Editing Learning curve (section)

==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.<ref>{{cite journal |bibcode= 1988ptw..conf..291P |title=Towards the Limits of Precision and Accuracy in Measurement|journal=Physics in a Technological World|issue=88|pages=291|last1=Petley|first1=Brian W.|year=1988}}</ref> 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, discussed at length in an [http://www.eoearth.org/article/Energy_return_on_investment_(EROI) Encyclopedia of the Earth article] and in an [http://www.theoildrum.com/node/3412 OilDrum article] and [http://www.theoildrum.com/node/3786 series] also referred to as [http://www.dani2989.com/matiere1/hubbertpeakoilgb.htm 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 diminishing EROI indicates an approach of whole system limits in our [[learning power|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.