The Baader-Meinhof Phenomenon and Littlewood's Law

I have a friend who recently became religious after becoming convinced that God was communicating with him through a series of highly improbable coincidences. He's extremely intelligent, but had recently gone through some devestating personal circumstances, which I suspect made him vulnerable to such thinking.

Anyway, I just saw this MonkeyFilter post and was interested that there is a name for this sort of thing.

Baader-Meinhof is the phenomenon where one happens upon some obscure piece of information– often an unfamiliar word or name– and soon afterwards encounters the same subject again, often repeatedly. Anytime the phrase "That's so weird, I just heard about that the other day" would be appropriate, the utterer is hip-deep in Baader-Meinhof.

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The phenomenon bears some similarity to synchronicity, which is the experience of having a highly meaningful coincidence… such as having someone telephone you while you are thinking about them. Both phenomena invoke a feeling of mild surprise, and cause one to ponder the odds of such an intersection. Both smack of destiny, as though the events were supposed to occur in just that arrangement… as though we're witnessing yet another domino tip over in a chain of dominoes beyond our reckoning.

Despite science's cries that a world as complex as ours invites frequent coincidences, observation tells us that such an explanation is inadequate. Observation shows us that Baader-Meinhof strikes with blurring accuracy, and too frequently to be explained away so easily. But over the centuries, observation has also shown us that observation itself is highly flawed, and not to be trusted.

The reason for this is our brains' prejudice towards patterns. Our brains are fantastic pattern recognition engines, a characteristic which is highly useful for learning, but it does cause the brain to lend excessive importance to unremarkable events. Considering how many words, names, and ideas a person is exposed to in any given day, it is unsurprising that we sometimes encounter the same information again within a short time. When that occasional intersection occurs, the brain promotes the information because the two instances make up the beginnings of a sequence. What we fail to notice is the hundreds or thousands of pieces of information which aren't repeated, because they do not conform to an interesting pattern. This tendency to ignore the "uninteresting" data is an example of selective attention.

In point of fact, coincidences themselves are usually just an artifact of perception. We humans tend to underestimate the probability of coinciding events, so our expectations are at odds with reality. And non-coincidental events do not grab our attention with anywhere near the same intensity, because coincidences are patterns, and the brain actually stimulates us for successfully detecting patterns… hence their inflated value. In short, patterns are habit-forming.

But when we hear a word or name which we just learned the previous day, it often feels like more than a mere coincidence. This is because Baader-Meinhof is amplified by the recency effect, a cognitive bias that inflates the importance of recent stimuli or observations. This increases the chances of being more aware of the subject when we encounter it again in the near future.

On a very related subject,

Littlewood's Law states that individuals can expect a miracle to happen to them at the rate of about one per month.

The law was framed by Cambridge University Professor J. E. Littlewood, and published in a collection of his work, A Mathematician's Miscellany; it seeks, inter alia, to debunk one element of supposed supernatural phenomenology and is related to the more general Law of Truly Large Numbers, which states that with a sample size large enough, any outrageous thing is likely to happen.

Littlewood's law, making certain suppositions, is explained as follows: a miracle is defined as an exceptional event of special significance occurring at a frequency of one in a million; during the hours in which a human is awake and alert, a human will experience one thing per second (for instance, seeing the computer screen, the keyboard, the mouse, the article, etc.); additionally, a human is alert for about eight hours per day; and as a result, a human will, in 35 days, have experienced, under these suppositions, 1,008,000 things. Accepting this definition of a miracle, one can be expected to observe one miraculous occurrence within the passing of every 35 consecutive days -- and therefore, according to this reasoning, seemingly miraculous events are actually commonplace.