Learning curve
Encyclopedia
A learning curve is a graphical representation of the changing rate of learning
(in the average person) for a given activity or tool. Typically, the increase in retention of information is sharpest after the initial attempts, and then gradually evens out, meaning that less and less new information is retained after each repetition.
The learning curve can also represent at a glance the initial difficulty of learning something and, to an extent, how much there is to learn after initial familiarity. For example, the Windows program Notepad is extremely simple to learn, but offers little after this. On the other extreme is the UNIX terminal editor Vim
, which is difficult to learn, but offers a wide array of features to master after the user has figured out how to work it. It is possible for something to be easy to learn, but difficult to master or hard to learn with little beyond this.
in 1885. He found that the time required to memorize a nonsense word
increased sharply as the number of syllables increased. Psychologist Arthur Bills gave a more detailed description of learning curves in 1934. He also discussed the properties of different types of learning curves, such as negative acceleration, positive acceleration, plateaus, and ogive
curves. In 1936, Theodore Paul Wright
described the effect of learning on labor productivity
in the aircraft industry
and proposed a mathematical model of the learning curve.
The economic learning of productivity and efficiency generally follows the same kinds of experience curves and have interesting secondary effects. Efficiency and productivity improvement can be considered as whole organization or industry or economy learning processes, as well as for individuals. The general pattern is of first speeding up and then slowing down, as the practically achievable level of methodology improvement is reached. The effect of reducing local effort and resource use by learning improved methods paradoxically often has the opposite latent effect on the next larger scale system, by facilitating its expansion, or economic growth
, as discussed in the Jevons paradox
in the 1880s and updated in the Khazzoom-Brookes Postulate
in the 1980s.
and behavioral psychology, the term has acquired a broader interpretation over time, and expressions such as "experience curve", "improvement curve", "cost improvement curve", "progress curve", "progress function", "startup curve", and "efficiency curve" are often used interchangeably. In economics the subject is rates of "development
", as development refers to a whole system learning process with varying rates of progression. Generally speaking all learning displays incremental change over time, but describes an "S" curve
which has different appearances depending on the time scale of observation. It has now also become associated with the evolutionary theory of punctuated equilibrium
and other kinds of revolutionary change in complex systems generally, relating to innovation
, organizational behavior and the management
of group learning, among other fields. These processes of rapidly emerging new form appear to take place by complex learning within the systems themselves, which when observable, display curves of changing rates that accelerate and decelerate.
Early uses of the metaphor focused
on the pattern's positive aspect, namely the potential for quick progress in learning (as measured by, e.g., memory accuracy or the number of trials required to obtain a desired result) at the introductory or elementary stage. Over time, however, the metaphor has become more commonly used to focus on the pattern's negative aspect, namely the difficulty of learning once one gets beyond the basics of a subject.
In the former case, the "steep[ness]" metaphor is inspired by the initially high rate of increase featured by the function characterizing the overall amount learned versus total resources invested (or versus time when resource investment per unit time is held constant)—in mathematical terms, the initially high positive absolute value
of the first derivative of that function. In the latter case, the metaphor is inspired by the pattern's eventual behavior, i.e., its behavior at high values of overall resources invested (or of overall time invested when resource investment per unit time is held constant), namely the high rate of increase in the resource investment required if the next item is to be learned—in other words, the eventually always-high, always-positive absolute value and the eventually never-decreasing status of the first derivative of that function. In turn, those properties of the latter function dictate that the function measuring the rate of learning per resource unit invested (or per unit time when resource investment per unit time is held constant) has a horizontal asymptote at zero, and thus that the overall amount learned, while never "plateauing" or decreasing, increases more and more slowly as more and more resources are invested.
This difference in emphasis has led to confusion and disagreements even among learned people.
for the limits of waste reduction generally. Approaching limits of perfecting things to eliminate waste meets geometrically increasing effort to make progress, and provides an environmental measure of all factors seen and unseen changing the learning experience. Perfecting things becomes ever more difficult despite increasing effort despite continuing positive, if ever diminishing, results. The same kind of slowing progress due to complications in learning also appears in the limits of useful technologies and of profitable markets applying to product life cycle management
and software development cycles). Remaining market segments or remaining potential efficiencies or efficiencies are found in successively less convenient forms.
Efficiency and development curves typically follow a two-phase process of first bigger steps corresponding to finding things easier, followed by smaller steps of finding things more difficult. It reflects bursts of learning following breakthroughs that make learning easier followed by meeting constraints that make learning ever harder, perhaps toward a point of cessation.
Learning
Learning is acquiring new or modifying existing knowledge, behaviors, skills, values, or preferences and may involve synthesizing different types of information. The ability to learn is possessed by humans, animals and some machines. Progress over time tends to follow learning curves.Human learning...
(in the average person) for a given activity or tool. Typically, the increase in retention of information is sharpest after the initial attempts, and then gradually evens out, meaning that less and less new information is retained after each repetition.
The learning curve can also represent at a glance the initial difficulty of learning something and, to an extent, how much there is to learn after initial familiarity. For example, the Windows program Notepad is extremely simple to learn, but offers little after this. On the other extreme is the UNIX terminal editor Vim
Vim (text editor)
Vim is a text editor written by Bram Moolenaar and first released publicly in 1991. Based on the vi editor common to Unix-like systems, Vim is designed for use both from a command line interface and as a standalone application in a graphical user interface...
, which is difficult to learn, but offers a wide array of features to master after the user has figured out how to work it. It is possible for something to be easy to learn, but difficult to master or hard to learn with little beyond this.
Learning curve in psychology and economics
The first person to describe the learning curve was Hermann EbbinghausHermann Ebbinghaus
Hermann Ebbinghaus was a German psychologist who pioneered the experimental study of memory, and is known for his discovery of the forgetting curve and the spacing effect. He was also the first person to describe the learning curve...
in 1885. He found that the time required to memorize a nonsense word
Nonsense word
A nonsense word, unlike a sememe, may have no definition. If it can be pronounced according to a language's phonotactics, it is a logatome. Nonsense words are used in literature for poetic or humorous effect. Proper names of real or fictional entities are sometimes nonsense words.-See...
increased sharply as the number of syllables increased. Psychologist Arthur Bills gave a more detailed description of learning curves in 1934. He also discussed the properties of different types of learning curves, such as negative acceleration, positive acceleration, plateaus, and ogive
Ogive
An ogive is the roundly tapered end of a two-dimensional or three-dimensional object.-Applied physical science and engineering:In ballistics or aerodynamics, an ogive is a pointed, curved surface mainly used to form the approximately streamlined nose of a bullet or other projectile.The traditional...
curves. In 1936, Theodore Paul Wright
Theodore Paul Wright
Theodore Paul Wright was a U.S. aeronautical engineer and educator. Born in Galesburg, Illinois, he served as acting president of Cornell University in 1951. Theodore P...
described the effect of learning on labor productivity
Labor productivity
Workforce productivity is the amount of goods and services that a worker produces in a given amount of time. It is one of several types of productivity that economists measure. Workforce productivity can be measured for a firm, a process, an industry, or a country...
in the aircraft industry
Aircraft industry
The aircraft industry is the industry supporting aviation by building aircraft and manufacturing aircraft parts for their maintenance. This includes aircraft and parts used for civil aviation and military aviation. Most production is done pursuant to type certificates and Defense Standards issued...
and proposed a mathematical model of the learning curve.
The economic learning of productivity and efficiency generally follows the same kinds of experience curves and have interesting secondary effects. Efficiency and productivity improvement can be considered as whole organization or industry or economy learning processes, as well as for individuals. The general pattern is of first speeding up and then slowing down, as the practically achievable level of methodology improvement is reached. The effect of reducing local effort and resource use by learning improved methods paradoxically often has the opposite latent effect on the next larger scale system, by facilitating its expansion, or economic growth
Economic growth
In economics, economic growth is defined as the increasing capacity of the economy to satisfy the wants of goods and services of the members of society. Economic growth is enabled by increases in productivity, which lowers the inputs for a given amount of output. Lowered costs increase demand...
, as discussed in the Jevons paradox
Jevons paradox
In economics, the Jevons paradox is the proposition that technological progress that increases the efficiency with which a resource is used, tends to increase the rate of consumption of that resource...
in the 1880s and updated in the Khazzoom-Brookes Postulate
Khazzoom-Brookes postulate
In the 1980s, the economists Daniel Khazzoom and Leonard Brookes independently put forward ideas about energy consumption and behavior that argue that increased energy efficiency paradoxically tends to lead to increased energy consumption...
in the 1980s.
Broader interpretations of the learning curve
Initially introduced in educationalEducational psychology
Educational psychology is the study of how humans learn in educational settings, the effectiveness of educational interventions, the psychology of teaching, and the social psychology of schools as organizations. Educational psychology is concerned with how students learn and develop, often focusing...
and behavioral psychology, the term has acquired a broader interpretation over time, and expressions such as "experience curve", "improvement curve", "cost improvement curve", "progress curve", "progress function", "startup curve", and "efficiency curve" are often used interchangeably. In economics the subject is rates of "development
Economic development
Economic development generally refers to the sustained, concerted actions of policymakers and communities that promote the standard of living and economic health of a specific area...
", as development refers to a whole system learning process with varying rates of progression. Generally speaking all learning displays incremental change over time, but describes an "S" curve
Sigmoid function
Many natural processes, including those of complex system learning curves, exhibit a progression from small beginnings that accelerates and approaches a climax over time. When a detailed description is lacking, a sigmoid function is often used. A sigmoid curve is produced by a mathematical...
which has different appearances depending on the time scale of observation. It has now also become associated with the evolutionary theory of punctuated equilibrium
Punctuated equilibrium
Punctuated equilibrium is a theory in evolutionary biology which proposes that most species will exhibit little net evolutionary change for most of their geological history, remaining in an extended state called stasis...
and other kinds of revolutionary change in complex systems generally, relating to innovation
Innovation
Innovation is the creation of better or more effective products, processes, technologies, or ideas that are accepted by markets, governments, and society...
, organizational behavior and the management
Management
Management in all business and organizational activities is the act of getting people together to accomplish desired goals and objectives using available resources efficiently and effectively...
of group learning, among other fields. These processes of rapidly emerging new form appear to take place by complex learning within the systems themselves, which when observable, display curves of changing rates that accelerate and decelerate.
Common terms
The familiar expression "steep learning curve" may refer to either of two aspects of a pattern in which the marginal rate of required resource investment is initially low, perhaps even decreasing at the very first stages, but eventually increases without bound.Early uses of the metaphor focused
Association (psychology)
In psychology and marketing, two concepts or stimuli are associated when the experience of one leads to the effects of another, due to repeated pairing. This is sometimes called Pavlovian association for Ivan Pavlov's pioneering of classical conditioning....
on the pattern's positive aspect, namely the potential for quick progress in learning (as measured by, e.g., memory accuracy or the number of trials required to obtain a desired result) at the introductory or elementary stage. Over time, however, the metaphor has become more commonly used to focus on the pattern's negative aspect, namely the difficulty of learning once one gets beyond the basics of a subject.
In the former case, the "steep[ness]" metaphor is inspired by the initially high rate of increase featured by the function characterizing the overall amount learned versus total resources invested (or versus time when resource investment per unit time is held constant)—in mathematical terms, the initially high positive absolute value
Absolute value
In mathematics, the absolute value |a| of a real number a is the numerical value of a without regard to its sign. So, for example, the absolute value of 3 is 3, and the absolute value of -3 is also 3...
of the first derivative of that function. In the latter case, the metaphor is inspired by the pattern's eventual behavior, i.e., its behavior at high values of overall resources invested (or of overall time invested when resource investment per unit time is held constant), namely the high rate of increase in the resource investment required if the next item is to be learned—in other words, the eventually always-high, always-positive absolute value and the eventually never-decreasing status of the first derivative of that function. In turn, those properties of the latter function dictate that the function measuring the rate of learning per resource unit invested (or per unit time when resource investment per unit time is held constant) has a horizontal asymptote at zero, and thus that the overall amount learned, while never "plateauing" or decreasing, increases more and more slowly as more and more resources are invested.
This difference in emphasis has led to confusion and disagreements even among learned people.
Learning curve models
The page on "learning & experience curve models" offers more discussion of the mathematical theory of representing them as deterministic processes, and provides a good group of empirical examples of how that technique has been applied.General learning limits
Learning curves, also called experience curves, relate to the much broader subject of natural limits for resources and technologies in general. Such limits generally present themselves as increasing complications that slow the learning of how to do things more efficiently, like the well-known limits of perfecting any process or product or to perfecting measurements. These practical experiences match the predictions of the second law of thermodynamicsSecond law of thermodynamics
The second law of thermodynamics is an expression of the tendency that over time, differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system. From the state of thermodynamic equilibrium, the law deduced the principle of the increase of entropy and...
for the limits of waste reduction generally. Approaching limits of perfecting things to eliminate waste meets geometrically increasing effort to make progress, and provides an environmental measure of all factors seen and unseen changing the learning experience. Perfecting things becomes ever more difficult despite increasing effort despite continuing positive, if ever diminishing, results. The same kind of slowing progress due to complications in learning also appears in the limits of useful technologies and of profitable markets applying to product life cycle management
Product life cycle management
Product life-cycle management is the succession of strategies used by business management as a product goes through its life-cycle. The conditions in which a product is sold changes over time and must be managed as it moves through its succession of stages.Product life-cycle Like human beings,...
and software development cycles). Remaining market segments or remaining potential efficiencies or efficiencies are found in successively less convenient forms.
Efficiency and development curves typically follow a two-phase process of first bigger steps corresponding to finding things easier, followed by smaller steps of finding things more difficult. It reflects bursts of learning following breakthroughs that make learning easier followed by meeting constraints that make learning ever harder, perhaps toward a point of cessation.
- Natural Limits One of the key studies in the area concerns diminishing returns on investments generally, either physical or financial, pointing to whole system limits for resource development or other efforts. The most studied of these may be Energy Return on Energy Invested or EROEI, discussed at length in an Encyclopedia of the Earth article and in an OilDrum article and series also referred to as Hubert curves. The energy needed to produce energy is a measure of our difficulty in learning how to make remaining energy resources useful in relation to the effort expended. Energy returns on energy invested have been in continual decline for some time, caused by natural resource limits and increasing investment. Energy is both nature's and our own principal resource for making things happen. The point of diminishing returns is when increasing investment makes the resource more expensive. As natural limits are approached, easily used sources are exhausted and ones with more complications need to be used instead. As an environmental signal persistently dimishing EROI indicates an approach of whole system limits in our ability to make things happen.
- Useful Natural Limits EROEI measures the return on invested effort as a ratio of R/I or learning progress. The inverse I/R measures learning difficulty. The simple difference is that if R approaches zero R/I will too, but I/R will approach infinity. When complications emerge to limit learning progress the limit of useful returns, uR, is approached and R-uR approaches zero. The difficulty of useful learning I/(R-uR) approaches infinity as increasingly difficult tasks make the effort unproductive. That point is approached as a vertical asymptote, at a particular point in time, that can be delayed only by unsustainable effort. It defines a point at which enough investment has been made and the task is done, usually planned to be the same as when the task is complete. For unplanned tasks it may be either foreseen or discovered by surprise. The usefulness measure, uR, is affected by the complexity of environmental responses that can only be measured when they occur unless they are foreseen.
See also
- Experience curve effectsExperience curve effectsModels of the learning curve effect and the closely related experience curve effect express the relationship between equations for experience and efficiency or between efficiency gains and investment in the effort....
- LearningLearningLearning is acquiring new or modifying existing knowledge, behaviors, skills, values, or preferences and may involve synthesizing different types of information. The ability to learn is possessed by humans, animals and some machines. Progress over time tends to follow learning curves.Human learning...
- Learning speed
- Labor productivityLabor productivityWorkforce productivity is the amount of goods and services that a worker produces in a given amount of time. It is one of several types of productivity that economists measure. Workforce productivity can be measured for a firm, a process, an industry, or a country...
- Learning-by-doingLearning-by-doingLearning-by-doing is a concept within economic theory. It refers to the capability of workers to improve their productivity by regularly repeating the same type of action...
- Population growthPopulation growthPopulation growth is the change in a population over time, and can be quantified as the change in the number of individuals of any species in a population using "per unit time" for measurement....