How Many Holes Does a Human Have?

[Music] 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 humans 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 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 doesn'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 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 [Music] 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 doesn'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 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 doesn'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 [Music] 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 [Music] you

Channel: Vsauce

Views: 7,862,856

Rating: 4.9361062 out of 5

Keywords: topology, math, holes, anatomy, learn, science, vsauce, michael stevens, genus, geometry

Id: egEraZP9yXQ

Length: 21min 27sec (1287 seconds)

Published: Mon Feb 17 2020

Reddit Comments

[u/PsychicTempestZero]

What a classic-vsauce feeling video; like something that would have been uploaded in 2014.

I was arguing about this same topic on a hentai thread literally 2 days ago so it's nice to get some conformation

[u/franklollo]

He uploaded a hour ago but where is the new video? It's been since 1 hour. Miss you Michael

[u/gooztrz]

No fking way

[u/Maciek300]

Wow, the 3d imagery looked impressive. Respect to Eric Langlay.

[u/The_Flying_Jew]

"Could I eat a donut without eating its hole?"

-Michael "Vsauce" Stevens

[u/[deleted]]

^{You could always make more holes...}

[u/FGHIK]

OH GOD HE ATE THE DONUT THAT'S NASTY

[u/WonderPhil92]

He DEFINITELY had meme material in mind when he made this. God bless Michael Stevens.

[u/ShinyBredLitwick]

ive been on a HUGE mindfield/vsauce kick lately, so this was unexpected and perfectly timed. wow i didnt realize a youtube channel could make me this happy