Mendeleev and the Mathematical Treatment of Observations in Natural Science

AbstractD. I. Mendeleev (1834–1907), the eminent chemist, rejected doubtful experiments and spoke out against amassing observations. He gave thought to eliminating systematic errors and offered a simple test of the “harmony” of observations. Modern statistics has recognized harmony as symmetry of the appropriate density function and has independently quantified asymmetry in accordance with Mendeleev's idea. Mendeleev made mistakes in estimating the plausibility of his data, and he hardly knew Gauss's second formulation of the method of least squares. An analysis of his work sheds light on the level of statistical knowledge in the natural sciences beyond astronomy and geodesy in the late 19th century.Der berühmte Chemiker D. I. Mendeleev (1834–1907) warf zweifelhafte Beobachtungen weg und trat gegen die Anhäufung von Beobachtungen auf. Er hat nach Eliminierung systematischer Fehler gestrebt und ein einfaches Kriterium für die “Harmonie” der Beobachtungen vorgeschlagen. Die moderne Statistik hat Harmonie als Symmetrie der entsprechenden Dichtefunktion anerkannt und hat selbst ein quantitatives Maß der Asymmetrie, das Mendeleev's Idee entspricht, eingeführt. Mendeleev irrte sich bei der Abschätzung der Sicherheit seiner Beobachtungen und war kaum mit der zweiten Gauss'schen Begründung der Methode der kleinsten Quadrate bekannt. Eine Analyse seines Werkes bringt Licht in den Stand der statistischen Kenntnis der Naturwissenschaft des späten 19. Jahrhundert außerhalb der Astronomie und Geodäsie

C.F. Gauss and the method of least squares

Gauss introduced the MLSq and Helmert completed its development whereas Bessel made important discoveries in astronomy and geodesy but was often extremely inattentive. Gauss’ final condition of least variance led to effective estimators of the unknowns sought, jointly effective in case of the normal distribution of the observational errors. Gauss’ memoire of 1823 leads to the principle of least squares much easier than generally thought

Around the theory of errors

The aims of the theory of errors and its relations with statistics are described. The term true value of a constant and the subjective approach in the error theory and statistics are explained and illustrated and a hint at the emergence of a new theory of errors is provided

Addendum No. 2 Antistigler

Stigler is the author of two books (1986; 1999) in which he dared to profane the memory of Gauss. Stigler is considered as the best historian of statistics of the 20th century. This paper contains my critical remarks on his works

KEPLER AS A STATISTICIAN

Drawing on my previous publications (see Bibliography), I describe Kepler’s work on the mathematical treatment of observations and astrology. In particular, I investigate how he rejected the Ptolemaic system of the world and note that his astrology had the features of qualitative correlation

Social Statistics: Its History and Some Modem Issues

Based on my previous publications and many other sources, I trace the history of social statistics before the 20th century and link it with the development of the statistical method in natural sciences. Many recent statistical issues had scarcely, or not at all existed then, and before Lexis probability theory had hardly entered statistics. Moreover, its introduction met with real and imaginary difficulties. Other topics discussed here are the present situation regarding "mathematical" versus "theoretical" statistics and the similarities and differences between statistics and the theory of errors.History of social statistics, statistics and the theory of probability, statistics and error theory.