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View Full Version : Are human beings donuts?


Liberal
12-14-2005, 06:45 PM
Topologically speaking, as in tori.

Johnny L.A.
12-14-2005, 06:49 PM
I've often said that animals are just complicated tubes.

Colibri
12-14-2005, 06:53 PM
Yes.

minor7flat5
12-14-2005, 06:54 PM
Topologically speaking, as in tori.
Too many holes. Mouth and two nostrils already goes beyond what you could do with a doughnut without piercing it.

Mama Zappa
12-14-2005, 06:54 PM
Topologically speaking, as in tori.
If we are, we're imperfect. Obviously the mouth-to-anus connection could serve as a donut hole (I imagine that's what you're thinking of), however the nasal passages, which connect through to that same doughnut hole (when not blocked off by the assorted flaps of flesh that prevent us from aspirating our Boston Creme treats) kind of mess up the perfection. Not to mention the other holes (eyes, ears, urethra etc.) that take advantage of holes in our skin, but don't actually offer free passage to an exit elsewhere on the body (well, not normally anyway!).

IANAT(opologist) but I would guess the extra ventilation passages mean we're not true doughnuts, despite the old adage "You are what you eat" :). Perhaps we're "second order tori" or something?

Q.E.D.
12-14-2005, 06:59 PM
Not to mention the other holes (eyes, ears, urethra etc.) that take advantage of holes in our skin, but don't actually offer free passage to an exit elsewhere on the body (well, not normally anyway!).
Topologically speaking, those are irrelevant, since they will still map to a flat surface. Through holes are what matters here. I agree, however, that the nostrils and nasal passages complicate things, making each of us an imperfect torus, at best.

lizardling
12-14-2005, 07:02 PM
So every living thing that has a GIGO system is a donut? Don't plants have microscopic holes in their leaves for uptake and release? (from admittedly hazy memories of middle/high school biology)

Colibri
12-14-2005, 07:16 PM
So every living thing that has a GIGO system is a donut? Don't plants have microscopic holes in their leaves for uptake and release? (from admittedly hazy memories of middle/high school biology)

Everything that has a mouth and an anus is a donut. This does not include jellyfish, sea anemones, corals, and flatworms.

The holes in plant leaves do not go through the whole organism. They are mainly located on the underside of the leaves.

Johnny L.A.
12-14-2005, 07:16 PM
Interesting factoid:

If an average-sized man were to face north, and the intestines on the right side of his body were cut and stretched outside of his body as far as they would go to the east, and the intestines on the left side of his body were cut and stretched outside of his body as far as they would reach to the west...
He'd die.

Bippy the Beardless
12-14-2005, 08:08 PM
Is there a topological name for an object with two non-connected holes going through it?

CookingWithGas
12-14-2005, 08:25 PM
Is there a topological name for an object with two non-connected holes going through it?It is called a 2-torus; such an object is of genus 2. I don't know if they have names once you get past genus 2.

Orbifold
12-14-2005, 09:43 PM
It is called a 2-torus; such an object is of genus 2. I don't know if they have names once you get past genus 2.

Another generic term is "solid handlebody".

Duckster
12-14-2005, 09:47 PM
So are men creme-filled while women are jelly?

:D

ultrafilter
12-14-2005, 10:28 PM
Topologically speaking, those are irrelevant, since they will still map to a flat surface. Through holes are what matters here. I agree, however, that the nostrils and nasal passages complicate things, making each of us an imperfect torus, at best.

The bladder's got an intake somewhere, though, and I think that makes it count as an exit hole.

picunurse
12-14-2005, 10:33 PM
Once the zygote begins dividing, it forms a tube (neural tube (http://uoguelph.ca/zoology/devobio/210labs/brainchart.html)) Everything else is window dressing.

Q.E.D.
12-14-2005, 10:34 PM
The bladder's got an intake somewhere, though, and I think that makes it count as an exit hole.
Not quite. The bladder connects to the outside world via the urethra, and is filled through a pair of tubes, one from each kidney. The kidneys have no other connection to the outside--all the fluids and waste products cross over from the bloodstream via osmosis. I wouldn't really count that.

Hail Ants
12-14-2005, 10:43 PM
Kennedy said he was!

:D

R. P. McMurphy
12-14-2005, 11:24 PM
Krispy Kremes, I hope!

Liberal
12-15-2005, 04:34 AM
Everything that has a mouth and an anus is a donut.That's pretty much what I was thinking, but I didn't know whether the sphincter mattered. Is a torus allowed to have a shut-off valve, so to speak? Or does the fact that the sphincter is elastic make it a non-issue?

butler1850
12-15-2005, 09:52 AM
That's pretty much what I was thinking, but I didn't know whether the sphincter mattered. Is a torus allowed to have a shut-off valve, so to speak? Or does the fact that the sphincter is elastic make it a non-issue?

No matter how much of a "tightass" one might be, there is always some part of it that's not completely closed. (very small, but present)

CookingWithGas
12-15-2005, 09:55 AM
Is a torus allowed to have a shut-off valve, so to speak? Or does the fact that the sphincter is elastic make it a non-issue?The sphincter is not a closed surface, topologically, so it's technically a hole even if it puckers so tight you couldn't drive an ice pick up there with a sledge hammer.

Bryan Ekers
12-15-2005, 09:56 AM
When your head's up your ass, does that make you a cruller?

Malacandra
12-15-2005, 10:04 AM
Similarly, ISTR that the length/width/height dimensions quoted for Noah's Ark are in roughly the same proportions as the human body (tho' differently oriented). So not only are we ambulatory doughnuts, but we are roughly the same shape as Noah's Ark.

Robot Arm
12-15-2005, 12:33 PM
For a really thorough count of the number of through-apertures on the human body, don't forget to include piercings.

bordelond
12-15-2005, 01:13 PM
Kennedy said he was!

:D
Nice!

Bosda Di'Chi of Tricor
12-15-2005, 02:05 PM
Are human beings donuts?


"MMMmmmm! Long pork!"~~Homer Simpson.

jawdirk
12-15-2005, 03:07 PM
A Human is not a donut. Nostrils and ears connect to the throat. So a human has 5 distinct holes.

And don't forget piercings.

You could also argue that each hair is a separate object topologically, but still part of the human.

ultrafilter
12-15-2005, 04:07 PM
Not quite. The bladder connects to the outside world via the urethra, and is filled through a pair of tubes, one from each kidney. The kidneys have no other connection to the outside--all the fluids and waste products cross over from the bloodstream via osmosis. I wouldn't really count that.

If stuff can get in, there's at least one hole there.

Actually, if you want to get really picky, humans are mostly empty space filled with a lot of electrons and nuclei. So no, we're not donuts--we're not even connected.

Q.E.D.
12-15-2005, 05:07 PM
...ears connect to the throat.
Only if the eardrum is perforated. The eustacian tubes run from the back of the throat to the middle ear, which is separated from the outside world by the normally airtight tympanum.
Actually, if you want to get really picky, humans are mostly empty space filled with a lot of electrons and nuclei. So no, we're not donuts--we're not even connected.
Ah ha! Here's the real crux of the question: how does one define a "hole" in this context? I think we need a definition which excludes the spaces between atoms and molecules, since common sense dictates that we think of these as being contiguous, for our purposes.

ultrafilter
12-15-2005, 05:14 PM
Ah ha! Here's the real crux of the question: how does one define a "hole" in this context? I think we need a definition which excludes the spaces between atoms and molecules, since common sense dictates that we think of these as being contiguous, for our purposes.

The hole in your mouth is a wider space between molecules than elsewhere in your body. I guess you could set a minimum size, but if you're getting into topology, it's not fair to expect common sense to have any input.

jawdirk
12-15-2005, 06:18 PM
Only if the eardrum is perforated. The eustacian tubes run from the back of the throat to the middle ear, which is separated from the outside world by the normally airtight tympanum.

I don't know about you, but if I plug my nose and close my mouth, I can blow a very small amount of air out of my ears. I can depressurize my ears in an airplane with my nose and mouth closed. So I think ears are only airtight in the same way that your mouth is airtight when it is closed.

Actually, if you want to get really picky, humans are mostly empty space filled with a lot of electrons and nuclei. So no, we're not donuts--we're not even connected.

Or maybe we are all just wrinkles on a contiguous 13-dimensional M-brane?

iamthewalrus(:3=
12-15-2005, 06:22 PM
Interesting factoid:

If an average-sized man were to face north, and the intestines on the right side of his body were cut and stretched outside of his body as far as they would go to the east, and the intestines on the left side of his body were cut and stretched outside of his body as far as they would reach to the west...
He'd die.But how much salt would it take to cover him?

Q.E.D.
12-15-2005, 06:28 PM
I don't know about you, but if I plug my nose and close my mouth, I can blow a very small amount of air out of my ears.
I used to be able to, after one of my eardrums was ruptured in a fight, but once that healed up it was sealed. However, I just thought of another set of holes we've overlooked: At the bottom of each eye is a tear drainage tube called the nasolacrimal duct. These connect to the nasal passages, and are therefore connected to the mouth and throat.

Cervaise
12-15-2005, 08:05 PM
if you're getting into topology, it's not fair to expect common sense to have any inputDo you get into a lot of fistfights at math conferences? ;)

Bob Scene
12-16-2005, 01:36 AM
Once the zygote begins dividing, it forms a tube (neural tube (http://uoguelph.ca/zoology/devobio/210labs/brainchart.html)) Everything else is window dressing.

I think you're talking about gastrulation, which happens pretty early in embryonic development and forms the archenteron, which becomes the digestive tract. The neural tube forms later in a completely different process.

Trunk
12-16-2005, 10:56 AM
When your head's up your ass, does that make you a cruller?
It makes you a Klein Bottle.

HA HA HA HA HA!!!

Dr. Rieux
12-16-2005, 11:06 AM
When your head's up your ass, does that make you a cruller?
Or a Klein Bottle.

Dr. Rieux
12-16-2005, 11:08 AM
Much like me...
:smack:

Trunk
12-16-2005, 11:12 AM
Much like me...
:smack:
Interesting how no one posted that joke for 24 hours, and then two of us did it within ten minutes.

I'm still laughing, by the way.

SentientMeat
12-16-2005, 11:59 AM
Since the mouth attaches to two other exits (nasal and anal), we are donuts with a sidehole, topologically speaking (or more sideholes if we consider the tear ducts). True genus 2 donuts would require extra separate holes. I suppose stigmata could make you genus 5!

Chronos
12-16-2005, 12:59 PM
I don't think that distinction exists, SentientMeat. Smoothly deform a human as follows: Open the mouth really wide. Prolapse the inside of the mouth cavity, to the point where the connection to the nasal passages is outside. Migrate the mouth end of the nasal passage to elsewhere on the body. You now have two "separate" holes through the manifold, just as if you had a stigma. But since the deformations were all smooth, we haven't changed the topology at all, so those extra holes were there and "separate" to begin with.

Flowch
12-16-2005, 07:39 PM
But Chronos, The mouth is still one hole.

There is the hole mouth to anus and the hole mouth to nostrils. For there to be two distinct holes one would have to stitch the mouth in the middle somewhere. I get what you are trying to say, but from the way I see it, you would end up essentially with a sphere with a "H" shaped hole in it (mouth, anus and two nostrils). No matter which way you manipulate it I can't see how you can separate the mouth - nostril connection.

Flowch

Robot Arm
12-16-2005, 08:18 PM
Nobody's trying to separate the mouth-nostril connection. (Did I really just type that?) It's just that every hole in an object is topologically equivalent. Mouth-to-anus is a hole, nostril-to-nostril is a hole, they're all the same.

Picture it this way: You've got a donut made of infintely stretchable clay. You can squeeze the clay around to one side to make a really lopsided donut. Then you can make an indentation and turn it into a coffee cup. And you haven't poked any extra holes in the thing, so you haven't changed it topologically. But it will never be a two-handled sugar bowl.

(Special thanks to my uncle for letting me spend hours with his Time-Life science series of books, and then giving them to me several years ago.)

Dr. Rieux
12-17-2005, 12:19 AM
Interesting how no one posted that joke for 24 hours, and then two of us did it within ten minutes.

I'm still laughing, by the way.
Great minds think alike--and so does mine.

inkleberry
12-17-2005, 01:25 AM
Yes. And ironically, topology is the only math (besides logic) I was ever good at.

I can also turn a mobius strip into a pretty watermelon-fruit-basket looking thing.

Of course, I'm not as cool as the guy who makes real-life glass klein bottle beer steins.

inkleberry
12-17-2005, 01:34 AM
Apparently, mytopology dorkdom (http://web.archive.org/web/20010802121232/dogbert.pitzer.edu/~llionett/topology.html) lives on to this day. Learn to make pretty colored world maps with only 4 crayons. Find a whole list of children's lit that's topology oriented. Be warned: it's a very knotty site..... ;) :D

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