Abstract
When the historians came to realize that “they had to count”— which occurred on a visible scale only during the last 50 years — quantitative analyses became a legitimate element of historical narratives. Such analyses were needed very badly, for we know the astounding errors in texts written by earlier historians, who were not accustomed to handling figures and did not realize what precision was required on that point. They would send to battles armies which were so enormous that the entire adult population of a given state would not suffice to man them; they would make towns be inhabited by immense masses, and would send thousands to death when describing effects of plagues. Lelewel alleged that 193,000 people died in Cracow in 1652 as a result of an epidemic,1 which was at least 10 times more than the whole population of that city could amount to at that time. He assumed that in the boom period from two to five million tons of grain used to be exported from Poland through Gdańsk.2 To realize how far he overshot his mark note that in Poland in 1961–3 the total annual four grain crops averaged 14.5 million tons; at the time referred to by Lelewel they could average 1.4 million tons,3 not more than 10 per cent of which would be exported. These data visualize the scale of the methodological upheaval in historical research over the last few decades. Those who are willing to use the term revolution might call that upheaval the quantitative revolution in historical research.
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References
J. Lelewel, “Uwagi nad dziejami Polski i ludu jej”(Comments on the History of Poland and Her People) (1854), in: Polska, dzieje i rzeczy jej (Polish History and Things Polish), vol. III, Poznań 1855, p. 327.
J. Lelewel, “Historia Polski az do konca panowania Stefana Batorego” (History of Poland to the End of the Reign of Stefan Batory) (1813), op. cit., vol. XIII, Poznań 1863, p. 579.
A. Wyczański, “Próba oszacowania obrotu żytem w Polsce w XVI w.”(A Tentative Estimate of the Rye Trade in 16th Century Poland), in: Kwartalnik Historii Kultury Materialnej, No. 1/1961, p. 70.
A. Soboul, “Opis i miara w historii spolecznej”(Descriptions and Measures in Social History), quoted after the Polish-language version in: Kwartalnik Historyczny, No. 2/1966, pp. 282–3.
K. T. Inama-Sternegg, “Geschichte und Statistik”, Statistische Monatschrift, VIII, 1882.
Z. Daszyńska-Golińska, “Metoda statystyki historycznej i jej dotychczasowe zdobycze”(Methods in Historical Statistics and the Achievements of That Discipline To Date), in: Ekonomista Polski, vol. XI, 1892.
This pioneer work is often underestimated when the applications of quantitative methods in the study of social structures are discussed.
Some French historians exaggerate greatly when assessing the role which F. Simiand had played in giving precision to methods of historical research. Even P. Vilar wrote (in connection with his otherwise correct criticism of R. Aron, who fails to notice modern historical research) that Simiand, by laying foundations for historical econometrics, “avait fair passer l’histoire du stade de la description au stade de la mesure”(P. Vilar, “Marxisme et histoire dans te développement des sciences humaines”, Studi storici, vol. I, No. 5/1959-60, p. 1016).
A. Soboul, op. cit., p. 280
Cf. J. Marczewski, “Histoire quantitative — Buts et méthodes”, Cahiers de l’Institut de Science Economique Appliquée, No. 115, Series AF 1, Paris 1962.
Here are some major items concerned with general and historical statistics: S. Szulc, Metody statystyczne (Statistical Methods), vol. I, Warszawa 1952, vol. II, Warszawa 1954; A. Piatier, Statistique et observation économique, vol. I, Paris 1961; E. P. Heckscher, “Quantitative Measurement in Economic History”, Quarterly Journal of Economics, vol. LIII, 1939; W. Kula, “Statystyka histo-ryczna”(Historical Statistics), in: Problemy i metody historii gospodarczej (Problems and Methods in Economic History), ed. cit., pp. 343-406; S. Kuznetz, “Statistics and Economic History”, Journal of Economic History, vol. I, 1941; J. Rutkowski, “Metoda statystyczna”(The Statistical Method) in: Historia gos-podarcza Polski (An Economic History of Poland), vol. I, ed. cit., pp. 8-11; J. Topolski, “Uwagi o metodach statystyki historycznej”(Comments on the Methods Used in Historical Statistics), in: Studia z metodologii historii (Studies in the Methodology of History), ed. cit., pp. 79-113; A. P. Usher, “The Application of the Quantitative Method to Economic History”, Journal of Political Economy, vol. XL, 1932; R. Mols, Introduction à la démographie historique des villes d’Europe du XIV e au XVIII e siècle, vols. I & II, Louvain 1955; S. Bo-rowski, “Charakter i klasyfikacja źródeł statystycznych”(The Nature and Classification of Statistical Sources), Studia Źródloznawcze, vol. IX, Poznan 1964, and the same author’s “Charakter i krytyka oceny źródeł statystycznych”(The Nature of Statistical Sources and a Criticism of Their Evaluation), Studia Źródloznawcze, vol. X, Poznan 1965. In the present chapter we are concerned only with the most general and elementary applications of statistics in historial research, especially that concerned with economic history. See also note 53.
“Identity”is, of course, a limiting concept, or what is termed an idealization; in mathematics, it is an abstract concept; in practice we have to do with identity as restricted to a certain object under consideration, that is, with in-distinguishability.
The present writer accepts that classification, even though W. Kula’s terminology lacks precision. First of all, it is difficult to notice any difference between mass phenomena and individual phenomena which occur on a mass scale. Do mass phenomena not consist of individual ones? The difference is to be sought in the origin of those two kinds of sources.
See J. Czekanowski’s works. An example is provided by W. Kočka, “Obli-czanie pojemności naczyń metodą. korelacji”(Computing the Capacity of Vessels by the Correlation Method), Slavia Antiqua, vol. I, pp. 239–46. Note also E. Vielrose, “Zmiany w odzywianiu się rybaków gdańskich w wieku XII i XIII. Próba oceny statystycznej”(Changes in the Diet of Gdańsk Fishermen in the 12th and 13th centuries. A Tentative Statistical Appraisal), Kwartalnik Historii Kultury Materialnej, No. 2/1956; Vielrose analyses remnants of food found on excavation sites to establish changes in the proportions of the various kinds of food.
J. Rutkowski, Historia gospodarcza Polski (An Economic History of Poland), vol. I, ed. cit., p. 10.
J. P. Guilford, Fundamental Statistics in Psychology and Education, London 1942 (quoted after the Polish-language 1964 edition).
On the grouping of data in historical statistics see W. Kula, Problemy i me-tody historii gospodarczej (Problems and Methods in Economic History), ed. cit., pp. 369-73, and J. Meuvret’s essay in: L’histoire et ses méthodes, ed. cit., pp. 914-24. W. Kula singles out institutional grouping (referring to a specified institution), such as the classification of peasants according to their relation to the manorial farm, conventional grouping (e.g., classification of farms by size: 0 to 2 hectares, 2 to 5 hectares, 5 to 10 hectares, etc.), and analytical (theoretical) grouping, i.e., one made by the historian from the point of view of the requirements of his investigations. He also assumes that theoretical grouping must be verified by the dispersion method, which takes into account the clusters of data and draws the classificational boundaries through areas of Tarification).
W. Kula, op. cit., p. 589. This statement comes from his excellent analysis of problems of historical metrology (Chap. XIII of his book).
A. Pawinski, Polska XVI w. pod względem geograficzno-statystycznym (16th Century Poland. Geography and Statistics), vols. 1 & 2-Greater Poland, Warszawa 1883; vols. 3 & 4-Lesser Poland, Warszawa 1886; vol. 5-Masovia, Warszawa 1895; A. Jablonowski’s contribution covers vol. 6-Podlasie, Warszawa 1908-10; vol. 7-Red Ruthenia, Warszawa 1902-3; vol. 8-the Volhynia and the Podolia, Warszawa 1889; vols. 9 to 11-the Ukraine, Warszawa 1894-7.
T. Ladenberger, Zaludnienie Polski na poczqtku panowania Kazimierza Wielkiego (The Population of Poland at the Beginning of the Reign of Casimir the Great), Lwów 1930; see also T. Ladogórski, Studio, nod zaludnieniem Polski XIV wieku (Studies in the Population of Poland in the 14th Century), Wroclaw 1955.
J. Rutkowski, Statystyka zawodowa ludności wiejskiej w Polsce w drugiej polowie XVI wieku (The Occupational Statistics of the Rural Population in Poland in the Second Half of the 16th Century), Krakow 1918, pp. 29–30.
S. Hoszowski, “Dynamika rozwoju zaludnienia Polski w epoce feudalnej (X-XVIII w.)”(The Growth of Poland’s Population in the Feudal Period, 10th Time When the Congress Kingdom of Poland was Being Organized), Kraków to 18th Centuries), Roczniki Dziejów Spolecznych i Gospodarczych, vol. XIII,. p. 173.
Z. Kirkor-Kiedroniowa, Wloscianie i ich s prow a w dobie organizacyjnej i konstytucyjnej Królestwa Polskiego (The Peasants and Their Cause at the 1912.
H. Grossman, “Struktura społeczna i gospodarcza Księstwa Warszawskiego na podstawie spisów ludności 1808–1810”(The Social and Economic Structure of the Duchy of Warsaw as Reflected in the Censuses, 1808-10), Kwartalnik Statystyczny, No. 2/1928.
Generalne tabele statystyczne Śląska 1787 roku (General Statistical Tables of Silesia for 1787); edited and introduced by T. Ładogórski, Wroclaw 1954.
J. Fierich, “Kultury rolnicze, zmianowania i zbiory w Katastrze Jozefin-skim 1785–1787”(Cultures, Rotation of Crops, and Volume of Crops as Shown by the Josephine Cadaster, 1785-7), Roczniki Dziejów Spolecznych i Gospodarczych, vol. XII, Poznań 1950.
This suggestion was first made at the 8th Congress of Polish Historians, held in Kraków in 1958 (see Historia Gospodarcza Polski (Economic History of Poland), Proceedings of the 8th Congress of Polish Historians, Warszawa 1960, p. 19.), and came to be criticized by W. Kula (ibid., p. 54, and also in Problemy i metody historii gospodarczej (Problems and Methods in Economic History), p. 362). The present writer’s approach won the support of a statistician (see S. Borowski, “Charakter i kryteria oceny źródeŁ statystycznych”(The Nature of Statistical Sources and the Criteria of Their Appraisal), Studia Źródło-znawcze, vol. IX, pp. 1-14). See also J. Topolski’s comments on W. Kula’s book quoted in this footnote in Ekonomista, No. 4/1964, p. 831.
Cf. S. Szulc, Metody statystyczne (Statistical Methods), vol. II, ed. cit., p. 173.
We are not concerned here with the mathematical foundations of the representation method, since that would require extensive comments and explanations; the reader is referred to text-books of statistics, such as Part V of vol. II of S. Szulc’s book quoted in footnote 28. The issues of probability as related to statistical methods are discussed by J. P. Guilford (see footnote16 above). See also H. Kryński, Matematyka dla ekonomistów (Mathematics for Economists), Warszawa 1964, pp. 354-67.
In random sampling we can use tables of random numbers.
Cf. K. J. Arrow, “Mathematical Models in the Social Sciences”in: The Policy Sciences, (eds.) D. Lerner & H. D. Lasswell, Stanford 1957.
J. P. Guilford, op. cit., p. 226.
The chi-square test was used by E. Vielrose in his paper quoted in footnote 14 above. The present writer is obliged to Prof. Vielrose for his extensive explanations in a personal letter.
The example is drawn from O. Lange and A. Banasinski, Teoria statystyki (Statistical Theory), Warszawa 1968, p. 123.
L. Zytkowicz, “Uwagi o gospodarstwie chlopskim w dobrach kościelnych w XVI wieku”(Comments on Peasant Holdings on Church-owned Lands in the 16th Century) in: Studia z dziejów gospodarstwa wiejskiego (Studies in the History of Peasant Holdings), vol. I, Wroclaw 1957.
J. Wiśniewski, Rozklad dochodow wedlug wysokości w rolqu 1929 (Income Distribution by Size in 1929), Warszawa 1934.
S. Borowski, “Rozwój mechanizacji pracy w rolnictwie Wielkopolski w la-tach 1890–1918”(Growing Mechanization of Agriculture in Greater Poland, 1890–1918), in: Roczniki Dziejów Społecznych i Gospodarczych, vol. XIX, Poznań 1958.
A. Jezierski, “Próba analizy statystycznej rozwarstwienia wsi na początku XX wieku”(A Tentative Statistical Analysis of the Stratification of the Rural Population in the Early 20th Century), in: Roczniki Dziejów Spolecznych i Gospodarczych, vol. XVIII, Poznań 1957.
Cf. O. Lange & A. Banasinski, Teoria statystyki (Statistical Theory), ed. cit., pp. 172–3.
S. Borowski, see footnote 37.
Among theoretical studies concerned with such fluctuations see G. Imbert, Des mouvements de longue durée Kondratieff, Aix-en-Provence 1956.
The advantages of chain idicators are stressed by W. Kula in Problemyi metody historii gospodarczej (Problems and Methods in Economic History), ed. cit., pp. 378-80.
The example is drawn from O. Lange & A. Banasinski, Teoria statystyki (Statistical Theory), ed. cit., pp. 201–2.
These data are drawn from A. Sauvy, Histoire économique de la France entre les deux guerres (1918–1931), Paris 1965, p. 462.
For considerations of space we do not give examples of the computation of trends; the reader is referred to works on econometrics, e.g., O. Lange, Introduction to Econometrics, Oxford—Warszawa 1962.
Cf. S. H. Coontz, Population Theories and Their Economic Interpretation, London 1957.
S. Kurowski, Historyczny procès wzrostu gospodarczego (The Historical Process of Economic Growth), Warszawa 1963.
On apparent relationships see S. Nowak, Studio z metodologii nauk spo-lecznych (Studies in the Methodology of the Social Sciences), ed. cit., pp. 81 ff.
W. Kula, Teoria ekonomiczna ustroju feudalnego (The Economic Theory of the Feudal System), Warszawa 1962, p. 105. See also I. Rychlikowa, “Nie-ktore zagadnienia metodyczne w badaniach cen i rynku w drugiej polowie XVIII wieku”(Some Methodological Issues in the Study of Prices and Markets in the Second Half of the 18th Century), Kwartalnik Historii Kultury Material-nej, No. 3/1964, pp. 375-405.
J. Purš, “Model závilosti rústu stávkového hunti na rozvoji továrni výdoby v obdobě předmonopolniho kapitalismu”(A Model of the Effect of Growing Strikes on Development of Industrial Production Under Premonopolistic Capitalism), Československy Časopis Historicky, vol. XI, 1963, pp. 34–45.
S. Ossowski, O. osobliwościach nauk spolecznych (On the Peculiarities of the Social Sciences), ed. cit., pp. 253–4.
The applications (mostly associated with the name of J. Czekanowski) of correlation co-efficients to studies in the history of culture were discussed by S. Klimek, “Metoda ilościowa w badaniach nad historią kultury”(The Quantitative Method in the Study of the History of Culture), Roczniki Dziejów Spolecznych i Gospodarczych, vol. III, Poznan 1934, pp.57-76.
Books and papers on the applications of information theory and computers to historical research are too many to be quoted here. We shall mention here only those guides for using computers in historical research which we consider the most useful for historians: Ch. M. Dollar, R. J. Jensen, Historian’s Guide to Statistics. Quantitative Analysis and Historical Research, New York, Chicago, San Francisco, Atlanta, Dallas, Montreal, Toronto, London, Sidney 1971; E. Shorter, The Historian and the Computer. A Practical Guide, Englewood Cliffs, N.Y. 1971. See also the elementary introduction to statistics for historians: R. Floud, An Introduction to Quantitative Methods for Historians, Princeton 1973. Literature of the subject is given in the book by Dollar and Jensen
For information’s sake we give here binary system equivalents of the first numerals in the decimal system: 0-0, 1-1, 2-10, 3-11, 4-100, 5-101, 6-110, 7-111, 8-1000, 9-1001, 10-1010, 11-1011, etc. For instance, 2 in the decimal system is rewritten in the binary system thus: 2 = l.21 + 0.20, i.e., as a sequence of powers of 2 multiplied, as the case may be, by 1.
J. C. Gardin and M. P. Garelli used an IBM computer to process mathematically the data provided by the numerous cuneiform tablets dating from the 19th century B.C. and excavated in Mesopotamia; they contain data about commercial transactions concluded among some 2000 merchants over a period of about 50 years. The study was intended to establish the merchants’ places of origin, the commodities they specialized in, etc. (Cf. “Étude sur les etablissements assyriens en Cappadoce”, Annales ESC, vol. 16, No. 5/1961, pp. 837–76.J. de Launuy also used an IBM computer to study opinions to be found in historical literature on many issues of contemporary history (cf. Les grandes controverses de l’histoire contemporaine, Lausanne 1964). The progress in the applications of computers in historical research up to 1970 was largely discussed at the 13th International Congress of Historical Sciences in Moscow. Special mention is due to the following papers: D. V. Deopik, G. M. Dobrov, J. J. Kahk, I. D. Kovalchenko, H. E. Palli, V. A. Ustinov, Quantitative and Machine Methods of Processing Historical Information, Moscow 1970; J. Schneider, La machine et l’histoire. De l’emploi des moyens mécaniques et électroniques dans la recherche historique, Moscou 1970; C. G. Andrae, Sven Lundkvist, The Use of Historical Mass Data. Experiences from a Project on Swedish Popular Movements, Moscow 1970. For general comments see J. H. Hexter, History, the Social Sciences and Quantification, Moscow 1970. Current advances in modern quantitative methods are discussed by Historical Methods Newsletter, published by The University Center for International Studies and The Department of History at the University of Pittsburgh.
That such research has a fairly long tradition is shown by W. W. Grey, The Calculus of Variant. An Essay on Textual Criticism, Oxford 1927. See also Poetyka i matematyka (Poetics and Mathematics), M. R. Mayenowa (ed.), Warszawa 1965 (reviewed in Poland by J. Kmita in Studia Metodologiczne, No. 3)
An example is provided by the study of the authorship of St. Paul’s epistles. See B. Jewsiewicki, “Uwagi o zastosowaniu maszyn cyfrowych w ba-daniach historycznych”(Comments on the Applications of Digital Computers in Historical Research), Kwartalnik Historii Kultury Materialnej, No. 4/1965, p. 734.
An example is provided by an analysis of the Koran. See K. Wyczańska, “Prace nad mechanizacją. informacji w naukach spolecznych”(Mechanization of Information in the Social Sciences), Kwartalnik Historii Kultury Materialnej, No. 4/1965, p. 741.
E. Rostworowski, Legendy i fakty XVIII w. (Legends and Facts of the 18th Century), Warszawa 1963, pp. 68–144
Ibid., p. 124.
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Topolski, J. (1976). Quantitative Methods in Historical Research. In: Methodology of History. Synthese Library, vol 88. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1123-5_22
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