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翻译人员: Steven Li
校对人员: Jenny Yang
00:06
If you line up the entire text
of “Moby Dick,”
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要是你把 "白鲸迪克",
00:09
which was published in 1851,
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一本在 1851 年发表的小说,
00:11
into a giant rectangle,
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的字拼成一个很大的长方形,
00:13
you may notice some peculiar patterns:
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你可能会发现一些奇怪的规律。
00:16
like these words,
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像这些字:
00:17
which seem to predict the assassination
of Martin Luther King.
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看起来像是预料到了马丁路德金的暗杀,
或者看一看"戴安娜王妃"的死亡。
00:22
Or these references
to the 1997 death of Princess Di.
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00:27
So, was Herman Melville a secret prophet?
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所以呢?"赫尔曼梅尔维尔" 是人们不知道的先知吗?
00:31
The answer is no,
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答案是:他不是,
00:32
and we know that thanks to a mathematical
principle called Ramsey theory.
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因为一个数学定理:"拉姆齐理论”。
00:37
It's the reason we can find geometric
shapes in the night sky,
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这个理论让我们能够在空中找到几何形状,
00:41
it's why we can know without checking
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让我们,不用检查就能够知道
00:43
that at least two people in London
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伦敦肯定有至少两个人
00:45
have exactly the same number
of hairs on their head,
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在头上会有一样多的头发,
00:49
and it explains why patterns can be found
in just about any text...
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这个定理很好的解释了为什么在无论那个文本当中都会有一些的规律,
00:54
even Vanilla Ice lyrics.
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包括 ”Vanilla Ice“ 的歌词里。
00:56
So what is Ramsey theory?
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所以呢?什么是"拉姆齐理论”。
00:58
Simply put, it states that given enough
elements in a set or structure,
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简单来讲,"拉姆齐理论” 告诉我们要是有很多的项目,
01:03
some particular interesting pattern
among them is guaranteed to emerge.
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肯定在那些项目中会有一些奇特的规律。
01:09
As a simple example, let’s look
at what’s called the Party Problem—
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一个非常基本的例子是 “派对” 题,
01:12
a classic illustration of Ramsey theory.
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一个非常传统的例子。
01:15
Suppose there are at least six people
at a party.
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假设有至少6人一起在一个派对。
01:18
Amazingly enough, we can say for sure
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令人吃惊的是,我们可以肯定地说
01:21
that some group of three of them
either all know each other,
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会有一个三人组办的组会都认识对方,
01:25
or have never met before,
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或没见过面,
01:26
without knowing a single thing about them.
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虽然我们不了解这些人的具体情况。
01:29
We can demonstrate that by graphing
out all the possibilities.
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我们可以用个图面来演示所有的可能性。
01:33
Each point represents a person,
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每个点表示一个人,
01:35
and a line indicates
that the pair know each other.
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每条线表示两个人认识对方。
01:38
Every pair only has two possibilities:
they either know each other or they don't.
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每两个人只有两个可能性:他们认识对方或不认识对方。
01:43
There are a lot of possibilities,
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这个案件有很多的可能性,
01:46
but every single one has the property
that we're looking for.
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但是每个可能性都会体现我所说的这个规律。
01:49
Six is the lowest number of guests
where that's guaranteed to be the case,
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这个规律已验证要是派对中有至少六个人,
01:54
which we can express like this.
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我们能这么表示。
01:56
Ramsey theory gives us a guarantee
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"拉姆齐理论” 能够为我们保证
01:59
that such a minimum number exists
for certain patterns,
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存在这样的最小数量特定的规律,
02:02
but no easy way to find it.
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但是没有简单的方法来找到这最少的数量。
02:05
In this case, as the total number
of guests grows higher,
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在这个具体的例子当中,随着人数增大,
02:08
the combinations get out of control.
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可能性会变得无穷大。
比如说你想要找出派对最少的人数
02:11
For instance, say you're trying
to find out the minimum size of a party
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02:15
where there's a group of five people
who all know each other or all don't.
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鉴于有五个人都认识对方或者都不认识对方。
02:19
Despite five being a small number,
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虽然五是个非常少的数量,
02:21
the answer is virtually
impossible to discover
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找出这道题的答案会非常难
02:24
through an exhaustive search like this.
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要是我们一个一个可能性的来看。
02:27
That's because of the sheer
volume of possibilities.
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这是因为这道题有太多的可能性了。
02:30
A party with 48 guests
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一个有48个人的派对有2^(1128)个可能性,
02:32
has 2^(1128) possible configurations,
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02:38
more than the number of atoms
in the universe.
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多余在宇宙中的原子的数量。
02:41
Even with the help of computers,
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即使使用计算机的帮助下,
02:43
the best we know is that the answer
to this question
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我们只能知道我们的答案
02:46
is somewhere between 43 and 49 guests.
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是介于43和49之间的客人。
02:50
What this shows us
is that specific patterns
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这让我们体验到具体的规律
02:53
with seemingly astronomical odds
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虽然有非常小的概率
02:55
can emerge from a relatively small set.
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能从一个非常小的数据集中起源。
02:58
And with a very large set,
the possibilities are almost endless.
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而要是数据集非常大,可能性会无穷多。
03:02
Any four stars where no three
lie in a straight line
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哪四颗星,要是至少三颗星不落在一条直线上
03:06
will form some quadrilateral shape.
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会产生一个随便的四边形。
03:09
Expand that to the thousands
of stars we can see in the sky,
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要是我们拿我们天空中上千颗星星来看,
03:12
and it's no surprise that we can
find all sorts of familiar shapes,
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我们能看到许多我们能认识的形状,
03:16
and even creatures if we look for them.
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而且要是我们更仔细看我们也能看到某些生物。
03:18
So what are the chances of a text
concealing a prophecy?
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那么摸个文本隐藏这一个秘密的概率是多少呢?
03:22
Well, when you factor
in the number of letters,
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要是你想到英文中有多少个字母,
03:25
the variety of possible related words,
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这些字母能成立多多的字或词,
03:28
and all their abbreviations
and alternate spellings,
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和所有的缩写和不同的拼写,
03:31
they're pretty high.
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有许多的可能性。
03:33
You can try it yourself.
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你可以自己试试。
03:34
Just pick a favorite text,
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调出来你最喜欢的文本,
03:36
arrange the letters in a grid,
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把文本里的字评到一个表格上,
03:37
and see what you can find.
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看一看你能不能发现一个奇特的规律。
03:40
The mathematician T.S. Motzkin
once remarked that,
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一个数学家,”T.S. Motzkin“ 过去说过,
03:43
“while disorder is more probable
in general,
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”虽然一般来说紊乱的概率非常高,
03:46
complete disorder is impossible."
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完整的紊乱是不可能的."
03:49
The sheer size of the universe guarantees
that some of its random elements
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宇宙的大小已经保证了莫些东西
03:53
will fall into specific arrangements,
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会陷入具体的排列,
03:56
and because we evolved to notice patterns
and pick out signals among the noise,
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而因为人们进化了,我们可以发现我们世界当中的一些规律,和从紊乱中调出来有用的规律,
04:01
we are often tempted to find intentional
meaning where there may not be any.
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我们有时会太积极的在没规律的范围中想要发现出规律。
04:07
So while we may be awed by hidden messages
in everything from books,
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所以,虽然我们会被奇怪的规律恐吓,特别是在书中,
04:11
to pieces of toast,
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烤面包中,
04:12
to the night sky,
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夜空中,等等,
04:14
their real origin
is usually our own minds.
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这些奇特的规律中的真正出处通常是我们的脑海。
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