One is one ... or is it?

一就是一...还是？ ── Christopher Danielson

翻译人员: Minji Seo 校对人员: Dong Mao

(音乐)

哪个是正确的──a dozen eggs 'is' 还是 a dozen eggs 'are'？

Which is correct: "A dozen eggs is?" Or "A dozen eggs are?"

我记得当我在小学的时候

I remember being in elementary school,

and my teachers making a big deal about the unit.

我们老师教了很多关于数量单位词

但我从没有学会 直到有一天我到杂货店

And I never really got that,

until one day, I was in the grocery store,

我想买一颗苹果（an apple）， 不过我却不能买「一」苹果 （one apple）

and I wanted to buy an apple, but I couldn't buy one apple.

I had to buy a whole bag of apples.

这表示我必须买一整袋的苹果

So I did. I bought one bag of apples,

所以我做了 我买了一整袋的苹果

I took it home, I took one apple out of the bag, and I cut it up.

我把它拿回家 我从袋子拿出一颗苹果并切开

然后吃了一片

And then I ate one slice.

一袋、一颗、一片

One bag, one apple, one slice.

Which of these is the real "one"?

哪一个才是真实的那一个？

好吧 他们都是 当然 那正是我小学老师一直试着告诉我的

Well, they all are of course,

and that's what my elementary teachers were trying to tell me.

因为这是一个重要的概念关于

Because this is the important idea behind whole number place value,

整数字、小数点位与分数

decimal place value and fractions.

Our whole number system depends

我们所使用的数字系统要能够转换我们所熟悉的「一」

on being able to change what we count as "one".

Our whole number system depends on being able to change units.

我们所使用的数字系统要能够转换「单位」

有两个方式能够转换单位

There are two ways to change units.

We can compose, and we can partition.

我们可以组合 也可以分割

当我们组合多个单位时

When we compose units,

we take a bunch of things, we put them together to make a bigger thing,

我们把一大堆的东西放在一起 让他们变成更大的东西

like a dozen eggs.

就像一打鸡蛋一样

我们把十二颗鸡蛋放在一起 组合成一组

We take 12 eggs, put them together to make a group,

and we call that group a dozen.

然后我们叫这一组「一打」

一打鸡蛋就是一种组合单位

A dozen eggs is a composed unit.

其他组合单位的例子包括：

Other examples of composed units

include a deck of cards, a pair of shoes, a jazz quartet

一副牌、一双鞋、爵士四重奏

当然还有 芭比和肯尼组合成一对情侣

and of course, Barbie and Ken make a couple.

但想想看一条面包

But think about a loaf of bread.

That's not a composed unit,

那不是一种组合单位

because we don't get a bunch of slices from a bunch of different bakeries

因为我们不会从不同的面包店拿一片片切好的面包

and put them together to make a loaf.

将它们放在一起变成一条面包

No, we start with a loaf of bread

不是这样的 我们是把一条面包切成更小的面包

and we cut it into smaller pieces called slices,

并叫它「一片」面包 所以每一片面包就是一个分割单位

so each slice of bread is a partitioned unit.

其他分割单位的例子包括：

Other examples of partitioned units

include a square of a chocolate bar, a section of an orange

一块巧克力、一片柳橙，

还有一片披萨

and a slice of pizza.

重要的是 一旦我们创造新的单位

The important thing about units is that once we've made a new unit,

we can treat it just like we did the old unit.

我们就能用跟旧的单位同样的方法使用它

We can compose composed units,

我们可以组成组合单位 也可以分成分割单位

and we can partition partitioned units.

Think about toaster pastries.

想想看那些零食

他们两片包成一袋

They come in packs of two,

然后再把四袋放在一起

and then those packs get put together in sets of four

to make a box.

变成一盒

So when I buy one box of toaster pastries,

所以当我买一盒零食时

我是买了「一个」？

am I buying one thing,

「四个」？还是「八个」？

four things, or eight things?

这取决于单位

It depends on the unit.

One box, four packs, eight pastries.

一盒、四袋、八片

And when I share a slice of pizza with a friend,

当我跟我的朋友分享一片披萨

我们必须将它切成更小的两个

we have to cut "it" into two smaller pieces.

所以一盒零食

So a box of toaster pastries is composed of composed units,

是一个组合单位的组成

而当我切开一片披萨时

and when I split a slice of pizza,

I'm partitioning a partitioned unit.

我正在切出一个分割单位

But what does that have to do with math?

但这些到底跟数学有甚么关系？

数学中，所有东西都是确定的

In math, everything is certain.

Two plus two equals four,

2+2=4 1就是1

and one is just one.

但那不全然正确

But that's not really right.

One isn't always one.

1不一定永远是1

Here's why: we start counting at one,

这就是原因：我们从1开始数

and we count up to nine: 1, 2, 3, 4, 5, 6, 7, 8, 9,

一直数到9──1、2、3、4、5、6、7、8、9

and then we get to 10, and in order to write 10,

接下来我们数到10了 而为了写下10这个数字，

we write a one

我们写了一个1和一个0

and a zero.

其中的1就表示我们有了一个群组

That one means that we have one group,

and the zero helps us remember

而0帮助我们记得这是指一组 而不是一个

that it means one group, not one thing.

但是10 就像1

But 10, just like one,

just like a dozen eggs,

就像一打鸡蛋 就像一颗鸡蛋

just like an egg,

10 is a unit.

10是一个单位

而十个10变成100

And 10 tens make 100.

So when I think about 100,

所以当我们在想100是什么的时候 它就像那一盒零食

it's like the box of toaster pastries.

Is 100 one thing,

100是一个东西？

10个？

10 things

or 100 things?

或是100个？

And that depends on what "one" is,

那就取决于那个「一」指什么

it depends on what the unit is.

单位就是什么

所以碰到数学需要写「一」的时候 要一直想着这件事

So think about all the times in math when you write the number one.

不管这个「一」是放在哪个位置，

No matter what place that one is in,

no matter how many things that one represents,

不管这个「一」里有多少东西

one is.