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How Many Holes Does a Human Have? — Vsauce shadowing | TryShadowing
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Vsauce
How Many Holes Does a Human Have?
How Many Holes Does a Human Have?
Vsauce
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21:27 · Feb 17, 2020
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hey Vsauce Michael here come
0:04
on in if you keep going you
0:08
will eventually emerge out my other end
0:11
and for this reason it has been said that the human body is
0:16
like a doughnut yeah
0:20
you are just a bunch of meat packed
0:23
around a central Hulk
0:24
or are you humans
0:27
have more than one hole right
0:29
I mean we've got nostrils
0:30
and ears the whole sweetpea
0:31
out of the holes were born from nipples our pores yes
0:35
there are subatomic gaps
0:36
between the molecules were made out of where
0:39
don't we have holes well
0:41
that is the rub
0:44
literally if you cut a clove
0:51
of garlic in half and then rub that fresh
0:55
raw end on your foot
0:57
about an hour later you
0:59
will start to taste garlic
1:00
in your mouth that's
1:03
because the molecules that give garlic its taste are small
1:06
enough and have just the right properties
1:08
to permeate skin cells in your foot enter
1:12
your bloodstream and reach your mouth but
1:15
you are even holier
1:16
than that every second
1:19
day and night about 60
1:21
billion neutrinos from the Sun pass through
1:24
just your thumbnail so
1:26
clearly at small enough scales how
1:29
many holes does a human have becomes
1:31
a meaningless question ultimately
1:33
the human body isn't a solid thing that can even have holes it's
1:37
just a loose constellation
1:39
of atoms and molecules
1:40
but if we accept
1:42
a minimum hole size the
1:45
answer becomes pretty interesting
1:46
and a good choice for this minimum is about twenty
1:49
to sixty millionths of a meter about
1:52
the width of a human hair a
1:53
magic spaceship 60 microns wide could
1:57
fly into your pores like
1:58
they were giant holes like craters but
2:01
it couldn't continue on through the vasculature
2:04
at the other end or diffuse
2:06
through cells or slip
2:07
between molecules and that
2:09
is significant it highlights the fact that
2:12
not all holes are
2:13
equal a 60 micron wide ship or string
2:17
could be threaded into your mouth and come out somewhere
2:20
else but it couldn't do that by entering a pore or hair
2:25
this makes the GI tract what engineers
2:27
call a through-hole where
2:30
as pores urethras nipples
2:32
ears hair follicles birth canals and the sinuses
2:35
are blind holes they
2:37
can be entered but eventually dead
2:39
end usually at narrow capillaries
2:42
permeable only by things smaller
2:44
than a single blood cell and the
2:46
determination to not be stopped the
2:48
eyeball can be squeezed under
2:50
but you'll eventually be stopped by the conjunctiva the
2:54
sinuses are nice big rooms and our skulls
2:56
but the only way out is the same
2:59
Ostia you came in through as for
3:02
the ear well the ear is a blast
3:04
to go inside but if you're 60 microns wide the
3:07
airtight eardrum will block further passage it's a blind hole now
3:12
altogether counting all of your pores and hair follicles you've
3:16
got millions of blind holes all over your body
3:20
but are they actually holes
3:22
that's a real humdinger because
3:25
you know what a hole is what what a hole really is
3:29
it's a word a
3:31
colloquial fuzzy imprecise lexeme
3:35
that refers to a host of disparate
3:37
utterly unreconciled things that eludes a single precise
3:41
mathematical definition in fact
3:44
holes might not even exist I
3:48
mean think about it if
3:50
I eat a whole
3:51
doughnut have I eaten
3:53
the whole like is the hole inside me or
3:56
could I eat a doughnut without
3:58
eating its hole could
4:00
I go to a store and
4:01
buy Swiss cheese but
4:04
leave the holes at the store
4:07
clearly holes are at best ontologically
4:11
parasitic their existence depends
4:14
upon the existence of something else that they can inhabit
4:17
or be a disturbance
4:19
in of course the philosophy
4:22
of holes rarely matters in your day-to-day life you
4:25
can call something a hole and context
4:27
will do its work and people will know what you're talking about but
4:30
take a look at this does
4:31
this have a hole in it well
4:34
yeah right obviously right
4:36
here there's a hole I can put my hand in it it can store
4:38
things it's got a hole but
4:40
now imagine that I could mold
4:42
it like it was made out of clay and
4:44
I molded it down into the shape of a
4:47
drinking glass you could see how that could happen right well
4:50
does a drinking glass have a hole in it if this does then
4:53
this should - right I mean I didn't pinch
4:56
the hole shut or glue anything together all
4:58
right sure fine I mean I can accept that a drinking
5:02
glass technically has a hole in it but
5:04
now imagine that I took this glass and
5:06
I molded it out and I widened
5:09
its opening until I had a shape like this a bowl
5:12
now does a bowl have a hole in it now
5:16
we're really stretching the use of the word hole I mean if someone said
5:19
their ball had a hole in it I would think that it had a
5:21
hole somewhere else and it was leaking but
5:24
sure let's call this a hole it's not a very prototypical
5:27
one but I think you see where I'm going with this if I didn't
5:30
molded the bowl and flattened its sides all the way out until I had
5:34
a plate a shape
5:36
like this well does
5:38
a plate have a hole in it
5:39
not really so if a plate doesn't have a hole in it but
5:45
this shape did and I
5:46
continuously molded from here to the glass to the bowl to the plate and
5:50
I never glued anything shut where'd
5:53
the hole go clearly
5:55
blind holes are pretty unique they
5:58
can be removed without closing
6:00
or pinching anything shut
6:02
compare that to the
6:04
through hole of a doughnut there
6:07
is no way to remove
6:09
a Donuts through hole or add a new through hole without
6:13
gluing stuff together squishing
6:15
things together that used to not be together or ripping
6:18
pieces apart poking a hole through and breaking it that
6:22
is extremely significant but let's go back to the body before
6:27
we get ahead of ourselves
6:30
the mouth is an entrance to both blind
6:34
and through holes a 60
6:37
micron wide traveler could enter it meander
6:40
down the esophagus and keep going until they were well
6:42
dumped out but turn down the trachea and they
6:46
would dead end in the lungs now
6:48
the area of the throat behind
6:50
the mouth is called the pharynx
6:52
it's a pretty chill place
6:54
except not really it's actually quite warm it plays a role in warming
6:58
and moistening and filtering the air that we breathe before
7:01
it enters the lungs including
7:03
the air we inhale through our nostrils
7:06
now each nostril leads
7:08
into a separate nasal vestibule that's
7:10
the tunnel that you can explore when you pick your nose
7:13
eventually those tunnels meet
7:15
and sniffed air enters
7:17
the nasal cavity a hollow air
7:20
filled room in your face
7:22
protruding from the walls of the nasal cavity are
7:24
mucusy fins called the nasal Concha
7:27
or turbinates that warm and moist in the air that passes around them from
7:31
there the air flows via the pharynx down the trachea
7:34
so your nostrils and your mouth are connected
7:38
a string could go into your mouth or nose
7:41
and come out your butt the
7:43
nasal cavity is quite
7:45
the hub I mean your ear holes would almost lead
7:49
into it but the eardrum blocks the way if it didn't
7:52
there would be clear passage
7:54
from the outside into
7:55
the middle ear and then
7:57
down the eustachian tube
7:59
into the nasal cavity via an opening
8:01
about here the eustachian tube controls air pressure in the middle ear behind the
8:06
eardrum and is normally collapsed
8:08
shut but if the outside pressure
8:10
is dramatically different than the air pressure in the middle
8:13
ear swallowing and yawning
8:15
can get it open equalizing
8:17
the pressure that's what happens when
8:20
you pop your ears
8:21
it's cool but it's not a through-hole
8:24
and that's what we're looking for and
8:26
as it turns out there
8:27
are four more four
8:29
more orifices that lead from the outside into
8:32
this place your nasal cavity and
8:34
they are the lacrimal
8:36
punctum there is one near each of your eyelids
8:40
they're tiny openings about a third of a millimeter wide into which tears
8:44
the fluid constantly moistening
8:46
and protecting your eyeball drain once
8:49
inside the lacrimal punctum
8:51
ASA lacrimal ducts tear
8:54
ducts into your nasal cavity which
8:57
is why when you're making a lot
9:00
of tear fluid and
9:05
have to blow your nose
9:07
that's not snot that's
9:09
mainly tears the point is a 60
9:12
micron wide string could be pushed into any of your four lacrimal
9:16
punctum threaded through your tear ducts into your nasal cavity into
9:19
the pharynx and then pushed all the way out your butt pretty
9:23
cool that gives us eight
9:25
external openings that don't dead-end
9:28
but how many through
9:31
holes is that I mean
9:33
how many holes does
9:35
a straw have this
9:36
clearly has two holes but how
9:39
many does this have is it
9:41
one hole that Forks
9:43
is it two that combined gosh
9:46
maybe it's three well
9:47
what about this how many holes does this thing have or
9:50
this topology can help us answer every
9:54
single one of those questions
9:56
here I have two essentially
9:58
identical pieces of material
10:10
now they are no longer identical
10:14
or are they geometrically
10:18
sure their shapes are now different
10:20
but what didn't change about them well
10:23
that is what topology
10:25
studies topology is concerned
10:27
with the properties that persist
10:29
so long as something isn't ripped
10:31
apart the famous joke that a topologist
10:34
doesn't know the difference between a doughnut and a coffee cup is based on
10:37
the fact that a coffee cup can
10:39
be gently continuously molded
10:42
into a doughnut by simply stretching
10:44
and squashing no cutting gluing
10:46
ripping or sewing required
10:48
topologists call these gentle
10:51
continuous transformations homeomorphisms and the
10:56
cutting and ripping and gluing
10:59
that they disallow are exactly
11:01
the kinds of actions required
11:03
to make new holes or remove
11:05
old ones so since a coffee cup and a doughnut are homeomorphic
11:09
they must have the same number of through holes and they do one
11:13
we can now more precisely
11:15
describe the difference we saw earlier between blind
11:18
holes and through holes and understand why we are separately
11:21
counting them now blind holes can
11:23
be erased through a homeomorphism as
11:26
such topologists don't even really consider
11:29
them they're just geometric
11:31
disturbances topological holes on the other hand cannot
11:34
be massage it away and unlike
11:37
a blind hole where what qualifies
11:39
and what doesn't is a matter of opinion the
11:42
number of through holes a surface
11:44
like your body and three dimensions has can
11:47
be clearly defined if
11:49
we are having a hard time counting
11:51
through holes all we need to do is find something with an easy to
11:55
count arrangement of through holes that
11:56
it is homeomorphic with
11:58
but first let's play around with some topological
12:02
puzzles here is a to hold donut
12:05
with an infinitely long unbreakable
12:07
unmovable rod through one of its holes without
12:11
cutting or separating any part of the shape can
12:14
you figure out how to manipulate it
12:16
such that the rod goes
12:17
through both holes pause
12:19
the video if you want to think about it
12:24
remember this shape it
12:26
looks like it might have three
12:27
holes right it's got a hole there a second
12:30
hole there and a third hole here
12:31
but if I flatten
12:32
it you can see that it only has two
12:34
holes it has one there and one there
12:36
if the rod is threaded through the shape such that one wire is in
12:41
front and I choose one of the other wires to be the middle of
12:44
the doughnut for example this one then
12:47
the rod passes through just one of the two holes but
12:51
if I choose the
12:52
wire in the front to be the middle of the donut well then the
12:56
rod is seen to be passing through two holes
12:59
likewise if you continuously
13:01
deform our original to hold donut into
13:04
the three tube thing and pick
13:06
this tube to be the new middle tada
13:08
the rod is now going through
13:11
two holes no cutting or gluing
13:14
required one more puzzle without
13:17
cutting or breaking can you unlock
13:19
this shapes intertwined loops well
13:21
pause if you want to figure it out yourself
13:24
here's a solution simply
13:26
inflate the bulb of the shape until you can skate a leg of each
13:29
loop around until they're untangled
13:31
and tada freedom alright
13:35
let's define homeomorphism a little
13:38
better we said it was a rubber
13:39
sheet or clay like molding
13:41
procedure with no cutting
13:43
or breaking or gluing and that's
13:45
a good introduction but
13:47
honestly you can cut all you
13:50
want during a homeomorphism so
13:51
long as you glue everything
13:53
back together the way it was in the end more
13:57
precisely a homeomorphism is
13:59
a bijective and by
14:02
continuous function it's a function because
14:05
it is a list of ordered pairs where
14:07
each point starts is paired with where it goes requiring
14:11
that it be a by jek ssin means that it must be a special
14:14
kind of function where there is a one-to-one
14:17
correspondence between points in one object and in
14:20
the other no two points
14:22
can map to the same location
14:23
and no point can get magically turned into multiple new points basically material
14:28
cannot be added or subtracted
14:30
by continuous means that any cuts made must be later mended
14:35
perfectly with points going back amongst
14:38
the same neighboring points they
14:40
had before in a
14:42
homeomorphism if parts are scooched
14:44
over everything else must flow
14:47
with the scootch as if all the points are kind of
14:51
there is no smooth
14:52
sliding along abrupt fissures
14:54
the precise test for whether a function is by continuous
14:58
is pretty cool now first I consider
15:01
a point in one arrangement now
15:03
where the function takes that point is its image okay
15:06
now I choose some neighborhood
15:08
around the image with a radius larger than zero and I consider all of
15:12
the points within it if the
15:14
function is continuous in
15:16
this direction I should
15:17
be able to find a neighborhood around the
15:19
preimage the input point that
15:22
only contains points that map inside
15:24
the images neighborhood in this
15:27
case I can but
15:29
in this case we've
15:30
got an original point
15:31
and where it went but given
15:33
a neighborhood around where it went every
15:36
neighborhood around the original no matter how small
15:38
will always contain some stuff that didn't make it over which means points got
15:43
separated but not put back so
15:46
the function is not
15:47
continuous by continuity means that a function must be continuous
15:52
in both directions okay
15:55
now that we can homey amorphous
15:56
let's start using it to count holes
15:59
remember this shape it wasn't immediately obvious earlier
16:03
how to count its holes but it is easy if we can use a
16:06
homeomorphism to turn it into something with an easy to count number of holes
16:11
which we can both
16:12
of these shapes are homeomorphic
16:14
they both have two holes to
16:17
see why simply drag
16:18
in mold and flow
16:20
the opening of one
16:22
of these shapes holes into the
16:24
tunnel of the other and
16:25
there we go since
16:28
we didn't cut or glue the number of holes hasn't
16:30
changed so this thing just
16:32
like this thing always
16:34
had two okay what about a straw well
16:38
short informally it can often make sense depending
16:41
on the context to differentiate between two
16:44
openings in a straw the one you put in your drink and the one
16:48
you put in your mouth but
16:49
that does not mean it has two
16:51
holes it only has one a
16:53
straw is homeomorphic to
16:55
a torus both openings
16:57
are part of the same single
16:59
hole but this process is a homeomorphism
17:01
and thus does not create any new holes you
17:05
can also see that openings
17:06
aren't holes by stretching one of the straws openings
17:09
until it becomes the outer part
17:11
of a doughnut there really was only ever just one hole
17:15
but enough about straws
17:16
let's get back to the body we
17:19
found eight external openings orifices
17:22
interconnected by tunnels but
17:25
openings aren't holes they're
17:27
parts of holes and we
17:29
can count those holes
17:31
as it turns out at a scale of 60 microns
17:34
the human body has
17:36
seven through holes the
17:39
human body is not a
17:41
doughnut it is a seven hold doughnut
17:44
this shape can be molded
17:46
and stretched into you
17:48
first we choose a hole to be the GI tract the mouth anus
17:53
tunnel now into this we roll half of the other orifices okay
17:56
now we've got something that looks pretty
17:58
dang human seven holes with eight external
18:01
orifices that meet in a common space the
18:03
nasal cavity if we squish all the matter in towards
18:07
the tunnels will notice that our seven hold torus is topologically
18:11
equivalent to four pairs of pants sewn
18:14
together at the waists your
18:16
body isn't a doughnut it's
18:18
a bodysuit for a spider okay
18:21
now to finish let's
18:22
make two of the legs the nostrils
18:25
and four of them the tear ducts one the mouth and inflate
18:28
the material into the form of a head now
18:31
let's inflate the boundary of the final tube into the shape of a body
18:34
with its opening in the rear and we've
18:36
done it the human body is a seven
18:45
hold doughnut or is
18:49
it for every piercing
18:51
you have that's one more hole in your body well
18:56
two more if the piercing goes through
18:58
a through hole like I don't know if you had a thin
19:00
piercing into your face that
19:02
went through a tear duct and came back out or if
19:05
something like a bullet pierced into your chest through
19:08
your esophagus and came out the other side that
19:11
would mathematically count as two
19:13
new holes and there's
19:16
more some people have supernumerary
19:19
lacrimal punctum on their
19:21
eyes each additional punctum they have over four total adds an
19:25
additional hole to the standard seven and
19:29
remember the sinuses and the Ostia
19:32
connecting them into the nasal cavity
19:34
well they're just blind holes depressions
19:36
but as many as half
19:38
of us may have at least one
19:40
accessory ostium an extra
19:43
hole connecting a sinus to the nasal cavity
19:45
well now we're talking about a through
19:47
hole you can enter one opening and exit
19:49
via another now these may
19:52
not be external orifices
19:54
but for every accessory Ostia
19:55
you have that's another topological
19:58
hole you need to add to
19:59
your bodies total the
20:01
thing is though most
20:02
of us have no idea how many accessory
20:05
Ostia we have unless
20:07
you've had serious sinus problems
20:08
or have had extensive
20:10
scans of your nasal region that have been studied from multiple angles
20:13
so to answer this videos question the
20:17
human body has millions
20:19
of blind holes like at least five million and at
20:23
Birth seven through holes it
20:26
would be better if there was a clear answer that applied to all of
20:30
us for our entire
20:31
lives or if finding out how many you
20:34
had right now was
20:36
easier but you'll have to speelunk
20:38
in your sinuses to know for sure and
20:40
that's beautiful isn't it we
20:42
can rigorously define the properties
20:45
of holes in all sorts of dimensions and we can study
20:49
that temperatures at the bottom of craters on Pluto but
20:52
few of us will ever truly
20:54
know the whole truth
20:57
of our own bodies and as
20:59
always thanks for watching
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