One of the funny things about owning a brain

is that you have no control over the things that it gathers and holds onto,

the facts and the stories. And as you get older, it only gets worse.

Things stick around for years sometimes

before you understand why you're interested in them,

before you understand their import to you.

Here's three of mine.

When Richard Feynman was a young boy in Queens,

he went for a walk with his dad and his wagon

and a ball. And he noticed that when he pulled the wagon,

the ball went to the back of the wagon.

And he asked his dad, "Why does the ball go to the back of the wagon?"

And his dad said, "That's inertia."

He said, "What's inertia?" And his dad said, "Ah.

Inertia is the name that scientists give

to the phenomenon of the ball going to the back of the wagon.

But in truth, nobody really knows."

Feynman went on to earn degrees

at MIT, Princeton, he solved the Challenger disaster,

he ended up winning the Nobel Prize in Physics

for his Feynman diagrams describing the movement of subatomic particles.

And he credits that conversation with his father

as giving him a sense

that the simplest questions could carry you out to the edge of human knowledge,

and that that's where he wanted to play.

And play he did.

Now Eratosthenes was the third librarian at the great Library at Alexandria,

and he made many contributions to science.

But the one he is most remembered for

began in a letter that he received as the librarian,

from the town of Swenet, which was south of Alexandria.

The letter included this fact that stuck in Eratosthenes' mind,

and the fact was that the writer said at noon

on the solstice, when he looked down this deep well,

he could see his reflection at the bottom, and he could also see that his head

was blocking the sun.

Now, I should tell you -- the idea that Christopher Columbus discovered that the world is spherical

is total bull. It's not true at all.

In fact, everyone who was educated understood that the world was spherical

since Aristotle's time, and Aristotle had proved it

with a simple observation.

He noticed that every time you saw the Earth's shadow on the Moon

it was circular,

and the only shape that constantly creates a circular shadow

is a sphere, Q.E.D. the Earth is round.

But nobody knew how big it was

until Eratosthenes got this letter with this fact.

So he understood that the sun was directly above the city of Swenet,

because looking down a well, it was a straight line

all the way down the well, right past the guy's head up to the sun.

Eratosthenes knew another fact.

He knew that a stick stuck in the ground in Alexandria

at the same time and the same day, at noon,

the sun's zenith, on the solstice,

the sun cast a shadow that showed that it was 7.2 degrees off-axis.

Now, if you know the circumference of a circle,

and you have two points on it,

all you need to know is the distance between those two points,

and you can extrapolate the circumference.

Three hundred and sixty degrees divided by 7.2 equals 50.

I know it's a little bit of a round number, and it makes me suspicious of this story too,

but it's a good story, so we'll continue with it.

He needed to know the distance between Swenet and Alexandria,

which is good because Eratosthenes was good at geography.

In fact, he invented the word geography.

The road between Swenet and Alexandria

was a road of commerce,

and commerce needed to know how long it took to get there.

It needed to know the exact distance, so he knew very precisely

that the distance between the two cities was 500 miles.

Multiply that times 50, you get 25,000,

which is within one percent of the actual diameter of the Earth.

He did this 2,200 years ago.

Now, we live in an age where

multi-billion-dollar pieces of machinery are looking for the Higgs boson.

We're discovering particles that may travel faster than the speed of light,

and all of these discoveries are made possible

by technology that's been developed in the last few decades.

But for most of human history,

we had to discover these things using our eyes and our ears and our minds.

Armand Fizeau was an experimental physicist in Paris.

His speciality was actually refining and confirming other people's results,

and this might sound like a bit of an also-ran,

but in fact this is the soul of science,

because there is no such thing as a fact that cannot be independently corroborated.

And he was familiar with Galileo's experiments

in trying to determine whether or not light had a speed.

So, Galileo had worked out this really wonderful experiment

where he and his assistant had a lamp,

each one of them was holding a lamp. And Galileo would open his lamp, and his assistant would open his lamp.

And they got the timing down really good.

They just knew their timing. And then they stood at two hilltops,

two miles distant, and they did the same thing, on the assumption

from Galileo that if light had a discernable speed,

he'd notice a delay in the light coming back from his assistant's lamp.

But light was too fast for Galileo.

He was off by several orders of magnitude when he assumed

that light was roughly 10 times as fast as the speed of sound.

Fizeau was aware of this experiment. He lived in Paris,

and he set up two experimental stations,

roughly five and a half miles distant,

in Paris. And he solved this problem of Galileo's,

and he did it with a really relatively trivial piece of equipment.

He did it with one of these.

I'm going to put away the clicker for a second

because I want to engage your brains in this.

So this is a toothed wheel. It's got a bunch of notches

and it's got a bunch of teeth.

This was Fizeau's solution to sending discrete pulses of light.

He put a beam behind one of these notches.

If I point a beam through this notch at a mirror,

five miles away, that beam is bouncing off the mirror

and coming back to me through this notch.

But something interesting happens as he spins the wheel faster.

He notices that it seems like a door is starting to close

on the light beam that's coming back to his eye.

Why is that?

It's because the pulse of light, it's not coming

back through the same notch. It's actually hitting a tooth.

And he spins the wheel fast enough

and he fully occludes the light. And then,

based on the distance between the two stations

and the speed of his wheel and the number of notches in the wheel,

he calculates the speed of light to within two percent of its actual value.

And he does this in 1849.

This is what really gets me going about science.

Whenever I'm having trouble understanding a concept, I go back and I research the people that discovered that concept.

I look at the story of how they came to understand it.

And what happens when you look at what the discoverers were thinking about

when they made their discoveries, is you understand

that they are not so different from us.

We are all bags of meat and water. We all start with the same tools.

I love the idea that different branches of science are called fields of study.

Most people think of science as a closed, black box,

when in fact it is an open field.

And we are all explorers.

The people that made these discoveries just thought a little bit harder

about what they were looking at, and they were a little bit more curious.

And their curiosity changed the way people thought about the world,

and thus it changed the world.

They changed the world, and so can you.

Thank you.

(Applause)