The Model Thinker summary

In politics, polls are a fact of life. Polls help people visualize the state of a race, and in the past, they were usually taken to be more or less reliable predictors of who’d win. In recent elections, though, this hasn't always been the case – presidential candidates have been favored to win states by a landslide, only to lose or squeak by with a narrow win when the day comes.

There are a lot of theories about why this is, but one reason surely has to be the creators of the polls: human beings. Humans are fallible. We make mistakes. So the same holds true for our models. Although they may rely on logic and math, models are ultimately things that we’ve created – meaning they can be wrong, just like us.

Most teachers would probably say that C students are pretty common. Intuitively, that seems to make sense – a C is, by definition, pretty average. But why is that? What makes us think of a C as the average grade? The answer’s simple: Grades tend to follow a normal distribution.

Now, a distribution assigns probabilities to events or values. A normal distribution is a spread of values that cluster in a symmetrical pattern around one central mean. It’s also known as “the bell curve,” because the cluster of values forms the shape of a bell, gently rising, then peaking and falling again.

Normal distribution isn't the only important type of distribution. Some data sets conform to what’s called a long-tailed distribution. Remember how normal distribution is shaped like a symmetrical bell? Well, long-tailed distribution looks like the tail of a creature standing just outside the graph, its “long tail” running along the horizontal axis when the distribution is graphed.

One common type of long-tailed distribution is what’s known as a power-law distribution, or “power law.” A power law usually describes a system in which something is amplified or exaggerated.

Although linear models are some of the simplest of all models, they can help to explain quite a few of the systems in operation in our world – like the effects of education on income, or of exercise on gains in life expectancy. So how do we know if a phenomenon can be explained using a linear model?

Well, when you graph a linear function you get a straight line. This fact is important: it means that if you plot a set of values on a graph and can then draw a line straight through them, the relationship between the variables can be described using a linear model.

Imagine that you’ve been on a long hike and you haven’t eaten in hours. You’re hungry, to say the least – and so, to reward yourself, you order a large pizza as soon as you get home.

The first slice is divine. The second is delicious too. But by the time you’re nearing the end of your meal, you’re not even paying attention to how it tastes. Your attention has simply drifted.

People can be troublesome: if that’s true when it comes to real life, then it’s doubly true when it comes to modeling.

Unlike bowling balls or weather cycles, humans have agency. We have minds of our own and we use them to make decisions. We experience social pressure, we have different preferences, and we often make mistakes. Sometimes, we might even learn from those mistakes.