The concept of a "learning curve" is a graphical representation illustrating how proficiency in a task improves with experience. While commonly understood today, its origins trace back to psychological studies in the late 19th century. Over time, this idea has expanded significantly, moving beyond individual learning to encompass broader interpretations in economics, industry, and even machine learning, reflecting its versatility in describing improvement
over time.
Early Psychological Foundations
The earliest known work contributing to the concept of the learning curve comes from Hermann Ebbinghaus, whose memory tests were published in 1885. Ebbinghaus conducted a series of experiments involving memorizing nonsense syllables and recording the success rate over multiple trials. Although his translated work does not explicitly use the term "learning curve," his diagrams clearly show learning plotted against the number of trials. He also observed that scores could decrease or even oscillate, indicating the complex nature of learning.
The term "learning curve" itself first appeared in 1903, stemming from a study by Bryan and Harter on the acquisition of telegraphic language. Their research identified a learning curve characterized by a rapid initial rise in proficiency, followed by a period of slower learning. This early description highlighted the convex shape of the curve relative to the vertical axis. Psychologist Arthur Bills further elaborated on learning curves in 1934, providing detailed descriptions of various properties, including negative acceleration, positive acceleration, plateaus, and ogive curves, thereby solidifying its place in psychological research.
Mathematical Modeling and Examples
In its essence, a learning curve plots proxy measures for implied learning or progression toward a limit against experience. The horizontal axis typically represents experience, which can be measured directly as time spent on an activity, or indirectly through related metrics like the number of trials or total units produced. The vertical axis quantifies "learning" or "proficiency," which can either increase (e.g., a test score) or decrease (e.g., time to complete a task).
While an individual's performance curve can be erratic, showing increases, decreases, or plateaus, averaging the results of many individual trials often yields a smooth curve that can be described mathematically. Several main functions are used to model these curves. The S-curve, or sigmoid function, is considered the idealized general form, depicting a slow start, followed by rapid improvement, and then a leveling off as the learning activity approaches its limit. Other common models include exponential growth, where proficiency can increase without bound, and exponential rise or fall to a limit, where skill approaches a maximum in a manner similar to a capacitor charging or discharging. The power law, often used for decreasing performance metrics like cost, is another significant model, appearing as a straight line when plotted logarithmically. This specific application, plotting unit cost against total production, is known as the experience curve and is widely used in industry for cost projections.
Broader Interpretations and Applications
Initially rooted in educational and behavioral psychology, the concept of the learning curve has evolved to encompass a much wider range of applications. Terms such as "experience curve," "improvement curve," "cost improvement curve," "progress curve," "progress function," "startup curve," "efficiency curve," and "learning rate" are now often used interchangeably to describe similar phenomena of improvement over time. In economics, the subject extends to rates of "development," referring to a system-wide learning process with varying rates of progression.
Generally, all learning processes exhibit incremental change over time, often following an S-curve pattern, though its appearance can vary depending on the observation timescale. This broader interpretation has also become linked with the evolutionary theory of punctuated equilibrium and other forms of revolutionary change in complex systems. It applies to fields such as innovation, organizational behavior, and the management of group learning. These processes, characterized by the rapid emergence of new forms, are understood to involve complex learning within the systems themselves, displaying curves of changing rates that accelerate and decelerate.
