41. Prime Numbers benjamin gompertz applied the calculus to actuarialquestions. He is best rememberedfor gompertz s Law of Mortality in which he showedthat the mortality http://hypatia.math.uri.edu/~kulenm/diffeqaturi/m381f00fp/andrea/andreamp.html

DIFFERENCE EQUATIONS Difference Equations and Recursive Relations in this period have been studied by several mathematicians. Some of these mathematicians include: Babbage Bessel Farey Gauss ... Gompertz ,and Legendre Babbage and the DifferenceEngine Ordinary arithmeticcalculating machines, in Babbage's day, could only carry out individualcalculations.They were useful only in the computation of single sums involvingaddition,subtraction, multiplication or division. Charles Babbage worked on a calculating machine that could be adapted specially to performthe Method of Differences. The Method of Differences is away of integrating"differences". A"difference", written D f(x), is simply the difference between the values of a function taken attwodifferent values of its variable, x. For example: D f(x)=f(x )-f(x ). A "differential" is much the same thingexcept that the difference between the two valuesof x used, x andx , is reduced [gradually by a limiting process] by an infinitesimalamount, df(x). A "differential" is thus an infinitesimal "difference".Conversely, a "difference" can be seen as akind of finite"differential",one which uses an interval of a finite sizeinstead of an infinitesimal. The Method of Differences is a practical numerical technique. It can beused to calculate exactly the numerical values of any mathematical functionthat can be expressed as a simple polynomial .

42. Tilastokeskus - Tilastokoulutus - Verkkokoulu - Johdatus Väestötieteen Peruste 2.10 benjamin gompertz ja kuolevuuden laki. 1800luvulla tutkijat alkoivat ollayhä enemmän kiinnostuneita väestöllisten ilmiöiden tarkastelusta. http://www.stat.fi/tk/tp/verkkokoulu/vk/vt/oppitunnit/vt02/vt02_10/view.html

Väestöön liittyvää tietoa: StatFin-palvelu Suomi lukuina Tilasto-opas Verkkokoulu ... Verkkokoulu Kurssi: Johdatus väestötieteen perusteisiin Oppitunti 2: Väestötieteen historia 2.10 Benjamin Gompertz ja kuolevuuden laki 1800-luvulla tutkijat alkoivat olla yhä enemmän kiinnostuneita väestöllisten ilmiöiden tarkastelusta. Aivan kuin 1700-luvun lopulla Thomas Malthus julkaisi olettamuksensa väestönkasvun kiihtymisestä ja oletti kasvun jatkuvan geometrisesti, niin vuonna 1825 englantilainen matemaatikko Benjamin Gompertz (1779-1865) havaitsi, että samalla geometrisella kasvulla voidaan kuvata myös kuolevuutta. Todennäköisyys kuolla on korkea juuri syntymähetken jälkeen, tämän jälkeen todennäköisyys kuolla on alhainen aina noin 15:een ikävuoteen saakka, mutta alkaa siitä jälleen kasvaa. Kasvu jatkuu kiihtyvänä ja tulee kaksinkertaiseksi joka seitsemäs vuosi. Tätä tilastollista laskelmaa kutsutaan Gompertzin kuolevuuden laiksi . Tosin nykyisin tuo kaksinkertaistuminen joka seitsemäs vuosi ei enää pidä paikkaansa. Sivua muokattu viimeksi maanantaina 03.11.2003 klo 15:11

43. RAS LETTERS Damoiseau—Kupffer - Royal Astronomical Society gompertz, benjamin 24,1. GORTON, Sandford 63,1; 71,1. GOTHARD, Eugen von 84,1;87,1; 88,1; 92,2; 93,2; 95,1; 96,1; 1900,1. GOULD, benjamin Apthorp 51,1; http://www.ras.org.uk/index.php?option=content&task=view&id=107

44. Could People Live To 120? The FinchPike study uses the gompertz model named after benjamin gompertz,the British actuary who first described it in 1825 to predict maximum life http://www.albionmonitor.com/5-27-96/agingmax.html

Could People Live to 120? by Eric Mankin (AR) LOS ANGELES Can we cross out the biblical three score and ten as the span of a human life and write in a round six score? A life span of about 120 years is the maximum that humans can attain under current medical and environmental conditions. But 120 might become the average life expectancy if medical advances could duplicate the mechanisms at work in the only life-extension technique now known to be effective in lab rodents extremely low-calorie diets say two University of Southern California scientists. Environment and "alpha factor" determines how long we live In a new analysis published in the May issue of the Journal of Gerontology, USC scientists Caleb E. Finch, Ph.D., and Malcolm C. Pike, Ph.D., use updated comparative data from animals and a well-known mathematical relation to recalculate the potential human life span. Their analysis also suggests an explanation for certain discrepancies that scientists have previously found in mortality data. 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.

45. KeepMedia | Esquire: It's Jesus Time developed in 1825 by a London insurance actuary named benjamin gompertz.The gompertz Curve calculates survivorship, a logarithmic computation that http://www.keepmedia.com/pubs/Esquire/2005/06/01/844771?extID=10026

46. Health Library.com -- Reading Room: Words Of Wisdom I had written earlier about the great English actuary, benjamin gompertz, wholived in the early part of the nineteenth century. This man conceived a human http://www.healthlibrary.com/reading/hegde/chap19.html

Find Out Everything Your Doctor Would Tell You If Only He Had the Time ! Press article of HELP Helping patients and doctors to talk to each other! Search the entire Healthlibrary.com site. The search is powered by Google. Here we will present you with regular Book Reviews of our latest arrivals. Find out how your help can HELP to improve its services. Would you like to read what others have to say. We would love to hear from you... Also read the Visitor's Comments HELP initiates a seminar and releases two books on improving the doctor patient relationship This section presents your favourite consumer health site Words Of Wisdom by Prof B. M. Hegde Reductio Ad Absurdum Outright contradiction ! Looks absurd, but true all the same. Medical scientists are talking about prolonging life and increasing life span etc. in every conceivable forum. I wonder if anyone has really looked at this seriously. We have achieved increased life expectancy at birth even in the poorer countries in the last fifty odd years, but to say that we have increased life span is far from the truth. Many times even scientists fall into this trap of giving opinions without hard data to support their opinions. In many areas in medicine dogma and opinions abound. Depending on the stature of the person dogmas stick for very long times to the detriment of genuine truth, hindering progress in our knowledge. Let us come back to our question on hand. Is there a biological limit to human life span ? Is it the same for all animals or is it different for man? What are the evidences? I had written earlier about the great English actuary, Benjamin Gompertz, who lived in the early part of the nineteenth century. This man conceived a human life curve and documented it properly, but the whole thing was lost after his death. Recently they have been able to discover the same from Nottingham where he lived. Surprisingly it compared very well with the present data. 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.

47. Milestones: Section 5. 1800-1849 as a function of time benjamin gompertz (1779-1865), England 98. TXT The gompertz model; 1827 First successful photograph produced (an 8-hour http://www.math.yorku.ca/SCS/Gallery/milestone/sec5.html

Milestones in the History of Thematic Cartography, Statistical Graphics, and Data Visualization Dupin's cartogram of rates of illiteracy in France Lalanne's windrose diagram, the first plot in polar coordinates Minard's Tableau graphique Up: Index Introduction References Related ... Pre-1600 1800-1849: Beginnings of modern data graphics With the fertilization provided by the previous innovations of design and technique, the first half of the 19th century witnessed explosive growth in statistical graphics and thematic mapping, at a rate which would not be equalled until modern times. In statistical graphics, all of the modern forms of data display were invented: bar and pie charts, histograms, line graphs and time-series plots, contour plots, and so forth. In thematic cartography, mapping progressed from single maps to comprehensive atlases, depicting data on a wide variety of topics (economic, social, moral, medical, physical, etc.), and introduced a wide range of novel forms of symbolism. Use of coordinate paper in published research (graph of barometric variations)- Luke Howard (1772-1864), England [ PIC Luke Howard portrait (170 x 207; 13K)

48. Benjamin Gompertz Université Montpellier II benjamin Franklin benjamin gompertz benjamingompertz (1779-1865). Cette image et la biographie complète en anglais résident http://ens.math.univ-montp2.fr/SPIP/article.php3?id_article=1200

49. Glossary Of Terms gompertz Model – A class of statistical models first proposed by the nineteenthcenturyBritish actuary benjamin gompertz, in which the hazard rate for http://images.antiagingconference.com/files/1103/aagateway/glossaryofterms.asp

Home Latest E-Journal Industry News Call for White Papers White Paper Library Suggested Reading Glossary of Terms Glossary for Anti-Aging Medicine To help you understand some of the terms used in Gerontology that may be unfamiliar to clinicians (or even specialists in other biological disciplines)... Aging molecules organelles (small membrane-bound cellular components with specialized functions); (3) cells tissues with various histological architectures; (5) organs organ systems ; and ultimately (7) the entire organism itself. Intrinsic aging or senescence occurs silently from within starting at the molecular level, in the same sense that termites, if unchecked, will, sooner or later, destroy the structural integrity of even the largest wooden house. Extrinsic aging corresponds to external trauma or predation, in the same sense that a lightning bold from above can start a fire that burns your house down. Aging is not normally observed in wild populations, but typically manifests itself in zoos, as virtually all post-reproductive feral creatures are removed from the population by predators once they lose their agility. Aging is a physical process that affects inanimate objects as well as living creatures (in the same way that the Egyptian pyramids are subject to wind and rain erosion). The related concept of Longevity determination , however, is the result of a species-specific genomic expression during early development that positions the somatic tissues of an organism to survive long after its reproductive period has been completed.

50. BBC - Radio 4 - Reith Lectures 2001 - The End Of Age form in 1825 by benjamin gompertz, a pioneer of actuarial science. What gompertzfound was that, like compound interest, adult mortality rates increase http://www.bbc.co.uk/radio4/reith2001/lecture1.shtml

@import url('/includes/tbenh.css') ; Home TV Radio Talk ... A-Z Index 1 September 2005 Text only BBC Homepage BBC Radio Radio 4 ... Help Like this page? Send it to a friend! Lecture 1: Brave Old World Listen to Lecture 1 Printable version of Lecture 1 Never in human history has a population so wilfully and deliberately defied nature as has the present generation. How have we defied it? We have survived. Our unprecedented survival has produced a revolution in longevity which is shaking the foundations of societies around the world and profoundly altering our attitudes to life and death. At the same time, science has made hitherto undreamed-of advances in human biology. The explosive force of these two revolutions coming together lies at the heart of my series of Reith Lectures, as it has been at the heart of my work. Science has new things to tell us about the process of ageing. We know now that ageing is neither inevitable nor necessary. It is particularly fitting that the first lecture in a series that will explore the revolution in human longevity should be given at the Royal Institution. This establishment, founded in 1799, has played a pioneering role in science and technology. It was here, exactly two hundred years ago, that the young Humphry Davy was appointed to arrange scientific demonstrations for the public. Davy's demonstrations were spectacular events, often explosive and dangerous. There is delicious irony in the fact that Davy's best-known legacy is the miner's safety lamp, expressly designed to prevent explosions from occurring. My home city of Newcastle upon Tyne, famously associated in earlier times with coal mining, has had good reason to bless the life-preserving qualities of the Davy lamp.

51. BJR -- Table Of Contents (November 1988, 61 [731]) EY Yeung, P McCarthy, RH gompertz, S benjamin, RN Gibson, and P DawsonThe ultrasonographic appearances of hilar cholangiocarcinoma (Klatskin tumours) http://bjr.birjournals.org/content/vol61/issue731/

HOME HELP FEEDBACK SUBSCRIPTIONS ... SEARCH TABLE OF CONTENTS Receive this page by email each issue: [Sign up for eTOCs] Contents: November 1988, Volume 61, Issue 731 [Index by Author] Other Issues: Articles Find articles in this issue containing these words: [Search ALL Issues] To see an article , click its [Full Text] link. To review many abstracts , check the boxes to the left of the titles you want, and click the 'Get All Checked Abstract(s)' button. To see one abstract at a time , click its [Abstract] link. Articles: S Karstrup Ultrasound diagnosis of cholangiocarcinoma at the confluence of the hepatic ducts (Klatskin tumours) Br J Radiol 1988 61: 987-990. [Abstract] EY Yeung, P McCarthy, RH Gompertz, S Benjamin, RN Gibson, and P Dawson The ultrasonographic appearances of hilar cholangiocarcinoma (Klatskin tumours) Br J Radiol 1988 61: 991-995. [Abstract] DC Anderson, JB O'Driscoll, HM Buckler, J Cantrill, and JD Brown Relapse of osteoporosis circumscripta as a lytic ring after treatment of Paget's disease with intravenous 3-amino-1-hydroxypropylidene-1,1-bisphosphonate Br J Radiol 1988 61: 996-1001.

52. The Ultrasonographic Appearances Of Hilar Cholangiocarcinoma (Klatskin Tumours) EY Yeung, P McCarthy, RH gompertz, S benjamin, RN Gibson and P Dawson Departmentof Diagnostic Radiology, Royal Postgraduate Medical School, http://bjr.birjournals.org/cgi/content/abstract/61/731/991

HOME HELP FEEDBACK SUBSCRIPTIONS ... TABLE OF CONTENTS Services Similar articles in this journal Similar articles in PubMed Alert me to new issues of the journal Download to citation manager ... Cited by other online articles PubMed PubMed Citation Articles by Yeung, E. Y. Articles by Dawson, P. ARTICLES The ultrasonographic appearances of hilar cholangiocarcinoma (Klatskin tumours) EY Yeung, P McCarthy, RH Gompertz, S Benjamin, RN Gibson and P Dawson Department of Diagnostic Radiology, Royal Postgraduate Medical School, Hammersmith Hospital, London. The findings on ultrasound of 40 patients presenting between 1984 and 1987 who were subsequently proven pathologically to have hilar cholangiocarcinoma were reviewed. The sonograms of 17 other patients in whom pathological confirmation was not obtained but who were also presumed to have Klatskin tumours on clinical and radiological grounds, were also reviewed. All patients demonstrated intrahepatic bile duct dilatation with no evidence of free communication between the right and left hepatic ducts.

53. Royal Society | About The Society | History Of Science | Biographies Of Fellows gompertz, benjamin. Proceedings 18661867 vol 15 pp xxiii-xxiv. Goodeve, SirCharles Frederick. Biographical Memoirs 1981 vol 27 pp 307-353, plate, http://www.royalsoc.ac.uk/page.asp?id=2370

54. Jossey-Bass::Encyclopedia Of Actuarial Science, 3-Volume Set gompertz, benjamin (17791865). Good Faith. Graduation. Graphical Methods.Graunt, John (16201674). Greeks. Gross Net Premium Income. http://www.josseybass.com/WileyCDA/WileyTitle/productCd-0470846763,descCd-tableO

By Keyword By Title By Author By ISBN By ISSN Shopping Cart My Account Help Contact Us ... Statistics for Finance and Business Encyclopedia of Actuarial Science, 3-Volume Set Related Subjects Survival Analysis Biometrics Engineering Statistics Related Titles More By These Authors Statistics of Extremes: Theory and Applications (Hardcover) Stochastic Processes for Insurance and Finance (Hardcover) Statistics for Finance and Business Risk and Financial Management: Mathematical and Computational Methods (Hardcover) by Charles Tapiero by Wim Schoutens Financial Derivatives in Theory and Practice, Revised Edition (Paperback) by Philip Hunt, Joanne Kennedy Forecasting with Univariate Box - Jenkins Models: Concepts and Cases (Hardcover) by Alan Pankratz Methods for Business Analysis and Forecasting: Text and Cases (Hardcover) by Peter Tryfos Statistics for Finance and Business Encyclopedia of Actuarial Science, 3-Volume Set Jozef Teugels (Editor-in-Chief), Bjørn Sundt (Editor-in-Chief) ISBN: 0-470-84676-3 Hardcover 1944 pages November 2004 US $1,745.00

55. USC Trojan Family Magazine - Spring 2001: Rock Of Aging The gompertz model, used to predict maximum life spans for different species, isnamed after 19thcentury British actuary benjamin gompertz. http://www.usc.edu/dept/pubrel/trojan_family/spring02/Aging/Aging_pg3.html

Continued from page 2 IN 1996, FINCH AND USC However, in a study published in the May 1996 issue of the Journal of Gerontology, Finch and Pike found that people living in wealthy, developed regions are at a 10-times lower risk for disease and environmental hazards than those living in parts of Asia and Africa. By reducing infectious disease, accidents and natural disasters to one-50th the current level, the scientists calculate, half of all 50-year-olds could live up to 120 years. This, however, depends on huge medical advances. FINCH HAS BEEN INTERESTED As an undergraduate at Yale University in the late 1950s, Finch studied physics, as did many young men caught up in the post-Sputnik science boom. Finch completed a thesis on the molecular mechanisms of aging and took a post at Cornell University in 1970, but was lured to Los Angeles in 1972 by the prospect of starting a new school of gerontology, the first of its kind in the United States. Finch and Thomas Kirkwood of the University of Newcastle, in England, had the notion that chance variation, while clearly recognized for years, has never been properly observed. How else to explain genetically identical worms, raised under the same laboratory conditions, dying over a three-fold range of ages? Or inbred mice, born of the same mother and reared in the same environment, dying over a similarly wide variation? Human twin studies also exhibit unusual differences in life spans. ON THE IRON MOUNTAIN Photographed by Joe Pugliese Eric Niiler is a reporter for public radio station KPBS-FM in San Diego. His freelance articles have appeared in Scientific American, the Christian Science Monitor, the Los Angeles Times and the Boston Globe.

56. BSHM: Gazetteer -- LONDON People D-G benjamin gompertz (17791865) was actuary to the Alliance Assurance Company whenhe formulated the gompertz Curve for human mortality. http://www.dcs.warwick.ac.uk/bshm/zingaz/LondonPeopleD.html

The British Society for the History of Mathematics HOME About BSHM BSHM Council Join BSHM ... Search BSHM Gazetteer LONDON People D-G Main Gazetteer A B C D ... Z Written by David Singmaster (zingmast@sbu.ac.uk ). Links to relevant external websites are being added occasionally to this gazetteer but the BSHM has no control over the availability or contents of these links. Please inform the BSHM Webster (A.Mann@gre.ac.uk) of any broken links. [When the gazetteer was edited for serial publication in the BSHM Newsletter, references were omitted since the bibliography was too substantial to be included. Publication on the web permits references to be included for material now being added to the website, but they are still absent from material originally prepared for the Newsletter - TM, August 2002] Because of its size, the London section of the Gazetteer is divided into eight pages: the main index page scientific institutions and societies the British Museum, British Library and Science Museum other institutions and places ; and mathematical people: A - C , D - G (this page), H - M N - R and S - Z . Inevitably these categories are somewhat arbitrary so use of the index page and / or the Search facility is recommended.

57. Glossary gompertz Model A class of statistical models first proposed by the nineteenthcenturyBritish actuary benjamin gompertz, in which the hazard rate for death http://www.kronosinstitute.org/glossary.html

A B C D ... Back to About Us Adenosine Triphosphate (ATP). The high energy chemical that is used for all energy requiring processes in our cells 95% confidence interval: This is the range of values above and below an estimate of risk, within which the actual risk has a 95% probability of falling by chance alone. Thus, if the 95% confidence interval for a risk does not include 1.0 (1.0 is always the risk for the control group), then there is less than a 5% chance that the risk estimated for treatment is not meaningfully different from that of a control group. Adenosine triphosphate (ATP): The high energy chemical that is used for all energy requiring processes in our cells Anthocyanins: Any of a variety of polycyclic compounds, with nitrogen in some rings and most with nitrogen side groups, and double bonds between some of the carbon atoms. These compounds absorb light selectively so that they tend to be highly colored (usually purple, blue, or red). They are found in high concentrations in colored vegetables and most are effective antioxidants. Antioxidant: One of many types of molecule in our cells which can safely combine with oxygen free radicals, thus rendering them harmless.

58. Table Of Contents For Encyclopedia Of Actuarial Science Geometric Distribution Gibbs Sampling Girsanov s Theorem Going Concern gompertz,benjamin (17791865) Good Faith Graduation Graphical Methods Graunt, http://www.loc.gov/catdir/toc/ecip0419/2004014696.html

Table of contents for Encyclopedia of actuarial science / editors-in-chief, Jozef L. Teugels, Bjorn Sundt. Bibliographic record and links to related information available from the Library of Congress catalog. Note: Contents data are machine generated based on pre-publication provided by the publisher. Contents may have variations from the printed book or be incomplete or contain other coding. Library of Congress Subject Headings for this publication: Insurance Mathematics Encyclopedias.

59. GLOSSARY gompertz Model A class of statistical models first proposed by the nineteenthcenturyBritish actuary benjamin gompertz, in which the hazard rate for http://www.grg.org/resources/glossary.html

GLOSSARY of Selected Terms in Gerontology [*] that may be unfamiliar to specialists in other biological disciplines... The glossary is an alphabetical list of selected terms in aging and longevity medicine that are commonly employed in gerontology Aging A gradual and relentless process by which sexually-reproducing organisms lose their youthful capacity for homeostasis . Aging doesn't normally begin until the completion of a characteristic interval of reproductive competence during which a species rears its progeny to independence (See Life History As a result of aging, older organisms are increasingly vulnerable to a wide variety of age-related diseases, ultimately culminating in their death. The tradeoff between aging and repair processes is extremely complex and observed to operate systematically within a hierarchy of at least seven different interacting levels: (1) molecules organelles (small membrane-bound cellular components with specialized functions); (3) cells tissues of various architectures; organs organ systems ; and ultimately (7) the entire organism Aging occurs silently from within, in the same sense that termites, if unchecked, will ultimately destroy the structural integrity of a large wooden house.

60. Hospital Practice: Screening In The Elderly: Principles And Practice benjamin gompertz (17791865) was the first to describe the complex relationshipbetween remaining life expectancy and annual mortality. http://www.hosppract.com/issues/2000/10/eldrich.htm

Screening in the Elderly: Principles and Practice J. SCOTT RICH HAROLD C. SOX Veterans Affairs Medical Center White River Junction, Vt. Dartmouth-Hitchcock Medical Center Lebanon, N. H. Data on the benefits of screening that have been obtained from studies of middle-aged adults cannot be extrapolated to the elderly; indeed, benefits decline appreciably with age. In addition, recommendations based on expert opinion are conflicting. The authors present an tailored, stepwise approach that weighs the benefits of screening against the risks and cost for each patient. Dr. Rich is Outcomes Group Research Fellow, Veterans Affairs Medical Center, White River Junction, Vt. Dr. Sox is Chair and Joseph M. Huber Professor, Department of Medicine, Dartmouth-Hitchcock Medical Center, Lebanon, N. H. As more people live into the eighth and ninth decades of life, physicians increasingly will have to decide whether to routinely screen older patients. Because few clinical trials of screening and prevention have enrolled patients aged 70 years and older, an evidence-based answer to this question is unlikely in the near future. Until then, one way to decide about screening in the elderly is to follow recommendations that are based on expert opinion. Unfortunately, current guidelines differ, no doubt reflecting the scientific uncertainty that exists. For example, the American College of Physicians and American Society of Internal Medicine recommend against routine screening mammography for breast cancer in women older than 75 years; the U. S. Preventive Services Task Force states that evidence for or against routine screening in women older than 70 is insufficient to make recommendations; and the American Cancer Society and American Medical Association cite no upper age limit for routine screening. The recommendations for other conditions are similarly inconsistent.

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