that you've heard in the last several fabulous days

各位這幾天

have been from people who have the characteristic

所聽到的大多數精彩演說

that they have thought about something,

都是具有專業特長

they are experts, they know what's going on.

學有專精的專家

All of you know about the topic

經過深思熟慮所發表的演說

that I'm supposed to talk about.

大家都知道

That is, you know what simplicity is,

我將發表的講題是什麼

you know what complexity is.

各位都知道什麼是「簡單」

The trouble is, I don't.

知道什麼是「複雜」

And what I'm going to do is share with you

問題是：我並不知道

my ignorance on this subject.

因此我將與各位

I want you to read this,

分享我對講題的無知

because we're going to come back to it in a moment.

請大家讀這段引述

The quote is from

因為不久後我們還會回到這段話

the fabled Potter Stewart

這是鼎鼎大名的最高法院

opinion on pornography.

大法官波特•司徒華談論

And let me just read it,

色情所發表的一段話

the important details here:

那麼我現在念

"Shorthand description, ['hardcore pornography'];

其中的重要細節

and perhaps I could never succeed in intelligibly defining it.

「簡略的描述，重鹹濕的色情

But I know it when I see it."

我恐怕無法給它清楚的定義

I'm going to come back to that in a moment.

但一看就知道」

So, what is simplicity?

我還會回到這段話

It's good to start with some examples.

那麼，什麼是「簡單」？

A coffee cup -- we don't think about coffee cups,

我們先舉個例子

but it's much more interesting than one might think --

咖啡杯，我們不會想太多

a coffee cup is a device,

但它可能比你認為的還有趣得多

which has a container and a handle.

咖啡杯是一種器具，對

The handle enables you to hold it

是一種容器，對；還有握柄，對

when the container is filled with hot liquid.

如果容器裡裝滿熱水的話

Why is that important?

握柄讓你能握住杯子，是吧

Well, it enables you to drink coffee.

那有什麼重要呢？

But also, by the way, the coffee is hot,

嗯，它讓你能喝咖啡

the liquid is sterile;

而且咖啡是熱的

you're not likely to get cholera that way.

液體是煮沸消毒過的

So the coffee cup, or the cup with a handle,

這樣你就不會感染霍亂

is one of the tools used by society

那麼咖啡杯或是有握柄的杯子

to maintain public health.

是社會上用來維護

Scissors are your clothes,

公共衛生的工具之一

glasses enable you to see things

剪刀用來剪裁衣服

and keep you from being eaten by cheetahs

眼鏡讓你能看見東西

or run down by automobiles,

也讓你不被印度豹給吃了

and books are, after all, your education.

或讓汽車給撞著了

But there's another class of simple things,

還有書，這是用來教育你的

which are also very important.

不過還有其它

Simple in function,

簡單的東西，同樣重要

but not at all simple in how they're constructed.

功能簡單

And the two here are just examples.

構造卻不簡單

One is the cellphone, which we use every day.

這裡有兩個例子

And it rests on a complexity,

一是我們天天使用的行動電話

which has some characteristics

其構造極其複雜

very different from those that my friend

所具有的特性和我的朋友

Benoit Mandelbrot discussed,

貝諾特•曼德爾博特談到的

but are very interesting.

有很大不同

And the other, of course, is a birth control pill,

但是也很有趣

which, in a very simple way,

另一例當然是避孕藥了

fundamentally changed the structure of society

它既簡單又根本地

by changing the role of women in it

改變了社會結構

by providing to them

避孕藥為婦女所提供的

the opportunity to make reproductive choices.

選擇懷孕與否的機會

So, there are two ways of thinking about this word, I think.

改變了婦女的角色

And here I've corrupted

我想有兩種方式來思考這個詞

the Potter Stewart quotation

那麼我稍微修改一下

by saying that we can think about something --

波特•司徒華的那段話

which spans all the way from scissors

從剪刀開始

to the cell phone,

一直到行動電話

Internet and birth control pills --

網際網路和避孕藥

by saying that they're simple,

等等，都有一個

the functions are simple,

共通點：它們都很簡單

and we recognize what that simplicity is

在功能上都是簡單的

when we see it.

大家都看見它們的「簡單」

Or there may be another way of doing it,

一看就知道

which is to think about the problem in terms of what --

也許另有別的方式來看事情

if you associate with moral philosophers --

也就是從道德哲學家的觀點

is called the teapot problem.

來思考這個問題

The teapot problem I'll pose this way.

那就是所謂的茶壺問題

Suppose you see a teapot,

茶壺問題嘛，這麼說吧

and the teapot is

假設你看到把茶壺

filled with hot water.

茶壺裡

And you then ask the question:

盛滿了熱水

Why is the water hot?

你提出問題啦：

And that's a simple question.

為什麼水是熱的？

It's like, what is simplicity?

這個問題很簡單

One answer would be:

就像問：「簡單」是什麼？

because the kinetic energy of the water molecules is high

有個答案是：

and they bounce against things rapidly --

因為水分子運動能量高

that's a kind of physical science argument.

撞擊的速度很快

A second argument would be:

這是物理的論點

because it was sitting on a stove with the flame on --

第二個論點是：

that's an historical argument.

因為它剛剛在爐子上燒

A third is that I wanted hot water

這是歷史的論點

for tea --

第三個是：我要用熱水

that's an intentional argument.

泡茶

And, since this is coming from a moral philosopher,

這是交代意圖的論點

the fourth would be that it's part of God's plan for the universe.

這是道德哲學家的回答

All of these are possibilities.

第四個是：這是上帝對宇宙的安排的一部分

The point is that you get into trouble

這些答案都有可能

when you ask a single question

重點是，你會有麻煩

with a single box for an answer,

如果你只問一個問題

in which that single question actually is many questions

只要一個答案

with quite different meanings,

但那個問題其實包含許多問題

but with the same words.

意義大不相同

Asking, "What is simplicity?" I think falls in that category.

卻使用相同的字彙

What is the state of science?

問「簡單」什麼是，我想就是這類的問題

And, interestingly, complexity

科學的現況是什麼？

is very highly evolved.

有趣的是其中

We have a lot of interesting information

所牽涉到的極其複雜

about what complexity is.

關於複雜

Simplicity, for reasons

我們有許多有趣的資訊

that are a little bit obscure,

不太清楚到底

is almost not pursued,

出於什麼原因

at least in the academic world.

幾乎無人探討簡單

We academics -- I am an academic --

至少學界情況是如此

we love complexity.

我們學界中人，我是學界的

You can write papers about complexity,

我們喜歡複雜

and the nice thing about complexity is

論文談的盡是複雜

it's fundamentally intractable in many ways,

談論複雜，最棒的是

so you're not responsible for outcomes. (Laughter)

基本上在許多方面是屹立不搖的

Simplicity -- all of you really would like

因此你可以不必為結果負責

your Waring Blender in the morning

「簡單」呢，早上起來

to make whatever a Waring Blender does,

大家都會用果汁機

but not explode or play Beethoven.

打些什麼吃的喝的

You're not interested in the limits of these things.

你不會希望它爆炸或彈奏貝多芬

So what one is interested in

你對這類東西的侷限沒多大興趣

has a lot to do with the rewards of the system.

那麼大家有興趣的

And there's a lot of rewards in thinking

其實跟回報很有關係

about complexity and emergence,

思考「複雜」和「顯現」

not so much in thinking about simplicity.

能帶來許多的獎賞

One of the things I want to do

思考「簡單」獎賞就沒那麼多了

is to help you with a very important task --

我想做的事情之一是

which you may not know that you have very often --

幫助你應付一個重要的場面

which is to understand

這種情況不難理解

how to sit next to a physicist at a dinner party

你可能常常不知道

and have a conversation. (Laughter)

在餐宴上坐在一位物理學家旁邊

And the words that I would like you to focus on

該跟他說些什麼

are complexity and emergence,

那我告訴你要注意的兩個詞是：

because these will enable you to start the conversation

「複雜」和「顯現」

and then daydream about other things.

它們讓你能開始聊

(Laughter)

還能繼續跟他一起作其它的白日夢

All right, what is complexity in this view of things,

（笑聲）

and what is emergence?

好吧，「複雜」是什麼？

We have, actually, a pretty good working definition of complexity.

「顯現」又是什麼？

It is a system, like traffic,

我們對於複雜其實有個很好的定義

which has components.

它是一種系統，像是交通系統

The components interact with one another.

有其組成的零件

These are cars and drivers. They dissipate energy.

零件之間有互動

It turns out that, whenever you have that system,

汽車和開車的人，他們消耗能量

weird stuff happens,

結果呢，只要有了這樣的系統

and you in Los Angeles

奇怪的事情就會發生

probably know this better than anyone.

各位住在洛杉磯

Here's another example,

可能比別人都清楚這一點

which I put up because

這裡還有另一個例子

it's an example of really important current science.

我提出來是因為

You can't possibly read that. It's not intended that you read it,

這是當前科學上重要的例子

but that's a tiny part

這不可能看得清楚，本來就不要大家讀的

of the chemical reactions going on

但這是你們的

in each of your cells at any given moment.

每一個微小細胞裡

And it's like the traffic that you see.

隨時都在進行的化學反應

The amazing thing about the cell is that

就像是大家看到的交通狀況

it actually does maintain a fairly stable

關於細胞，令人訝異的是

working relationship with other cells,

它確實與其它的細胞

but we don't know why.

維持著相當穩定的運作關係

Anyone who tells you that we understand life,

我們不知道為何如此

walk away.

那些聲稱懂得生命的人

And let me reduce this to the simplest level.

沒有解釋就走了

We've heard from Bill Gates recently.

那麼，我把這一切簡化到最簡單的層次

All of us, to some extent, study

我們最近聽了比爾•蓋茲演說

this thing called a Bill Gates.

我們大家多多少少都研究了

Terrific. You learn everything you can about that.

這個叫「比爾•蓋茲」的東西

And then there's another kind of thing that you might study,

你盡量學習了關於他的一切

and you study that hard.

你可能另外還研究別的東西

That's a Bono, this is a Bono.

你很用功研究

But then, if you know everything you can know about those two things,

這是波諾

and you put them together,

你盡所能了解有關這兩者的一切後

what can you say about this combination?

把他們放在一起

The answer is, not a lot.

你能得到的組合是什麼？

And that's complexity.

答案是：不多

Now, imagine building that up to a city, or to a society,

那就是複雜

and you've got, obviously, an interesting problem.

那麼，推而及之於一個城市或一個社會

All right, so let me give you an example

顯然的這是個有趣的問題

of simplicity

好吧，讓我舉一個

of a particular kind.

一種特殊的

And I want to introduce a word

「簡單」的例子

that I think is very useful,

然後我要介紹一個

which is stacking.

我認為很有用的詞

And I'm going to use stacking for a kind of simplicity

那就是「堆疊」

that has the characteristic

我將「堆疊」出一種「簡單」

that it is so simple

這種「簡單」具有

and so reliable

可以說是既簡單

that I can build things with it.

又可靠的特性

Or I'm going to use simple to mean

可以用來建構別的東西

reliable, predictable, repeatable.

當我說「簡單」，意思是

And I'm going to use as an example the Internet,

可靠、可預測、可重複

because it's a particularly good example

拿網際網路來說

of stacked simplicity.

這是個很好的

We call it a complex system, which it is,

「堆疊簡單」的特例

but it's also something else.

我們稱網際網路為「複雜系統」，確實也是

The Internet starts with mathematics,

但也有別的意思

it starts with binary.

網際網路始於數學

And if you look at the list of things on the bottom,

始於二進位系統

we are familiar with the Arabic numbers

各位如果看看底下的清單

one to 10 and so on.

大家都熟悉阿拉伯數字

In binary, one is 0001,

一到十等等的

seven is 0111.

在二進位系統裡一是0001

The question is: Why is binary

七是0111

simpler than Arabic?

問題是：為什麼使用二進位

And the answer is, simply,

會比使用阿拉伯數字簡單？

that if I hold up three fingers, you can count that easily,

答案很簡單：

but if I hold up this,

如果我伸出三根指頭，你能輕易的數

it's sort of hard to say that I just did seven.

但如果是這個

The virtue of binary is that it's the simplest possible way

要說我剛才比了個七可不容易

of representing numbers.

二進位的好處是：它是表示數字

Anything else is more complicated.

最簡單的辦法

You can catch errors with it,

其它都更複雜

it's unambiguous in its reading,

二進位很容易找到錯誤

there are lots of good things about binary.

只有一種解讀法

So it is very, very simple

二進位系統有許多好處

once you learn how to read it.

只要懂得解讀法

Now, if you like to represent

它就非常非常簡單

this zero and one of binary,

那麼，如果要表示

you need a device.

二進位系統的零和一

And think of things in your life

需要使用一種裝置

that are binary,

那麼，想一想生活中

one of them is light switches.

有什麼二進位的東西

They can be on and off. That's binary.

其中之一就是電燈開關

Now wall switches, we all know, fail.

開關非開即關－這就是二進位

But our friends who are condensed matter physicists

牆上的開關有時會壞掉

managed to come up, some 50 years ago,

但是五十年前

with a very nice device, shown under that bell jar,

我們那些積體物理學家朋友們發明了

which is a transistor.

鐘形罐裡的那個很棒的裝置

A transistor is nothing more than a wall switch.

也就是電晶體

It turns things on and off,

電晶體其實和牆上的開關

but it does so without moving parts

沒有兩樣，非開即關

and it doesn't fail, basically, for a very long period of time.

但不必移動零件

So the second layer of simplicity

而且很長時間不會壞掉

was the transistor in the Internet.

那麼，「簡單」的第二個層次

So, since the transistor is so simple,

是進入電晶體和網際網路時代

you can put lots of them together.

由於電晶體構造非常簡單

And you put lots of them together and you come with

可以把很多個

something called integrated circuits.

放在一起做成

And a current integrated circuit

積體電路

might have in each one of these chips

現在的積體電路

something like a billion transistors,

每一個晶片上可能

all of which have to work perfectly every time.

有大約十億個電晶體

So that's the next layer of simplicity,

每個晶體都必須完美運作

and, in fact, integrated circuits

這就是「簡單」的另一個層次

are really simple in the sense that they,

事實上，積體電路

in general, work really well.

真的非常簡單，因為

With integrated circuits, you can build cellphones.

運作一般都很暢順

You all are accustomed to having your cellphones work

用積體電路可以做行動電話

the large majority of the time.

大家都習慣行動電話可以打得通

In Boston ... Boston is a little bit like Namibia

大部分的時候是打得通的

in its cell phone coverage, (Laughter)

波士頓行動電話的涵蓋率

so that we're not accustomed to that all the time,