Topological genus of the human body
Stuart Anderson
is its genus? How many holes do we have in our bodies; what counts as
a hole?
Ioannis
news:pan.2004.01.23....@unsound.tv...
>
> If we treat the human body as a topological surface, male and female, what
> is its genus? How many holes do we have in our bodies; what counts as
> a hole?
Ignoring the nasal cavity altogether, it's a torus with a single hole
(running from mouth to anus). So in this case, it's genus 1.
Taking the nasal cavity into account, you have an additional hole (nose)
which is furthermore divided into two separate ones by the nasal diaphragm.
So in this case the (actual) genus is 3.
All that, ignoring any artificial, pathological or otherwise induced
passages (such as doubly communicating internal cysts) that communicate with
each other.
(My own body, for example, was at least genus 300, since on my back's skin I
have cysts which have created self communicating corridors, because of
cystic acne. At least 300, because at least this many were removed by a skin
surgeon)
--
Ioannis Galidakis
http://users.forthnet.gr/ath/jgal/
------------------------------------------
Eventually, _everything_ is understandable
Daniel Grubb
>If we treat the human body as a topological surface, male and female, what
> is its genus? How many holes do we have in our bodies; what counts as
>a hole?
This may depend on whether your mouth is open or closed.
--Dan Grubb
Robin Chapman
>
> (My own body, for example, was at least genus 300, since on my back's skin
> I have cysts which have created self communicating corridors, because of
> cystic acne. At least 300, because at least this many were removed by a
> skin surgeon)
Fascinating... have you a picture on your website?
--
Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html
"Needless to say, I had the last laugh."
Alan Partridge, _Bouncing Back_ (14 times)
Ioannis
news:burqe4$b18$3...@news8.svr.pol.co.uk...
>
> Ioannis wrote:
>
> >
> > (My own body, for example, was at least genus 300, since on my back's
skin
> > I have cysts which have created self communicating corridors, because of
> > cystic acne. At least 300, because at least this many were removed by a
> > skin surgeon)
>
> Fascinating... have you a picture on your website?
No, but I have a nice picture of something else there. Wanna see it?
> --
> Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html
> "Needless to say, I had the last laugh."
> Alan Partridge, _Bouncing Back_ (14 times)
Rick Decker
Robin Chapman wrote:
> Ioannis wrote:
>
>
>>(My own body, for example, was at least genus 300, since on my back's skin
>>I have cysts which have created self communicating corridors, because of
>>cystic acne. At least 300, because at least this many were removed by a
>>skin surgeon)
>>
>
> Fascinating... have you a picture on your website?
>
EWWWW! One hopes not.
Regards,
Rick
p.s. Counting pores, I'd suggest that the number is far higher than
300 for most, if not all, people.
Jake Wildstrom
"Mathematics made difficult" had a chapter on topology, which drew a
distinction between a 'Quiet Man' (closed orifices, so a surface of
genus 0) and a 'Loud Man' (constantly flatulent and speaking, so, with
an oversimplified view of the digestive system, a surface of genus
1). They made the rather disturbing point that two loud men could be
interlocked, which is probably best not visualized.
+-------------------------------------------------------------+
| D. Jacob Wildstrom -- Math monkey and freelance thinker |
| Graduate Student, University of California at San Diego |
| "A mathematician is a device for turning coffee into |
| theorems." -Alfred Renyi |
+-------------------------------------------------------------+
The opinions expressed herein are not necessarily endorsed by the
University of California or math department thereof.
Ioannis
news:401179E4...@hamilton.edu...
[snip]
> Regards,
>
> Rick
>
> p.s. Counting pores, I'd suggest that the number is far higher than
> 300 for most, if not all, people.
Wrong. Pores are all dead ends, so they are essentially skin folds, so they
don't alter the genus count. All orifices on the human body with the
exception of the three main cavities (nasal, mouth, rectal) eventually dead
end. Including urethral cavities, which eventually dead end on the kidneys
and ear cavities which dead end inside the cochlea.
Makes sense, too, since if you look at the blastula while the embryo grows,
it only forms a single fold, which eventually wraps around to form the
digestive tract. All other organs are formed by folding surface cells. The
zygote starts as genus 0, becomes genus 1 when it folds once upon itself to
form the digestive system and changes to genii 2 and 3 when the nasal cavity
and diaphragm form. The formation of the rest of the organs do not change
the genus, which stays 3, unless some external procedure changes it. For
example a tracheaectomy (given to free aerial passages), would change the
genus to 4, while shooting one on the head, would change the genus to 4
also.
The rest about "closed" and "open" orifices is nonsense, since no matter how
tight, the openings are still there, unless somebody cauterizes the opening
to form a skin/muscle joint that seals the cavity permanently.
Michael Varney
"Stuart Anderson" <stu...@unsound.tv> wrote in message
news:pan.2004.01.23....@unsound.tv...
> If we treat the human body as a topological surface, male and female, what
> is its genus? How many holes do we have in our bodies; what counts as
> a hole?
Genus 3 to first order. However, if one counts the rupture of an ear drum
then the Eustachian
tube could add a genus +1.
Now remember that this is gross topology at the macro scale.
Michael Varney
"Ioannis" <morp...@olympus.mons> wrote in message
news:10748929...@athnrd02.forthnet.gr...
> ? "Rick Decker" <rde...@hamilton.edu> ?????? ??? ??????
I wonder how to designate rectal Kleins like James Harris or Peter Brown?
Jesse F. Hughes
> The Prophet Daniel Grubb known to the wise as gr...@math.niu.edu, opened the Book of Words, and read unto the people:
>>
>>>If we treat the human body as a topological surface, male and female, what
>>> is its genus? How many holes do we have in our bodies; what counts as
>>>a hole?
>>
>>This may depend on whether your mouth is open or closed.
>
> "Mathematics made difficult" had a chapter on topology, which drew a
> distinction between a 'Quiet Man' (closed orifices, so a surface of
> genus 0) and a 'Loud Man' (constantly flatulent and speaking, so, with
> an oversimplified view of the digestive system, a surface of genus
> 1). They made the rather disturbing point that two loud men could be
> interlocked, which is probably best not visualized.
But a so-called "closed orifice" isn't closed in the relevant
topological sense, right? After all, a continuous function turns a
closed mouth into an open mouth, right?
At least, I don't recall tearing or ripping in order to open my
mouth. Seems to me that topology oughtn't distinguish between open
and closed mouths.
--
"This confused and outraged many Matrix fans, who'd already spent hours
on the web explaining that man and computers could never really live
in such a state of harmony and mutual benefit."
-- http://www.pointlesswasteoftime.com
KRamsay
I think many piercings have to count. A friend once commented
that some of her acquaintances possessed a rapidly increasing
genus.
Keith Ramsay