×

Scientific method, statistical method and the speed of light. (English) Zbl 1059.62507

Summary: What is ”statistical method”? Is it the same as ”scientific method”? This paper answers the first question by specifying the elements and procedures common to all statistical investigations and organizing these into a single structure. This structure is illustrated by careful examination of the first scientific study on the speed of light carried out by A. A. Michelson in 1879. Our answer to the second question is negative. To understand this a history on the speed of light up to the time of Michelson’s study is presented. The larger history and the details of a single study allow us to place the method of statistics within the larger context of science.

MSC:

62A01 Foundations and philosophical topics in statistics
62P35 Applications of statistics to physics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Alexander, A. F. O’D. (1970). James Bradley. In Dictionary of Scientific Biography (C. C. Gillispie, ed.) 2 387- 389. Scribner’s, New York.
[2] Aristotle. Nicomachean ethics. In The Complete Works of Aristotle: The Revised Oxford Translation (J. Barnes, ed.)
[3] 1729-1867. Princeton Univ. Press (1984). (Translated by W. D. Ross with revision by J. O. Urmson.)
[4] Aristotle. On the heavens. In The Complete Works of Aristotle: The Revised Oxford Translation (J. Barnes, ed.) 1
[5] -511. Princeton Univ. Press (1984). (Translated by J. L. Stocks.)
[6] Aristotle. On the soul. In The Complete Works of Aristotle: The Revised Oxford Translation (J. Barnes, ed.) 1
[7] -692. Princeton Univ. Press (1984). (Translated by J. A. Smith.)
[8] Aristotle. Sense and sensibilia. In The Complete Works of Aristotle: The Revised Oxford Translation (J. Barnes, ed.)
[9] 693-713. Princeton Univ. Press (1984). (Translated by J. I. Beare.)
[10] Bacon, F. (1620). Novum organum. In Novum Organum: With Other Parts of the Great Instauration (P. Urbach and J. Gibson, ed.) 33-293. Open Court, Chicago. (1994 translation.)
[11] Barnett, V. (1982). Comparative Statistical Inference, 2nd ed. Wiley, New York. · Zbl 0593.62002
[12] Beeckman, I. (1629). Folio 340, 19 March 1629. In Journal Tenupar Isaac Beeckman de 1604 a 1634 (C. de Waard,
[13] Ed.) 3 112. Nijoff, The Hague (1939-1953).
[14] Bipm, (1983). Comptes Rendus des Séances de la 17e CGPM. BIPM, Sévres, France.
[15] Box, G. E. P. (1976). Science and statistics. J. Amer. Statist. Assoc. 71 791-799. JSTOR: · Zbl 0335.62002 · doi:10.2307/2286841
[16] Chatfield, C. (1995). Problem Solving. A Statistican’s Guide, 2nd ed. Chapman and Hall, London. · Zbl 0867.62002
[17] Cohen, I. B. (1940). Roemer and the first determination of the velocity of light. Isis 31 327-379.
[18] Cotter, C. H. (1968). A History of Nautical Astronomy. North-Holland, Amsterdam.
[19] Deming, W. E. (1953). On the distinction between enumerative and analytic surveys. J. Amer. Statist. Assoc. 48 244-255.
[20] Descartes, R. (1634). Letter to Beeckman, August 22 1634. In Oeuvres de Descartes 1 307-312. (C. Adam and P. Tannery, eds.) 1969, Librairie Philosophique J. VRIN, Paris.
[21] Drake, S., ed. (1957). Discoveries and Opinions of Galileo. Anchor Books, Doubleday, New York. (Translated with an introduction and notes by Stillman Drake.)
[22] Drake, S. (1978). Galileo at Work: His Scientific Biography. Univ. Chicago Press. · Zbl 0392.01008
[23] Durbin, J. (1987). Statistics and statistical science. J. Roy. Stat. Soc. Ser. A 150 177-191. JSTOR: · doi:10.2307/2981472
[24] Edgeworth, F. Y. (1885). Methods of statistics, In Proceedings of the Silver Jubilee of the Royal Statistical Society 181-217.
[25] Feyerabend, P. (1988). Against Method, rev. ed. Verso of New Left Books, New York.
[26] Fisher, R. A. (1925). Statistical Methods for Research Workers. Oliver & Boyd, Edinburgh. (13th ed. published 1958.)
[27] Galilei, G. (1610). The starry messenger. In Discoveries and Opinions of Galileo (G. S. Drake, ed.) 21-58.
[28] Galilei, G. (1615). Letter to Madame Christina of Lorraine Grand Duchess of Tuscany concerning the use of Biblical quotations in matters of Science. In Discoveries and Opinions of Galileo (S. Drake, ed.) 173-216.
[29] Galilei, G. (1638). Two New Sciences Including Centers of Gravity and Force of Percussion. Univ. Wiscon · Zbl 0286.01007
[30] s
[31] Gaukroger, S. (1995). Descartes: An Intellectual Biography. Clarendon, Oxford.
[32] Good, I. J. (1988). Scientific method and statistics. In Encyclopedia of Statistical Sciences 8 291-304. Wiley, New York.
[33] Hacking, I. (1985). Representing and Intervening: Introductory Topics in the Philosophy of Natural Science. Cambridge Univ. Press.
[34] Hahn, G. J. and Meeker, W. Q. (1993). Assumptions for statistical inference. Amer. Statist. 47 1-11.
[35] Hand, D. J. (1994). Deconstructing statistical questions. J. Roy. Statist. Soc. Ser. A 157 317-356.
[36] Hume, D. (1739-1740). A Treatise on Human Nature. Oxford Univ. Press. [Analytical Index by L. A. SelbyBigge (1888); 2nd ed. (1978), with text revised and notes by P. H. Nidditch.]
[37] Kendall, M. G. and Stuart, A. (1958). The Advanced Theory of Statistics 1. Distribution Theory. Griffin, London. [First published in 1943; revised in 1958 with A. Stuart.] · Zbl 0223.62001
[38] Kobal, Z. (1975). Ole Christensen Römer. In Dictionary of Scientific Biography 11 525-527. Scribner’s, New York.
[39] Kuhn, T. S. (1962). The Structure of Scientific Revolutions. Princeton Univ. Press. (2nd ed., 1970.)
[40] Lakatos, I. (1978). Falsification and the methodology of scientific research programmes. In The Methodology of Scientific Research Programmes: Philosophical Papers (J. Worrall and G. Currie, ed.) 1 8-101. Cambridge Univ. Press. (First published in 1970.) · Zbl 0373.02002 · doi:10.1017/CBO9780511621123
[41] Lindberg, D. C. (1978). Medieval Latin Theories of the Speed of Light. In Roemer et la Vitesse de la Lumi ere (R. Taton, ed.) 45-72. Librairie Philosophique J. VRIN, Paris.
[42] Losee, J. (1993). A Historical Introduction to the Philosophy of Science, 3d ed. Oxford Univ. Press.
[43] Madden, E. H., ed. (1966). Theories of Scientific Method: The Renaissance through the Nineteenth Century. Univ. Washington Press.
[44] Michelson, A. A. (1880). Experimental determination of the velocity of light made at the U. S. Naval Academy, Annapolis. Astronomical Papers 1 109-145.
[45] Michelson, A. A. and Morley, E. W. (1887). The motion of the earth relative to the luminiferous ether. Amer. J. Sci. 34 333ff.
[46] Michelson, A. A., Pease, F. G. and Pearson, J. (1935). Measurement of the velocity of light in a partial vacuum. Astrophysics Journal 82 26-61.
[47] Moore, D. and MCCabe, G. (1993). Introduction to the Practice of Statistics, 2nd ed. Freeman, New York. · Zbl 0701.62002
[48] Nelder, J. A. (1986). Statistics, science and technology. J. Roy. Statist. Ser. A 149 109-121.
[49] Newcomb, S. (1882). Measures of the velocity of light made under the direction of the Secretary of the Navy during the years 1880-82. Astronomical Papers 3 107-239.
[50] Pearson, K. (1911). The Grammar of Science. Meridian Books, New York. [First published in 1892, revised 1900, final edition in 1911. Reprinted (1957) with introduction by Ernest Nagel.]
[51] Popper, K. R. (1959). The Logic of Scientific Discovery. Basic Books, New York. (First English edition; original German edition published 1934.) · Zbl 0083.24104
[52] Sakellariadis, S. (1982). Descartes’ experimental proof of the infinite velocity of light and Huygens’ rejoinder. Archive for History of Exact Sciences 26 1-12. · Zbl 0484.01002
[53] Sobel, D. (1995). Longitude: The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time. Walker, New York.
[54] Stigler, S. M. (1977). Do robust estimators work with REAL data? (with discussion). Ann. Statist. 5 1055-1098. · Zbl 0374.62050 · doi:10.1214/aos/1176343997
[55] Stigler, S. M. (1986). The History of Statistics: The Measurement of Uncertainty before 1900. Harvard Univ. Press. · Zbl 0656.62005
[56] Swenson, L. S., Jr. (1972). The Ethereal Aether: A History of the Michelson-Morley-Miller Aether-Drift Experiments 1880-1930. Univ. Texas Press.
[57] Taton, R. (1971). Gian Domenico Cassini. In Dictionary of Scientific Biography 3 100-104. Scribner’s, New York.
[58] Tukey, J. W. (1980). We need both exploratory and confirmatory. Amer. Statist. 34 23-25. [Reproduced in Collected Works of John Tukey 4.] JSTOR: · doi:10.2307/2682998
[59] Wheeler, D. J. and Lyday, R. W. (1989). Evaluating the Measurement Process. SPC Press, Knoxville, TN.
[60] Wild, C. J. and Pfannkuch, M. (1999). Statistical thinking in empirical enquiry. Internat. Statist. Rev. 67 223-248. · Zbl 0963.62115 · doi:10.1111/j.1751-5823.1999.tb00442.x
[61] Youden, W. J. (1985). Experimentation and Measurement. National Science Teachers’ Association, Washington, DC.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.