Invest a little time in reading this and reap the value - which is in itself an example of a power-law!Ī power law is often represented by an equation with an exponent:Įach letter represents a number. Understanding the math behind power laws is worthwhile to grasp their many applications. If parts of this post look intimidating to non-mathematicians, bear with us. As a mental model, power laws are versatile, with numerous applications in different fields of knowledge. Power laws are interesting because they reveal surprising correlations between disparate factors. In both of our examples, a small investment of time at the beginning of the endeavor leads to a large increase in performance. While the first few runs are incredibly difficult, the person’s endurance increases rapidly with the passing of each week, until it levels off and diminishing returns set in again.īoth of these situations are examples of power laws - a relationship between two things in which a change in one thing can lead to a large change in the other, regardless of the initial quantities. Now, let’s imagine that our frustrated weightlifter decides to take up running instead. Their motivation is sapped, and they find themselves getting injured, without any real change in the amount of weight they can lift.

Perhaps they resort to taking performance-enhancing drugs or training more often. At first, they could increase their strength by as much as 10% per session now it takes months to improve by even 1%.

Eventually, however, their progress slows down. But as they invest more time, they find that for each training session, their strength increases a surprising amount.įor a while, they make huge improvements.

“The greatest shortcoming of the human race is our inability to understand the exponential function.” - Albert Allen Bartlett Defining A Power LawĬonsider a person who begins weightlifting for the first time.ĭuring their initial sessions, they can lift only a small amount of weight.

Inverse fourth power law