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\noindent{\bf John ARBUTHNOT }\\
b. 29 April 1667 - d. 27 February 1735
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\noindent{\bf Summary.} A physician and writer, the creator of John Bull,
John Arbuthnot is
known in statistics for his translation of Huygens' book on probability and for
the first use of a test of significance.
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In assessing the eminent writers from the time of Queen Anne (1702 -
1714), James Boswell during the 1760's quoted the English
lexicographer and writer Samuel Johnson as saying, ``I think
Dr.~Arbuthnot the first man among them. He was the most universal
genius, being an excellent physician, a man of deep learning, and a
man of much humour.'' ({\em Boswell's Life of Johnson\/})
By profession, Arbuthnot was a physician, receiving the degree of
Doctor of Medicine from St.~Andrews in 1696. His medical practice
included many leading figures of English society. By chance he
provided medical services to Prince George, Queen Anne's consort. As a
result he was appointed Physician Extraordinary to the Queen in 1705
and later Physician in Ordinary to the Queen in 1709. The range of his
interests beyond his profession were great. Arbuthnot was an amateur
musician with connections to the composer George Frederick
H\"andel. He was active in the Royal Society serving on two committees
in support of Sir Isaac Newton.
He was a political satirist and an excellent conversationalist.
Arbuthnot was also the author of eight scientific works which reflect
a breadth of interest from mathematics to numismatics to
dietetics. Today Arbuthnot is best known as a literary wit, the
creator of the character John Bull, and as a close friend and
collaborator of the leading writers of the day: Jonathan Swift, John
Gay and Alexander Pope.
Arbuthnot's contributions to the development of probability were minor
yet indicative of the status of probability as a subject of inquiry in
the late seventeenth and early eighteenth centuries. Following the
publication of Huygens's (q.v.)
{\em De Ratiociniis in Ludo Aleae\/} in 1657,
very little was published in probability, either in volume or in
substance, until Montmort's (q.v.) {\em Essai d'Analyse sur les Jeux de
Hazards\/} in 1708. Stephen Stigler refers to this time period as the
dark ages of the theory of probability.
In 1692 Arbuthnot published {\em Of the Laws of Chance}, a translation
of {\em De Ratiociniis in Ludo Aleae\/} with some additions containing
probability calculations on various dice and card games. {\em Of the
Laws of Chance\/} was a popular book. It went through four editions,
the last published three years after Arbuthnot's death. Each edition
was printed by Benjamin Motte, a Tory in politics as was Arbuthnot.
The 1692 edition appears to have been one of the first books off
Motte's press. Later Motte published the first edition of Swift's {\em
Gulliver's Travels}. {\em Of the Laws of Chance\/} was written
anonymously as were all of Arbuthnot's writings. Some of Arbuthnot's
serious works appear under his own name.
The preface to {\em Of the Laws of Chance\/} shows that the book was
intended as a gambling manual which perhaps explains its popularity.
Arbuthnot probably wrote the book as a means to make money. The first
edition was written during a time of personal upheaval for Arbuthnot.
His father, an Episcopalian-Jacobite clergyman, had been deposed after
the Glorious Revolution (1688) and died three years later. Arbuthnot,
who probably intended to follow his father into the Church, left
Scotland in 1691 for London where initially he established himself as
a gentlemen's tutor in mathematics. The initial 1692 publication on
probability falls naturally into a time period when Arbuthnot was
apparently viewing mathematics as leading to a possible
profession. {\em Of the Laws of Chance\/} appeared in a second edition
in 1714 and a fourth edition posthumously in 1738.
In 1694 Arbuthnot entered University College, Oxford, as a
fellow-com\-mo\-ner where he met David Gregory, Savilian Professor of
Astronomy. Both were alumni of the University of Aberdeen. Probably at
this time Gregory obtained a manuscript on chance written by Arbuthnot
and dated 1694 by Gregory. Arbuthnot may have used the manuscript as
his own personal introduction to Gregory. The manuscript contains some
generalisations of the work appearing in {\em Of the Laws of Chance\/}
and an anticipation, including the first use of significance tests, of
Arbuthnot's later work on the sex ratio published in 1710 in {\em
Philosophical Transactions of the Royal Society}. The 1710 paper is an
attempt using statistics on the relative number births of males and
females to demonstrate one aspect of the providence of God.
Arbuthnot's mathematical career ended and his medical career began
after he received his medical degree in 1696. There are some possible
probabilistic twists to the beginning of this career. Archibald
Pitcaime, a Scottish physician, was closely involved in helping
Arbuthnot take his doctoral examination. Between 1693 and 1695
Pitcaime tried to apply Huygens's work in probability to medicine, in
particular to the secretion of blood and to the cure of fevers. It is
likely that Pitcaime's introduction to the work of Huygens was through
Arbuthnot.
In philosophy Arbuthnot was a Newtonian, defined by the {\em Cambridge
Dictionary of Philosophy\/} as one who has a ``view of nature as a
universal system of mathematical reason and order divinely created and
administered''. This is readily apparent in Arbuthnot's preface to
{\em Of the Laws of Chance}. For example at one point in the preface
there is a short discussion of providence as it relates to chance or
casual events. Later in the preface Arbuthnot states, ``all the
Politicks in the World are nothing else but a kind of Analysis of the
Quantity of Probability in casual Events, and a good Politician
signifies no more, but one who is dexterous at such Calculations''.
Arbuthnot had a continuing interest in mathematics in general and
probability in particular. His library was sold in 1779 and contained
at the time of sale the 1718 edition of DeMoivre's {\em Doctrine of
Chances}, DeMoivre's {\em Miscellanea Analytica\/} published 1730 and
other mathematical books.
Biographical material on Arbuthnot may be found in [1, 7] and his
known publications with probability content are listed in [2, 3, 4,
5]. Discussion of his work in probability may be found in [6, 8, 10,
12, 15]. Other references of interest are [9, 11, 13, 14].
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\begin{thebibliography}{3}
\bibitem{1} [1] Aitken, G.~A. (1892). {\em The Life and Works of John
Arbuthnot}. Clarendon Press, Oxford.
\bibitem{2} [2] Arbuthnot, J. (1692). {\em Of the Laws of Chance}.
Motte, London.
\bibitem{3} [3] Arbuthnot, J. (1710). An argument for divine providence,
taken from the constant regularity observed in the births of both
sexes. {\em Philosophical Transactions of the Royal Society\/} {\bf 27}:
186-190. Reprinted in {\em Studies in the History of Statistics and
Probability} (1977), {\bf 2}, Ed.~M.~G.~Kendall and R.~L.~Plackett,
Griffin, London, pp.~30-34.
\bibitem{4} [4] Arbuthnot, J. (1714). {\em Of the Laws of Chance}, 2nd ed.\
Motte, London.
\bibitem{5} [5] Arbuthnot, J. (1738). {\em Of the Laws of Chance}, 4nd ed.\
Motte and Bathurst, London.
\bibitem{6} [6] Bartholomew, D.~J. (1984). {\em God of Chance}. SCM, London.
\bibitem{7} [7] Beattie, L.~M. (1935). {\em John Arbuthnot, Mathematician
and Satirist}. Russell $\&$ Russell, New York.
\bibitem{8} [8] Bellhouse, D.~R. (1989). A manuscript on chance written by
John Arbuthnot. {\em International Statistical Review\/} {\bf 57},
249-259.
\bibitem{9} [9] Boswell, J. (1934). {\em Boswell's Life of Johnson}, edited
by G.~B.~Hill and L.~F.~Powell. Clarendon Press, Oxford.
\bibitem{10} [10] Pearson, K. (1978). {\em The History of Statistics in the
17th $\&$ 18th Centuries}. Griffin, London.
\bibitem{11} [11] Shuttleton, D.~E. (1995). `A modest examination': John
Arbuthnot and the Scottish Newtonians. {\em British Journal for
Eighteenth Century Studies\/} {\bf 18}, 47-62.
\bibitem{12} [12] Stigler, S.~M. (1986). {\em The History of Statistics: The
Measurement of Uncertainty before 1900}.
Belknap Press, Cambridge, MA.
\bibitem{13} [13] Stigler, S.~M. (1988). The dark ages of probability in
England: the seventeenth century work of Richard Cumberland and Thomas
Strode. {\em International Statistical Review\/} {\bf 56}, 75-88.
\bibitem{14} [14] Stigler, S.~M. (1992). Apollo Mathematicus: a story of
resistance to quantification in the seventeenth century. {\em
Proceedings of the American Philosophical Society\/} {\bf 136}, 93-126.
\bibitem{15} [15] Todhunter, I. (1865). {\em A History of the Mathematical
Theory of Probability}. Cambridge University Press. Printed by
Chelsea, New York, 1965.
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\hfill{David Bellhouse}
\end{thebibliography}
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