Editing Demography (section)

==The doomsday equation for the Earth's population==
A 1960 issue of ''[[Science (magazine)|Science]]'' magazine included an article by [[Heinz von Foerster]] and his colleagues, P. M. Mora and L. W. Amiot, proposing an equation representing the best fit to the historical data on the Earth's population available in 1958:
<blockquote>
Fifty years ago, ''Science'' published a study with the provocative title “[https://www.researchgate.net/publication/233822850_Doomsday_friday_13_November_AD_2026 Doomsday: Friday, 13 November, A.D. 2026]”. It fitted world population during the previous two millennia with ''P'' = 179 × 10<sup>9</sup>/(2026.9 − ''t'')<sup>0.99</sup>. This “quasi-hyperbolic” equation (hyperbolic having exponent 1.00 in the denominator) projected to infinite population in 2026—and to an imaginary one thereafter.
:—Taagepera, Rein. [https://www.sciencedirect.com/science/article/abs/pii/S0040162513001613 A world population growth model: Interaction with Earth's carrying capacity and technology in limited space] ''Technological Forecasting and Social Change'', vol. 82, February 2014, pp. 34–41
</blockquote>
[[File:World population since 10,000 BCE (OurWorldInData series), OWID.svg|thumb|The global population is equal to <math>\tfrac{179000000000}{2026.9 - t}</math> and [[Hyperbolic growth|hyperbolically grows]] as ''t'' approaches 2026.9. When ''t'' surpasses 2026.9, the number of people living on the planet Earth suddenly becomes negative—on 13 November 2026 AD, all humans instantaneously disappear.]]
In 1975, [[Sebastian von Hoerner|von Hoerner]] suggested  that von Foerster's doomsday equation can be written, without a significant loss of accuracy, in a simplified [[Hyperbolic growth|hyperbolic]] form (''i.e.'' with the exponent in the denominator assumed to be 1.00):
:<math>\text{Global population}=\frac{179000000000}{2026.9 - t},</math>
where
* 2026.9 is 13 November 2026 AD—the date of the so-called "demographic singularity"<ref>Korotayev, Andrey. [https://jbh.journals.villanova.edu/article/view/2329/2251 The 21st Century Singularity and its Big History Implications: A re-analysis] ''Journal of Big History'', II(3), June 2018, pp. 73–119</ref> and von Foerster's 115th anniversary;
* ''t'' is the number of a year of the [[Gregorian calendar]].<ref>Korotayev, Andrey. [https://jbh.journals.villanova.edu/article/view/2329/2251 The 21st Century Singularity and its Big History Implications: A re-analysis] ''Journal of Big History'', II(3), June 2018, pp. 73–119. "We have already mentioned that, as was the case with equations (8) and (9) above, in von Foerster’s Eq. (13) the denominator’s exponent (0.99) turns out to be only negligibly different from 1, and as was already suggested by von Hoerner (1975) and Kapitza (1992, 1999), it can be written more succinctly as ''N<sub>t</sub>'' = ''C''/(''t<sup>*</sup>'' − ''t'')."</ref>

Despite its simplicity, von Foerster's equation is very accurate in the range from 4,000,000 BP<ref>Korotayev, Andrey. [https://jbh.journals.villanova.edu/article/view/2329/2251 The 21st Century Singularity and its Big History Implications: A re-analysis] ''Journal of Big History'', II(3), June 2018, pp. 73–119. "Note that von Foerster and his colleagues detected the hyperbolic pattern of world population growth for 1 CE –1958 CE; later it was shown that this pattern continued for a few years after 1958, and also that it can be traced for many millennia BCE (Kapitza 1996a, 1996b, 1999; Kremer 1993; Tsirel 2004; Podlazov 2000, 2001, 2002; Korotayev, Malkov, Khaltourina 2006a, 2006b). In fact Kremer (1993) claims that this pattern is traced since 1,000,000 BP, whereas Kapitza (1996a, 1996b, 2003, 2006, 2010) even insists that it can be found since 4,000,000 BP."</ref> to 1997 AD. For example, the doomsday equation (developed in 1958, when the Earth's population was 2,911,249,671<ref name=Worldometer>[https://www.worldometers.info/world-population/world-population-by-year/ World Population by Year] Worldometer</ref>) predicts a population of 5,986,622,074 for the beginning of the year 1997:
:<math>\frac{179000000000}{2026.9 - 1997}=5986622074.</math>

The actual figure was 5,924,787,816.<ref name=Worldometer/>

The doomsday equation is called so because it predicts that the number of people living on the planet Earth will become maximally ''positive'' by 13 November 2026, and on the next moment will become ''negative''.  Said otherwise, the equation predicts that on 13 November 2026 all humans will instantaneously disappear.