Where does fertility collide?

The observed reproductive output of a population, that is, how many children are actually born, usually scaled as an average number of children per woman. John Graunt's 1662 Natural and Political Observations Made upon the Bills of Mortality founded the quantitative study of a population's births and deaths, and the modern treatment of fertility as births per woman across the childbearing years was set out by demographers, with Bongaarts (1978) describing the proximate factors that determine it. In demography this word names actual births counted in a population, and it is deliberately kept apart from a couple's biological capacity to conceive. That referent shares nothing with a soil's power to feed a crop, a theory's power to generate new work, or the number of words one word produces in a translation model.[1][2]

Unit

An average number of children born per woman over her childbearing years

Recovery means

Not applicable

Measured by

Computed from registered births using age-specific rates, summed into measures such as the total fertility rate

The capacity of a soil to supply the nutrients a plant needs, in the right amounts and at the right time, so that a crop can grow. Justus von Liebig's 1840 Organic Chemistry in its Application to Agriculture and Physiology established that plants draw specific mineral nutrients from the soil and that growth is held back by whichever needed nutrient is scarcest, and later texts such as Brady and Weil's The Nature and Properties of Soils developed how this capacity rests on a soil's chemical, physical, and biological properties. Here the word describes a property of the ground, gauged by nutrient content and the yield it can support. It has no relation to a count of human births, the fruitfulness of a scientific theory, or a parameter in a translation program.[3][4]

Unit

A soil's nutrient-supplying capacity, read through its chemistry and the yield it sustains

Recovery means

Rebuilt over time by fertilisation, crop rotation, and organic matter as nutrients are removed at harvest

Measured by

Assessed by soil tests for available nutrients, organic matter, and pH, and by measured crop yield

A property of a scientific theory: its power to keep generating new and successful predictions, questions, and lines of research beyond the facts it was first built to explain. Ernan McMullin's 1976 essay The Fertility of Theory and the Unit for Appraisal in Science argued that this fruitfulness over time is one of the things by which a theory should be judged, alongside virtues such as accuracy and scope that Kuhn (1977) also weighed. In philosophy of science the word names how much fresh, useful work a theory goes on to produce. That referent is unrelated to births in a population, nutrients in the ground, or a numeric parameter inside a translation model.[5][6]

Unit

A theory's ongoing yield of new predictions, questions, and research

Recovery means

Not applicable

Measured by

Judged qualitatively by the volume and success of the new work a theory later generates

In statistical machine translation, the fertility of a source word is the number of words it produces in the translated output: a word may map to zero, one, or several words in the other language, and that count is its fertility. Brown, Della Pietra, Della Pietra, and Mercer's 1993 The Mathematics of Statistical Machine Translation introduced fertility as a formal parameter in their word-alignment models, giving each source word a probability distribution over how many output words it generates. Here the word is a whole number attached to a word inside a translation model. It has nothing to do with births in a population, the nutrients in a soil, or the fruitfulness of a scientific theory.[7]

Unit

A whole number: how many output words one source word produces

Recovery means

Not applicable

Measured by

Estimated as a probability distribution over word counts from aligned bilingual text during model training