How Many Holes Does a Human Have?Feb 19, 2020
hello Vsauce Michael come on if you continue you will eventually emerge from my other end and for this reason it has been said that the
humanbody is like a doughnut yes you are just a bunch of meat packed around a central Hulk or is it you, Humans
havemore than one hole, right? I mean, we
havenostrils and ears. All the sweet pea in the
holeswas born from the nipples. Our pores. Yes, there are subatomic gaps between the molecules. that's the problem, literally, if you cut a garlic clove in half and then rub that fresh, raw end on your foot about an hour later, you'll start to taste the garlic in your mouth, that's because the The molecules that give garlic its flavor are small enough and have the right properties to penetrate the skin cells on your foot, enter your bloodstream, and reach your mouth, but they're even holier than that every other day and nights, approximately 60 billion neutrinos from the Sun pass through the thumbnail so clearly on scales small enough that How
humanhave becomes a meaningless question, ultimately the human body is not something solid that can even have holes in it, it's just a loose constellation of atoms and molecules, but if we accept a minimum hole size, the answer becomes quite interesting and a good option for this minimum is twenty to sixty millionths of a meter, about the width of a human hair.
A magical 60 micron wide spaceship could enter your pores as if they were giant crater-like holes, but it couldn't continue through the vasculature at the other end or it diffuses through the cells or slips between the molecules and that is significant, it highlights the fact that not all holes are the same, a boat or a rope of 60 microns wide could be coiled in the mouth and come out the other side, but it could not do so by entering a pore or hair follicle ago that the GI tract is what engineers call a through-hole where the pores, urethras, nipples, ears, hair follicles, birth canals, and sinuses are all blind holes to enter, but ultimately they end up in a dead end, usually in narrow capillaries permeable only by things smaller than a single blood cell and the determination not to be stopped the eyeball may be crushed but eventually you will 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 through the ear well the ear is great to get in but if it's 60 microns wide the airtight eardrum will block further passage it's a blind hole now, counting all his pores and hair follicles, he has millions of blind holes all over his body, but are they really holes?
That's a real wonder because you know what a hole is, what a hole really is. mathematical definition, in fact, holes may not even exist, I mean think about it if I eat a whole donut, have I eaten it all like I had a hole in me or could I eat a donut without eating its hole? Could I go to a store and buy Swiss? cheese but leave the holes in store clearly holes are at best ontologically parasitic their existence depends on the existence of something else they can inhabit or be a disturbance of course the philosophy of holes rarely matter in your everyday life.
I can call something a hole and the context will do its job and people will know what you're talking about, but take a look at this,
doesthis have a hole? Yeah, obviously, there's a hole here that I can put my hand through. it can store things it has a hole in it but now imagine i could mold it like it was made of clay and i molded it into the shape of a drinking glass you can see how that could happen well does a drinking glass have a hole in it if this does then this should - ok i mean i didn't pinch the hole shut or glue anything ok sure ok i mean i can accept that a drinking glass technically has a hole but now imagine i took this glass and i shaped it and enlarged its opening until i had a shape like this a bowl now has a bowl has a hole 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 it had a hole elsewhere and it was leaking but ok 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 mold the bowl and flatten its sides completely until I had a one shaped plate how is it ok, does a plate have a hole?
It doesn't, if a plate doesn't have a hole, but this shape does and I molded continuously from here to glass to bowl to plate and never glued anything to close it off where the hole was clearly the knockouts are pretty unique they can be removed without close or pinch anything to close compared to a donut through hole there is no way to remove a Donuts through hole or add a new through hole without gluing things together by squashing things that didn't used to be together or ripping pieces off by drilling a hole and breaking it off which is extremely significant but let's go back to the body before let's get ahead of ourselves the mouth is an entrance for both blind and through holes a 60 micron wide traveler could meander down the esophagus and continue until they were well emptied but lower the windpipe and would now end in the lungs the area of the throat behind the mouth is called the pharynx it's a pretty cold place except it's not actually quite warm it plays a role in warming, moistening and filtering the air we breathe before it gets inside to the lungs including the air we inhale through our nostrils now each nostril leads to a separate nasal vestibule which is the tunnel you can explore when you pick your nose eventually those tunnels meet and the sniffed air enters the nasal cavity a hollow, air-filled room in your face that protrudes from the walls of the nasal cavity are mucous flaps called the nasal concha or turbinates that become warm and humid in the air passing around them from there the air flows through the pharynx into the windpipe so his nostrils and mouth are connected a string could go into his mouth or nose and out his butt the nasal cavity is pretty central i mean his ear holes would almost lead into it but the eardrum blocks the way, if it didn't there would be a clear passage from the outside into the middle ear and then down the Eustachian tube. the nasal cavity through an opening here, the Eustachian tube controls the air pressure in the middle ear behind the eardrum and normally closes collapsed, but if the outside pressure is dramatically different than the air pressure in the middle ear , swallowing and yawning can cause it to open equalizing the pressure that happens when you plug your ears is great but it's not a through hole and that's what we're looking for and it turns out there are four more holes leading from the outside to this place , your nasal cavity and are the lacrimal puncta there is one near each of your eyelids they are small openings about a third of a millimeter wide into which the fluid that constantly moistens and protects your eyeball drains once inside the puncta tear ducts ASA tear ducts empty into the nasal cavity tear ducts which is why when you're producing a lot of tear fluid and you have to blow your nose that's not mucus it's mostly tears the point is you could push a string 60 microns wide at any of his four puncta through his tear ducts into his nasal cavity into his pharynx and then pushed his whole butt out pretty nicely that gives us eight external openings that don't end in a dead end outlet, but how
manythrough 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 a hole that Forks is two that combined God maybe is three? Well, what about this? How many holes does this thing have or can this topology help us answer each of those questions here I have? two essentially identical pieces of material are now no longer identical or are geometrically sure their shapes are now different but what didn't change about them well that's what topology studies topology deals with properties that persist while something is taken apart The famous joke that a topologist can't tell the difference between a donut and a coffee cup is based on the fact that a coffee cup can be smoothly and continuously molded into a donut simply by stretching and squashing without cutting, gluing, tearing or stitching.
Required topologists call these smooth continuous transformations homeomorphisms, and the cutting, tearing, and pasting they don't allow are exactly the kinds of actions required to make new holes or remove old ones, so since a cup of coffee and a donut are homeomorphic , they should have the same number of through holes and make one, we can now more accurately describe the difference we saw earlier between blind holes and through holes and understand why we are counting them separately now blind holes can be erase via a homeomorphism, since topologists don't even consider them to really be just geometric disturbances, topological holes, on the other hand, cannot be massaged and, unlike a blind hole, where what qualifies and what doesn't it's a matter of opinion, the number of through holes a surface like your body has and three dimensions can be clearly defined if we have difficulty counting through holes all we have to do is find something with an easy to count arrangement of through holes whichever is homeomorphic but first let's play with some topological puzzles here is a donut to hold with an infinitely long unbreakable immovable bar through one of its holes without cutting or separating any part of the shape you can figure out how to manipulate it so that the bar go through both holes pause the video if you want to think about it remember this shape looks like it could have three holes right it has one hole there a second hole there and a third hole here but if i flatten it you can see it only has two holes, you have one there and one there if the rod is threaded. the shape such that one wire is in front and I choose one of the other wires to be the center of the donut, for example, this then the rod goes through only one of the two holes, but if I choose the wire in the front to be in the middle of the donut, then the rod is seen to pass through two holes in the same way if you continuously deform our original to hold the donut on all three tubes and select this tube to be the new center tada, the rod is now going through two holes no need to cut or glue one more puzzle no cutting or breaking can you unlock these shapes interlocking loops ok pause if you want to figure it out yourself here is a solution just inflate the bulb of the shape until you can skate one leg of each loop around until they are untangled and given freedom ok let's define homeomorphism a little bit better we said it was a molding procedure similar to a sheet of rubber or clay with no cutting, breaking or gluing and that's a good introduction, but honestly, you can cut as much as you want during a homeomorphism, so as long as you put everything back together as it was at the end, more precisely, a homeomorphism is a bijective and per continuous function is a function because it is a list of pairs sorted where each point starts and is matched with where it goes which requires it to be a by jek ssin means 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 two points can't be mapped to the same location and no point can magically become multiple new points, basically material can't be continuously added or subtracted so any cuts made need to be neatly patched up with points going back to the same locations. same neighboring points as before in a homeomorphism if parts overlap everything else should flow with the scootch as if all points are a bit sticky no smooth sliding along abrupt cracks the accurate test of whether a function is continuous is pretty good now first i consider a point in an array now where the function takes that point is its image ok now i choose a neighborhood around the image with radius greater than zero and consider all points inside ella if the function is continuous in this direction it should be able to find a neighborhood around the preimage the entry point that only contains points that map inside the image neighborhood in this case i can but in this case we have 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 doesn't redo it, which means the points were split but not repositioned, so the function doesn't is continuous by continuity means that a function must be continuous in both directions, it isok now that we can be amorphous let's start using it to count holes remember this shape was Immediately Before it's obvious how to count its holes but it's easy if we can use a homeomorphism to turn it into something with an easy to count number of holes that we can.
Both shapes are homeomorphic both have two holes to see why just drag the mold and flow the opening of one of these shape holes into the tunnel of the other and there we go since we don't cut and paste the number of holes it hasn't changed so this thing like this always had two holes ok what about a really short straw? 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 doesn't mean it has two holes. you only have one, a straw is homeomorphic to a torus, both openings are part of the same single hole, but this process is a homeomorphism and therefore does not create any new holes, you can also see that the openings are not holes by stretching a of the openings of the straws until it becomes the outer part of a donut, actually there was only a single hole, but enough straws, let's go back to the body, we found eight holes of external openings interconnected by tunnels, but the openings are not holes. they are parts of holes and we can count those holes as it turns out that on a 60 micron scale the human body has seven through holes the human body is not a donut it is a seven grip donut this shape can be molded and stretched on you First , we choose a hole to be the GI tract, the tunnel of the mouth and the anus.
Now in this one we roll half of the other holes. Well now we have something that looks quite human. Seven holes with eight external holes that meet in a common space, the nasal. cavity if we squash all the matter into the tunnels you will realize that our seven grasp torus is topologically equivalent to four pairs of pants sewn together at the waist your body is not a donut it is a suit for a spider ok now to finish let's do two of the legs the nostrils and four of them the tear ducts one the mouth and inflate the material into the shape of a head now let's inflate the edge of the final tube into the shape of a body with its opening at the rear and we have done it, the human body is it a seven grip donut or is it for every piercing you have it'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 skinny piercing in your face that went through a tear duct and came back out or if something like a bullet went through your chest through your esophagus and out the other side that would mathematically count as two new holes and there are more some people have a supernumerary punctum in their eye, each additional punctum that they have about four in total adds an extra hole to the standard seven and reminds of the paranasal sinuses and the ostia that connects them to the nasal cavity, well they're just blind foramina depressions but up to half of us can have at least one ostium attachment an additional hole that connects a sinus to the nasal cavity ok now we are talking about a through hole you can go in one opening and out another now they may not be external holes but for every Ostia attachment you have that is another topological orifice that you need to add to your body total, although most of us have no idea how many accessory Ostia we have, unless you have had severe sinus problems or have had extensive scans of your nasal region studied from multiple angles to answer the question of this video is that 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 throughout our lives or if Finding out how many she had right now was easier, but you'll have to peer into your sinuses to be sure, and that's beautiful, isn't it?
We can rigorously define the properties of holes in all kinds of dimensions, and we can study the temperatures at the bottom of craters on Pluto, but few of us will really know the whole truth about our own bodies, and as always, thanks for looking.
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