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?
若把1851年出版的 《白鯨記》整本書的文字, 排成大的矩形文字格, 你可能會注意到一些奇特的模式, 像這些字 似乎預言馬丁‧路德‧金會被暗殺, 或是關於1997年 黛安娜王妃的死亡。 那麼,赫爾曼‧梅爾維爾 是個秘密先知嗎?
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.
當然不是, 我們之所以知道,是因為根據 「拉姆西理論」這個數學原理。 因著這個理論, 我們能在夜空中發現幾何圖形, 也因著它,我們不用查就知道 在倫敦至少有兩個 頭髮數量完全一樣的人, 它也解釋了 何以在任何形式的文字裡, 幾乎都能找到所謂的模式,
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.
甚至在香草冰的歌詞中 也能找到。 什麼是「拉姆西理論」? 簡單說,若組合或結構中 有足夠的元素, 那麼一些奇特有趣的模式 必然會發生。 簡單舉例,讓我們來看看 拉姆西理論中典型的例證 ── 派對習題。
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.
假設至少有6個人出席派對, 很奇妙地, 我們確知必定有3個人認識彼此, 或者從未見過面, 即使我們完全不知 他們的任何背景資料。 我們可以圖解, 來說明所有的可能性。 每一點代表一個人, 一條線表示兩個人彼此相識。 任何兩人只存在兩種可能性: 他們認識或者不認識對方。 有眾多的可能性, 但是,每一種 都有我們想尋找的特性。 6是讓這個例子成立的 最少賓客人數, 可以用這式子表示。 拉姆西理論保證 像這樣的最小數, 必定存在某些模式中, 但未必容易找得出來。 在這情形下,當賓客數增多, 組合數就會超出可控制的範圍。
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.
例如,假設你要找一組 5人彼此認識 或是互不認識的最少賓客數, 雖然,5是一個小數目, 但實際上,無法以窮舉搜索法 來找出來答案。 原因是可能性極為龐大。 在有48位賓客的派對中, 存在2的1128次方種可能性。 遠超過全宇宙中的原子總數。 即使有電腦的幫忙, 我們對這問題所能求得的最佳解答, 只能得出賓客人數 落在43~49這個區間。
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.
這告訴我們, 有著像天文數字般大的 可能性的特定模式, 可源自於相對小的組合。 而大組合的可能性, 幾乎是無窮大的。 任何4顆星,若有任3顆不共線, 就會組成某種四邊形。 因此,觀看天空中數千顆的星星, 我們能看到各種熟悉的形狀, 甚至動物的樣子, 就一點也不奇怪了。
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.
所以,文字中隱藏著預言 的可能性有多少? 如果你計入字母的總數, 它們所能組合的各式字詞, 還有簡寫,和替代拼法, 可能性非常的高。
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.
你可以自己試試。 選一篇你喜歡的文章, 把字母排成格子狀, 看看你能找到什麼。 數學家莫茲金曾說 : 「雖然一般而言, 混亂失序的機率較高, 但是, 全然的混亂失序是不可能的。」 在廣大遼闊的宇宙中, 必定有些隨機的元素 會形成特定的排列, 由於我們進化到 能從雜訊中找出訊號和模式, 所以,我們常禁不住想從可能 無意義的事物中找出隱含的訊息。
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.
因此,當我們驚嘆隱藏於 書中、吐司上、 或夜空中的訊息時, 其實,我們自己的心智 才是發出訊息的源頭。