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Perceiving Randomness

Cosmic Variance
By Sean Carroll
Apr 6, 2009 6:50 PMNov 5, 2019 8:15 AM


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The kind way to say it is: "Humans are really good at detecting patterns." The less kind way is: "Humans are really good at detecting patterns, even when they don't exist." I'm going to blatantly swipe these two pictures from Peter Coles, but you should read his post for more information. The question is: which of these images represents a collection of points selected randomly from a distribution with uniform probability, and which has correlations between the points? (The relevance of this exercise to cosmologists studying distributions of galaxies should be obvious.)

The points on the right, as you've probably guessed from the set up, are distributed completely randomly. On the left, there are important correlations between them. Humans are not very good at generating random sequences; when asked to come up with a "random" sequence of coin flips from their heads, they inevitably include too few long strings of the same outcome. In other words, they think that randomness looks a lot more uniform and structureless than it really does. The flip side is that, when things really are random, they see patterns that aren't really there. It might be in coin flips or distributions of points, or it might involve the Virgin Mary on a grilled cheese sandwich, or the insistence on assigning blame for random unfortunate events. Bonus link uncovered while doing our characteristic in-depth research for this post: flip ancient coins online!

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