Scott Young wrote a good post about two types of progress when learning something new: logarithmic and exponential.

Anything you try to improve will have a growth curve. Imagine you ran everyday and you tracked your speed to finish a 5-mile course. Smoothing out the noise, over enough time you’d probably get a graph like this:

Here, improvement works on a logarithmic scale. As you get better, it gets harder and harder to improve. Elite athletes expend enormous effort to shave seconds off their best times. Novice athletes can shave minutes with just a little practice.

Logarithmic growth is the first type of growth. This is where you see a lot of progress in the beginning, but continuing progress is more difficult.

Now imagine a different graph. This time you’ve build a new website you update regularly and you’re measuring subscribers. This graph would likely look very different:

This is exponential growth, the second type of growth. Website traffic is often exponential because as a blog attracts more readers, there are more opportunities for word about the blog to spread. A blog with zero traffic also has zero word of mouth.

I’ve noticed most things tend to be either logarithmic or exponential growth. Despite this, linear progress is what most people expect. We tend to expect things to move in the same direction or rate as they have in the past. This violation of our expectation leads to some mistakes in how we set goals and act on them.

 Scott later offers advice on how to tell whether a given activity is one or the other:

The easiest way to tell is to look at how other people have progressed in that field. Don’t pay attention to their rates, just pay attention to the shape of their growth trajectory. Is it the kind that slows down with mastery or speeds up?

I’ve written about related themes in the past. Here’s my post about efforts where you see continuous, ongoing improvement vs. quantum leaps. Here’s my post about how formal schooling is an information rich environment where you receive constant feedback on how you’re doing, whereas in the real world you sometimes have to go months without knowing if you’re on the right track.