Inflection point

When practicing a skill, at some point, an effect that is opposite to diminishing returns starts to show. The new skill begins to benefit other aspects of activity, even those that are seemingly unrelated to the original practice.

In photography, an example of this would be building a portfolio that attracts new work, which in turn enhances the portfolio even further. In other areas, examples of reaching the inflection point include learning the basics of a foreign language, which enables one to read books, connect with people, etc., or reaching a certain level of physical fitness, which enables a whole new range of activities: sports, work, travel, etc.. Malcolm Gladwell described a similar phenomenon of viral spread of ideas in his book “The Tipping Point.”

There is an interesting analogy between reaching the critical level of mastery of a skill and physical phenomena in fluid mechanics, which I teach to students. Particularly, separation of a boundary layer under the influence of an adverse pressure gradient happens after an inflection point (in a mathematical sense) in the local velocity profile occurs.

Just like in nature, though, predicting when the inflection occurs (in the case of skill development, how much practice is required before exponential changes start to happen) is most difficult. When we are just starting, the only comfort we can take is that the critical transition will happen for sure – this seems to be the law of nature.