Random walks

Computer-generated random walks

Random walks can create interesting visual effects. I came across a video from Khan Academy mentioning them, so I decided to create some simple drawings. In a random walk, a decision at each step is made where to go further. Different parameters like initial position, direction, speed of movement, length of the step and color can all play a role in how a final drawing can look like. The longer the sequence of unique decisions is, the more unique each path becomes. If we look more closely, we could almost perceive how this adds character to each color. In a sense, a complete random walk can act as a history or ID of something.

Companies often seek ways to learn more about the paths of their customers to serve them better. Starbucks has recently started to sell coffee with trucks that follow the movement of the students during the day. Wherever they go, they have access to fresh coffee for longer periods of time. When each preference and purchase can be tracked universally as they are today, companies will increasingly have the power to follow individual paths back in time. Although this allows them to make more informed business decisions, it can also intefere with our privacy. Individual purchases now no longer count as interesting, when more sustainable profits can be seen only through the examination of our paths—however random they might be,—possibly followed by DNA analysis in the future.

Random walks can be seen as a mechanism for exploration. Imagine that you are in a new city, where you don't know anyone and you also forgot to take your map-loaded mobile phone. You could buy a map just to see the names of the buildings and streets, but they aren't likely to tell you much. Instead, it may be more practical to go on a random walk. If you are lost by default, this may seem to be the wrong thing to do, but not when you realize that “lost” doesn't have a form “lost-er”. This will allow you to see new places and people you wouldn't otherwise see if you always went to the same city and always spoke with the same people. Everything becomes more memorable, since you are not merely looking at things in the way a regular passerby does. A potentially chaotic new environment asks for your orientation skills. But the heightened attention with which you approached your walk allows you to easily return to the starting point if needed. This means that you are safe not to go through the same path twice; doing this won't help you to learn much more about the some place—it is still there. At the end of the walk, which is likely to be exhaustive, you have learned where each building is located, why it exists and how it relates to you, how to reach some new destinations, how some important streets are called, how some people's names are pronounced. This means that a random walk also serves to gather important information.

Is our surfing on the web a random walk? Not always, but it can be. At least we may think so. In terms of exploration, what is valid for random walks in real life is also valid for those that happen online. On the surface, we see links that connect us to different sites and as we move from one to another, we leave a path trace that improves analytics software. Meanwhile, a hidden router somewhere is determining the best way to send us to the destination by considering the path of least resistance. Even in case we perceive our random clicks as a random walk, what happens in the background is that the router's decisions aren't random, but happen in knowledge of the current environment.

Some time ago I saw a photo of something resembling a large pond. It made me think of which way I would go to reach what was distant. The photographer was quite good, because from his viewpoint the pond looked perfectly oval and it seemed that you would need to sidestep a lot in either direction (either left or right) to avoid it. The fact that I couldn't decide which direction would be shorter made this photo so strangely interesting to me. At the same time, since it was taken at night, on the left was some extravagant looking building (possibly a hotel) and on the right were some very beautiful and romantic-looking lights. So in terms of which direction would lead to a better experience it seemed undecideable too. The roads and cars circumventing the pond looked quite small, almost surreal, which was a sign that both sides had a lot to explore. But the need to choose a direction in this case seemed to block my choosing. A machine can decide this in milliseconds. If we realized that we could toss a coin, this would be possible in a couple of seconds. But thinking seems to be endless.

What happens when we are presented with the infinite choice of the random walk in all directions and not just two possible paths? We feel terrified to the point of crumbling. But this doesn't change the fact that our life is the walk of choices we make every day. Introducing randomness in these choices, when we don't intend to learn/expand our worldview, but during our work, cancels our previous efforts and makes us forget what is important in our life. The dirigent pays attention to each small gesture and so should we.

When was the last time you were on a random walk? Did you see something beautiful or learn something unexpected? Which color were you?