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\noindent{\bf Ladislaus von BORTKIEWICZ}\\
b. 7 August 1868 - d. 15 July 1931
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\noindent{\bf Summary}. Bortkiewicz did more than investigate kicks by Prussian cavalry
horses. A pioneer faithful to his master Lexis, he extended in numerous and
original ways ways the application of the probability calculus to statistical
problems.
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Bortkiewicz was born into a Polish family in St.Petersburg, capital of the
Russian Empire. ``Bortkiewicz" is the Polish spelling of his surname, and most
of his works are written under this spelling. The German tranliteration from
the Russian version is ``Bortkewitsch", under which he wrote his best known
work {\it Das Gesetz der kleinen Zahlen (The Law of Small Numbers.)} An English
transliteration of his surname from the Russian is ``Bortkevich", with emphasis
on the ``ke". Correspondingly, his first name is variously given as Wladyslaw,
Ladislaus, and Vladislav. All three of his identifications: Polish, German and Russian are
evident in his life, contacts and writings. His father Joseph Ivanowitsch Bortkewitsch,
an aristocrat from Kaunas, now in Lithuania, but then a city of the Russian Empire
called Kovno, was a colonel who was also an instructor in artillery and in
mathematics, and had written several texts in mathematics, and
other works in economics and finance. His mother was Helene von Rokicka.
Bortkiewicz pursued his studies in the Faculty of Law of
the University of St. Petersburg, from which he graduated in 1890;
he left to improve his training in statistics and political
economy in Germany. After spending a short time at the university
of Strasburg (1891-1892), where he worked under the direction of
Georg Friedrich Knapp (1842-1926), then at G\"ottingen with
Wilhelm Lexis (q.v.), and also at Vienna and Leipzig, he
defended his doctoral thesis at the University of G\"ottingen in
1893. From 1895 to 1897 he taught actuarial studies and
theoretical statistics as a {\it Privatdozent} at the University of
Strasburg (the title page of the {\it Gesetz} describes him in this capacity),
where he influenced A.A.Chuprov (q.v.). He returned to Russia in 1897,
before coming back permanently to Germany four years later. While employed in the general
office of the Pensions Committee for the railways in St.
Petersburg between 1897 and 1901, he also taught statistics from
1899 until December 1900 at the prestigious Alexandrovsky Lyceum.
In 1901, he was appointed professor {\it extraordinarius} (Associate Professor)
at the University of Berlin, where he remained until his death in 1931.
From 1906 to 1923, he taught simultaneously at the
Handelshochschule of Berlin as a {\it Privatdozent}. It was only
after the introduction of university reforms under the Weimar
republic that Bortkiewicz was promoted to the rank of professor {\it ordinarius},
(full Professor) and then merely {\it ad personam} in statistics and political economy.
The Chair remained vacant after his death;
Bortkiewicz would have liked Gumbel (q.v.) to succeed him, but the latter
was marginalized by his anti-nationalist activities, which earned
him the hostility of the Berlin establishment. Thus the Chair
remained vacant for the entire period of the Third Reich. The short biography of
Bortkiewicz by Gumbel (1978), though politically tendentious, is that of a disciple.
In his generation, Bortkiewicz was the main representative of
mathematical statistics in Germany and within the sphere of German
influence. Scrupulous in the extreme, inclined to be critical and
polemical, Bortkiewicz was a highly respected and feared figure;
but he was rarely understood, so that his teaching as well as his
published work had few imitators. Yet, this work ranges from
political economy to probability, through
demography, actuarial studies, economic statistics and statistical
physics. His published works are mainly in German, although a number,
beginning in 1890 are in Russian; and three or so are in Polish.
Bortkiewicz contributed in a decisive manner to the modern
development of mathematical statistics, taking up the inheritance
of Laplace (q.v.), Poisson (q.v.), Bienaym\'e (q.v.), Cournot (q.v.)
and finally
Lexis (q.v.).
Demography and actuarial studies were still the dominant core of
statistics at the end of the 19th century, and these were
Botkiewicz's first areas of research in Russia and Germany. This
research was an extension of the work of his two German masters, Knapp
in ``theoretical demography" and Lexis in matters concerning the
study of mortality and births. Bortkiewicz lectured widely,
including at the Congress of the International Statistical Institute,
on his
methods and on his results on the treatment of tables, as well as on the
male ratio at birth.
Posthumous fame was ensured by his short work, the {\it Gesetz} of 1898, dedicated to
Lexis, in which he discussed his famous (but widely misunderstood subsequently)
``Law of Small Numbers". In this pamphlet he gave the first account and
application of the distribution
of rare events, established sixty years earlier by Poisson. What is
usually remembered is his famous example on the number of men
killed by horse kicks in the Prussian army. But on a less superficial level,
Bortkiewicz's
book may be interpreted as a twofold plea. First,
by giving theoretical proofs and many numerical examples,
Bortkiewicz consolidated Lexis's theory based on his famous
Q coefficient of dispersion. He proved that rare events whose
frequency is low have a sufficiently regular dispersion to
satisfy Lexis's criterion (Q close to 1). This achieved, Bortkiewicz
provided the first major validation of Lexis's idea,
raising it, somewhat clumsily, to the level of a ``Law of small
numbers". This title was used to recall, rather than contrast with
Poisson's ``Law of Large
Numbers". His success opened up a far more ambitious perspective.
While Lexis's theory provided a simultaneous measure of the
stability of statistical series and a criterion for the applicability of
probabilistic models, the contribution of Bortkiewicz was
essentially a plea for the use of probabilistic methods in
the treatment of statistical data. On this score, his work did not
fail to trigger some violent and contradictory reactions. One was with
Karl Pearson (q.v.) over the Lucy Whitaker paper (Quine and
Seneta, 1987). These controversies
lasted well after World War I and were followed
from time to time by
others, particularly one with Gini (q.v.) concerning priority.
At the turn of the century, German statistics, inheriting
a long administrative tradition with all its history, was
still thoroughly divided on the meaning and existence of
social laws established
mathematically. The ghost of Quetelet (q.v.)
still haunted statistical thinking when Bortkiewicz's work appeared. All the
old mistrust concerning advanced mathematics, and even more
acutely the aim of basing all statistics on the calculus of
probabilities, then resurfaced.
Throughout his career, Bortkiewicz never ceased to defend Lexis'
theory. Many of his publications were related to the study of dispersio;n
which may be regarded as one of the central themes of his work.
Together with Markov (q.v.) and Chuprov in particular,
Bortkiewicz tried
to develop, perhaps in vain, the basis of a real analysis of
variance starting from Lexis' theory, but this direction taken
by continental
statisticians was not followed up, in contrast to the English Biometric
School. While
Chuprov, Bortkiewicz's friend and rival, was able to redirect
his research and recognize the innovations of the English School,
Bortkiewicz for too long allowed himself to be entangled in his
interminable quarrels; another with Karl Pearson was about the
Chi-square distribution, which Bortkiewicz attributed quite
correctly to Helmert.
There remains, however, an area where Bortkiewicz's thinking found a
happier outlet: extremes and order statistics. One may set his
pioneering contribution to the study of extreme values
of 1922 within the framework of his research on dispersion. Starting from
the comments of Fechner on the range, he pursued an argument analogous
to that which had led him to the ``Law of Small Numbers" and showed
that the range, showed a remarkable regularity, similar to that of
rare events. His results and comments, echoing the research carried
out by the School of his old adversary Karl Pearson, would later be
discussed and fruitfully extended by his younger German colleagues
R. von Mises (q.v.), and particularly Gumbel, amongst others.
Bortkiewicz took an interest in every possible application of the
calculus of probabilities, and had a predilection for
intricate problems. In a pamphlet published in 1913, he considered
the question of radioactive radiation, and showed that its distribution
followed probabilistic laws.
In the 1920s Bortkiewicz concerned himself with questions of
economic statistics; the concentration of wealth, which resulted in
a new quarrel with the Italian Gini within the International
Statistical Institute. In 1923-24 his critical review of the
treatise by Irving Fisher (q.v.) on {\it Price Index Numbers} again
started yet another controversy.
Overall, there is only a single area where his name is as familiar as
at the dawn of the 20th century, namely Political
Economy. Like all statisticians trained in German universities
at the end of
the 19th century, Bortkiewicz had acquired a taste for economics,
and demonstrated it by a remarkably astute study of Book
III of {\it Das Kapital} in which Marx discussed his theory of the
transformation of value into price. This work warranted Bortkiewicz being
ranked by Schumpeter (1951) as ``one of the ten greatest economists from
Marx to Keynes" and
\begin{quote}
``By far his most important achievement is his analysis of the
theoretical framework of the Marxian system, much the best thing
ever written on it and, incidentally, on its other critics."
\end{quote}
Bortkiewicz maintained active contacts with Polish scientists, notably
Neyman (q.v.), and was sounded out on accepting a Chair at the University of Warsaw,
and in Krak\'ow. There is a posthumous survey of his work by Neyman - who regards Bortkiewicz's
{\it Die Iterationen} (1917) as his most important work - followed by an
anonymous obituary, both in Polish, in {\it Kwartalnik Statystyczny},
{\bf 8}(1931), 1116-1120.
A systematic study of Bortkiewicz as a
statistician would throw valuable light on this
crucial period in the history of mathematical statistics.
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\begin{thebibliography}{3}
\bibitem{1} Bortkiewicz, L.v. (1893). {\it Die Mittlere Lebensdauer.
Die Methoden ihrer Bestimmung und ihr Verh\"altnis zur
Sterblichkeitsmessung}, Fischer, Jena, 117 pp.
\bibitem{2} Bortkiewicz, L.v. (1898). {\it Das Gesetz der kleinen Zahlen},
Teubner, Leipzig, 52 pp.
\bibitem{3} Bortkiewicz, L.v.(1913). {\it Die radioaktive Strahlung
als Gegenstand wahrscheinlichkeitstheoretischer Untersuchung},
Springer, Berlin, 1913.
\bibitem{4} Gumbel, E.J.(1978). Bortkiewicz, Ladislaus von,
{\it International Encyclopedia of Statistics}, {\bf 1}, 24-27 (with a
Postscript by O.B. Sheynin).
\bibitem{5} Quine, M.P. and Seneta, E.(1987). Bortkiewicz's data and the Law of
Small Numbers. {\it International Statistical Review,} {\bf 55}, 173-181.
\bibitem{6} Schumpeter, J.A.(1951). Ladislaus von Bortkiewicz
(1868-1931),{\it Ten Great Economists, from Marx to Keynes},
Oxford Univ. Press, New York, pp. 302-305.
\bibitem{7} Sheynin, O.B. (1970). Bortkiewicz(or Bortkewitsch), Ladislaus (or
Vladislav) Josephowitsch. {\it Dictionary of Scientific Biography}, {\bf 2},
318-319.
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\hfill{S. Hertz}
\end{thebibliography}
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