Never be afraid to get dirty, but be sufficiently sure-footed to avoid the abyss of contamination.

Ramsey Theory

When the JonBenet Ramsey murder investigation began ten years ago, police gathered a lot of evidence, but the evidence as a whole did not lead conclusively to any particular suspect. Nevertheless, people found some patterns in smaller parts of the evidence, and certain pockets of the public as well as the media used these patterns to point blame on Ramsey’s parents. Within the past week, an unrelated man confessed to her murder and awaits formal charges.

How significant are patterns? One might notice patterns in clouds or in the stars, but does that necessarily mean we can draw conclusions from them? It turns out that order can arise even in randomness, and a whole branch of mathematics studies how this order arises.

Coincidentally, this field is called Ramsey Theory. The simplest example of Ramsey Theory is found in the following example. Suppose I have a drawer filled with black and red socks. If I draw any three socks from that drawer, then I am guaranteed at least one pair of matching ones. A little thought reveals that that if I have a drawer with socks of n different colors, I am guaranteed at least one matching pair if I draw n+1 socks from the drawer. This concept is often called the pigeon-hole principle, and Ramsey Theory generalizes it into new domains.

While patterns may exist, there is a question of whether these patterns lead to relevant conclusions. A good mystery novel is filled not only with relevant facts, but also red herrings, which mislead the reader into drawing false conclusions. Hopefully investigators now have enough evidence in the Ramsey murder to separate the relevant facts from the red herrings.

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