Learning curve

The term learning curve refers to the graphical relation between the amount of learning and the time it takes to learn. 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.

The first person to describe the learning curve was Herman Ebbinghaus in 1885. He found that the time required to memorize a nonsense syllable increased sharply as the number of syllables increased. [Wozniak, R. H. (1999). Introduction to memory: Hermann Ebbinghaus (1885/1913). [http://psychclassics.yorku.ca/Ebbinghaus/wozniak.htm "Classics in the history of psychology"] ] 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. [Bills, A. G. (1934). General experimental psychology. Longmans Psychology Series. (pp. 192-215). New York, NY: Longmans, Green and Co.] 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. [Wright, T.P., "Factors Affecting the Cost of Airplanes", "Journal of Aeronautical Sciences", 3(4) (1936): 122–128.]

The expression, "steep learning curve" is used in two opposite contexts. Originally it referred to quick progress in learning during the initial stages followed by gradually lesser improvements with further practice. [Ritter, F. E., & Schooler, L. J. " [http://ritter.ist.psu.edu/papers/ritterS01.pdf The learning curve] ". In "International Encyclopedia of the Social and Behavioral Sciences" (2002), 8602-8605. Amsterdam: Pergamon] The progress may be measured in different ways, e.g. memory accuracy vs. the number of trials. [Y. Kenneth and S. Gerald, " [http://citeseer.ist.psu.edu/790.html Sparse Representations for Fast, One-Shot Learning] ". MIT AI Lab Memo 1633, May 1998.] Over time, the misapprehension has emerged that a "steep" learning curve means that something requires a great deal of effort to learn because of the natural association of the word "steep" with a slope which is difficult to climb. This has led to confusion and disagreements even among "learned" people. ["Laparoscopic Colon Resection Early in the Learning Curve", "Ann Surg." 2006 June; 243(6): 730–737, see the [http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=1570580 "Discussions"] section, Dr. Smith's remark about the usage of the term "steep learning curve".]

Another specific context of the term "learning curve" involves the effort required to acquire a new skill (e.g., expertise with a new tool) over a specific period of time. In this context, expressions such as "fast learning curve", "short learning curve", and "steep learning curve" are used. This context involves a different interpretation of fast "initial" progress vs. time—namely, the amount of progress required at each stage of learning. In this sense, "steep learning curve" represents the need to make significant progress in the initial stages so that a person may start using the new skill with reasonable efficiency, a need often associated with increased efforts in learning. Conversely, the expressions "gradual" or "flat learning curve" imply that the acquisition of a skill may be gradual, so that a reasonable use of the new skill is possible at early stages with a relatively light amount of training.fact|date=May 2007

General Learning Limits

Learning curves, also called experience curves (Experience curve effects), 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 [http://adsabs.harvard.edu/abs/1988ptw..conf..291P perfecting measurements] . 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 [http://www.actapress.com/PaperInfo.aspx?PaperID=19159&reason=500 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 as also discussed on the Encyclopedia of the Earth as [http://www.eoearth.org/article/Energy_return_on_investment_(EROI) EROI] and referred to as [http://www.dani2989.com/matiere1/hubbertpeakoilgb.htm Hubert curves] in the discussions of [http://www.oildrum.com Peak Oil] . 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. Energy is both nature’s and our own principal resource for making things happen. Persistent declining returns on investment in energy have occurred as the use of easy sources has led to needing to use ones with more complications. As an environmental signal, if true, it would indicate an approach of whole system limits in our ability to make things happen.

*Useful Natural Limits EROI 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 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 forseen 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 forseen.

ee also

* Experience curve effects
* Learning

References