrum would topologically just be an infolding of the skin. ---
**Author:** ![johnpost](https://avatars.discourse-cdn.com/v4/letter/j/f17d59/32.png) [@johnpost](https://boards.straightdope.com/u/johnpost)\ **Post date:** [December 8, 2012, 6:26pm UTC](https://boards.straightdope.com/t/what-kind-of-topological-object-is-the-human-body/643432/10 "2012-12-08T18:26:06Z")
a donut with sprinkles. ---
**Author:** ![Exapno\_Mapcase](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/exapno_mapcase/32/1051_2.png) [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)\ **Post date:** [December 8, 2012, 6:38pm UTC](https://boards.straightdope.com/t/what-kind-of-topological-object-is-the-human-body/643432/11 "2012-12-08T18:38:03Z")
> [@johnpost](#): > > a donut with sprinkles. I don’t know about the sprinkles but I think many of us are cream-filled. ---
**Author:** ![Leo\_Bloom](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/leo_bloom/32/10377_2.png) [@Leo\_Bloom](https://boards.straightdope.com/u/Leo_Bloom)\ **Post date:** [December 8, 2012, 7:11pm UTC](https://boards.straightdope.com/t/what-kind-of-topological-object-is-the-human-body/643432/12 "2012-12-08T19:11:17Z")
I can’t figure out why anus counts but urethra doesn’t. ---
**Author:** ![Darwins\_Finch](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/darwins_finch/32/20304_2.png) [@Darwins\_Finch](https://boards.straightdope.com/u/Darwins_Finch)\ **Post date:** [December 8, 2012, 7:22pm UTC](https://boards.straightdope.com/t/what-kind-of-topological-object-is-the-human-body/643432/13 "2012-12-08T19:22:36Z")
> [@Leo\_Bloom](#): > > I can’t figure out why anus counts but urethra doesn’t. Because you can stick a long-enough hose down your throat and have it come out of your anus without rupturing anything. You can’t do that with with the urethra; it’s connected to the bladder, but the bladder is filled via the kidneys, not the gut. ---
**Author:** ![panache45](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/panache45/32/64_2.png) [@panache45](https://boards.straightdope.com/u/panache45)\ **Post date:** [December 8, 2012, 7:24pm UTC](https://boards.straightdope.com/t/what-kind-of-topological-object-is-the-human-body/643432/14 "2012-12-08T19:24:02Z")
> [@Exapno\_Mapcase](#): > > I don’t know about the sprinkles but I think many of us are cream-filled. And others are sometimes jelly-filled (I’ve heard). ---
**Author:** ![Smeghead](https://avatars.discourse-cdn.com/v4/letter/s/f1d935/32.png) [@Smeghead](https://boards.straightdope.com/u/Smeghead)\ **Post date:** [December 8, 2012, 7:25pm UTC](https://boards.straightdope.com/t/what-kind-of-topological-object-is-the-human-body/643432/15 "2012-12-08T19:25:02Z")
> [@Leo\_Bloom](#): > > I can’t figure out why anus counts but urethra doesn’t. Because the anus connects to the mouth via a tube. If you follow the urethra in, you hit the bladder, and go up to the kidneys, where the “outside” space branches out into a multitude of microscopic tubules. At no point does it connect to another opening, and so the entire system is essentially a complex infolding of the outer surface, which is what topology cares about. ---
**Author:** ![TriPolar](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tripolar/32/3008_2.png) [@TriPolar](https://boards.straightdope.com/u/TriPolar)\ **Post date:** [December 8, 2012, 7:30pm UTC](https://boards.straightdope.com/t/what-kind-of-topological-object-is-the-human-body/643432/16 "2012-12-08T19:30:39Z")
Yup. When you kiss someone on the mouth that’s the sweet end of a 27 foot digestive tract. ---
**Author:** ![Trinopus](https://avatars.discourse-cdn.com/v4/letter/t/2bfe46/32.png) [@Trinopus](https://boards.straightdope.com/u/Trinopus)\ **Post date:** [December 8, 2012, 8:56pm UTC](https://boards.straightdope.com/t/what-kind-of-topological-object-is-the-human-body/643432/17 "2012-12-08T20:56:57Z")
JBS Haldane had a punctured eardrum, and enjoyed blowing cigarette smoke out his ear. He called it a social accomplishment… Another trivial extension of the idea is pierced earlobes. +2 Genus count for some people. ---
**Author:** ![ftg](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/ftg/32/2801_2.png) [@ftg](https://boards.straightdope.com/u/ftg)\ **Post date:** [December 8, 2012, 9:29pm UTC](https://boards.straightdope.com/t/what-kind-of-topological-object-is-the-human-body/643432/18 "2012-12-08T21:29:35Z")
There are numerous complications to all this. Take the [nasolacrimal ducts](http://en.wikipedia.org/wiki/Nasolacrimal_duct) for example. Two holes from the eye openings into the nasal passage. Various performers, such as Teller from Penn and Teller, do stunts with these such as passing beans thru them. And then there are bile ducts that connect to the digestive system and have a complex arrangement. Not a straightforward tree arrangement with some differences among individuals. Etc. ---
**Author:** ![Senegoid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/senegoid/32/6606_2.png) [@Senegoid](https://boards.straightdope.com/u/Senegoid)\ **Post date:** [December 8, 2012, 10:03pm UTC](https://boards.straightdope.com/t/what-kind-of-topological-object-is-the-human-body/643432/19 "2012-12-08T22:03:20Z")
> [@leahcim](#): > > If you count the digestive tract as only one hole (which is what I’ve usually seen done), then “the surface of a human” is **an orientable manifold of genus 1**. Counting the nostrils, it’s an orientable manifold of genus 3. Not mentioned here yet: Counting the GI tract only (orientable manifold of genus 1), this is also called a torus. (Topologically, just a donut shape.) ---
**Author:** ![Hari\_Seldon](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hari_seldon/32/5173_2.png) [@Hari\_Seldon](https://boards.straightdope.com/u/Hari_Seldon)\ **Post date:** [December 8, 2012, 10:32pm UTC](https://boards.straightdope.com/t/what-kind-of-topological-object-is-the-human-body/643432/20 "2012-12-08T22:32:12Z")
It all depends on the scale you use. Get a fine enough microscope you will see the holes between the atomic nuclei. But I would accept an orientable manifold of genus 3. Or a sphere with three handles. But I have a tooth with a hole through it (big enough to insert something called a proxa-brush) so I have a fourth hole or handle. My daughter has pierced ears, giving her genus 5. [Next page](https://boards.straightdope.com/t/what-kind-of-topological-object-is-the-human-body/643432.md?page=2)