Where does erosion collide?

The gradual removal and transport of rock, soil, and sediment from the land surface by moving water, wind, ice, and gravity. Lyell's 1830 Principles of Geology set out how everyday processes acting over long spans wear down and reshape the land, and Horton's 1945 Erosional development of streams and their drainage basins turned that idea into quantitative laws linking rainfall, runoff, and the cutting of channels. Here the referent is physical material carried off a landscape, measured as mass or depth lost per unit area over time, and not the acid loss of a tooth, the shrinking of a shape in an image, or the fading of a firm's market position.[1][2]

Unit

Material lost from a surface, as mass or depth per unit area over time

Recovery means

Deposition elsewhere and slow soil formation can rebuild surfaces, usually far more slowly than material is lost

Measured by

Estimated from sediment yield, erosion pins, plot studies, and models such as the universal soil loss equation

The progressive loss of hard tooth surface caused by acid that is not produced by bacteria, for example from diet or stomach reflux, as distinct from decay or mechanical grinding. Miller's 1907 report in Dental Cosmos on the wasting of tooth tissue named and separated this chemical wearing from other kinds of tooth loss, and Lussi and Jaeggi's 2008 review set out modern diagnosis and risk factors. The referent is enamel and dentine dissolved from a living tooth, graded by clinical scoring of surface depth and area, and not soil stripped from a hillside, a set contracted by an operator, or a fading business advantage.[3][4]

Unit

Hard tooth tissue dissolved from a tooth surface

Recovery means

Lost enamel does not regrow; care aims to slow further loss and remineralize softened surface

Measured by

Graded clinically by indices of surface depth and extent, such as the basic erosive wear examination

One of the two basic operations of mathematical morphology, in which a shape is probed and shrunk by a small reference shape called a structuring element, keeping only the points where the probe fits entirely inside the original. Matheron and Serra developed the operation at Fontainebleau in the 1960s, formalized in Matheron's 1975 Random Sets and Integral Geometry and Serra's 1982 Image Analysis and Mathematical Morphology, and Haralick, Sternberg, and Zhuang's 1987 paper set it out for image analysis. The referent is a defined transformation on sets or digital images, exact and repeatable, and it shares nothing with worn rock, dissolved enamel, or a declining market lead beyond the word.[5][6][7]

Unit

A transformed set or image produced by one erosion operation

Recovery means

Not applicable; the paired dilation operation grows sets but does not exactly reverse an erosion

Measured by

Defined exactly by set inclusion, and computed on binary or grayscale images from the chosen structuring element

The decline over time of the advantage that lets a firm earn returns above its rivals, as competitors imitate, substitute, or outmaneuver it. D'Aveni's 1994 Hypercompetition argued that advantages are worn down faster in modern markets, and Wiggins and Ruefli's 2005 study measured how long superior performance lasts and found it shortening. The referent is a firm's relative position, tracked through profitability, market share, and how long an advantage endures, and not physical material lost from land, tissue stripped from a tooth, or a shape shrunk by a probe.[8][9]

Unit

A firm's advantage over rivals, its size and how long it lasts

Recovery means

A firm can rebuild advantage through innovation or new positions, though not always to the former level

Measured by

Tracked by profitability and market share over time, and by the persistence of above-normal returns