are the moments in which we are perplexed.

是在我們覺得困惑的時刻

Those moments in which you begin to wonder and question.

就是你開始疑惑及質疑的時刻

These moments have happened throughout history.

這些時刻曾在歷史上發生

and have led to some truly amazing discoveries.

這些時刻也曾導致一些驚人地發現

Take this story, for example.

舉這個故事為例

There once was a fellow named Archimedes.

曾經有個傢伙叫阿基米德

He was born in 287 B.C. in the city of Syracuse in Sicily.

他於公元前287年，在西西里島上的敘拉古城出生

He was a Greek mathematician, physicist, engineer,

他是古希臘的數學家、物理學家、工程師

inventor, and astronomer.

發明家及天文學家

One day, Archimedes was summoned by the king of Sicily

有一天，西西里王宣召阿基米德

to investigate if he had been cheated by a goldsmith.

來調查金匠是否欺騙了他

The king said he had given a goldsmith the exact amount of gold

國王說他已經給了金匠所需確切數量的金子

needed to make a crown.

來打造一頂皇冠

However, when the crown was ready, the king suspected that the goldsmith cheated

但是，當皇冠完成時，國王懷疑這個金匠騙了他

and slipped some silver into the crown,

在皇冠裡摻了銀

keeping some of the gold for himself.

污了一些金子留給自己

The king asked Archimedes to solve the problem.

國王要求阿基米德解決這個問題

But there was a catch: he couldn't do any damage to the crown.

但有個前提：他不能破壞這頂皇冠

One day, while taking his bath,

有一天，當他在洗澡的時候

Archimedes noticed that the water level in the bathtub rose

阿基米德注意到當他浸到澡盆的時候

and overflowed as he immersed himself into the tub.

洗澡盆的水面上升並溢出

He suddenly realized that how much water was displaced

他突然瞭解到水的排出量

depended on how much of his body was immersed.

跟他身體浸入多少有關

This discovery excited him so much that he jumped out of the tub

這項發現使他非常興奮，他甚至跳出澡盆

and ran through the streets naked, shouting "Eureka!"

裸體跑到街上大喊「Eureka!」

Which comes from the ancient Greek meaning "I found it."

即古希臘文「我發現了」的意思

What did he find?

他發現了什麼？

Well, he found a way to solve the king's problem.

嗯，他發現解決國王的問題的方法

You see, Archimedes needed to check the crown's density

就是，阿基米德需要查一下皇冠的密度

to see if it was the same as the density of pure gold.

看看它是否與純金的密度相符

Density is a measure of an object's mass divided by its volume.

密度測量法是把物體質量除以體積

Pure gold is very dense, while silver is less dense.

純金的密度非常高，而銀的密度稍低

So if there was silver in the crown, it would be less dense than if it were made of pure gold.

所以如果皇冠裡摻了銀，其密度會比純金打造的要低一些

But no matter what it was made of, the crown would be the same shape,

但不論此皇冠是什麼做的，它的形狀還是一樣

which means the same volume.

也就是說體積相同

So if Archimedes could measure the mass of the crown first,

所以如果阿基米德先測量皇冠的質量

and then measure its volume,

再測量其體積

he could find out how dense it was.

他就可以找到其密度

But it is not easy to measure a crown's volume - it has an irregular shape,

但是要量皇冠的體積也不容易—— 它是不規則形狀

that's different from a simple box or ball.

跟一個形狀簡單的盒子或球不一樣

You can't measure its size and multiply like you might for other shapes.

你不能先測量尺寸然後乘起來， 像你量其他形狀的東西一樣，

The solution, Archimedes realized,

而其解決方法，阿基米德想到

was to give the crown a bath.

是讓這個皇冠「洗個澡」

by placing it in water and seeing how much water was displaced,

把它放在水裡看它排出多少水量

he could measure the volume,

他可以測量水量

and he'd calculate the density of the crown.

然後他就能計算出這頂皇冠的密度

If the crown was less dense than pure gold,

如果這頂皇冠的密度小於純金

then the goldsmith most definitely cheated the king.

那麼這個金匠可斷定是欺騙了國王

When Archimedes went back to the king and did his test,

當阿基米德回到國王面前做這項試驗時

the story says, he found that the goldsmith had indeed cheated the king,

故事是這麼說的，他發現這金匠的確騙了國王

and slipped some silver in. These days,

掺了一些銀進去。現在

using the way an object displaces water to measure volume is called

使用物體的排水量來測體積被稱為

Archimedes' principle. The next time you take a bath,

阿基米德原理。所以下回你洗澡的時候

you can see Archimedes' principle in action,

你就可以觀察到阿基米德原理的實際運用

and maybe you'll have a genius idea of your own.

說不定你還會發現一些天才點子呢！