fifteen,

15 步、

twenty moves ahead.

甚至 20 步

And it's a great myth

這真的只是傳說

because I'm a Grandmaster

因為我就是西洋棋大師

and it makes me look like a super freaking genius.

大家看我像是超級怪胎天才

But the truth is,

不過事實上

in just the first four moves

光是前四步

there are 318 billion ways you could play.

就有 3,180 億種走法

Now that would be cool if I could pull that off,

如果我真能預測得到，那一定很酷

but Grandmasters just can't, it's too much.

但西洋棋大師也沒轍，太多可能了

So we use different techniques to be able to look ahead.

因此我們運用一些技巧 使預測變得可能

And some of these techniques include

這些技巧包括

chunking,

「分群」

which means taking a group, a chess position,

意思是只看盤面中的一群棋子

and seeing what possibilities can come just that group;

分析發展的可能性

or pattern recognition,

還有「類型識別」

which is just going over a lot of positions

由許多類似的盤面類型中

that look very similiarly

識別出最接近的一種

and extrapolating truths from that;

推斷出正確的下法

the stepping-stone method,

「跳板法」

which is to take a position,

就是把盤面

freeze it in your mind,

記在腦海裡

and go from there to guess the next position.

依據這個盤面猜出下一步

But one of my favorites

有種方法是我的最愛

that I love to solve these kind of chess puzzles,

我最喜歡用來解決殘局謎題

is called retrograde analysis.

叫做「回溯分析」

And what you do with retrograde analysis

意思是

is that in order to look ahead,

為了預測下一步

it pays to look backwards.

值得先看前一步

Now, why is this so useful?

為什麼很有用呢？

Well, in chess, it's a very complicated case.

西洋棋是很複雜的

You got all these chess pieces,

全部棋子

it's 32 pieces,

一共有 32 顆

but after 5 moves, the position starts to evolve a little bit.

五步過後，盤面開始改變

And the game starts to go on

比賽繼續進行

and you see the chess position get a little simpler,

盤面變得簡單些

and a little bit simpler,

然後更簡單些

and less pieces on the board,

棋子越來越少

until finally,

直到終局

in this case, a game that I played in a tournament in Foxwoods,

我在康州快活林錦標賽的一局

it gets to something like this.

就差不多是這樣

When great players play,

兩個高手對戰時

it often gets to something like this.

常會變成這樣

You don't see like some easy, early checkmate.

不太可能輕鬆或是幾步 就將死對方

Grandmasters see through all that stuff.

西洋棋大師一定會看穿

What you see is some end game,

有些殘局

something really, really simple.

盤面非常簡單

And we like to study things like this,

大家喜歡研究這種棋局

Grandmasters do,

西洋棋大師也是

so that if we get to them,

以後遇到這種局面時

we know how to play them cold,

就可冷靜取勝

but also so that we can steer

我們也可以

in the position that's in front of us,

引導棋局成為這種局面

the more complex ones you saw earlier,

之前看到的複雜情勢

to something this easy,

就變得很容易、

something this simple.

很簡單

So in this way, when you're dead,

以這種方式，你被將死時

I already knew like ten moves ago

我十步前就知道了

because I knew where we were going.

因為我知道接下來雙方會怎麼下

Now, why is this so effective?

為什麼這很有效呢？

Well, it's something about the human mind,

是因為人類的思考

the problem with the human mind.

因為人類思考的問題

We're very logical creatures.

我們是很有邏輯的生物

So I want you to play along with me a few games.

我希望你們跟我玩幾個遊戲

Take a look at this sentence.

看看這個句子

Now most of you reading the sentence

大多數人在讀這個句子的

the second time around

第二次時

will realize that you missed the word "the"

才發現在第一次讀的時候

the first time around.

漏掉了 the 這個字

Your mind is very logical,

大腦是很有邏輯的

it proceeds forward,

會一路向前

it just ignores anything that breaks with its logical stream,

忽略所有不合邏輯的東西

and so you don't see the word "the" the first time,

所以第一次你並沒有看到 the 這個字

the second "the," the first time you read it.

第二個 the 會被忽略

But if you read this sentence backwards,

如果你從句子後面看過來

you would automatically catch it.

自然而然就會看到它

You'd go backwards,

你反方向閱讀時

and you get to "brain",

先看到 brain

and you get to "the,"

再看到 the

and then you say, "Whoa, there are two 'the's' in the sentence."

接著你會說： 「哇，這句子有兩個 the 」

This is a really cool trick for proofreading papers.

這是個很酷的校對技巧

You know, you're writing your paper

寫報告時

and there are these silly mistakes.

常會有這種愚蠢的錯誤

Why are these mistakes in my paper?

為什麼報告會有這種錯誤？

You read it backwards, you'll catch all of them.

只要反向讀一次，就可以全部抓到

Alright, let's go on to this problem, an interesting problem.

再來看個有趣的問題

"Bacteria that double every 24 hours

「細菌每 24 小時分裂一次，

fill a lake it has infested after precisely 60 days.

60 天可覆蓋一整個湖，

On what day was the lake half-full?"

請問覆蓋半個湖需要幾天？」

Now, a lot of people had seen this problem

很多人看過這個問題

and they'd think, "30, like, you know, you split it in half."

他們會覺得： 「 30 天吧，就是一半。」

Well, that's not the right answer.

但這不是正確答案

And, also, people might want a calculator.

接著人們可能會想找一台計算機

It's too big, it's math, it's boring,

數字太大，數學問題很無聊

I don't want to do that either.

我也不想算

But, if you do that problem backwards,

但如果你反方向解題

you get the answer right away.

馬上就可以得到答案

What's the answer?

答案是？

59, obviously.

59，很明顯

You start at the end, you go backwards,

你從結局開始，反方向解題

it's like, "Oh yeah, it's half-full, the answer is 59."

就會說：「噢耶， 半滿的答案是 59 」

Here's another puzzle, a little bit more complicated.

另一個謎題複雜一點

You have six numbers, 1 through 6.

有六個數字，從 1 到 6

The cards are face-down.

牌都是蓋起來的

You and I are going to pick a card.

你我各挑一張

You pick a card and you look at it

你挑了一張，瞇了一下

and it says the number 2.

數字是 2

I look at my card,

我看了一下我的牌

I think about it for a minute

想了一分鐘

and I say, "I want to trade."

然後說：「我想跟你換牌。」

The reason I want to trade,

我想換的原因

we're going to trade to see

是因為我們在交換後

who has the highest number at the end.

要比看看誰的數字大

Do you trade with me?

你要跟我換嗎？

Most people say, "Of course, I got a 2, 2 sucks!

大多數人會說：「當然， 我只拿到 2 ， 2 很爛！」

There are four numbers higher,

有四個數字比我大

probability says I'm going to do better."

機率告訴我，牌很可能會變好

Wrong answer, you're playing a Grandmaster.

錯！你的對手是西洋棋大師

You start from the back and you work it out.

試著反方向思考，你就會懂了

If I had the number 6, would I offer to trade?

如果拿到 6 ，我會提議交換嗎？

Of course not, I'm not dumb.

當然不會，我又不是白痴

What about the number 5?

如果是 5 呢？

Probably not either,

應該也不會

because you're not going to say yes if you have a 6.

因為如果你是 6 你才不會答應跟我換

Well, if 5 is not going to trade and 6 is not going to trade,

5 不會換、6 也不會換

4 is going to be like,

4 的情況則是：

"I'm not trading either because 5's and 6's don't trade."

「我才不要換，因為 5 和 6 都不可能換給我。」

So you see what happens as we work backwards.

所以你看到反方向思考時 會發生什麼事

3 is going to realize 4, 5, and 6 - they don't trade,

3 和 4、5、6 一樣 不可能換給我

so the offer is definitely a 1

提議要換的人一定是 1

and all of you who said yes,

剛才說「好」的人

thanks for your money.

謝謝你們的賭金

So, this retrograde analysis is used in different places.

回溯分析可用在不同地方

It's used to prove intoxications hours after an alleged DUI

賓州警方用這方法證明

by Pennsylvania police officers,

酒駕案的駕駛真的有喝酒

which is kind of cool.

實在很酷

Well, it means don't drink and drive.

這告訴我們不要酒駕

The use of retro-analysis is used in

回溯分析也用在

law,

法律、

science,

科學、

medicine,

醫療、

insurance,

保險、

stock market,

股市、

politics,

政治、

career planning.

生涯規劃

But I find its use to be a more interesting place,

最有趣的應用可能是電影

maybe one of the most interesting uses is in

最有趣的應用可能是電影

this movie, which I know a lot of you know,

很多人知道這部片

The Curious Case of Benjamin Button,

《班傑明的奇幻旅程》

where Brad Pitt plays a guy

布萊得彼特扮演一個

who's living his life backwards.

人生倒著過的角色

And what this movie makes me think of

這部電影讓我想到

is that great quote that,

一句有名的格言

well, that quote you often hear from people who are older,

你常會從長輩口中聽到： (譯註：蕭伯納說的)

that youth is wasted on the young.

「青春總被年輕人白白浪費。」 (Youth is wasted on the young.)

Well, if you can see the end game,

如果你可以預見人生結局

your youth will not be wasted on you.

你就不會浪費青春了

Thank you very much.

非常感謝