Jens Høyrup

Bio: Jens Høyrup is an academic researcher from Roskilde University. The author has contributed to research in topics: Babylonian mathematics & Greek mathematics. The author has an hindex of 20, co-authored 169 publications receiving 1507 citations. Previous affiliations of Jens Høyrup include Chinese Academy of Sciences & University of Copenhagen.

Lengths, Widths, Surfaces: A Portrait of Old Babylonian Algebra and Its Kin

Abstract: I. Introduction / II. A New Reading / III. Select Textual Examples / IV. Methods / V. Further 'Algebraic' Texts / VI. Quasi-Algebraic Geometry / VII. Old Babylonian 'Algebra': A Global Characterization / VIII. The Historical Framework / IX. The 'Finer Structure' of the Old Babylonian Corpus / X. The Origin and Transformations of Old Babylonian Algebra / XI. Repercussions and Influences / XII. Index of Tablets / XIII. Index of Akkadian and Sumerian Terms and Key Phrases / XIV. Name Index / XV. Subject Index / XVI. Abbreviations and Bibliography

From Hesiod to Saussure, from Hippocrates to Jevons: An Introduction to the History of Scientific Thought between Iran and the Atlantic

Abstract: claims with real quantified laws). In order to solve this problem, one has to introduce a notion of the “price of production”, for which it holds true that producers will continue to supply the market with such goods that can be produced in unlimited quantity as long as the price they anticipate exceeds their price of production. Such a notion was introduced by Alfred Marshall in 1890 in his Principles of Economics [Marshall 1949]. As it turns out, Marshall’s determination of this price is mathematically equivalent to what Marx had developed on the foundation of the labour value theory in volume III of Das Kapital (published only in 1894 by Engels) when confronting the problem of real market prices (more precisely, the equilibrium prices toward around which real prices fluctuate – Marx’s thinking was dynamic, that of Marshall static). Ideology and political whitewashing were thus no longer the only determinants of the content and results of theory. Marshall’s general aim was still to prove that the prevailing economic system was optimal. He did so by combining arguments from mathematical curves with verbal exposition (shifting to the latter when the outcome of his mathematics threatened to make conflicts with his intended conclusion too glaring. But even Marshall was not the end point of the marginalist development. In 1933, Marshall’s most brilliant student Joan Robinson showed in her Economics of Imperfect competition (second edition [J. Robinson 1969]) that his methods and arguments when taken seriously lead to a conclusion that diverges strongly from what Marshall had believed. As she shows, an economy where each sector is dominated by a small number of agents (since decades the actual situation in the capitalist economy) will 1662 In one such case, Marshall [1949: 380 n.1] claims that “abstract reasonings [...] are apt to be misleading, not only in detail, but even in their general effect [...]. Some [...] follow their mathematics boldly, but apparently without noticing that their premises lead inevitably to the conclusion that, whatever firm first gets a good start will obtain a monopoly of the whole business of its trade in its district”. What made Marshall reject this conclusion was not that it was contradicted by empirical evidence; monopolization was indeed the unmistakeable trend since decades when Marshall wrote. The problem was that this “inevitable” conclusion following from “bold” use of Marshall’s mathematics not only contradicted his ideal picture but also eliminated the basis for many of his arguments. A brief postlude 1243 never operate optimally on global terms if each agent optimizes his behaviour according to his private interests. Beyond providing monopolists with conceptual tools that allow them to determine better than by instinct alone what their private interests ask for, Joan Robinson’s theory thus showed that the “invisible hand” is less beneficial than proclaimed by Jevons and Marshall. Though no full theory of the economic crisis that had broken out, Joan Robinson provided part of the explanation. The optimistic aspect of the moral is thus that even a mediocre contribution which gains undeserved prestige may, if only further work is done seriously and critically – that is, in agreement with the general norms for decent scientific work – become fruitful in the longer run. Done seriously and critically, scientific practice may then provide both functioning technical knowledge and such insights as can serve enlightenment purposes. (The pessimistic aspect is of course that may does not entail must.) One may like or dislike the uses to which the technical knowledge is put, but we must recognize that the production of applicable knowledge has been seen since the 17th century as one of the properties that characterizes valid science. Whoever does not welcome insights that can serve enlightenment purposes does not deserve the name of an intellectual.

Sociology of Science

Abstract: The Social Contexts of Research. Edited by Saad Z. Nagi and Ronald G. Corwin. Pp. xii + 409. (John Wiley: New York and London, August 1972.) £5.65.

A Complete Bibliography of Publications in Berichte zur Wissenschaftsgeschichte (Reports on the History of Science)

Abstract: [1140, 267, 446, 1024, 666, 348, 618, 217, 1038, 1152, 873, 81, 159, 198, 1075, 1142, 1189, 1196, 1036, 775, 835, 1145, 1178, 915, 1060, 1194, 1193, 885, 1192, 454, 360, 982, 407, 558, 669, 122, 196, 194, 218, 291, 349, 357, 446, 523, 545, 535, 158, 844, 976, 277, 217, 79, 950, 539, 493, 913, 1056, 159, 198, 403, 235, 702, 914, 237, 276, 120, 838, 1074, 840, 374, 197, 351, 372, 431, 581, 405, 293, 438]. -/48 [217]. -/Bd [198]. -/DM [446]. -arbeiten [1201]. -Geschichtsschreibung [1175]. -Mark [378]. -ÖS [1145]. -praxis [956]. -Schleinkofer [948]. -theoretische [1689].