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? 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. 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. 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. 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. 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. 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. 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. 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.
