The past two months, I’ve been completing University of Michigan’s fantastic Model Thinking course, available for free on Coursera. There’s so much to love about the modern world: you can learn interesting things through quality teaching, no matter where you are (well, you need a wifi), no matter when. And it doesn’t cost a cent!
Anyway, the course had a section about Random Walks, and it got me thinking. A while back I wrote about how the nonlinear life and our linear emotions aren’t exactly optimally suited to each other. Your brain craves signs of progress, so it could reward you with a burst of feel-good chemicals. Unfortunately, the nonlinear life doesn’t work like that. Often, you can spend days or weeks slaving away at the office/studio/whatever, not really moving forward – or even taking two steps back for each move forward. Despite the hours that you put in, the article/thesis/design never seems to be finished, making you question whether you’re really cut out for this kind of job. Perhaps you’d do the world a favor by setting your sights lower and working as a sales clerk instead.
Now, while watching one of the course lectures, I suddenly realized that the creative nonlinear work is exactly a random walk! I don’t claim this to be a unique insight or anything – I’m sure many of you have realized this before. But for the fun of it, it might be a nice exercise to show with a random walk model how the nonlinear life functions. At least in my own case, models often help to see the bigger picture, and forget about the noise in the short term. And who knows, maybe this will help to quell those linear emotions, too.
So, a random walk is very simple. In this case, let’s assume that we have a project that has a goal we’re trying to reach. Arbitrarily, let’s say that the completion means we reach a threshold of 100 points. Of course, these numbers are completely make-believe and I pulled them from my magical hat. Now, further, let’s assume that each unit of time – say 1 unit equals 1 day – means we have three possibilities: make progress, stay where we are, or take steps backward. In my personal experience, this is an ok model for work: sometimes you’re actually making progress, and things move smoothly. Sometimes, though, you’re actually hurting your project, for example by programming bugs into the software, which need to be fixed later on (just happened to me two weeks ago). Most often, though, you’re trying your best, but nothing seems to work. Maybe you’re stuck in a dead end with your idea, and need to change tack. Maybe you’re burdened with silly tasks that have nothing to do with the project. Well, I’m sure we all have these kinds of days.
So let’s again use my magical hat and pull out some probabilities for these options. Let’s say you have a 5% chance of making a great jump forwards (10 points), 25% chance of making 3 points of progress, 55% chance of getting stuck (0 points), 10% chance of making a mistake (-2 points), and a 5% chance of doing serious damage (-6 points). Now we just simulate these across and get a graph that shows your cumulative progress towards the goal (yes I'm doing this in Excel):
Anyway, the course had a section about Random Walks, and it got me thinking. A while back I wrote about how the nonlinear life and our linear emotions aren’t exactly optimally suited to each other. Your brain craves signs of progress, so it could reward you with a burst of feel-good chemicals. Unfortunately, the nonlinear life doesn’t work like that. Often, you can spend days or weeks slaving away at the office/studio/whatever, not really moving forward – or even taking two steps back for each move forward. Despite the hours that you put in, the article/thesis/design never seems to be finished, making you question whether you’re really cut out for this kind of job. Perhaps you’d do the world a favor by setting your sights lower and working as a sales clerk instead.
Now, while watching one of the course lectures, I suddenly realized that the creative nonlinear work is exactly a random walk! I don’t claim this to be a unique insight or anything – I’m sure many of you have realized this before. But for the fun of it, it might be a nice exercise to show with a random walk model how the nonlinear life functions. At least in my own case, models often help to see the bigger picture, and forget about the noise in the short term. And who knows, maybe this will help to quell those linear emotions, too.
So, a random walk is very simple. In this case, let’s assume that we have a project that has a goal we’re trying to reach. Arbitrarily, let’s say that the completion means we reach a threshold of 100 points. Of course, these numbers are completely make-believe and I pulled them from my magical hat. Now, further, let’s assume that each unit of time – say 1 unit equals 1 day – means we have three possibilities: make progress, stay where we are, or take steps backward. In my personal experience, this is an ok model for work: sometimes you’re actually making progress, and things move smoothly. Sometimes, though, you’re actually hurting your project, for example by programming bugs into the software, which need to be fixed later on (just happened to me two weeks ago). Most often, though, you’re trying your best, but nothing seems to work. Maybe you’re stuck in a dead end with your idea, and need to change tack. Maybe you’re burdened with silly tasks that have nothing to do with the project. Well, I’m sure we all have these kinds of days.
So let’s again use my magical hat and pull out some probabilities for these options. Let’s say you have a 5% chance of making a great jump forwards (10 points), 25% chance of making 3 points of progress, 55% chance of getting stuck (0 points), 10% chance of making a mistake (-2 points), and a 5% chance of doing serious damage (-6 points). Now we just simulate these across and get a graph that shows your cumulative progress towards the goal (yes I'm doing this in Excel):
So, in the graph there are several periods when it’s just going downhill, or plateauing for several time periods. Even though the numbers are really made up, I feel the above graph is actually a pretty decent example of how the nonlinear work often feels. However, there’s still the additional complication: the emotions.
Suppose that our emotions work as follows. If you’re making progress, you feel good. And this is mostly irrespective of how much progress you’re making. Suppose the same holds for drawbacks – it hurts, but it hurts almost as much to look for a bug for two hours or the full day. Finally, I’ll assume that if you’re not moving anywhere, you inherit the feeling from the day before. Now, I realize this is probably not how emotions really work (we’re often annoyed by our administrative duties, for example). But on the other hand, when I have a day I have spent at a dull seminar, I seem to find myself looking back a bit to evaluate the progress. The “inherit from t-1” rule tries to describe this: I feel good if the past has been good, and I feel annoyed if the past wasn’t successful. Why just t-1 and not the actual level? Well, I’ve also found that it’s really hard to evaluate how far the project actually is, which makes that option unrealistic. And when looking back, our memories are much stronger from the immediate past than the long-gone part. In short, I’m modeling here the short-sightedness. The actual progress-emotions payoff table looks like this:
Suppose that our emotions work as follows. If you’re making progress, you feel good. And this is mostly irrespective of how much progress you’re making. Suppose the same holds for drawbacks – it hurts, but it hurts almost as much to look for a bug for two hours or the full day. Finally, I’ll assume that if you’re not moving anywhere, you inherit the feeling from the day before. Now, I realize this is probably not how emotions really work (we’re often annoyed by our administrative duties, for example). But on the other hand, when I have a day I have spent at a dull seminar, I seem to find myself looking back a bit to evaluate the progress. The “inherit from t-1” rule tries to describe this: I feel good if the past has been good, and I feel annoyed if the past wasn’t successful. Why just t-1 and not the actual level? Well, I’ve also found that it’s really hard to evaluate how far the project actually is, which makes that option unrealistic. And when looking back, our memories are much stronger from the immediate past than the long-gone part. In short, I’m modeling here the short-sightedness. The actual progress-emotions payoff table looks like this:
So with these assumptions, we get the following graph portraying emotions:
Now this is pretty interesting! You can see how 1) there’s a lot of fluctuations back and forth, and 2) how there’s still “runs”, ie. the same emotional state tends to linger for a while. If you run the numbers, with this particular string of successes and failures you get 99 positive time periods and 51 negative ones, out of the total 150 periods I ran the simulation for. I think the above graph is quite a good summary of how the nonlinear life often feels: you love you’re job, but you’re not above hating it when things are not going well.
A final word of warning: this was of course just one simulated outcome. With the exact same parameters, you can get project outcomes that never finish, that run into negative progress, that finish in less than 30 periods, etc. They are not very nice for terms of a presentation, but also capture the great amount of uncertainty in a nonlinear project. Sometimes it just falls apart, and after 50 periods you’re back to exactly where you started. Or that a project you thought takes 6 weeks takes 16 weeks instead. Well, I’m sure everyone has had these experiences.
A final word of warning: this was of course just one simulated outcome. With the exact same parameters, you can get project outcomes that never finish, that run into negative progress, that finish in less than 30 periods, etc. They are not very nice for terms of a presentation, but also capture the great amount of uncertainty in a nonlinear project. Sometimes it just falls apart, and after 50 periods you’re back to exactly where you started. Or that a project you thought takes 6 weeks takes 16 weeks instead. Well, I’m sure everyone has had these experiences.
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