Learning curves

I recently summarized the related work for two research projects in two fields. As both fields were new to me, this experience allowed me to practice and to think about self education.

When learning about a new field, we hope to gain maximal knowledge in minimal time. Visualize this process with a learning curve. The key is to do the right things at the right time, depending on the field, our goals, and our current stage.


  • Stage 1: solid preparation. At this stage, we gain a lot of information from almost every paragraph we read. Skimming doesn’t seem to help much here; it could tell us some keywords in the field, but these keywords are not self-explanatory. So, at this stage, read carefully and take notes promptly.
  • Stage 2: fast growth. This is the happiest stage where almost any effort can pay off and bring a sense of accomplishment. At this stage:
    • Skimming can be quite productive if our goals are specific, such as to summarize the related work for a research project. Since we now understand some jargons and important questions in the field, each paper fits easily into the big picture. So, in this case, skim lots of papers and understand how these papers relate to each other.
    • Careful reading can be worthwhile, too, if we our goals are more general, such as to see what’s going on. Random pieces of information can fill in gaps in our knowledge, even if they might not be the “most important” pieces.
  • Stage 3: bottleneck. At this stage, learning slows down. We now know a lot about the field in general, and we are quite satisfied about this accomplishment. The only remaining problem is not finishing some specific goals, such as concluding how a research project could contribute to the field. To achieve these specific goals, we need to understand the relevant technical details more deeply. So, at this stage, focus on the specific goals and work hard.

Different fields have different learning curves. After decorating the curves with milestones,* some fields may look like this:


In these fields, stage 1 is long. Concepts and theorems build upon each other. Entering these fields can be challenging. Experts in these fields are irreplaceable.

Other fields may look like this:


In these fields, stage 1 is short. Many concepts are comprehensible in isolation. Self-educating these fields can be quick and efficient. But to become real experts, we need to go through the longer stage 3.

Similar curves can describe not only the speed of learning knowledge. They can also desribe speeds of other processes, such as the speed of solving a problem or the speed of discoveries in a field.

In life, we deal with many problems at once. Each problem has a curve characterized by the problem, our goals, and our current stage. Visualize these curves. Estimate how much time is needed to make reasonable progress. Allocate time accordingly.

* Inspired by The illustrated guide to a Ph.D.