What kind of topological object is the human body?

[md2000]

Originally Posted by 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]

Originally Posted by 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]

Originally Posted by 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]

Originally Posted by 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.