It happened twice in the past few days… each time, I encountered the same fairly obscure (i.e. unlikely to appear in my life) concept in two (or more!) completely unrelated contexts.

• On Saturday, I went to see The Phantom of the Opera (an outstanding production, the kind of Broadway that elevates you). As I flipped through Playbill, I read an article about A Steady Rain, a show starring Hugh Jackman and Daniel Craig. Then, that night, I was flipping through a hotel brochure and read a different article about how Broadway starts attracting movie actors… A Steady Rain was mentioned. Finally, on Sunday I was talking to a producer who brought up the same show. Quite a coincidence
• I just finished watching House, M.D. (one of two TV shows I religiously watch). The case (SPOILERS!!) revolved around the “hygiene hypothesis”, an idea that living in an environment that’s too germ-free actually makes us sicker^*. Coincidentally, just a few hours earlier I was listening to a not-too-recent RadioLab episode and the same hypothesis was brought up! Uncanny

I was quick to burst my own bubble–selection bias is definitely at play here. We perceive coincidences as rare, weird and somewhat mystical so that when they actually happen (and they are bound to every so often), we will definitely remember them, unlike the thousands of non-coincidences that happen to us every day.

But as I thought about it more, I thought of a curious, seemingly unlikely interpretation of this phenomenon: coincidences are equivalent to randomness; and the fact that they happen is simply an outcome of the fact that there is plenty of randomness around us. Without coincidences, there is no randomness.

Say what? Why would coincidences and randomness be equivalent? Getting 7 tails in a row in a series of 100 coin tosses is actually a rather likely event^†, but we’d consider it a big coincidence. As shown by a mathematician named Ramsey, in a complex enough system, you can find pretty much any structure you can think of. The world that surrounds us is an incredibly random (and thus complex) system–we are bombarded by terabytes of information every minute, and most of this information is linked^‡. It should therefore come as no surprise that the world we experience will feature plenty of structure, even of the most unlikely kind. It is this hard-to-believe structure that we call coincidence. Randomness, therefore, is the existence of unexpected structure.

This entry was posted on Thursday, November 19th, 2009 at 01:30 and is filed under paramathematics, reductions, whatis. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.