Random Clusters

The human mind is not good at randomness. The human mind is good at identifying and seeing patterns. The mind is so good at patter recognition and so bad at randomness that we will often perceive a pattern in a situation where no pattern exists. We have trouble accepting that statistics are messy and don’t always follow a set pattern that we can observe and understand.
 
 
Steven Pinker points this out in his book The Better Angels of Our Nature and I think it is an important point to keep in mind. He writes, “events that occur at random will seem to come in clusters, because it would take a nonrandom process to space them out.” This problem of our perception of randomness comes into play when our music streaming apps shuffle songs at random. If we have a large library of our favorite songs to chose from, some of those songs will be by the same artist. If we hear two or more songs from the artist back to back, we will assume there is some sort of problem with the random shuffling of the streaming service. We should expect to naturally get clusters of songs by the same artist or even off the same album, but it doesn’t feel random to us when it happens. To solve this problem, music streaming services deliberately add algorithms that stop songs from the same artist from appearing in clusters. This makes the shuffle less random overall, but makes the perception of the shuffle feel more random to us.
 
 
Pinker uses lightning to describe the process in more detail. “Lightning strikes are an example of what statisticians call a Poisson process,” he writes. “In a Poisson process, events occur continuously, randomly, and independently of one another. … in a Poisson process the intervals between events are distributed exponentially: there are lots of short intervals and fewer and fewer of them as they get longer and longer.”
 
 
To understand a Poisson process, we have to be able to understand having many independent events and we have to shift our perspective to look at the space between events as variables, not just look at the events themselves as variables. Both of these things are hard to do. It is hard to look at a basketball team and think that their next shot is independent of the previous shot (this is largely true). It is hard to look at customer complaints and see them as independent (also largely true), and it is hard to look at the history of human wars and think that events are also independent (Pinker shows this to be largely true as well). We tend to see events as connected even when they are not, a perspective error on our part. We also look just at the events, not at the time between the events. If we think that the time between the events will have a statistical dispersion that we can analyze, it shifts our focus away from the actual event itself. We can then think about what caused the pause and not what caused the even. This helps us see the independence between events and helps us see the statistics between both the event and the subsequent pause between the next event. Shifting our focus in this way can help us see Poisson distributions, random distributions with clusters, and patterns that we might miss or misinterpret. 
 
 
All of these factors are part of probability and statistics which our minds have trouble with. We like to see patterns and think causally. We don’t like to see larger complex perspective shifting statistics. We don’t like to think that there is a statistical probability without an easily distinguishable pattern that we can attribute to specific causal structures. However, as lightning and other Poisson processes show us, sometimes the statistical perspective is the better perspective to have, and sometimes our brains run amok with finding patterns that do not exist in random clusters.

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