Group learning to dance bachata

When we are learning a new skill, we usually expect that our results are going to be a linear function of the time we invest and that our progress is going to be quite fast. In this post, I will argue that these two expectations often lead to disappointment and wanting to give up when confronted with reality. However, learning has a compound effect. This means that your skill improvement will be tiny at the beginning, but over time the cumulative improvements will take off. This will have a massive impact on your skill level outperforming your initial expectations in the long run.

How Linear Improvement Looks Like

Imagine that today you are starting to learn a new skill and that you are going to focus on improving this skill for an hour a day for the next 365 days. In this scenario, the time and effort you invest in learning the new skill are constant. Let’s say that your initial level is 1 and that every day you improve 1%.

If learning worked as a linear function of the time you invest, the graph of your learning improvement over a year would look like the following figure.

How learning would look like with a 1% daily linear improvement

The figure shows a positive linear relationship between days of practice (on the x-axis) and the skill level (on the y-axis). Under the assumptions, after 1 day of practice, you are 1% better, after two days 2% better, etc. At the end of the year, your skill level would have improved 365%. That is, your level at the end of the year is 3.65 times your initial level!

An improvement of this magnitude is amazing. However, you should often be able to improve much more if you commit 1 hour a day for an entire year. Why? Because of the compound effect.

The Compound Effect of Learning

To understand how learning works, it is useful to think about saving. If you deposit $1000 into a saving account with a fixed interest rate of 1%, the yield it produces is not only 1% of your initial deposit. This is known as simple interest. Saving accounts don’t work in this way. The interest is calculated with the sum of your initial deposit and the accumulated interests from previous periods. That is, if the first 1% yield produced $10, the second yield would be calculated with the sum of your initial $1000 plus the $10, producing $10.1 in the second period instead of just $10. This is known as compound interest.

Learning a new skill is like the compound interest in your saving account and, thus, follows an exponential function. This entails that the improvement when learning a new skill won’t be very impressive at the beginning. In the initial stages, a 1% improvement following an exponential function would be difficult to distinguish from the linear function in the figure above. However, the compound effect of a daily 1% improvement makes your skill level skyrocket after a while. The consequence is that your skill level would be 37.38 times your initial level after a year!!!

The compound effect of learning a new skill. The graph shows a 1% daily exponential improvement in skill level. 

The Valley of Disappointment. Comparing 5% daily linear improvement to 1% daily exponential improvement

The figure shows that our skill level improves slower than our expectations at the beginning, which corresponds to the area labelled “the valley of disappointment”. This is a keystone in any learning project as it’s the time when many experience frustration and are tempted to quit. People in this mindset tend to self-talk in a defeated manner:

• “I’ve been studying French for two years and I still cannot hold a conversation. This must mean I’m very bad at French”.
• “After 6 months at the gym, I still don’t see results in the mirror. I’m wasting my time. I’ve never going to be smoking hot”.
• “Everybody seems to be doing better than me in my dance class. Oh, this is so frustrating”.

The valley of disappointment is probably the greatest threat to our progress in learning a new skill. It negatively affects our motivation. We start missing workouts in the gym, skip some hours of dancing practice, and begin to engage in other activities when we should be studying French. As a consequence, the moment in which your skill level takes off is moved further and further away. But it could be even worse: giving up and never learning a skill that we previously thought was going to make a positive change in our life.

Antidotes to the Valley of Disappointment

Think about Boiling Water

To overcome the temptation to quit when you feel you aren’t learning fast enough, it is important to know that this is the normal trajectory of learning [1]. The benefits of spending time learning a new skill are not immediate. They won’t be clearly perceptible until a certain amount of work has already been done.

It’s like boiling water. If you heat cold water in a cooking hob, the temperature will progressively increase. When the water is at 27 degrees nothing perceptible happens. It’s the same at 28 degrees, and 29, 30, and 31 degrees. But…what happens at 32 degrees? The water boils!

Learning is very similar to heating water. 

Be Aware that if You Don’t Keep Practicing Your Skill Will Deteriorate

One of the consequences of not continually practicing a skill is that we will tend to forget it. If you don’t play the guitar for over a decade, your skill will begin to be quite poor. If you don’t communicate in French after learning French, you will lose your fluency, etc. The rate of deterioration of your previous learning depends on multiple factors. However, the deterioration always happens when you don’t practice a complex skill. It’s important to be aware that, if you stop practicing, you won’t only be moving away from the moment in which your skill takes off. You also will make your skill poorer and will need to regain your previous level first before keeping up the progress.

Take Home Message

In this post, I showed the long-term consequences of regular learning practice. Over the short term, the improvement is tiny but over time the cumulative improvements have a compound effect. This will make your learning take off which can have a massive impact on your skill level. When doubt creeps, being aware of this phenomenon will help you to keep going.

Dr Ángel V. Jiménez

Notes

[1] There is variation in the pace people learn a skill and this depends on multiple variables. Some of them are the learner’s age, motivation, and natural talent; the number of hours of practice, the method used, the teacher’s effectiveness, and the similarity with skills previously learned. These variables can affect the improvement rate (say 3% improvement instead of 1%) but the long-term trajectory (the form of the curve) should be the same given identical intervals between training sessions.

References

This blog post is based on the first chapter of James’ Clear Atomic Habits, which is a book I strongly recommend.