Where does birth collide?

In demography a birth is the entry of a new person into a population, and the birth rate counts those entries against the population that produced them, usually as births per thousand people per year. John Graunt's 1662 Natural and Political Observations Made upon the Bills of Mortality was the first to tally christenings and burials year by year and reason about a city's births as a countable, comparable quantity, founding the quantitative study of populations. Here a birth is a demographic event attached to a living person, aggregated into a rate for a place and a period, and it is not a star condensing from gas or an abstract event in a stochastic model.[1]

Unit

One human birth; scaled as births per 1,000 people per year (the crude birth rate)

Recovery means

Not applicable

Measured by

Counted from vital registration or census-based estimates of live births, divided by mid-year population

In astrophysics the birth of a star is the collapse of a cold cloud of interstellar gas under its own gravity until its core grows hot and dense enough to begin nuclear fusion. James Jeans's 1902 The Stability of a Spherical Nebula derived the critical mass above which such a cloud cannot resist gravity and must contract, giving the physical account of how stars come to form. Stahler's 1983 The Birthline for Low-Mass Stars later named the birthline, the track on which a newly visible young star first appears. This birth is a physical process in gas and gravity, dated by a star's youth, and it has nothing to do with a person entering a population or an event counted in a probability model.[2][3]

Unit

One newly formed star; described by mass, age, and position relative to the birthline

Recovery means

Not applicable

Measured by

Inferred from infrared and radio observations of collapsing clouds and protostars, and from a young star's place on the Hertzsprung-Russell diagram

In probability theory a birth is an abstract arrival event that increases a counter by one in a continuous-time model of population change, and a birth-death process combines such arrivals with departures. George Udny Yule's 1925 A Mathematical Theory of Evolution introduced the pure birth model, now called the Yule process, in which each existing unit produces new units at random over time. David Kendall's 1948 On the Generalized Birth-and-Death Process set out the general form combining births and deaths and named it. Here a birth is a mathematical event in a model, carrying no biology of its own, and it need not describe people or stars at all.[4][5]

Unit

One arrival event that raises the count by one; the process is scaled by its per-unit birth rate

Recovery means

Not applicable

Measured by

Specified by transition rates and studied through the resulting distribution of the count over time