How Many Holes Does a Human Have?

Hi Vsauce Michael come in, if you continue you will eventually come out the other end of me and for this reason it has been said that the

human

body is like a doughnut, yes you are just a bunch of meat packed around a central Hulk or are you guys, Humans, they

have

more than one hole, right, I mean, we

have

nostrils and ears, all the sweet pea

holes

were born from the nipples, our pores, yes, there are subatomic spaces between the molecules they were made from, do they? where don't we have

holes

? That's the problem, 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'll start to taste the garlic in your mouth, that's because the molecules that give garlic its flavor are small enough and have just the right properties to permeate the skin cells of your foot, enter your bloodstream, and reach your mouth, but you're even holier than that.

Every second, day and night, about 60 billion neutrinos from the Sun pass just through your thumb so clearly at scales small enough that How

many

holes

does

a

human

being have becomes a meaningless question? Ultimately the human body is not a solid thing that can even have holes, it is just a loose constellation of atoms and molecules, but if we accept a minimum hole size the answer becomes quite interesting and a good choice for this. minimum is between twenty and sixty millionths of a meter, approximately the width of a human hair. A magical 60-micron-wide spaceship could fly into your pores like giant crater-like holes, but it couldn't continue 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 the same.

A boat or string 60 microns wide could be threaded into the mouth and come out the other side, but it couldn't do so by Entering a pore or hair follicle, this makes the gastrointestinal tract what engineers call a through orifice, where the pores, urethra, nipples, ears, hair follicles, birth canals, and sinuses are blind orifices that can be entered, but eventually are a dead end, usually in capillaries straits permeable only by things. smaller than a single blood cell and the determination not to be stopped the eyeball can be compressed 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 entered through As for the ear, it is wonderful to enter the ear, but if you are 60 microns wide, the airtight eardrum will block the further passage, it is a blind hole.

Now, counting all your pores and hair follicles, you have millions of blinds. holes all over the body, but are they really holes? That's really amazing because you know what a hole is, what a hole really is, it's a word, a colloquial, confusing and imprecise lexeme that refers to a series of disparate and completely irreconcilable things that eludes a single precise definition. mathematical definition, in fact, the holes may not even exist. I mean, think about it, if I eat a whole donut, have I eaten the whole thing? cheese, but leaves the holes in the 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 It rarely matters in your daily life.

I can call something a hole and the context will do its job and people will know what you're talking about, but look at this,

does

it have a hole? Well, yeah, obviously, there's a hole here that I can put my hand in. It can store things it has a hole, but now imagine I could mold it like it was made of clay and mold it into the shape of a glass. You could see how that could happen. Well, does a glass have a hole? hole in it, if this is so, then this should... right, I mean, I didn't close the hole or glue anything, okay, sure, okay.

I mean, I can accept that a glass technically has a hole, but now imagine I took this glass and shaped it and expanded its opening until I had a shape like this a bowl now does a bowl have a hole now are we really stretching the use of the word hole? I mean, if someone said their ball had a hole in it, I'd think it had a hole somewhere else and was leaking, but sure, let's call this a hole, it's not very prototypical, but I think you see where I'm going with This if I didn't shape the bowl and flatten its sides completely until I had a plate with a shape like this, well, does a plate have a hole?

Not really, if a plate doesn't have a hole, but this shape did and I continually shaped it. Here, to the glass, to the bowl, to the plate, and I never glued anything to close it, where did the hole go? Clearly blind holes are quite unique, they can be removed without closing or pinching anything, 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, crushing things that were not together before or separating pieces, making a hole and breaking it, that is extremely significant, but let's go back to the body before we begin. getting ahead of ourselves the mouth is an entry both blind and through holes a 60 micron wide traveler could enter snaking up the esophagus and continue until they were well removed, but turning towards the trachea and would now end up 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 very warm. It plays a role in warming, humidifying and filtering the air we breathe before it enters the lungs, including the air we inhale. 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 space filled with air in your face that protrudes From the walls of the nasal cavity are mucous flaps called nasal conchae or turbinates that are warmed and moistened by the air that passes around them.

From there, the air flows through the pharynx into the trachea, so the nasal passages and the mouth are connected. A thread could enter your mouth or nose and come out. outside your butt, the nasal cavity is quite a hub. I mean, the openings in your ears would almost lead there, but the eardrum blocks the way, if it didn't, there would be a clear path from the outside to the middle ear and then to 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 is normally closed, but if the outside pressure is dramatically different from the air pressure in the middle ear when swallowing and yawning can be opened to match it. the pressure that happens when you open your ears is great, but it's not a through hole and that's what we're looking for and it turns out that there are four more holes that lead from the outside to this place, your nasal cavity. and they are the tear point.

There is one near each of the eyelids. They are small openings about a third of a millimeter wide into which the liquid that constantly moistens and protects the eyeball is torn. Once inside the punctum, the tear ducts ASA, the tear ducts inward. nasal cavity, so when you're producing a lot of tear fluid and you have to blow your nose, which is not snot, but mainly tears, the point is that a 60 micron wide thread can be pushed into any of your four tear points and pass it through your tear ducts. into your nasal cavity into your pharynx and then pushed all the way out of your butt, which gives us eight external openings that don't end in a dead end, but how

many

through holes are 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 are two that combined? Oh my God, maybe it's three, well what's up with this? How many holes does this thing have? Or this topology can help us answer each of those questions that I have here. Two essentially identical pieces of material are now no longer identical or are geometrically certain that their shapes are now different, but what didn't change about them, well, that's what topology studies. Topology deals with properties that persist as long as something exists. t busted the famous joke that a topologist doesn't know the difference between a donut and a coffee cup is based on the fact that a coffee cup can be gently and continuously molded into a donut simply by stretching and squishing it without cutting, gluing, rip or sew Required topologists call these smooth continuous transformations homeomorphisms, and the cutting, tearing, and gluing they do not allow are exactly the types of actions required to make new holes or remove old ones, so, given that a cup of coffee and a donut are homeomorphic, they must have the same number of through holes and they make one, now we can more precisely describe the difference we saw earlier between blind holes and through holes and understand why we count them separately.

Now blind holes can be erased by homeomorphism, since those topologists don't even really consider them. are just geometric perturbations, topological holes, on the other hand, cannot be massaged out 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 its body and three dimensions can be clearly defined. If we are having difficulty counting through holes, all we need to do is find something with an easy-to-count arrangement of through holes that is homeomorphic, but first let's play with some topological puzzles. Here's a donut to hold.

With an infinitely long, unbreakable, immovable rod through one of its holes without cutting or separating any part of the shape, can you figure out how to manipulate it so that the rod passes through both holes? Pause the video if you want to think about it, remember this way. It 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 out you can see it only has two holes, it has one there and one there if the rod is threaded. the shape is 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 one, then the rod goes through only one of the two holes, but if I choose the wire in the front to let it be in the middle of the donut, then the rod is seen to pass through two holes in the same way, if you continuously warp our original to hold the donut in the three tubes and choose this tube to be the new middle, the rod now passes through two holes.

No need to cut and paste one more puzzle without cutting or breaking Can you unlock these interlocking loops of shapes? Pause if you want to figure it out yourself here's a solution, simply inflate the bulb of the shape until you can skate one leg of each loop until they are untangled and free, okay, let's define homeomorphism a little better. We said it was a molding procedure similar to a sheet of rubber or clay without cutting, breaking or gluing and that's a good introduction, but honestly, you can cut anything 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, by continuous function, it is a function because it is a list of ordered pairs where each point begins and is paired with the destination that requires it to be a by jek ssin means that it must be a special type of function where there is a one-to-one correspondence between the points of one object and in the other no two points can be assigned to the same location and no point can magically become multiple new points, basically the material is not can add or subtract by continuous means, any cuts made must be perfectly repaired afterwards with points that recede between the same neighboring points as they had before in a homeomorphism if the parts slide over everything else must flow with the scootch as if all the points are a little sticky, there is no smooth sliding along abrupt cracks, the precise test for whether a function is continuous is quite good.

Now first I consider a point in a layout, now where the function takes that point is its image, okay? I choose a neighborhood around the image with a radius greater than zero and consider all points within it. 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. within 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 which it went, every neighborhood around the original, no matter how small, will always contain some things that not do it on top, which means that the stitches were separated but not replaced, for example.what the function is not continuous by continuity means that a function must be continuous in both directions.

Okay, now that we can be amorphous, let's start using it to count holes. Remember it was this way. It's not immediately 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. Both forms are homeomorphic. Both have two holes to see why simply. drag into the mold and flow the opening of one of these shape holes into the tunnel of the other and there we go, since we didn't cut and glue the number of holes hasn't changed, so this thing like this always had two holes Well, in short, informally, it can often make sense, depending on the context, to differentiate between two openings on 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 . it only has one, a straw is homeomorphic to a torus, both openings are part of the same 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 one of the openings of the straws until it becomes the outside of a donut, there was actually only a single hole, but enough about straws, let's go back to the body, we find eight external openings, holes interconnected by tunnels, but the openings are not holes. They are parts of holes and we can count those holes as it results in a scale of 60 microns. The human body has seven through holes. The human body is not a donut, it is a seven-position donut. This shape can be molded and stretched inside you. first we choose a hole to be the gastrointestinal tract, the mouth, the anus, the tunnel, now inside this we place half of the other holes.

Well, now we have something that looks quite human, seven holes with eight external orifices that meet in a common space, the nose. cavity if we squash all the matter into the tunnels we will notice that our seven point 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 okay now to finish let's make two of the legs the nostrils and four of them the tear ducts one the mouth and we inflate the material in the shape of a head now let's inflate the limit of the final tube in the shape of a body with its opening at the back and I have done it, the human body is a seven-hole 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 thin piercing. your face that went through a tear duct and came back out or if something like a bullet went through your chest through the esophagus and came out the other side, that would mathematically count as two new holes and there are more, some people have supernumerary punctum in your eyes, each additional point that they have more than four in total adds an additional hole to the standard seven and remember the paranasal sinuses and the Ostia that connects them to the nasal cavity, well, they are just blind holes, depressions, but up to half of us can have at least one. accessory ostium, an additional opening that connects a sinus to the nasal cavity.

Well now we are talking about a through hole, you can enter through one opening and exit through another. These may not be external orifices, but for every accessory Ostia you have, that is another topological orifice. It is necessary to add to your body total. The thing is, although most of us have no idea how many Ostia accessories we have, unless you have had serious sinus problems or have undergone extensive scans of your nasal region that have been studied from multiple angles, to answer. This video asks 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 I found out how many you have. Right now it was easier but you'll have to scrutinize your sinuses to be sure and that's beautiful, right? 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 watching.