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