Benjamin Gompertz

Benjamin Gompertz

Benjamin Gompertz (born March 5, 1779 in London ; † July 14, 1865 there ) was a mathematician and self-taught .

life and work

Because he was Jewish, he was denied access to the university. Nevertheless, he became a Fellow of the Royal Society in 1819 . He was influenced by the work of Isaac Newton , Colin Maclaurin, and Augustus De Morgan .

In his work he dealt with Fourier series , the construction and the properties of astronomical instruments . From 1820 he used methods of analysis for the investigation of life probabilities. In 1824 he became an actuary and chief accountant for an insurance company. He also worked as a stockbroker in London.

Gompertz and his work in the area of population dynamics are still known today through the Gompertz growth model from 1825, which is named after him . This model is related to the later and more well-known logistic growth model by Pierre-François Verhulst .

It can be formulated mathematically in the following ways:

${\displaystyle N'(t)=-rN(t)\log \left({\frac {N(t)}{K}}\right)\,}$

Here describes the number of individuals at the time t and r the intrinsic growth rate. K stands for the capacity, i.e. the state of equilibrium. ${\displaystyle N(t)}$

The term that describes the capacity limit models the probable cause of epidemics that Thomas Robert Malthus postulated in his demographic model.

An article on Gompertz's model was published in Science in 1992. The population dynamics of Drosophila melanogaster were examined by keeping the flies in several closed rooms and counting the dead flies daily. The scientists started with 1 203 646 flies and recorded the flies lying on the ground every day. After 171 days, all the flies were dead.

The idea of ​​the equation is that the death rate of each individual in a population increases exponentially with age.

The Euler-Gompertz constant, which is often named after him, = 0.596347362323194 ... is not found in his work. ${\displaystyle G:=\int _{0}^{\infty }{\frac {e^{-t}}{1+t}}\,\mathrm {d} t}$

Gompertz was an early member of the Royal Astronomical Society since 1820 and a founding member of the Royal Statistical Society in 1834 .

See also

• Gompertz function
• Gompertz Makeham model

Fonts

A sketch of an analysis , 1820

• The Application of a Method of Differences to the Species of Series whose Sums are obtained by Mr. Landen, by the Help of Impossible Quatities . Philosophical Transactions of the Royal Society of London, vol. 96 (1806), pp. 147-194
• On the Nature of the Function Expressive of the Law of Human Mortality, and on a New Mode of Determining the Value of Life Contingencies . Philosophical Transactions of the Royal Society of London , Vol. 115 (1825), pp. 513-585.

Web links

• John J. O'Connor, Edmund F. Robertson :  Benjamin Gompertz. In: MacTutor History of Mathematics archive .
• Analysis of growth processes see Chap. 2.1.1: Gompertz function
• Anon .: Benjamin Gompertz. Monthly Notices of the Royal Astronomical Society, Vol. 26 (1865), p. 104 (obituary)

Individual evidence

1. ↑ Thomas Robert Malthus, An Essay on the Principle of Population (1st ed. 1798), ch. VII: "A probable Cause of Epidemics".
2. ↑ Tabular listing on StatLib ( Memento of the original from April 10, 2000 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. 
3. ↑ Graphical representation on StatLib ( Memento of the original from May 4, 1999 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice.