Thomas Simpson | |
|---|---|
| Born | 20 August 1710 |
| Died | 14 May 1761(1761-05-14) (aged 50) Market Bosworth, Leicestershire |
| Known for | Simpson's rule Simpson–Weber triangle problem |
Thomas SimpsonFRS (20 August 1710 – 14 May 1761) was a British mathematician and inventor known for theeponymousSimpson's rule to approximatedefinite integrals. The attribution, as often in mathematics, can be debated: this rule had been found 100 years earlier byJohannes Kepler, and in German it is calledKeplersche Fassregel, or roughly "Kepler's Barrel Rule".
Simpson was born inSutton Cheney, Leicestershire. The son of a weaver,[1] Simpson taught himself mathematics. At the age of nineteen, he married a fifty-year old widow with two children.[2] As a youth, he became interested inastrology after seeing asolar eclipse. He also dabbled in divination and caused fits in a girl after 'raising a devil' from her. After this incident, he and his wife fled toDerby.[3] He moved with his wife and children toLondon at age twenty-five, where he supported his family by weaving during the day and teaching mathematics at night.[4]
From 1743, he taught mathematics at theRoyal Military Academy, Woolwich. Simpson was a fellow of theRoyal Society. In 1758, Simpson was elected a foreign member of theRoyal Swedish Academy of Sciences.
He died inMarket Bosworth, and was laid to rest in Sutton Cheney. A plaque inside the church commemorates him.
Simpson's treatise entitledThe Nature and Laws of Chance andThe Doctrine of Annuities and Reversions were based on the work of De Moivre and were attempts at making the same material more brief and understandable. Simpson stated this clearly inThe Nature and Laws of Chance, referring toAbraham De Moivre'sThe Doctrine of Chances: "tho' it neither wants Matter nor Elegance to recommend it, yet the Price must, I am sensible, have put it out of the Power of many to purchase it". In both works, Simpson cited De Moivre's work and did not claim originality beyond the presentation of some more accurate data. While he and De Moivre initially got along, De Moivre eventually felt that his income was threatened by Simpson's work and in his second edition ofAnnuities upon Lives, wrote in the preface:[5]
"After the pains I have taken to perfect this Second Edition, it may happen, that a certain Person, whom I need not name, out of Compassion to the Public, will publish a Second Edition of his Book on the same Subject, which he will afford at a very moderate Price, not regarding whether he mutilates my Propositions, obscures what is clear, makes a Shew of new Rules, and works by mine; in short, confounds, in his usual way, every thing with a croud of useless Symbols; if this be the Case, I must forgive the indigent Author, and his disappointed Bookseller."
The method commonly calledSimpson's Rule was known and used earlier byBonaventura Cavalieri (a student of Galileo) in 1639, and later byJames Gregory;[6] still, the long popularity of Simpson's textbooks invites this association with his name, in that many readers would have learnt it from them.
In the context of disputes surrounding methods advanced byRené Descartes,Pierre de Fermat proposed the challenge to find a point D such that the sum of the distances to three given points, A, B and C is least, a challenge popularised in Italy byMarin Mersenne in the early 1640s. Simpson treats the problem in the first part ofDoctrine and Application of Fluxions (1750), on pp. 26–28, by the description of circular arcs at which the edges of the triangle ABC subtend an angle of pi/3; in the second part of the book, on pp. 505–506 he extends this geometrical method, in effect, to weighted sums of the distances. Several of Simpson's books contain selections of optimisation problems treated by simple geometrical considerations in similar manner, as (for Simpson) an illuminating counterpart to possible treatment by fluxional (calculus) methods.[7] But Simpson does not treat the problem in the essay on geometrical problems of maxima and minima appended to his textbook on Geometry of 1747, although it does appear in the considerably reworked edition of 1760. Comparative attention might, however, usefully be drawn to a paper in English from eighty years earlier as suggesting that the underlying ideas were already recognised then:
Of further related interest are problems posed in the early 1750s by J. Orchard, inThe British Palladium, and by T. Moss, inThe Ladies' Diary; or Woman's Almanack (at that period not yet edited by Simpson).
This type of generalisation was later popularised byAlfred Weber in 1909. TheSimpson-Weber triangle problem consists in locating a point D with respect to three points A, B, and C in such a way that the sum of the transportation costs between D and each of the three other points is minimised. In 1971,Luc-Normand Tellier[8] found the first direct (non iterative) numerical solution of theFermat and Simpson-Weber triangle problems. Long beforeVon Thünen's contributions, which go back to 1818, theFermat point problem can be seen as the very beginning of space economy.
In 1985,Luc-Normand Tellier[9] formulated an all-new problem called the “attraction-repulsion problem”, which constitutes a generalisation of both the Fermat and Simpson-Weber problems. In its simplest version, the attraction-repulsion problem consists in locating a point D with respect to three points A1, A2 and R in such a way that the attractive forces exerted by points A1 and A2, and the repulsive force exerted by point R cancel each other out. In the same book, Tellier solved that problem for the first time in the triangle case, and he reinterpreted thespace economy theory, especially, the theory of land rent, in the light of the concepts of attractive and repulsive forces stemming from the attraction-repulsion problem. That problem was later further analysed by mathematicians like Chen, Hansen, Jaumard and Tuy (1992),[10] and Jalal and Krarup (2003).[11] The attraction-repulsion problem is seen by Ottaviano andThisse (2005)[12] as a prelude to theNew Economic Geography that developed in the 1990s, and earnedPaul Krugman aNobel Memorial Prize in Economic Sciences in 2008.
