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\noindent{\bf Georges-Louis LECLERC, Comte de BUFFON}\\
b. 7 September 1707 - d. 16 April 1788
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\noindent{\bf Summary} Author of the monumental {\it Histoire Naturelle}, Buffon also
introduced several original ideas in probability and statistics, notably the
premier example in ``geometric probability" and a body of experimental and
theoretical work in demography.
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Georges-Louis Leclerc was born in Montbard, Burgundy, the son of a councillor
in the Burgundian
Parliament, who took the title of seigneur de Buffon in 1717. Following
his secondary studies at the Jesuit college in Dijon, he studied
for a degree in Law, possibly with the aim of following in his
father's footsteps, but his interests were more inclined to
mathematics. It would appear that he had read the {\it Elements} of
Euclid, the {\it Analyse des infiniment petits} of the Marquis de
l'H\^opital, and rediscovered Newton's binomial formula.
His early correspondence
with Gabriel Cramer (1704-1752), professor of analysis and geometry
at the University of Geneva dates back to 1727. Buffon
acknowledged that he owed to Cramer ``part of his first knowledge" of
mathematics, in particular the calculus of probabilities. During a
visit to Geneva in 1731, Cramer acquainted him with
the problem first
posed by Nicolas Bernoulli (q.v.) to Pierre-R\'emond de Montmort, commonly
known as the St Petersburg problem (Weil, 1961). Buffon suggested a solution
which foreshadowed
the future concepts of moral expectation and of utility function. In
1728, he moved to Angers, where he attended lectures in medicine.
These were interrupted as the result of a duel, and he later
studied botany.
In 1733, wishing to demonstrate that ``chance falls within the
domain of geometry as well as that of analysis" Buffon presented
his paper ``Solution de probl\`emes sur le jeu du franc-carreau",
to the Acad\'emie Royale des Sciences. In it, he applied infinitesimal
analysis to the calculus of probabilities, thus initiating the
study of geometrical probability. It contains a mention of the ``Buffon needle
problem" for which his name persists in probability theory.
In January 1734 he was elected Adjunct Member to the
Royal Academy in the Mechanics Section; in March 1739 he was
transferred to the Botany Section of which he became an Associate
Member in June 1739. Meanwhile, his main interests had shifted to
forestry (Hanks, 1966), and, more broadly, plant physiology; in 1735,
he translated the {\it Vegetable Staticks} of Stephen Hales,
originally published in English in 1727. In his Preface to this
work, Buffon praised the merits of Newton's experimental method,
whose fecundity in physics had been demonstrated. Buffon specifically
obtained a series of observations, from which he attempted to
establish the laws of resistance of wood by a comparable method.
However, as Hanks (1966, p.210) points out, these researches suffered
from a lack
of statistical methods for determining the significance level for the
differences between sample observations on the one hand, and
the theory and empirical data on the other. It
should be pointed out that some years later, in the first volume of
his {\it Histoire naturelle}, Buffon advocated the use of
statistics ``when subjects are too complex to allow us to apply to advantage
calculations and measurements".
In 1740, he published {\it M\'ethode des fluxions et des suites
infinies} a translation of Newton's work after the English text of
Colson, with a preface in which he adopted a position on the
Leibniz-Newton controversy about the discovery of the infinitesimal
calculus, and developed his views on the mathematical notion of
infinity. Eight years later, he communicated his {\it R\'eflexions
sur la loi d'attraction}, to the Academy, replying to Clairaut's
suggestion that Newton's law of gravitation be modified, and got
into a controversy on the relation of mathematics to reality.
In July 1739, he was named Superintendent of the King's Garden by
his patron, the minister Maurepas, and entrusted with the task of
producing an account of the King's Natural History
collection. He broadened the project considerably
and worked for 10 years in collaboration with Daubenton to write
the first volumes of his monumental {\it Histoire naturelle
g\'en\'erale et particuli\`ere avec la description du Cabinet du
Roy} consisting of 15 volumes published between 1749 and 1767. It
enjoyed great success, and provided Buffon with fame and honours: he
became a member of the Acad\'emie Fran\c{c}aise in August 1753, and spent
the main part of his subsequent researches in extending his {\it
Histoire Naturelle}. There followed {\it l'Histoire naturelle des
oiseaux} (in collaboration with Gu\'eneau de Montbeillard and the
abb\'e Bexon), then the {\it Suppl\'ement \`a l'Histoire
naturelle}, 7 volumes, 1774-1789, including the {\it Epoques de la
Nature} and {\it l'Histoire naturelle des min\'eraux} in
collaboration with Faujas de Saint-Fond, 5 volumes, 1783-1788. The
Count of Lac\'ep\`ede continued Buffon's enterprise after the
latter's death.
A number of Buffon's articles provide an
account of his probabilistic
and statistical analyses , as well as his philosophy of
mathematics.
The discourse in ``De la mani\`ere d'\'etudier et de traiter
l'histoire naturelle", with which Buffon began his {\it Histoire
naturelle}, gave him the opportunity of presenting his method and
putting forward a theory of knowledge influenced by English
thought, particularly that of Newton and Locke. He affirmed the
role of the senses and the supremacy of experience in
systematizing and presenting the laws of nature. Buffon drew a
distinction between mathematical truths ``which are only truths of
definition" and thus arbitrary, and physical truths ``which,
instead of being based on assumptions we have made, are based only
on facts". The certainty of a physical truth is to be measured by
the probability of the corresponding facts. Buffon was to refine
this epistemological thought in his ``Essai d'arithm\'etique
morale" of 1777 (within {\it Suppl\'ement \`a l'Histoire naturelle}, vol. IV),
which is concerned with ``the measurement of
uncertain things". But, more broadly, the work is devoted to
reflections on the concept of measurement, and the way in which it
can provide information on reality. In it Buffon develops his
thoughts on probability, which are dominated by the distinction
between physical and moral viewpoints, that is between what is
applicable to natural phenomena, and what counts in human affairs.
It was in the light of this distinction that Buffon had interpreted
the results of his probability table for life expectancy in
the paper ``De la vieillesse et de la mort", showing that the
first 15 years of an individual should be ``morally" considered as
non-existent. It was equally in the light of this distinction that
the ``Essai d'arithm\'etique morale" attempted to obtain a
numerical and probabilistic estimate of degrees of certainty, of
which the minimal limit was the moral certainty. Beyond this lay
the field of probabilities which were negligible in practice.
Applying these considerations to the study of the St Petersburg
problem, Buffon appealed for the first time to statistical
experiment to test calculations against reality, and suggested
an estimate of the ``moral value" of money, which led to a solution
of the problem similar to that given by Daniel Bernoulli (q.v.). Buffon had
already fallen back on statistical methods in his paper ``De la
vieillesse et de la mort" in Volume II of the {\it Histoire
naturelle}, in which he had studied human mortality in general, and
praised the excellence of the work of A. Deparcieux (1703-1768). It was
on the latter's {\it Essai sur
les probabilit\'es de la dur\'ee de la vie humaine} of 1746 that
he had prepared a report of 1745 for the Academy, in
collaboration with Nicolle, while expressing regret that the population
included only persons of private means. That was the reason why Buffon used
Dupr\'e de Saint-Maur's mortality tables, which included 3 Paris
parishes, and 12 country parishes in which there had been 23,994
deaths. The statistical parameter chosen to define the probability
of life expectancy was the median. These tables, published by
Buffon, were taken up by Moheau in his {\it Recherches et
consid\'erations sur la population de la France} in 1778. In 1777,
in his article ``Des probabilit\'es de la dur\'ee de la vie" in
Volume IV of the {\it Suppl\'ement \`a l'Histoire naturelle},
Buffon refined this statistical work, correcting the raw data,
particularly the anomalies observed in the ages corresponding
to whole numbers. Using a moving average method, he took
advantage of the comments in the work of Deparcieux, and thus
obtained his probabilities of life expectancy, whose knowledge he
wrote ``is one of the most interesting topics in the natural
history of man". Buffon added to his ``Probabilities de la
dur\'ee de la vie", a paper on the ``Etat g\'en\'eral des
naissances, mariages et morts dans la ville de Paris" for the
period 1709-1766, as well as for the main towns of Burgundy for 1770-1774.
From these, he tried to establish the fertility rate of marriages,
the ratio of births and deaths by sex, the rates of births and
deaths, and the evolution of marriages and deaths year by year. Using
the whole of these data, he endeavoured to compare mortality
in Paris and in the country, then made a comparison of mortality in
France and London, in which he took a position in the controversy
about the respective healths of the cities of London and Paris.
These statistical and demographic works of Buffon have attracted
widely diverging judgments from different authors; in particular
the reader might consult M. Fr\'echet (in Piveteau, 1954, pp. 435-436), L.
Badey (1929), K. Pearson (1978, pp. 188-197), and J. and M. Dup\^aquier
(1985, pp. 174-175 and 232).
Buffon's writings influenced Thomas Jefferson's {\it Notes on the State of
Virginia} (1782), and the two met in Paris during Jefferson's sojourn
(1784-1789) as U.S. Minister to France.
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\begin{thebibliography}{3}
\bibitem{1} Badey,L. (1929). Buffon, pr\'ecurseur de la science d\'emographique.
{\it Annales
de g\'eographie,} May, 206-220.
\bibitem{2} Buffon, G.L., (1749-1804). {\it Histoire naturelle,
g\'en\'erale et particuli\`ere}, 44 volumes, Imprimerie Royale [later
Plassan], Paris. [This is the original complete edition. The most
authoritative subsequent edition is that published in 1884-1885 (14
volumes in-8), annotated and preceded by an introduction by J.L.
Lanessan, followed by the general correspondence of Buffon,
collected and annotated by Nadault de Buffon, Librairie A.
Le Vasseur, Paris,].
\bibitem{3} Dupaquier, J. and M. (1985). {\it Histoire de la d\'emographie.} Perrin,
Paris.
\bibitem{4} Gayon, J., (1992). {\it Buffon 88}, Actes du colloque
international Paris-Montbard-Dijon, 14-22 June 1988, under the
direction of J. Gayon, Vrin, Paris,. [Contains a detailed
bibliography of Buffon's works and his published opus from 1954 to
1991.]
\bibitem{5} Hanks, L., (1966). {\it Buffon avant l'``Histoire naturelle"},
P.U.F., Paris.
\bibitem{6} Pearson, K. (1978). {\it The History of Statistics in the 17th and 18th
Centuries.} Griffin, London.
\bibitem{7} Piveteau, J., (1954). {\it Oeuvres philosophiques de Buffon},
edited by J. Piveteau, Corpus g\'en\'eral des philosophes
fran\c{c}ais, Volume XLI, Paris, PUF.. [Contains in particular the
paper ``De la mani\`ere d'\'etudier et de traiter l'histoire
naturelle" and ``Essai d'arithm\'etique morale". Apart from an
introduction to the philosophical work of Buffon by J. Piveteau and
a study of his mathematical philosophy by M. Fr\'echet, this work
contains a very detailed bibliography of works on Buffon and his
opus up to 1954].
\bibitem{8} Weil. F., (1961). La correspondance Buffon-Cramer,
{\it Revue d'histoire des sciences}, Volume XIV, pp. 97-136. [Annotates the
text of all known letters
between these two scholars from 1727 until Cramer's death in 1752.]
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\hfill{Yves Ducel, Thierry Martin}
\end{thebibliography}
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