# Learning Curve

Learning curve in psychology and economics The first person to describe the learning curve was Hermann Ebbinghaus in 1885. He found that the time required to memorize a nonsense word increased sharply as the number of syllables increased. [l] 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. 2] In 1936, Theodore Paul Wright described the effect of learning on labor productivity in the aircraft industry and proposed a mathematical odel of the learning curve. [3] 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 ften 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. edit] Broader interpretations of the learning curve Initially introduced in educational 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. 4] 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. edit] 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 on the pattern’s positive aspect, namely the potential for quick progress in learning (as measured by, e. . , memory accuracy or the number of trials required to obtain a desired result)[5] at the introductory or elementary stage. 6] 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]” characterizing the overall amount learned versus total resources invested (or versus time when resource investment per unit time is held constant)βin 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 learnedβin 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 earning 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. 7] The most effective solution to problems arising from a steep learning curve is to find a different method of learning that features a differently shaped (or at least less steep) curve. Such a discovery, often characterized as an ‘”aha! ‘ moment” or “breakthrough”, often results from a seemingly radical intuitive change in direction. [citation needed] [edit] 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. edit] 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. [8] These practical experiences match the predictions of the Second law of thermodynamics 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 hings 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. Π Natural Limits One of the key studies in the area concerns diminishing 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 s 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 dimininishing returns is when increasing investment makes the resource more expensive. As natural limits are approached, easily used sources are exhausted and nes 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. Π Useful Natural Limits EROEI measures the return on invested effort as a ratio of RII or learning progress. The inverse IIR measures learning difficulty. The simple difference is that if R approaches zero R/’ will too, but IIR 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 seful learning 1/(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.