Focus on the Trajectory, Not the Current State
(This article was initially published on 31.01.2023 on my website.)
During the winter semester, I was taking an Abstract Algebra I course. I struggled a lot with the topic and felt despair and anxiety, worrying about how I would pass the exam. The past exams were public, so I knew what to expect. However, achieving 50% of the exam necessary to pass seemed unreachable.
I did not have many exams this semester, so I had a lot of time to prepare. I devised a rough plan of things to learn: revisiting basic concepts, learning to solve exercises in every exam (with some variations), and memorizing bits of theory from past exams. I could see the progress I was making after a couple of days or a week, and about a week before the exam, I started to feel like I might be able to make it - which, fortunately, turned out to be correct.
Small Steps
The idea of making small but steady improvements is not anything new. It has been made clear to me in a great book Atomic Habits. However, my recent experience with the exam led me to think about the benefits and broader application of the idea. The framework looks something like this:
Set a goal and a path to get there
Focus on the rate of progress towards the goal
Occasionally reevaluate both the goal and means of getting there
Benefits
For me, the main benefit of the framework is the positive feedback loop of noticing the progress. It was difficult for me to focus on my improvements if I knew that I was still far away from knowing enough to pass the course. However, I could observe easily that now I can reliably use one more technique to solve one task from the exam. It also reduced anxiety - I could focus on what I was learning instead of the large remaining gap in my knowledge. This gap could be so intimidating as to hinder my resolve to work on the problem.
I also find that this makes learning more effective in two ways: It is easier to optimize the process of learning by focusing on small components. And by occasional reevaluations of the goal and the state, I could pause to think if the progress and the goal itself are still set correctly or try to change it accordingly.
Other Applications
I find thinking in trajectories useful in more broad domains. For example, extrapolating the idea to my life is valuable, although sometimes challenging: Where do I want to be in some time? What is necessary to achieve that? How to do that better/faster?
Another area where it is applicable is when observing other people who are more competent than me in some domain. I try to see them as a demonstration of what is possible, and then think about the path that would be needed to get there, and focus on that path instead of the gap between my and their abilities.
It is also useful in thinking about trends, e.g. in technology. Sometimes it is more insightful to see the pace of technological improvement rather than the current capabilities.
Anyway, I use these lenses to see this post as well. It is a long way to becoming a decent writer. But hopefully I am making progress, and that is what I should pay attention to.