DO YOU REALLY KNOW HOW MANY HOLES DOES A HUMAN BEING HAVE?

DO YOU KNOW HOW MANY HOLES DOES A HUMAN BEING HAVE?

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You keep going you will eventuallyemerge out my other end and for thisreason it has been said that the humanbody is like a doughnut yeah you arejust a bunch of meat packed around acentral Hulk or are you humans have morethan one hole right I mean we've gotnostrils and ears the whole sweetpea outof the holes were born from nipples ourpores yes there are subatomic gapsbetween the molecules were made out ofwhere don't we have holes well that isthe rub literally if you cut a clove ofgarlic in half and then rub that freshraw end on your foot about an hour lateryou will start to taste garlic in yourmouth that's because the molecules thatgive garlic its taste are small enoughand have just the right properties topermeate skin cells in your foot enteryour bloodstream and reach your mouthbut you are even holier than that everysecond day and night about 60 billionneutrinos from the Sun pass through justyour thumbnail so clearly at smallenough scales how many holes does ahuman have becomes a meaninglessquestion ultimately the human body isn'ta solid thing that can even have holesit's just a loose constellation of atomsand molecules but if we accept a minimumhole size the answer becomes prettyinteresting and a good choice for thisminimum is about twenty to sixtymillionths of a meter about the width ofa human hair a magic spaceship 60microns wide could fly into your poreslike they were giant holes like cratersbut it couldn't continue on through thevasculature at the other end or diffusethrough cells or slip between moleculesand that is significant it highlightsthe fact that not all holes areequal a 60 micron wide ship or stringcould be threaded into your mouth andcome out somewhere else but it couldn'tdo that by entering a pore or hairfolliclethis makes the GI tract what engineerscall a through-hole where as poresurethras nipples ears hair folliclesbirth canals and the sinuses are blindholes they can be enteredbut eventually dead end usually atnarrow capillaries permeable only bythings smaller than a single blood celland the determination to not be stoppedthe eyeball can be squeezed under butyou'll eventually be stopped by theconjunctiva the sinuses are nice bigrooms and our skulls but the only wayout is the same Ostia you came inthrough as for the earwell the ear is a blast to go inside butif you're 60 microns wide the airtighteardrum will block further passage it'sa blind hole now altogether counting allof your pores and hair follicles you'vegot millions of blind holes all overyour body but are they actually holesthat's a real humdinger because you know what a hole is what what a hole reallyis it's a word a colloquial fuzzyimprecise lexeme that refers to a hostof disparate utterly unreconciled thingsthat eludes a single precisemathematical definition in fact holesmight not even exist I mean think aboutit if I eat a whole doughnut have Ieaten the whole like is the hole insideme or could I eat a doughnut withouteating its hole could I go to a storeand buy Swiss cheese but leave the holesat the store clearly holes are at bestontologically parasitic their existencedepends upon the existence of somethingelse that they can inhabit or be adisturbance inof course the philosophy of holes rarelymatters in your day-to-day life you cancall something a hole and context willdo its work and people will know whatyou're talking about but take a look atthis does this have a hole in it wellyeah right obviously right here there'sa hole I can put my hand in it it canstore things it's got a hole but nowimagine that I could mold it like it wasmade out of clay and I molded it downinto the shape of a drinking glass youcould see how that could happen rightwell does a drinking glass have a holein it if this does then this should -right I mean I didn't pinch the holeshut or glue anything together all rightsure fine I mean I can accept that adrinking glass technically has a hole init but now imagine that I took thisglass and I molded it out and I widenedits opening until I had a shape likethis a bowl now does a bowl have a holein it now we're really stretching theuse of the word hole I mean if someonesaid their ball had a hole in it I wouldthink that it had a hole somewhere elseand it was leaking but sure let's callthis a hole it's not a very prototypicalone but I think you see where I'm goingwith this if I didn't molded the bowland flattened its sides all the way outuntil I had a plate a shape like thiswell does a plate have a hole in it notreally so if a plate doesn't have a holein it but this shape did and Icontinuously molded from here to theglass to the bowl to the plate and Inever glued anything shut where'd thehole go clearly blind holes are prettyunique they can be removed withoutclosing or pinching anything shutcompare that to the through hole of adoughnut there is no way to remove aDonuts through hole or add a new throughhole without gluing stuff togethersquishing things together that used tonot be together or ripping pieces apartpoking a hole through and breaking itthat is extremely significant but let'sgo back to the body before we get aheadof ourselvesthe mouth is an entrance to both blindand through holes a 60 micron widetraveler could enter it meander down theesophagus and keep going until they werewell dumped out but turn down thetrachea and they would dead end in thelungs now the area of the throat behindthe mouth is called the pharynx it's apretty chill place except not reallyit's actually quite warm it plays a rolein warming and moistening and filteringthe air that we breathe before it entersthe lungs including the air we inhalethrough our nostrils now each nostrilleads into a separate nasal vestibulethat's the tunnel that you can explorewhen you pick your nose eventually thosetunnels meet and sniffed air enters thenasal cavity a hollow air filled room inyour face protruding from the walls ofthe nasal cavity are mucusy fins calledthe nasal Concha or turbinates that warmand moist in the air that passes aroundthem from there the air flows via thepharynx down the trachea so yournostrils and your mouth are connected astring could go into your mouth or noseand come out your butt the nasal cavityis quite the hub I mean your ear holeswould almost lead into it but theeardrum blocks the way if it didn'tthere would be clear passage from theoutside into the middle ear and thendown the eustachian tube into the nasalcavity via an opening about here theeustachian tube controls air pressure inthe middle ear behind the eardrum and isnormally collapsed shut but if theoutside pressure is dramaticallydifferent than the air pressure in themiddle ear swallowing and yawning canget it open equalizing the pressurethat's what happens when you pop yourears it's cool but it's not athrough-hole and that's what we'relooking forand as it turns out there are four morefour more orifices that lead from theoutside into this place your nasalcavity and they are the lacrimal punctumthere is one near each of your eyelidsthey're tiny openings about a third of amillimeter wide into which tearsthe fluid constantly moistening andprotecting your eyeball drain onceinside the lacrimal punctum ASA lacrimalducts tear ducts into your nasal cavitywhich is why when you're making a lot oftear fluid and have to blow your nosethat's not snot that's mainly tears thepoint is a 60 micron wide string couldbe pushed into any of your four lacrimalpuncture threaded through your tear ductsinto your nasal cavity into the pharynxand then pushed all the way out yourbutt pretty cool that gives us eightexternal openings that don't dead-endbut how many through holes is that Imean how many holes does a straw havethis clearly has two holes but how manydoes this have is it one hole that Forksis it two that combined gosh maybe it'sthree well what about this how manyholes does this thing have or thistopology can help us answer every singleone of those questions here I have twoessentially identical pieces of material

now they are no longer identical or arethey geometrically sure their shapes arenow different but what didn't changeabout them well that is what topologystudies topology is concerned with theproperties that persist so long assomething isn't ripped apart the famousjoke that a topologist doesn't know thedifference between a doughnut and acoffee cup is based on the fact that acoffee cup can be gentlycontinuously molded into a doughnut bysimply stretching and squashing nocutting gluing ripping or sewingrequired topologists call these gentlecontinuous transformationshomeomorphisms and the cuttingand ripping and gluing that theydisallow are exactly the kinds ofactions required to make new holes orremove old ones so since a coffee cupand a doughnut are homeomorphic theymust have the same number of throughholes and they do one we can now moreprecisely describe the difference we sawearlier between blind holes and throughholes and understand why we areseparately counting them now blind holescan be erased through a homeomorphism assuch topologists don't even reallyconsider them they're just geometricdisturbances topological holes on theother hand cannot be massage it away andunlike a blind hole where what qualifiesand what doesn't is a matter of opinionthe number of through holes a surfacelike your body and three dimensions hascan be clearly defined if we are havinga hard time counting through holes allwe need to do is find something with aneasy to count arrangement of throughholes that it is homeomorphic with butfirst let's play around with sometopological puzzles here is a to holddonut with an infinitely longunbreakable unmovable rod through one ofits holes without cutting or separatingany part of the shape can you figure outhow to manipulate it such that the rodgoes through both holes pause the videoif you want to think about it rememberthis shape it looks like it might havethree holes right it's got a hole therea second hole there and a third holehere but if I flatten it you can seethat it only has two holes it has onethere and one there if the rod isthreaded through the shape such that onewire is in front and I choose one of theother wires to be the middle of thedoughnut for example this one then therod passes through just one of the twoholes but if I choose the wire in thefront to be the middle of the donut wellthen the rod is seen to be passingthrough two holes likewise if youcontinuously deform our original to holddonut into the three tube thing and pickthis tube to be the new middle tada therod is now going throughtwo holes no cutting or gluing requiredone more puzzle without cutting orbreaking can you unlock this shapesintertwined loops well pause if you wantto figure it out yourselfhere's a solution simply inflate thebulb of the shape until you can skate aleg of each loop around until they'reuntangled and tadafreedom alright let's definehomeomorphism a little better we said itwas a rubber sheet or clay like moldingprocedure with no cutting or breaking orgluing and that's a good introductionbut honestly you can cut all you wantduring a homeomorphism so long as youglue everything back together the way itwas in the end more precisely ahomeomorphism is a bijective and bycontinuous function it's a functionbecause it is a list of ordered pairswhere each point starts is paired withwhere it goes requiring that it be a byjek ssin means that it must be a specialkind of function where there is aone-to-one correspondence between pointsin one object and in the other no twopoints can map to the same location andno point can get magically turned intomultiple new points basically materialcannot be added or subtracted bycontinuous means that any cuts made mustbe later mended perfectly with pointsgoing back amongst the same neighboringpoints they had before in ahomeomorphism if parts are scooched overeverything else must flow with thescootch as if all the points are kind ofstickythere is no smooth sliding along abruptfissures the precise test for whether afunction is by continuous is pretty coolnow first I consider a point in onearrangement now where the function takesthat point is its image okay now Ichoose some neighborhood around theimage with a radius larger than zero andI consider all of the points within itif the function is continuous in thisdirection I should be able to find aneighborhood around the preimage theinput point that only contains pointsthat map inside the images neighborhoodin this case I can but in this casewe've got an original point and where itwent but given a neighborhood aroundwhere it went every neighborhood aroundthe original no matter how small willalways contain some stuff that didn'tmake it over which means points gotseparated but not put back so thefunction is not continuous by continuitymeans that a function must be continuousin both directions okay now that we canhomey amorphous let's start using it tocount holesremember this shape it wasn'timmediately obvious earlier how to countits holes but it is easy if we can use ahomeomorphism to turn it into somethingwith an easy to count number of holeswhich we can both of these shapes arehomeomorphic they both have two holes tosee whysimply drag in mold and flow the openingof one of these shapes holes into thetunnel of the other and there we gosince we didn't cut or glue the numberof holes hasn't changed so this thingjust like this thing always had twoholesokay what about a straw well shortinformally it can often make sensedepending on the context todifferentiate between two openings in astraw the one you put in your drink andthe one you put in your mouth but thatdoes not mean it has two holes it onlyhas one a straw is homeomorphic to atorus both openings are part of the samesingle hole but this process is ahomeomorphism and thus does not createany new holes you can also see thatopenings aren't holes by stretching oneof the straws openings until it becomesthe outer part of a doughnut therereally was only ever just one holebut enough about straws let's get backto the body we found eight externalopenings orifices interconnected bytunnels but openings aren't holesthey're parts of holes and we can countthose holes as it turns out at a scaleof 60 microns the human body has seventhrough holes the human body is not adoughnut it is a seven hold doughnutthis shape can be molded and stretchedinto you first we choose a hole to bethe GI tract the mouth anus tunnel nowinto this we roll half of the otherorifices okay now we've got somethingthat looks pretty dang human seven holeswith eight external orifices that meetin a common space the nasal cavity if wesquish all the matter in towards thetunnels will notice that our seven holdtorus is topologically equivalent tofour pairs of pants sewn together at thewaists your body isn't a doughnut it's abodysuit for a spider okay now to finishlet's make two of the legs the nostrilsand four of them the tear ducts one themouth and inflate the material into theform of a head now let's inflate theboundary of the final tube into theshape of a body with its opening in therear and we've done itThe human body is a seven hold doughnutor is it for every piercing you havethat's one more hole in your bodywell two more if the piercing goesthrough a through hole like I don't knowif you had a thin piercing into yourface that went through a tear duct andcame back out or if something like abullet pierced into your chest throughyour esophagus and came out the otherside that would mathematically count astwo new holes and there's moresome people have supernumerary lacrimalpunctum on their eyes each additionalpunctum they have over four total addsan additional hole to the standard sevenand remember the sinuses and the Ostiaconnecting them into the nasal cavitywell they're just blind holesdepressions but as many as half of usmay have at least one accessory ostiuman extra hole connecting a sinus to thenasal cavity well now we're talkingabout a through hole you can enter oneopening and exit via another now thesemay not be external orifices but forevery accessory Ostia you have that'sanother topological hole you need to addto your bodies total the thing is thoughmost of us have no idea how manyaccessory Ostia we have unless you'vehad serious sinus problems or have hadextensive scans of your nasal regionthat have been studied from multipleangles so to answer this videos questionthe human body has millions of blindholes like at least five million and atBirth seven through holes it would bebetter if there was a clear answer thatapplied to all of us for our entirelives or if finding out how many you hadright now was easier but you'll have tospeelunk in your sinuses to know forsure and that's beautiful isn't it wecan rigorously define the properties ofholes in all sorts of dimensions and wecan study that temperatures at thebottom of craters on Pluto but few of uswill ever truly knowthe whole truth of our own bodies .

Thank You .