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	Benjamin Gompertz -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-12)
		Gompertz is today mostly known for his Gompertz's law of mortality, a (A statistic characterizing human populations (or segments of human populations broken down by age or sex or income etc.)) demographic model published in 1825.
		It was used by insurance companies to calculate the cost of (Insurance paid to named beneficiaries when the insured person dies) life insurance.
		Gompertz's descendent Simon Gompertz is an (The branch of social science that deals with the production and distribution and consumption of goods and services and their management) economics (An advocate who presents a person (as for an award or a degree or an introduction etc.)) presenter for the BBC.
	www.absoluteastronomy.com /encyclopedia/b/be/benjamin_gompertz.htm (240 words)

	Discussion of the paper by Jack C. Yue
		The scientific literature on the deviation of mortality rates from the Gompertz law at advanced ages is abundant, starting with the study of Benjamin Gompertz himself (Gompertz,1825; Makeham, 1867; Brownlee, 1919; Perks, 1932; Greenwood and Irwin, 1939; Mildvan and Strehler, 1960; Strehler, 1960; Economos, 1979,1980,1983,1985; Gavrilov and Gavrilova, 1991).
		To summarize the coverage of scientific background, we may conclude that the Gompertz law is known to be not applicable to the oldest-old mortality, unless the data are spoiled by artificial introduction of this law during extrapolation/graduation procedures.
		Gompertz, B. (1825) On the nature of the function expressive of the law of human mortality and on a new mode of determining life contingencies.
	longevity-science.org /DYue.html (1012 words)

	benjamin gompertz
		That Benjamin Gompertz ever got the chance to develop his Law of Mortality was down to the help of another long-gone East End institution – the Spitalfields Mathematical Society.
		The Gompertz family were merchants who – like many others in the late 1700s – left Holland to try their luck in a London booming with trade.
		Gompertz was now marrying his mathematical brilliance to the cold science of insurance, and in 1824 he was appointed as actuary and head clerk of the Alliance Assurance Company.
	www.eastlondonhistory.com /gompertz.htm (992 words)

	Glossary for "Models of Systems Failure in Aging" (Site not responding. Last check: 2007-10-12)
		Gompertz law of mortality -- the law of exponential increase in death (failure) rates with age.
		According to the Gompertz law, the logarithm of death rates is increasing linearly with age.
		It was first suggested by the British actuary Benjamin Gompertz in 1825 for use in the life insurance business.
	www.omidyar.net /user/u863210052/news/26 (1350 words)

	Benjamin Gompertz - Wikipedia, the free encyclopedia
		Gompertz is today mostly known for his Gompertz's law of mortality, a demographic model published in 1825.
		It was used by insurance companies to calculate the cost of life insurance.
		Gompertz's descendent Simon Gompertz is an economics presenter for the BBC.
	en.wikipedia.org /wiki/Benjamin_Gompertz (174 words)

	Nat' Academies Press, Between Zeus and the Salmon: The Biodemography of Longevity (1997)
		Gompertz Models: Phenomenological Theory From age 15 years or so, the rate of mortality accelerates exponentially in long-industrialized human populations, and this has been a commonplace of both demography and gerontology (e.g., Comfort, 1964).
		The Gompertz equation attempts to summarize this pattern using what amounts to a linear regression of the logarithm of the mortality rate (µ) on age, x, where a gives the slope of that regression and α is the initial rate of mortality.
		While the Gompertz model is an excellent approximation to mortality rates for most individuals from some iteroparous populations, it appears inadequate for the description of even the qualitative pattern of the full life history of most organisms, granting that such full life histories are not usually adequately observed.
	www.nap.edu /books/0309057876/html/96.html (5106 words)

	Gompertz (Site not responding. Last check: 2007-10-12)
		Benjamin was self educated, learning mathematics by reading Newton and Maclaurin.
		[Gompertz's] rigid adherence to Newton's fluxional notation prevented wide recognition of his accomplishment, but he must be rated as a pioneer in actuarial science and one of the great amateur scholars of his day.
		Gompertz assisted Baily in calculating positions of stars which was eventually published as Baily's Catalogue giving the constants for 3000 fixed stars.
	www-groups.dcs.st-and.ac.uk /~history/Mathematicians/Gompertz.html (859 words)

	Refining the idea of ripe old age
		The study uses the Gompertz model - named after 19th century British actuary Benjamin Gompertz - to predict maximum life expectancies for various species.
		The Gompertz rule predicts that the risk of dying accelerates at a constant rate over time for all organisms, be they fruit flies or humans.
		According to Finch, the Gompertz model successfully accounts for a large volume of aging data, but seeming anomalies have been reported in some species, especially at the extreme-old-age end of the life span spectrum.
	www.usc.edu /uscnews/stories/1902.html (1084 words)

	[No title]
		One is the slope of the other, and to get at one from the other, you need a bit of math, and the two functions should be clearly kept separate when talking about aging, so as not to confuse.
		Benjamin Gompertz was an insurance actuary who in 1825 noticed that your risk of dying in any given year increased exponentially with time.
		If other non-time dependent stuff is left out (getting bombed in a war, or starving, or dying of plague, or getting eaten by wild animals), this equation should (when integrated and graphed) produce a pretty good look at what aging in the absence of external causes looks like, in terms of population survival.
	www.cs.cmu.edu /afs/cs.cmu.edu/user/tsf/Public-Mail/cryonics/194 (566 words)

	Dr.James Moore (Site not responding. Last check: 2007-10-12)
		In 1825, an English actuary named Benjamin Gompertz observed that death rates in humans rise exponentially after sexual maturity, and he proposed a simple formula to define the relationship between the force of mortality and age within a population.
		The crucial question now is: Can the slope of the Gompertz curve be altered by biological interventions, i.e., can basic research on aging provide interventions to improve quality of life by decelerating the rate of senescence.
		A different, but simpler way to present survival data is to plot the fraction of individuals remaining in a population as a function of the age of the population, i.e., a survival curve.
	www.herbalconsults.com /research25.html (546 words)

	Population dynamics - Open Encyclopedia (Site not responding. Last check: 2007-10-12)
		Population dynamics is the dominant branch of mathematical biology, which has a history of more than 200 years.
		The early period was dominated by demographic studies such as the work of Benjamin Gompertz (5 March1779-14 July1865) and Pierre François Verhulst (28 October1804-15 February1849), who refined and adjusted the Malthusian demograhical model.
		A more general model formulation was proposed by F.J. Richards in 1959, by which the models of Gompertz, Verhulst and also Ludwig von Bertalanffy are covered as special cases of the general formulation.
	open-encyclopedia.com /Population_dynamics (152 words)

	A Matter of Life and Death
		Benjamin Gompertz devised the famous Gompertz model of mortality, utilized still in many areas of survival analysis, in 1825.
		Gompertz, a brilliant mathematician, was the first actuary of the Alliance Assurance Company of
		Gompertz’ model was based on the instantaneous mortality rate – a function we now call the force of mortality in actuarial science, and which statisticians call the hazard rate or failure rate.
	www.fenews.com /fen46/topics_act_analysis/topics-act-analysis.htm (1729 words)

	Gompertz - new and used books
		GOMPERTZ, BENJAMIN.: - A Sketch of an Analysis and Notation applicable to the estimation of the value of Life Contingencies.
		Benjamin Gompertz was a pioneer in actuarial science and one of the great amateur scholars of his day.
		Gompertz first describes what celadon wares are, and where and how they were made.
	www.isbn.pl /A-Gompertz (1358 words)

	Longevity First: Cashing in on Protandim (Site not responding. Last check: 2007-10-12)
		Gompertz Law is a formulation of an interesting fact about aging and death.
		The standard definition of the rate of aging of a population is the slope of its Gompertz regression.
		This means that in order to add 7–8 years to someone’s lifespan, the Gompertz Curve must be shifted down by lowering one’s mortality rate at all ages by at least 50% (in practice, it must be lowered even further, depending on the age of the person).
	www.longevityfirst.org /archives/2005/06/cashing_in_on_p_1.html (3227 words)

	"Borderlands of Science" - Population Problems
		That model is known as "Gompertz law." It was proposed by a British actuary, Benjamin Gompertz, back in 1825, and it states that mortality rates increase exponentially with age.
		Their need for special care will be great, as will the demands that they place on an economic system already struggling to cope with a graying population in their 60s and 70s.
		The failure of the Gompertz law may sound like bad news for the future, but not, I would argue, for anyone alive today and reading this.
	www.fenrir.com /free_stuff/columns/science/sci-072.htm (1238 words)

	"The Quest for the General Theory of Aging and Longevity" - Synopsis
		Gompertz also proposed the first mathematical model to explain the exponential increase in mortality rate with age (Gompertz, 1825).
		The Gompertz law of exponential increase in mortality rates with age is observed in many biological species (Strehler, 1978; Finch, 1990), including humans, rats, mice, fruit flies, flour beetles, and human lice (Gavrilov and Gavrilova, 1991), and, therefore, some general theoretical explanation for this phenomenon is required.
		Gompertz also found that at advanced ages mortality rates increase less rapidly than an exponential function, thus forestalling two centuries ago the recent fuss over 'late-life mortality deceleration', 'mortality leveling off', and 'late-life mortality plateaus'.
	longevity-science.org /Synopsis.html (2330 words)

	International Longevity Center - USA
		In 1825, Benjamin Gompertz, a British actuary, observed that after establishment of maturity at about 30 years of age there is a logarithmic increase, a doubling of the "force of mortality" every seven years, at least until the eighth or ninth decade.
		The Gompertz equation reflects underlying cellular and molecular deterioration that predisposes to disease and death.
		This workshop is organized to explore up-to-date perspectives of the role of aging in health and disease, with special attention to the Gompertz Curve, including epidemiology, the disorders of longevity, theories of aging, animal models and biomarkers.
	www.ilcusa.org /prj/agingfactor.htm (1169 words)

	Goodhealth n You
		In 1825 or so Gompertz wrote that human mortality increases with age in a geometric proportion, doubling every eight years, between the ages of twenty and eighty years.
		Gompertz died before he could prove his hypothesis.
		Another biologist Raymond Pearl, thought that Gompertz was right, by his experiments on Drosophila in the year 1926, nearly hundred years after Gompertz.
	www.goodhealthnyou.com /library/reading/hegde/lifespan.php3 (1180 words)

	References for Gompertz (Site not responding. Last check: 2007-10-12)
		M N Adler, Memoirs of the late Benjamin Gompertz, Journal of the Institute of Actuaries 13 (1866), 1-20.
		Benjamin Gompertz, Monthly Notices of the Royal Astronomical Society 26 (1865-6), 104-109.
		P F Hooker, Benjamin Gompertz, Journal of the Institute of Actuaries 91 (1965), 203-212.
	www-groups.dcs.st-and.ac.uk /~history/References/Gompertz.html (119 words)

	Longevity Science » Mortality Deceleration and Aging Theories (Site not responding. Last check: 2007-10-12)
		Here we focus on one particular topic raised by Dr. George Martin – the departures of mortality trajectories from the Gompertz curve – a paradoxical phenomenon known in scientific literature as late-life mortality deceleration, mortality levelling-off, and late-life mortality plateaus.
		The first of these essential observations was the Gompertz law of mortality, while the second essential observation stated that “the Gomperzian period is followed by a gradual reduction in their rate of increase of the mortality” (see page 14 in Strehler, B. L., & Mildvan, A. General theory of mortality and aging.
		A year later the same author analyzed data for thoroughbred horses (mares), Dall mountain sheep, houseflies and some other species, and came to a conclusion that “Gompertz’s law is only an approximation, not valid over a certain terminal part of the lifespan, during which force of mortality levels off.
	longevity.scienceboard.net /index.php?p=17 (1782 words)

	eMJA: Hassan, Social consequences of manufactured longevity
		In 1825, a British actuary, Benjamin Gompertz, discovered a distinctive pattern in human mortality statistics.
		He found that the probability of dying was high at birth, and then continued declining until sexual maturity, after which it increased at an exponential rate.
		Gompertz B. On the nature of the function expressive of the law of human mortality and on a new mode of determining life contingencies.
	pandora.nla.gov.au /pan/10180/20030809/www.mja.com.au/public/issues/173_11_041200/hassan/hassan.html (1988 words)

	Britannica Concise Encyclopedia - The online encyclopedia you can trust!
		The viability (survival ability) of a population is characterized in two actuarial functions: the survivorship curve (A in Figure 1) and the age-specific death rate, or Gompertz function (B in Figure 1).
		The relation of such factors as aging characteristics, constitutional vigour, physical factors, diet, and exposure to disease-causing organisms to the actuarial functions is complex; there is, nevertheless, no substitute for them as measures of the aging process and of the effect of environmental or genetic modifiers.
		It was first pointed out by an English actuary, Benjamin Gompertz, in 1825 that the mortality rate increases in geometric progression—i.e., by a constant ratio in successive equal age intervals.
	www.britannica.com /ebc/print_toc?tocId=9110653 (515 words)

	Force of Mortality
		The "Force of Mortality" - reflections on the survival curve and the "ageing" process with some implications for new directions in research.
		The exponential rate of mortality after age 30 is held to be caused by "ageing" - i.e., Gompertz' "force of mortality".
		(1) Gompertz B, 1825; On The Nature Of The Functions Expressive Of The Law Of Human Mortality And On A New Mode Of Determining Life Contingencies; Philosophical Transactions of the Royal Society, 1825 (A115) 513.
	www.fis.org /public/obiterdicta/forceofmortality.html (994 words)

	Could People Live to 120? (Site not responding. Last check: 2007-10-12)
		The Finch-Pike study uses the Gompertz model -- named after Benjamin Gompertz, the British actuary who first described it in 1825 -- to predict maximum life expectancies for various species.
		While the Gompertz model successfully accounts for a large volume of aging data for a number of species, seeming anomalies have been reported in some species, especially at the extreme old age end of the life-span spectrum.
		All of the animal data, they found, fit Gompertz curves closely, with mortality rates showing no sign of leveling off at extreme old ages.
	www.monitor.net:16080 /monitor/5-27-96/agingmax.html (1104 words)

	Intl. Trans. Failures, Pt. 2 (Site not responding. Last check: 2007-10-12)
		The most influential parametric mortality model in published actuarial literature is that proposed in 1825 by Benjamin Gompertz, who recognized that an exponential pattern in age captured the behavior of human mortality.
		In 1860, W.M. Makeham modified the Gompertz equation because it failed to capture the behavior of mortality due to accidental death, by adding a constant term in order to correct for this deficiency.
		In 1932, Perks proposed modifications to the Gompertz formula to allow the curve to more closely approximate the slower rate of increase in mortality at older ages.
	www.hsb.com /thelocomotive/Story/FullStory/ST-FS-LOTRAN04-2.html (2370 words)

	BENJAMIN (Site not responding. Last check: 2007-10-12)
		Search the BENJAMIN Family Message Boards at Ancestry.com (if available).
		Search the BENJAMIN Family Resource Center at RootsWeb.com (if available).
		Find graves of people named BENJAMIN at Find-a-Grave.com (or add one that you know).
	www.worldhistory.com /surname/US/B/BENJAMIN.htm (73 words)

	Population dynamics - Wikipedia, the free encyclopedia
		Population dynamics has tradionally been the dominant branch of mathematical biology, which has a history of more than 200 years, although more recently the scope of mathematical biology has greatly expanded.
		The early period was dominated by demographic studies such as the work of Benjamin Gompertz and Pierre François Verhulst in the early 19th century, who refined and adjusted the Malthusian demographical model.
		The computer game SimCity and the MMORPG Ultima Online, among others, tried to simulate some of these population dynamics.
	en.wikipedia.org /wiki/Population_dynamics (404 words)

	HDE 19: Lecture 2
		One of the most fundamental and important parameters in demography, gerontology and actuarial studies is the rate of change or slope of the age-specific mortality schedule with age.
		In 1825 the English actuary Benjamin Gompertz observed that "the number of living corresponding to ages increasing in arithmetical progression, decreased in geometrical progression." He proposed that a geometrical decrease in survival with age existed because of a geometric increase in the "force of mortality" with age.
		is the mortality at age x, a is the initial mortality rate and b is the Gompertz parameter which denotes the exponential rate of change in mortality with age.
	entomology.ucdavis.edu /courses/hde19/lecture2.html (3237 words)

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