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

Everest—in fact, all of Earth's ruggedness—barely 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 orbits… here,

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 ratio—the 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 surface—every mountain and valley,

every bump on every rock—this 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 pancake—it'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 water—your 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