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How Many Holes Does a Human Have?

How Many Holes Does a Human Have?
hey Vsauce Michael here come on in if you keep going you will eventually emerge out my other end and for this reason it has been said that the

human

body is like a doughnut yeah you are just a bunch of meat packed around a central Hulk or are you

human

s

have

more than one hole right I mean we've got nostrils and ears the whole sweetpea out of the

holes

were born from nipples our pores yes there are subatomic gaps between the molecules were made out of where don't we

have

holes

well that
how many holes does a human have
is the rub literally if you cut a clove of garlic in half and then rub that fresh raw end on your foot about an hour later you will start to taste garlic in your mouth that's because the molecules that give garlic its taste are small enough and

have

just the right properties to permeate skin cells in your foot enter your bloodstream and reach your mouth but you are even holier than that every second day and night about 60 billion neutrinos from the Sun pass through just your thumbnail so
clearly at small enough scales how

many

holes

does

a

human

have

becomes a meaningless question ultimately the

human

body isn't a solid thing that can even

have

holes

it's just a loose constellation of atoms and molecules but if we accept a minimum hole size the answer becomes pretty interesting and a good choice for this minimum is about twenty to sixty millionths of a meter about the width of a

human

hair a magic spaceship 60 microns wide could fly into your pores like they were giant

holes

like craters but it couldn't continue on through the vasculature at the other end or diffuse through cells or slip between molecules and that is significant it highlights the fact that not all

holes

are equal a 60 micron wide ship or string could be threaded into your mouth and come out somewhere else but it couldn't do that by entering a pore or hair follicle this makes the GI tract what engineers call a through-hole where as pores urethras nipples ears hair follicles birth canals
and the sinuses are blind

holes

they can be entered but eventually dead end usually at narrow capillaries permeable only by things smaller than a single blood cell and the determination to not be stopped the eyeball can be squeezed under but you'll eventually be stopped by the conjunctiva the sinuses are nice big rooms and our skulls but the only way out is the same Ostia you came in through as for the ear well the ear is a blast to go inside but if you're 60 microns wide the airtight
eardrum will block further passage it's a blind hole now altogether counting all of your pores and hair follicles you've got millions of blind

holes

all over your body but are they actually

holes

that's a real humdinger because you know what a hole is what what a hole really is it's a word a colloquial fuzzy imprecise lexeme that refers to a host of disparate utterly unreconciled things that eludes a single precise mathematical definition in fact

holes

might not even exist I mean
think about it if I eat a whole doughnut

have

I eaten the whole like is the hole inside me or could I eat a doughnut without eating its hole could I go to a store and buy Swiss cheese but leave the

holes

at the store clearly

holes

are at best ontologically parasitic their existence depends upon the existence of something else that they can inhabit or be a disturbance in of course the philosophy of

holes

rarely matters in your day-to-day life you can call something a hole and context will do its
work and people will know what you're talking about but take a look at this

does

this

have

a hole in it well yeah right obviously right here there's a hole I can put my hand in it it can store things it's got a hole but now imagine that I could mold it like it was made out of clay and I molded it down into the shape of a drinking glass you could see how that could happen right well

does

a drinking glass

have

a hole in it if this

does

then this should - right I mean I didn't pinch
the hole shut or glue anything together all right sure fine I mean I can accept that a drinking glass technically has a hole in it but now imagine that I took this glass and I molded it out and I widened its opening until I had a shape like this a bowl now

does

a bowl

have

a hole in it now we're really stretching the use of the word hole I mean if someone said their ball had a hole in it I would think that it had a hole somewhere else and it was leaking but sure let's call this a hole
it's not a very prototypical one but I think you see where I'm going with this if I didn't molded the bowl and flattened its sides all the way out until I had a plate a shape like this well

does

a plate

have

a hole in it not really so if a plate

does

n't

have

a hole in it but this shape did and I continuously molded from here to the glass to the bowl to the plate and I never glued anything shut where'd the hole go clearly blind

holes

are pretty unique they can be removed
how many holes does a human have
without closing or pinching anything shut compare that to the through hole of a doughnut there is no way to remove a Donuts through hole or add a new through hole without gluing stuff together squishing things together that used to not be together or ripping pieces apart poking a hole through and breaking it that is extremely significant but let's go back to the body before we get ahead of ourselves the mouth is an entrance to both blind and through

holes

a 60 micron wide traveler could
enter it meander down the esophagus and keep going until they were well dumped out but turn down the trachea and they would dead end in the lungs now the area of the throat behind the mouth is called the pharynx it's a pretty chill place except not really it's actually quite warm it plays a role in warming and moistening and filtering the air that we breathe before it enters the lungs including the air we inhale through our nostrils now each nostril leads into a separate nasal vestibule
that's the tunnel that you can explore when you pick your nose eventually those tunnels meet and sniffed air enters the nasal cavity a hollow air filled room in your face protruding from the walls of the nasal cavity are mucusy fins called the nasal Concha or turbinates that warm and moist in the air that passes around them from there the air flows via the pharynx down the trachea so your nostrils and your mouth are connected a string could go into your mouth or nose and come out your butt
the nasal cavity is quite the hub I mean your ear

holes

would almost lead into it but the eardrum blocks the way if it didn't there would be clear passage from the outside into the middle ear and then down the eustachian tube into the nasal cavity via an opening about here the eustachian tube controls air pressure in the middle ear behind the eardrum and is normally collapsed shut but if the outside pressure is dramatically different than the air pressure in the middle ear swallowing and
yawning can get it open equalizing the pressure that's what happens when you pop your ears it's cool but it's not a through-hole and that's what we're looking for and as it turns out there are four more four more orifices that lead from the outside into this place your nasal cavity and they are the lacrimal punctum there is one near each of your eyelids they're tiny openings about a third of a millimeter wide into which tears the fluid constantly moistening and protecting
your eyeball drain once inside the lacrimal punctum ASA lacrimal ducts tear ducts into your nasal cavity which is why when you're making a lot of tear fluid and

have

to blow your nose that's not snot that's mainly tears the point is a 60 micron wide string could be pushed into any of your four lacrimal punctum threaded through your tear ducts into your nasal cavity into the pharynx and then pushed all the way out your butt pretty cool that gives us eight external openings that
don't dead-end but how

many

through

holes

is that I mean how

many

holes

does

a straw

have

this clearly has two

holes

but how

many

does

this

have

is it one hole that Forks is it two that combined gosh maybe it's three well what about this how

many

holes

does

this thing

have

or this topology can help us answer every single one of those questions here I

have

two essentially identical pieces of material now they are no longer identical or are they geometrically sure their shapes are now
different but what didn't change about them well that is what topology studies topology is concerned with the properties that persist so long as something isn't ripped apart the famous joke that a topologist

does

n't know the difference between a doughnut and a coffee cup is based on the fact that a coffee cup can be gently continuously molded into a doughnut by simply stretching and squashing no cutting gluing ripping or sewing required topologists call these gentle continuous
transformations homeomorphisms and the cutting and ripping and gluing that they disallow are exactly the kinds of actions required to make new

holes

or remove old ones so since a coffee cup and a doughnut are homeomorphic they must

have

the same number of through

holes

and they do one we can now more precisely describe the difference we saw earlier between blind

holes

and through

holes

and understand why we are separately counting them now blind

holes

can be erased through a homeomorphism as
how many holes does a human have
such topologists don't even really consider them they're just geometric disturbances topological

holes

on the other hand cannot be massage it away and unlike a blind hole where what qualifies and what

does

n't is a matter of opinion the number of through

holes

a surface like your body and three dimensions has can be clearly defined if we are having a hard time counting through

holes

all we need to do is find something with an easy to count arrangement of through

holes

that it is
homeomorphic with but first let's play around with some topological puzzles here is a to hold donut with an infinitely long unbreakable unmovable rod through one of its

holes

without cutting or separating any part of the shape can you figure out how to manipulate it such that the rod goes through both

holes

pause the video if you want to think about it remember this shape it looks like it might

have

three

holes

right it's got a hole there a second hole there and a third hole here but if
I flatten it you can see that it only has two

holes

it has one there and one there if the rod is threaded through the shape such that one wire is in front and I choose one of the other wires to be the middle of the doughnut for example this one then the rod passes through just one of the two

holes

but if I choose the wire in the front to be the middle of the donut well then the rod is seen to be passing through two

holes

likewise if you continuously deform our original to hold donut into the
three tube thing and pick this tube to be the new middle tada the rod is now going through two

holes

no cutting or gluing required one more puzzle without cutting or breaking can you unlock this shapes intertwined loops well pause if you want to figure it out yourself here's a solution simply inflate the bulb of the shape until you can skate a leg of each loop around until they're untangled and tada freedom alright let's define homeomorphism a little better we said it was a rubber
sheet or clay like molding procedure with no cutting or breaking or gluing and that's a good introduction but honestly you can cut all you want during a homeomorphism so long as you glue everything back together the way it was in the end more precisely a homeomorphism is a bijective and by continuous function it's a function because it is a list of ordered pairs where each point starts is paired with where it goes requiring that it be a by jek ssin means that it must be a special kind of
function where there is a one-to-one correspondence between points in one object and in the other no two points can map to the same location and no point can get magically turned into multiple new points basically material cannot be added or subtracted by continuous means that any cuts made must be later mended perfectly with points going back amongst the same neighboring points they had before in a homeomorphism if parts are scooched over everything else must flow with the scootch as if all the
points are kind of sticky there is no smooth sliding along abrupt fissures the precise test for whether a function is by continuous is pretty cool now first I consider a point in one arrangement now where the function takes that point is its image okay now I choose some neighborhood around the image with a radius larger than zero and I consider all of the points within it if the function is continuous in this direction I should be able to find a neighborhood around the preimage the input point
that only contains points that map inside the images neighborhood in this case I can but in this case we've got an original point and where it went but given a neighborhood around where it went every neighborhood around the original no matter how small will always contain some stuff that didn't make it over which means points got separated but not put back so the function is not continuous by continuity means that a function must be continuous in both directions okay now that we can
homey amorphous let's start using it to count

holes

remember this shape it wasn't immediately obvious earlier how to count its

holes

but it is easy if we can use a homeomorphism to turn it into something with an easy to count number of

holes

which we can both of these shapes are homeomorphic they both

have

two

holes

to see why simply drag in mold and flow the opening of one of these shapes

holes

into the tunnel of the other and there we go since we didn't cut or glue the number of

holes

hasn't changed so this thing just like this thing always had two

holes

okay what about a straw well short informally it can often make sense depending on the context to differentiate between two openings in a straw the one you put in your drink and the one you put in your mouth but that

does

not mean it has two

holes

it only has one a straw is homeomorphic to a torus both openings are part of the same single hole but this process is a homeomorphism and thus

does

not create any new

holes

you can also see that openings aren't

holes

by stretching one of the straws openings until it becomes the outer part of a doughnut there really was only ever just one hole but enough about straws let's get back to the body we found eight external openings orifices interconnected by tunnels but openings aren't

holes

they're parts of

holes

and we can count those

holes

as it turns out at a scale of 60 microns the

human

body has seven through

holes

the

human

body is not a
doughnut it is a seven hold doughnut this shape can be molded and stretched into you first we choose a hole to be the GI tract the mouth anus tunnel now into this we roll half of the other orifices okay now we've got something that looks pretty dang

human

seven

holes

with eight external orifices that meet in a common space the nasal cavity if we squish all the matter in towards the tunnels will notice that our seven hold torus is topologically equivalent to four pairs of pants sewn together
at the waists your body isn't a doughnut it's a bodysuit for a spider okay now to finish let's make two of the legs the nostrils and four of them the tear ducts one the mouth and inflate the material into the form of a head now let's inflate the boundary of the final tube into the shape of a body with its opening in the rear and we've done it the

human

body is a seven hold doughnut or is it for every piercing you

have

that's one more hole in your body well two more if
the piercing goes through a through hole like I don't know if you had a thin piercing into your face that went through a tear duct and came back out or if something like a bullet pierced into your chest through your esophagus and came out the other side that would mathematically count as two new

holes

and there's more some people

have

supernumerary lacrimal punctum on their eyes each additional punctum they

have

over four total adds an additional hole to the standard seven and remember
the sinuses and the Ostia connecting them into the nasal cavity well they're just blind

holes

depressions but as

many

as half of us may

have

at least one accessory ostium an extra hole connecting a sinus to the nasal cavity well now we're talking about a through hole you can enter one opening and exit via another now these may not be external orifices but for every accessory Ostia you

have

that's another topological hole you need to add to your bodies total the thing is though most
of us

have

no idea how

many

accessory Ostia we

have

unless you've had serious sinus problems or

have

had extensive scans of your nasal region that

have

been studied from multiple angles so to answer this videos question the

human

body has millions of blind

holes

like at least five million and at Birth seven through

holes

it would be better if there was a clear answer that applied to all of us for our entire lives or if finding out how

many

you had right now was easier but you'll

have

to
speelunk in your sinuses to know for sure and that's beautiful isn't it we can rigorously define the properties of

holes

in all sorts of dimensions and we can study that temperatures at the bottom of craters on Pluto but few of us will ever truly know the whole truth of our own bodies and as always thanks for watching you