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  • Hey, Vsauce, Michael here

  • And here, I am the real Michael

  • This Michael was created by a brilliant young man named Mitchell,

  • who brought it to me at a meet-and-greet after Brain Candy Live

  • It is phenomenal and obviously the most handsome jack-in-the-box ever

  • Ever-est is a mountain that's 8.848 km tall

  • Its size is impressive

  • Or is it?

  • (Characteristic music of Vsauce, get prepared to be mind = blown)

  • Let's cut Earth, the entire planet, right in half,

  • straight through Everest, and then start zooming out

  • As you can see, Everest's monumentality quickly disappears against Earth's planetary ginormosity

  • Compared to Earth's diameter

  • Everestin fact, all of Earth's ruggednessbarely registers

  • That can seem surprising, since we are often surrounded by diagrams and maps and globes

  • that exaggerate Earth's topography

  • There is a good reason to do that,

  • but it leads to a misconception about just how smooth Earth is

  • Here's a typical example:

  • a cross section of the United States that I found on reddit

  • The vertical axis spans about 10,000 ft,

  • but the horizontal axis represents nearly 14 million ft

  • Stretched to the same scale so as to mirror reality,

  • the actual smoothness of the Earth becomes apparent

  • On this 1 ft diameter globe,

  • Everest is a bump about 2 mm high

  • Feels good!

  • But if the Earth was actually this small,

  • Everest would be a bump only 0.2 mm high

  • It's 10 times taller than it should be

  • Only 24 people have seen the Earth, with their own eyes, as a circle small enough to be looked right at;

  • not as the whole world, but as a little thing suspended alone in space

  • The further away you are from a ball, the more of its surface you can see

  • We don't always notice this,

  • because in our day-to-day lives,

  • most of the balls we deal with are so small

  • they're almost always many of their own radii away from us,

  • and the available amount of their surface visible is near a maximum

  • Or, they're so big, like the Earth, that we rarely get far enough away fast enough to notice this property

  • But the next time you are near a ball, get close to it

  • You'll see that as you get nearer, more of its surface disappears behind the horizon,

  • but moving back up will make it available again

  • For most of us, stuck our whole lives on Earth's surface,

  • such an experience is impossible

  • WIth nothing around to block your view,

  • 5 km (about 3 mi) is about the furthest you can see

  • Haze can limit your view and atmospheric refraction can slightly extend it,

  • but for the most part, everything you can see happens within an area of just 80 km^2

  • That's not bad, but it's tiny compared with what there is to see

  • The higher up you go, of course, the further away you will be able to see

  • That's why it's great to be a satellite

  • Here's the International Space Station

  • Yeah, look at that nice bit portion of the surface in view

  • Unfortunately, this isn't to scale

  • If the Earth were the size of an apple,

  • how far away would the International Space Station orbit?

  • Like this far away?

  • Maybe this far away

  • Maybe this far away

  • Actually, it orbitshere,

  • 2.7 mm above the surface

  • That's how far the stem of this apple sticks up

  • It's not very far

  • Oh, here's another fun little to scale fact:

  • if the Earth were the size of an apple, your eyeball would be about the size of the moon

  • We often imagine that from the International Space Station,

  • astronauts see the Earth like this, but they're just not that far away

  • From where they actually orbit,

  • International Space Station residents only see about 3% of Earth's surface at any one time

  • And that 3% is too wide to all fit within a window

  • When I was in Pittsburgh, their science museum had a mock-up of part of the ISS

  • And as you can see, out of the window, Earth is still quite expansive

  • Using special lenses, images can be taken from the ISS that look like circular disk Earths,

  • but the lens is distorting things here

  • It's fitting much more into the picture

  • In order to truly witness Earth's entire shape with your own eyes,

  • you would need to either smash your face right up against the window

  • or just be floating outside the station

  • And even then, you would have to move your head to see from edge to edge

  • So, how high up do you have to go to see the edges of Earth all at once?

  • And, even if you did that, how much would you actually see?

  • How much is there to see?

  • Earth is made of stuff,

  • lots of stuff: water and dirt and rocks and air, all of which are composed of atoms

  • tiny things so teeny that a single drop of water contains not a million atoms,

  • not a billion atoms, or a trillion, or a quadrillion, or a quintillion but 5 sextillion atoms

  • Earth is made of even more stuff:

  • not a septillion atoms, not an octillion, nonillion,

  • decillion, undecillion, duodecillion, tredecillion,

  • not even a quattuordecillion but 100 quindecillion atoms

  • But since we live only on the surface of our planet, we unfortunately can't see most of those atoms

  • If the Earth was shaped like a disk or an icosahedron,

  • or, say, a cube, or a rectangular prism, or two stellated rhombic dodecahedrons,

  • we could see more of the Earth than we normally can

  • But as things are, we actually see nearly the least of Earth's matter possible

  • because of all solids, a sphere, which the Earth approximately is,

  • has the smallest surface-area-to-volume ratiothe most stuff inside and the least stuff outside

  • So, how many of these 10^50 atoms that make up Earth are on the surface for us to see?

  • That's not an easy question

  • For one thing, technically, atoms on the surfaces of opaque things like rocks and dirt

  • aren't the only parts involved in their appearances

  • Sub-surface scattering can and does happen

  • Regardless, attempting even a rough approximation is illuminating

  • I asked Grant from the YouTube channel 3Blue1Brown for some help

  • And he pointed out that if you calculate the number of circles with atom-sized radii

  • that could, packed optimally, cover a sphere with the surface area of Earth, you'll get about 1.5×10^34

  • That's a lot of atoms

  • But then he pointed out that the Earth's surface isn't smooth

  • Its roughness provides extra surface area for atoms to occupy

  • Without a complete description of the shape of Earth's surfaceevery mountain and valley,

  • every bump on every rockthis is just gonna be hopeless, right?

  • Well, here's the thing, Earth is made of little rugged shapes that from far away make big rugged shapes

  • In other words, Earth's surface can be described as a fractal

  • There is a regularity to its roughness

  • In fact, mathematicians have even assigned a fractal dimension to Earth's surface: 2.3

  • To see what that means, I highly recommend Grant's video on fractal dimensions

  • It's fascinating

  • Using 2.3 and assuming that it applies from the scale of a human hair up to that of a mountain,

  • Grant found that the number of atoms on Earth's surface changes significantly:

  • up from a power of 34 to a power of 37

  • That's 1000 times more atoms

  • So, maybe we shouldn't count Earth's roughness out just yet

  • It's smooth, but not perfectly

  • To put that number in perspective, the human body contains about 10^27 atoms

  • That's 10 powers of 10 less than the surface of the Earth

  • 10 powers of 10 is 10 billion

  • There are about 7.5 billion humans

  • So, more or less, it can be said that there are the same number of atoms in every human body right now

  • as there are on the surface of the Earth

  • As I've shown before, all human bodies piled into one place would barely even fill the Grand Canyon,

  • but all human atoms spread across the Earth would almost perfectly cover it just one atom deep

  • Fun fact: the mass of the atmosphere is about 2.5% less

  • than what you would get by multiplying sea level pressure (14.7 psi) by the surface area of the Earth

  • because Earth's terrain displaces about that much air

  • Huh, Earth's surface is pretty cool

  • Obviously, I mean it got lichen and monster trucks

  • and an island in a lake on an island in a lake on an island

  • But from down here, on its surface, we just can't see that much of it

  • Your view of Earth is obstructed by lots of opaque things: walls, buildings, trees, rocks, terrain

  • If Earth was flat, you could see further, but sorry, it's a rough world out there

  • Or is it?

  • If you could hold the Earth in your hands like this, how bumpy would it actually feel?

  • We already saw that even our planet's biggest bumps barely register relative to Earth's size

  • But let's go somewhere famously flat,

  • where relative to our size, terrain rarely gets in the way of seeing lots of the planet:

  • the US state of Kansas

  • I grew up here and took this footage while driving across the state last year

  • You can probably see why Kansas is often called "flatter than a pancake"

  • However, although it is famously flat, Kansas is not the flattest US state

  • In a fantastic piece of research, Jerome Dobson and Joshua Campbell defined "looks flat" like this:

  • if, from a given point, any part of the terrain within the horizon rises more than 0.32° up

  • (about the height of a 30 m hill at the horizon),

  • a typical person would say, "Hey! That part's not flat!"

  • By cleverly applying this rule to topographical data, they were able to give every state a flatness score

  • West Virginia was the least flat

  • Kansas was only the seventh flattest

  • Delaware, Minnesota, Louisiana, North Dakota and Illinois are all, by this method, flatter than Kansas

  • As was the number 1 flattest state: Florida

  • Adam Savage and I had the pleasure of visiting Florida with our Brain Candy Live show this year,

  • and as this footage from atop the King Center in Melbourne, Florida shows, it's pretty gosh dang flat

  • Even though Kansas is not the flattest,

  • it is the state most often ranked flattest when the general population is asked

  • It is truly, scientifically flatter than a pancakeit's been demonstrated

  • But there's more to the story than that

  • In 2003, researchers took a 130 mm wide pancake procured from IHOP and analysed its local reliefs

  • They found the difference between high and low points was on the order of about 2 mm

  • If a typical pancake like this was the size of Kansas, 5 million times larger,

  • 2 mm high peaks would be 10 km high mountains

  • In comparison, Mount Everest is only about 8.8 km tall

  • and Earth's deepest scar, the Marianas Trench, is thought to be just under 11 km deep

  • So, not only is Kansas about as smooth as a pancake, but so is every other state in the union

  • and so is the entire world

  • If you were a giant holding the planet in your hands like this,

  • you and it would be torn apart by the immense tidal forces created by your gravities

  • If somehow you could avoid that though,

  • the planet would feel not much rougher than running your hands over a pancake

  • But a soggy one, right?

  • I mean, most of Earth's surface is covered in wateryour hands would get wet

  • Or would they?

  • Yes, Earth is covered in liquid, but the depth of that liquid, like the mountains above,

  • just doesn't compare to the total size of the planet

  • As it turns out, if the Earth was the size of a typical classroom globe like this one, 1 ft in diameter,

  • the volume of water contained in, above and on it would only be about 14 mL

  • That's this much water

  • It's kinda hard to believe because at this scale, spreading this much water across all of the ocean surfaces

  • would be pretty much impossible due to surface tension

  • But, this is it:

  • all of Earth's water compared to all of Earth

  • 90% of the space on our planet life can live in is in here

  • The other 10% is dry land

  • So, no, you wouldn't get wrinkly fingers playing with an Earth like this

  • You could sop it dry just with a paper towel

  • Despite the incredible area oceans cover on our planet,

  • their depth is just nothing compared to the size of our entire planet

  • You may have heard it said that if the entire planet were shrunk down to the size of a billiard ball,

  • it would be smoother than a billiard ball

  • After all we've seen so far, that seems believable, but as it turns out, it's not true

  • The misconception stems from the interpretation of the World Pool-Billiard Association's rules

  • According to them, a ball must have a diameter of 2.25 in ± 0.005 in

  • Some writers have taken this to mean that pits and bumps of 0.005 in are allowed

  • Proportionately, on Earth, that would mean a mountain that was 28 km high

  • So, since Earth has none of those, Earth must be smoother than a billiard ball

  • Except if bumps that high were actually allowed on a pool ball,

  • a ball covered with 120 grit sandpaper would be within regulation

  • Clearly, the 0.005 in rule is more about roundness, deviation from a sphere, and not texture

  • In fact, as microscopic photography has shown, imperfections on regulation balls are only 1/100,000 in,

  • or about 0.5 μm deep and high

  • Scaled to the size of a billiard ball, Earth's Marianas Trench would be 49 μm deep

  • So, Earth is smoother than a pancake but not smoother than a billiard ball

  • Nor, as xkcd wonderfully showed, is Earth smoother than a bowling ball

  • But hold on, earlier we were using the word "flat", now we were using the word "smooth"

  • That distinction is important

  • You see, the Earth isn't flat like a plane (or is it?)

  • Instead, it curves

  • It's a ball

  • Pieces of Earth, like Kansas, might be quite smooth, but they curve along with Earth

  • If you were to stand in the middle of Kansas,

  • people on the eastern or western edges of the state would appear to be, not level with you,

  • but about 8.1 km below you

  • That's nearly the height of Everest

  • And if they stood straight up, they'd be tilted nearlyrelative to where you thought up was

  • Here is an interesting coincidence:

  • generally speaking, 1 mi from where you are, Earth curves down about 8 in;

  • 1 km from where you stand, it curves down about 8 cm

  • The rate of drop due to curvature isn't a linear one

  • You can't just multiply any distance by 8 to get the drop due to curvature

  • Instead, use an online calculator like the one I have linked down in this video's description

  • You can put in any distance you want

  • Anyway, the visibility limit caused by Earth's curvature is your horizon

  • It encircles you like a visual cage,

  • but it's a cage whose radius is determined by how high up your eyes are

  • Conan O'Brien, at 6 ft 4 in tall, can see up to 5 km in any direction,

  • but Snooki, at 4 ft 8 in, can only see about 4.3 km

  • To find out how far away your horizon is,

  • geometrically, just use the online tools I've put down in the description below

  • Earth's texture can get in the way of your horizon but can also cause things beyond the horizon to peek into view

  • HeyWhatsThat.com factors all of this in

  • If Earth was a smooth sphere, the view from atop Ben Nevis, the highest mountain in the British Isles,