# Central Limit Theorem of behaviour

Dawid Laszuk published on
5 min, 977 words

As we get older, our thoughts solidify a bit. We are unintentionally drawn into more experiments, we get more data, and we learn more theories that help us to make sense of the world. If we're lucky, these experiments are diverse enough to sample from "real-life" distribution, rather than repeating the same situation over and over again. If we're super lucky, we also get to learn about the Central Limit theorem.

What does armchair psychology have to do with the Central Limit theorem? Or, what actually the Central Limit theorem is? Loosely, on the latter, it's a statistical theory that states that the sum of many independent random variables will tend to a normal (Gaussian) distribution. It's a very powerful theory that explains why so many things in the world are "normal." In layman terms, summing many observations from many distributions will result in a normal distribution, even though each one of the distributions might be very different. For example, adding the height and weight of a person, and their hair's RBG (red, blue, green) colour, and a score from a fair 20-sided die will result in a normal distribution, even though each one of these characteristics is distributed differently. (Actually, I don't know if these 7 characteristics are independent, but you get the point.)

What about psychology? Well, we all are different, obviously. The scale of the difference is dictated by many things, including past experiences and genes. Physical characteristics are easy to observe and throughout one's life they vary a little. The psychological characteristics, on the other hand, are much harder to observe, and they vary on a daily basis, depending on the "mood" we're in. For example, I was growing fast until I was 18, then maybe a tiny bit and as I get older I'll start shrinking a bit. The measured height is dependent on the time of the day; in the morning, assuming night of horizontal sleep, joints are relaxed and I'm about 1 cm taller than in the evening, after the whole day of gravity. It's a tiny change that no one notices. However, whether I like to be surrounded by people depends on if I had a good night sleep followed by a good cup of coffee. The others will, unfortunately, notice if I'm in the mood to chat, or I'd rather be on my own for a bit. That's all to say that people have many characteristics, both physical and psychological, and they are described with different distributions. Averaging that over the whole human population, we can get a normal distribution for each characteristic, and that statistical person is the Normal person.

It's a bit subjective how important the existence of the Normal person is. Some people care a lot about whether they're perceived as either "very normal" or "very not-normal" which, ironically, is also very normal. Some people might intentionally introduce sampling bias to subdivide the population such that they'll fit better with their wanted category. They might pick a specific value of a characteristic, call it "normal," and then measure everyone against that value. I might be tall for some people, others might call me average. Some people might be appalled by my stance on certain social issues, others would say it isn't enough. The Normal person is rather an intuitive and strong concept; even kids can tell you whether someone is normal or not. Maybe my upbringing was special but folks that stand out in a few characteristics were often called "weird" or "strange" or "not normal."

If that's so intuitive why the blog post? Because the Central Limit Theorem also applies to individual characteristics. I might react differently to the same situation. My reaction depends on yesterday's interaction with a spouse, whether I could get enough sleep, and whether the coffee was good. Everyone has some probability distribution of certain characteristics. Sampling from these distributions will result in an observation that someone might then call with a single word, like "introvert," or "pessimist," or "funny." Interacting with others means sampling from their distributions. The more time you spend with someone, in a wide variety of situations, the better approximation of their "normal" behaviour you'll get. The "normal," in this case, is what you'd mostly expect; however, same as with the global population, there is no "normal" me. Fortunately, we also have a built in pattern recognition that if we know of some characteristics we can deduce what others might be. For example, one does expect physically different people in Japan and in Namibia; Namibians are typically taller and have darker complexion. There exist many very tall and dark skin Japanease, but they aren't the "normal" (the most common) Japanease.

I guess the point I'm trying to make is that everyone needs to have a few observations before they can make a judgement about someone. The more observations the better approximation of the "normal" behaviour we'll get. However, bear in mind that through interacting, you're affecting the sampling and you're a random variable in someone else's distribution. Their next response will depend on your current response so the less "bad" samples you give them, the less they'll give back. Also, try to change your environment every once in a while. Every once in a while we'll sample an extreme value from the distribution, and we'll be "very extroverted" or "just assholes." When you're interacting with people in the same situation and the outcome is the same, and it's unpleasant, change the situation. Interact with them at a different time of the day, or in a different place, or in a different way. Or, have them interact with different you. Same as you draw from their characteristics, they draw from yours. If they seem strange or "not normal" to you, it might be because you're not normal to them.