This is the second in a series of posts on mathematical metaphors. Don’t let the topic scare you. We all use these metaphors, most of us use them every day.
This is a graph of an exponential function. It is the second most common metaphor, and almost as often wrong as the first.
This is the graph of compound interest. While the previous linear graph is often misapplied to daily life, relationships, jobs, and happiness, the exponential graph is usually misapplied in business and science.
Scientists take a broader view. Even though a small section of an exponential curve looks linear, the whole picture is radically different. An exponential is accurate over a longer period than the linear metaphor, but still misleading.
The population of earth is an exponential. The growth of a successful start-up company is also exponential. In fact, this is the definition of success for most companies. For years the capability of computers matched this metaphor. (See Moore’s Law).
Some people see the world as exponentials. They expect each success to be followed by two more and then four more, as small successes give birth to large successes.
In politics, this metaphor breeds extreme responses to elections, with the both the winners and the losers expecting dramatic changes.
Reality has never delivered on this model of exponential growth for the long term, yet people continue to hold onto this idea.
Stay tuned. There are better metaphors.