What kind of topological object is the human body?

[AaronX]

@cmyk

See, now we’re talking volumes.

And this is why I kinda feel this whole “the human body is topographically a torus or a coffee mug!” quite a bit of an oversimplification—and only true in the most broadest of terms.

Our bodies are an overwhelming amalgam of thousands of organs, structures, cavities, hair, pours, and a mind-boggling network of, well, tubes… made up of trillions of cells all pushing solids, fluids and molecules. Sure, it’s all bound by connective tissue, but we’re hardly a homogenous abstract entity like a mathematically idealized, geometric toroidal surface.

I mean, I get the feeling that in 4D, a hollow 3D object is the same as having a hole. Is that true?

[Xema]

@TriPolar

A styrofoam coffee cup is no different than a sheet of paper.

I think we should ask you to drink a cup of hot coffee from each and then report as to their equivalence.

[md2000]

Hmm, basically topologically a human is equivalent to a set of brass knuckles, not a tube or a donut. Too many holes.

[Darth_Panda]

@Musicat

A human body considered as a hole in, connected to a hole out, is topologically equivalent to a donut.

Worst donut hole ever.

[Smeghead]

It all depends on what you define as a “surface”. And that question is one of semantics, with a bit of biology thrown in for fun. It’s not really a topological question.

[Leo_Bloom]

@Smeghead

It all depends on what you define as a “surface”. And that question is one of semantics, with a bit of biology thrown in for fun. It’s not really a topological question.

Then does topology not deal with surfaces (or surface sets) enclosing other surface sets?

Please excuse the grade-school questions.

[Learjeff]

Ignoring the eyes but just considering two nostrils (that collapse to one passageway, ignoring sinus anomalies), mouth (which collapses to the same passageway along with the nostrils), and anus, that makes us a manifold.

A manifold is something that has one intake and multiple outlets (or vice versa … or ignore “in and out” but retain the multiple openings to one cavity). That’s a different topology from adding pierced ears, which simply adds two new passageways.

So is the characterization of a person with pierced ears a genus-5 manifold incorrect? I would think so.

[Chronos]

A manifold is something that has one intake and multiple outlets (or vice versa … or ignore “in and out” but retain the multiple openings to one cavity). That’s a different topology from adding pierced ears, which simply adds two new passageways.

It’s not a different topology, since “inside” and “outside” aren’t well-defined here.

[ftg]

@foolsguinea

I guess the relevant void has mostly closed up, but I used to be able to hold my nose closed and exhale around one of my eyeballs. I’m not sure if I was forcing air through the tear duct or something else. But yeah, at least genus 5, what with mouth, 2 nostrils, 2 tear ducts, and anus.

See post 18.

[Johanna]

@panache45

And others are sometimes jelly-filled (I’ve heard).

Only one of those that I’ve ever heard of: President John F. Kennedy.

[md2000]

@Learjeff

Ignoring the eyes but just considering two nostrils (that collapse to one passageway, ignoring sinus anomalies), mouth (which collapses to the same passageway along with the nostrils), and anus, that makes us a manifold.

A manifold is something that has one intake and multiple outlets (or vice versa … or ignore “in and out” but retain the multiple openings to one cavity). That’s a different topology from adding pierced ears, which simply adds two new passageways.

So is the characterization of a person with pierced ears a genus-5 manifold incorrect? I would think so.

but 3-in-one-out generally collapses topologically to a donut with 3 donut holes. 5 if we count eustacian tubes. 7 with ear piercings. A manifold is no different than a multi-hole donut - or a set of brass knuckles.

[Leo_Bloom]

@Leo_Bloom

Then does topology not deal with surfaces (or surface sets) enclosing other surface sets?

Please excuse the grade-school questions.

Wait, so has this been answered and I missed it?

[cmyk]

@Leo_Bloom

Then does topology not deal with surfaces (or surface sets) enclosing other surface sets?

Please excuse the grade-school questions.

It does, but discrete surfaces (and in the mathematical/geometrical study, usually idealized, abstract ones). So, we really would have to break the body down into as many discrete “objects” as possible. But as an highly complex organism, this is virtually impossible and full of gray areas to take it out of a topological context.

That said, you can sever the eyeball from its nerve, blood supply and muscles, then say, topologically, the surface is a 2-sphere, but the iris inside is a torus.

We all know the skin is full of thousands of pours, the lungs are full a millions of alveoli, and even the circulatory system is a mind-fuck if you go all the way down to the capillary level.

So, saying topologically a human is a torus based on the GI track alone barely cuts it. Where does the GI track begin and end?

[Leo_Bloom]

@cmyk

…We all know the skin is full of thousands of pours, the lungs are full a millions of alveoli, and even the circulatory system is a mind-fuck if you go all the way down to the capillary level…

Thanks for the reply.

But I must add that the mind fuck is ameliorated considerably if you must pry white-blood cells off Raquel Welch, or so I’ve heard.