What if we could use mathematics to figure out how to make ourselves happier? I submit for your consideration that it is, in fact, possible. In this post, I construct a simple mathematical model of experiencing the world, and then derive some principles from the model which I believe are applicable to real life. Let’s begin! Consider the following graph of my happiness over the course of a day:
![[Happiness on a Typical Day]](http://markpneyer.com/images/happiness_graph/HappinessGraph_SampleDay.png)
The day starts off well, and reaches a peak when I eat my breakfast of eggs and turkey bacon. Yum. I get into my car, and there’s a wreck on 15-501, so I’m late getting to work. My mood goes down, but it’s still positive. Upon arriving at work, I realize that I’ve fallen seriously behind in a big important project, so my mood falls. As I work harder and harder, I keep realizing how much more work I have to do. My mood plummets, until lunch time. A dozen buffalo wings provide a brief respite and put me in a better mood, but I’m still frustrated about work. I have time to think at lunch, though, and I realize I can save myself some time if I take a new approach that I hadn’t though of. My mood improves, and by the end of the work day I’m happy again. After I get home from work, I relax by playing a game of Left 4 Dead with some friends, and my mood improves back to where it was.
The above graph was generated using a type of randomized noise function called Perlin noise. In other words, I modeled happiness as simply the summation of random waves. What better models can we use to describe and predict how people can become more happy? If happiness is a function of time, the simplest model says that we just choose to be happy all of the time. I would argue that the ‘choose to be happy’ model is too simple to be very useful. Happiness isn’t a simple binary choice: It’s hard to choose to be happy when it’s cold and dark outside, and you feel tired, lonely, and hopeless about the future. Conversely, It’s easy to choose to be happy when it’s sunny outside, you’ve just enjoyed a nice meal with friends, and now you’re playing a sweet designer German board game, like Dominion. These examples are taken from points in my life. Your mileage may vary. The examples demonstrate that, very often, external factors in your life play a huge role in how happy you are. I believe it is possible to influence those external factors, but influencing them Isn’t as simple as just saying “I choose the happy path.”
A more predictive model of happiness must therefore take into account external factors as well as personal choices. After giving this idea a lot of thought, I came up with a model, based upon the concept of ‘Experience-Space.’ Experience-Space is the set of all possible experiences that an individual could have. Points in Experience-Space are points in both time-space and sensation-space. In other words, a single point in experience space describes the exact feelings you feel at a given time. To make things as easy to understand as possible, we will say that the only sensation one can experience is happiness, and that, at any given instant in life, one can make one of three choices. Why three? When there is only one sensation, Experience-Space becomes two dimensional: time is one dimension, and the experience you have is the other dimension. We can represent life with an image. Your experience of life is a path traced by a pixel through that that image from left to right. At each step in time, the pixel can either go straight forward, diagonally up, or diagonally down. We will label these choices straight, up, and down.
Look at this example:
In this example, the person is currently happy. They have a choice to make: in the next time tick, they will be happy if they choose straight or down, unhappy if they choose up. This is a very simple model, but it proves surprisingly powerful in generating useful predictions about how we can make ourselves happier.
Suppose you know everything about the universe, and your goal is to be as happy as you possibly can. You start out at some initial point in experience-space, and your goal is to maximize the sum of the happiness of the experiences you have over the course of your entire life. (Is that a reasonable goal? A question for another blog post!). Suppose that experience space looks like this:
If this is your universe, wherever you start out, your most logical move is to always choose to go down (when possible) and then go straight along the bottom edge of the graph, when (if) you ever reach it. That’s easy enough. Let’s consider a more complicated model of the world:
In this model, most experiences are either slightly positive or slightly neutral. There are quite a few “great” experiences, and a small number of “terrible” experiences. These big experiences are so big that they affect you for some time after you experience them. How would you navigate this graph, in order to maximize your happiness? The problem begins to look like an artificial intelligence. I’m not going to go into artificial intelligence algorithms such as A* search (as much as I’d like to.) Instead, I’m going to draw to draw some conclusions from this model.
In the real world, we don’t know the entire universe ahead of time: we only know the choices that we have made, and their ramifications. In other words, our graphs look like this:
That’s not a lot to go on. It would be hard to take that information and build a model of the world and use it to predict where to go next. While walking like this, you’d probably notice that some areas were nicer than others, and that the really nice areas and really bad areas tended to clump together, but you’d still have a hard time determining which areas to go towards. Suppose there are 50 people in the universe, and you all share information about the choices you have made and the results those choices have brought you. Then, your picture of the universe looks like this:
This picture is much more complete than the picture you were able to generate by yourself. By using information you glean from asking others about the choices they make, you can make yourself happier.
Conclusion: Talk to as many people as you can, and learn about their experiences. Doing this talking will allow you to gain a much more accurate model of the world as a whole, in order to determine what will make you happy. Ask people about their history, and specifically about choices they have made that made them happy or unhappy.
I hope to write more on this subject in the future. Stay tuned!