Understanding the Patterns in Chaos


id you know that bags of M&Ms are not random? Plain-M&Ms-Pile If they were you’d occasionally get a bag that was completely devoid of blues or comprised of only greens. The Mars Company employs mechanisms during the packaging process to ensure that each bag of candy is not entirely random, but conforms to our false concept of randomness.[1] Real randomness is full of patterns.

Our brains are not wired to fathom probabilities. Our cognitive biases permit us to believe we stand a worthwhile chance of winning the lottery but that terrible accidents will befall other people and not us. We are rather dumb about luck. We want to thank God for our blessings and blame Satan for our curses. We are stunned when we acquire diseases we do not deserve, and take personally what is impersonal and random. “Why me?” cries the victim to the heavens, and the heavens do not respond.

Suppose you wished to play a game of chance that involved flipping a fair coin five times. Which of the following two sequences of Heads and Tails seems more likely to you?

Sequence A: H T T H T
Sequence B: T T T T T

Most people assume that sequence A is more likely than B because the latter contains a long run of all Tails. But in fact the two sequences are just as likely.

Each time you flip a fair coin there a two possible outcomes. When you flip a coin five times there are 2 * 2 * 2 * 2 * 2 possible sequences, or 32. Each sequence is equally likely. So there’s a one in 32 chance of getting sequence A, and the same chance of getting sequence B, and the same chance of getting any of the other 30 possible sequences.

Here are all 32 sequences with some highlighted:

table of coin sequences

I’ve highlighted the rows containing perfect striping patterns (e.g. H T H T H) or runs of four or more consecutive Heads or Tails. These are the rows that may not feel random to us because we notice patterns in them. We might consider sequences like these to be spooky. We expect our chaos to appear pattern-less, and these sequences defy that expectation. Nevertheless, these sequences are just as probable as any of the others. And notice that there are eight of these rows, meaning that with five flips of a fair coin there is a 25% chance you’ll see spooky results. Spookiness is not very unlikely.

Flip coins for a while and inevitably you’ll eventually get runs of Heads or runs of Tails, or you’ll notice repeating combinations. These apparent patterns do not defy randomness; on the contrary, they’re tell-tail signs of it. It is only due to our cognitive biases that we mistakenly believe randomness does not result in runs or repeated combinations.

The tendency to notice patterns in random sequences is called apophenia. Noticing patterns (and in the process filtering out non-patterns) is something our brains do particularly well.

We are prone to assume that patterns we find in the universe must have meaning, but these patterns are a natural consequence of true chaos. We underestimate the power of chaos to generate coincidences and wrongly assume great coincidences must be the product of cosmic intelligence at work. They are not. It is naïve to think otherwise – a sign of ignorance, not spirituality.

Add to this the fact that we are extremely adept at noticing these patterns, and you have an explanation for the countenance of Jesus Christ showing up on a tortilla, and all the other holy simulacra that have caused sensations over the ages. Supernaturalists will accept every tiny coincidence – a series of green lights on a drive through town, a convenient parking spot in a busy parking lot, a phone call from a sister while daydreaming about her – as proof of synchronicity, psychic powers, Jesus, or whatever it is they believe. But even if supernatural forces do exist, coincidences are not proof of them. They are only proof that chaos is busy doing its thing and that it’s wonderfully weirder than we normally acknowledge.

“There are no coincidences,” says the supernaturalist. “Everything happens for a reason.”

This might seem like innocuous, feel-good drivel, but it’s a cruel and harmful lie. It encourages people to take paths in life that lead to dead ends they wouldn’t otherwise take, to waste time searching for meaning where it isn’t, and to deny ugly realities that can only be surmounted if faced boldly and honestly.

Coincidences have histories but not reasons. They are beautifully meaningless. And this is good! The supernaturalist feels that imposing meanings upon meaningless events makes them somehow better. The naturalist embraces them just as they are, raw and au naturel, without drizzling any goopy sauces over them to disguise their native flavor, which is – though the taste must be acquired – ambrosial.

Cloudy Skies

Pareidolia is a type of apophenia. It is the psychological phenomenon of perceiving significant patterns in vague images or sounds, like seeing animal shapes in clouds. Spotting bulls in a buttermilk sky is a marvelous pastime. But there is another equally marvelous way to enjoy clouds: behold them without seeking patterns, in all their gorgeous, billowy randomness, and let their glory strike your heart like a mallet strikes a gong. Accept them just as they are.

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  1. [1]Actually, the Mars Company researches how appetizing various M&M colors are to consumers, and based on their findings they target certain percentages of each color.
 Posted by on February 18, 2012
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