Topological homeomorphisms and other musings...
Having just given a talk on Random Field Theory, a technique designed to combine topology with probability to allow one to carry out extreme statistics, it is unsurprising to find my brain primed to look at the world in a homeomorphic fashion. Fortunately I choose very safe examples in my talk to explain the concept in relation to the Euler Characteristic, utilising donuts and coffecups, tennis balls and cubes...
... However, as I walked in this morning in the crisp autumn air, it struck me how topological homeomorphisms are employed frequently comedy. For some reason Bill Hicks was on my mind:
"Tie me to your headboard, throw your legs over my shoulders and let me wear you like a feed-bag"
I'm sure there are other examples, but that got me thinking just what is the topological characteristic of a human, and is it the same for men and women? Having worked through this problem I notice that different people are getting different answers depending on their definitions of an orifice (.. religious problem if you will...). Now technically speaking there are 9 orifices, and if you wanted to get smart and include sweat pores these are just blind ending tubes and so don't count! In my calculations I am merely thinking about the human 'surface' and not anything bound within cavities. So vasculature, brain etc., are out as they are within a seperate compartment. It divides up as follows (based on surface continuity):
Group 1 (Purple):
Mouth -> Anus (obvious tube)... However includes nostrils (linked to mouth via oropharynx), and ear canal (eustian tubes to oropharynx).
Group 2 & 3 (red and green) - Eyes, or rather the hole formed by your eyelids. Again one might try to argue the case for the lacrimal duct->nasal cavity, but this actually empties into the lacrimal sac and is discontinious with the eyelid per se.
Group 4 - Vagina-> Fallopian tubes (which open out into the peritoneal cavity).
N.B. Urethra, no matter which way you follow it, ends up as a blind ending tube and hence does not contribute
As you can see from below that means that men are topologically isomorphic with a triple torus (and hence are not dissimilar from pretzels)
Now obviously anyone with piercings completely changes the topology only while the piercing is in place (with some exceptions). Every pircing raises the human-n-Torus representation by n+3 for blokes and n+4 for women. Hence a dude with just one piercing is topologically equivilent to a woman.... And the more piercings you get, the closer you become to a chav bracelet...
That's enough procrastination for now, back to research....
... However, as I walked in this morning in the crisp autumn air, it struck me how topological homeomorphisms are employed frequently comedy. For some reason Bill Hicks was on my mind:
"Tie me to your headboard, throw your legs over my shoulders and let me wear you like a feed-bag"
I'm sure there are other examples, but that got me thinking just what is the topological characteristic of a human, and is it the same for men and women? Having worked through this problem I notice that different people are getting different answers depending on their definitions of an orifice (.. religious problem if you will...). Now technically speaking there are 9 orifices, and if you wanted to get smart and include sweat pores these are just blind ending tubes and so don't count! In my calculations I am merely thinking about the human 'surface' and not anything bound within cavities. So vasculature, brain etc., are out as they are within a seperate compartment. It divides up as follows (based on surface continuity):
Group 1 (Purple):
Mouth -> Anus (obvious tube)... However includes nostrils (linked to mouth via oropharynx), and ear canal (eustian tubes to oropharynx).
Group 2 & 3 (red and green) - Eyes, or rather the hole formed by your eyelids. Again one might try to argue the case for the lacrimal duct->nasal cavity, but this actually empties into the lacrimal sac and is discontinious with the eyelid per se.
Group 4 - Vagina-> Fallopian tubes (which open out into the peritoneal cavity).
N.B. Urethra, no matter which way you follow it, ends up as a blind ending tube and hence does not contribute
As you can see from below that means that men are topologically isomorphic with a triple torus (and hence are not dissimilar from pretzels)
Now obviously anyone with piercings completely changes the topology only while the piercing is in place (with some exceptions). Every pircing raises the human-n-Torus representation by n+3 for blokes and n+4 for women. Hence a dude with just one piercing is topologically equivilent to a woman.... And the more piercings you get, the closer you become to a chav bracelet...
That's enough procrastination for now, back to research....