Learning curve

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The term learning curve refers to a graphical representation of the "average" rate of learning for an activity or tool. It can 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 vi, 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.

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, organization behavior and the management of group learning, among other fields[1]. 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.

The first person to describe the learning curve was Hermann Ebbinghaus in 1885. He found that the time required to memorize a nonsense syllable increased sharply as the number of syllables increased.[2] 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.[3] 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.[4]

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 it's expansion, or Economic growth, as discussed in Jevon's paradox in the 1880s and updated in the Khazzoom-Brookes Postulate in the 1980s. That it means that the effect of saving energy may generally be to increase energy use has not yet been widely appreciated in the sustainability or global warming discussions.


[edit] Common Terms

The familiar expression "steep learning curve" may refer alternately to rapid learning that is easy, or especially hard, or to steady progress that is increasingly difficult. Which is referred to needs to be clarified by context. The difference is specifically whether one is referring to the rate of learning or the rate of investment needed to learn. Typically for a steady rate of learning, the rate of effort or time invested first decreases and then increases without bound in approaching the limits of learning or perfection for a given subject and method. Originally it referred to quick progress in learning during the initial stages followed by gradually lesser improvements with further practice.[5] The progress may be measured in different ways, e.g. memory accuracy vs. the number of trials.[6] Over time, the misunderstanding 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.[7]

Frequently a "learning curve" is used to describe the effort required to acquire a new skill (e.g., expertise with a new tool) over a specific period of time. If it's a complex task requiring you to reorient your way of thinking as with learning new software, what makes it a "steep learning curve" in the mental strain of comprehending a new language rather than the time or physical effort involved. The effort to achieve significant progress and sufficient skill to start using a tool may be fairly predictable, but achieving real mastery requiring much more time, effort and making original discoveries about its use. Often learning brings one to an "impasse", only resolved by a seemingly radical intuitive change in direction, an "ah-ha moment" or "breakthrough" representing "S" curve learning of a different kind and on a different scale.

[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 (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 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 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 dimninishing 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 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 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.

[edit] See also

[edit] References

  1. ^ Connie JG Gersick 1991 "Revolutionary Change Theories: A Multilevel Exploration of the Punctuated Equilibrium Paradigm" The Academy of Management Review, Vol. 16, No. 1 pp. 10-361
  2. ^ Wozniak, R. H. (1999). Introduction to memory: Hermann Ebbinghaus (1885/1913). Classics in the history of psychology
  3. ^ Bills, A. G. (1934). General experimental psychology. Longmans Psychology Series. (pp. 192-215). New York, NY: Longmans, Green and Co.
  4. ^ Wright, T.P., "Factors Affecting the Cost of Airplanes", Journal of Aeronautical Sciences, 3(4) (1936): 122–128.
  5. ^ Ritter, F. E., & Schooler, L. J. The learning curve. In International Encyclopedia of the Social and Behavioral Sciences (2002), 8602-8605. Amsterdam: Pergamon
  6. ^ Y. Kenneth and S. Gerald, "Sparse Representations for Fast, One-Shot Learning". MIT AI Lab Memo 1633, May 1998.
  7. ^ "Laparoscopic Colon Resection Early in the Learning Curve", Ann Surg. 2006 June; 243(6): 730–737, see the "Discussions" section, Dr. Smith's remark about the usage of the term "steep learning curve".
  8. ^ "Towards the Limits of Precision and Accuracy in Measurement". http://adsabs.harvard.edu/abs/1988ptw..conf..291P. 
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