The Transformation of Aristotle's Mechanical Questions: A Bridge Between the Italian Renaissance Architects and Galileo's First New Science

The reception process of Aristotle's Mechanical Questions during the early modern period began with the publication of the corpus aristotelicum between 1495 and 1498. Between 1581 and 1627, two of the thirty-five arguments discussed in the text, namely Question XIV concerning the resistance to fracture and Question XVI concerning the deformation of objects such as timbers, became central to the work of the commentators. The commentaries of Bernardino Baldi (1581–1582), Giovanni de Benedetti (1585), Giuseppe Biancani (1615) and Giovanni di Guevara (1627) gradually approached the doctrine of proportions of the Renaissance architects, some aspects of which deal with the strength of materials according to the Vitruvian conception of scalar building. These aspects of the doctrine of proportions were integrated into the Aristotelian arguments so that a theory of linear proportionality concerned with the strength of materials could be formulated. This very first theory of strength of materials is the theory to which Galileo critically referred in his Discorsi where he published his own theory of strength of materials. Economic and military constraints are determined as the fundamental reasons for the commentators’ commitment to developing a theory of strength of materials that later linked Galileo's work to the practical knowledge of the architects and machine-builders of his time.     

Knowing what would happen: The epistemic strategies in Galileo's thought experiments

While philosophers have subjected Galileo's classic thought experiments to critical analysis, they have tended to largely ignored the historical and intellectual context in which they were deployed, and the specific role they played in Galileo's overall vision of science. In this paper I investigate Galileo's use of thought experiments, by focusing on the epistemic and rhetorical strategies that he employed in attempting to answer the question of how one can know what would happen in an imaginary scenario. Here I argue we can find three different answers to this question in Galileo later dialogues, which reflect the changing meanings of ‘experience’ and ‘knowledge’ (scientia) in the early modern period. Once we recognise that Galileo's thought experiments sometimes drew on the power of memory and the explicit appeal to ‘common experience’, while at other times, they took the form of demonstrative arguments intended to have the status of necessary truths; and on still other occasions, they were extrapolations, or probable guesses, drawn from a carefully planned series of controlled experiments, it becomes evident that no single account of the epistemological relationship between thought experiment, experience and experiment can adequately capture the epistemic variety we find Galileo's use of imaginary scenarios. To this extent, we cannot neatly classify Galileo's use of thought experiments as either ‘medieval’ or ‘early modern’, but we should see them as indicative of the complex epistemological transformations of the early seventeenth century.     

The Curie's Lab and its Women (1906–1934) Le laboratoire Curie et ses Femmes (1906–1934)

When Bouvet discovered the relationship between the binary arithmetic of Leibniz and the hexagrams of the I ching—in reality only a purely formal correspondence—he sent to Leibniz a woodcut diagram of the Fu-Hsi arrangement, which provides the key to the analogy. This diagram, in a re-drawn version, was first published by Gorai Kinzō in a study of Leibniz's interpretation of the I ching and Confucianism which has been influential in providing, indirectly, the principal source for the accounts of Wilhelm and Needham. Yet this pioneering study of Leibniz's interpretation of the hexagrams is virtually unknown. Even the account of Needham, who saved it from complete obscurity, contains one or two inaccuracies about it and these are repeated by Zacher in his otherwise excellent monograph on Leibniz's binary arithmetic.     

Different shades of Newton: Herman Boerhaave on Newton mathematicus,philosophus, and optico-chemicus

In this paper I will probe into Herman Boerhaave's (1668–1738) appropriation of Isaac Newton's natural philosophy. It will be shown that Newton's work served multiple purposes in Boerhaave's oeuvre, for he appropriated Newton's work differently in different contexts and in different episodes in his career. Three important episodes in, and contexts of, Boerhaave's appropriation of Newton's natural philosophical ideas and methods will be considered: 1710–11, the time of his often neglected lectures on the place of physics in medicine; 1715, when he delivered his most famous rectorial address; and, finally, 1731/2, in publishing his Elementa chemiae. Along the way, I will spell out the implications of Boerhaave's case for our understanding of the reception, or use, of Newton's ideas more generally.     

Galileo and Descartes on Copernicanism and the cause of the tides

Galileo and Descartes were on the front lines of the defense of Copernicanism against theological objections that took on special importance during the seventeenth century. Galileo attempted to overcome opposition to Copernicanism within the Catholic Church by offering a demonstration of this theory that appeals to the fact that the double motion of the earth is necessary as a cause of the tides. It turns out, however, that the details of Galileo's tidal theory compromise his demonstration. Far from attempting to provide a demonstration of the earth's motion, Descartes ultimately argued that his system is compatible with the determination of the Church that the earth is at rest. Nonetheless, Descartes's account of the cause of the tides creates difficulty for this argument.     

Did Samuel Clarke really disavow action at a distance in his correspondence with Leibniz?: Newton,Clarke, and Bentley on gravitation and action at a distance

In this paper I ague against John Henry's claim that Newton embraced unmediated action at a distance as an explanation of gravity (Henry, 1994, 1999, 2011, 2014). In particular, I take issue with his apparent suggestion that the fact, as he sees it, that two of Newton's prominent followers, namely, Richard Bentley and Samuel Clarke, embraced unmediated action at a distance as an explanation of gravity provides significant supporting evidence that Newton did as well (see Henry, 1994 and 1999). Instead, I argue that while Bentley did ultimately defend the notion of unmediated action at a distance as an explanation of gravity, Newton himself accepted that notion neither in his correspondence with Bentley, as Henry has maintained, nor in any of his later works. I also provide evidence that suggests that Newton did, in fact, accept both the principle of local causation and the passivity of matter. Finally, I argue that whatever the case may be with respect to Newton on the matter, it is clear from his correspondence with Leibniz, as well as from his Boyle lectures, that contrary to what Henry has maintained, Clarke was a stalwart opponent of unmediated action at a distance due to his strong commitment to both the principle of local causation and the passivity of matter.     

Instruments of Music,Instruments of Science: Hermann von Helmholtz's Musical Practices,his Classicism,and his Beethoven Sonata

The young Hermann Helmholtz, in an 1838 letter home, declared that he always appreciated music much more when he played it for himself. Though a frequent concert-goer, and celebrated for his highly influential 1863 work on the physiological basis of music theory, Die Lehre von den Tonempfindungen, it is likely that Helmholtz's enduring engagement with music began with his initial, personal experience of playing music for himself. I develop this idea, shifting the discussion of Helmholtz's work on sound sensation back to its origins, and examine the role of his material interaction with musical instruments and music itself. In his sound sensation studies, Helmholtz understood sound as an external, physical object. But Helmholtz also conceived of sound in musical terms. Further, Helmholtz's particular musical tastes as well as his deeply personal interaction with musical instruments allowed him to reconcile his conception of sound as physical object with his conception of sound as music. Helmholtz's physiological theory of sound sensation was both the product of and constitutive of how he heard and created sound. I argue that Helmholtz himself was the embodied reconciliation of his physiological theory of sound sensation and his belief that musical aesthetics were historically and culturally contingent.     

Huygens at work: Annotations in his rediscovered personal copy of Hooke's Micrographia

It is well known that Hooke's wave theory of light, set forth in his Micrographia of 1665, is viewed as a step towards Huygens's famous theory of light. This view depends mostly on some short remarks given by Huygens in his Traité de la Lumi`ere (1690) and the earlier Projet du Contenu de la Dioptrique (1673). Huygens's personal copy of Micrographia was believed to be lost until found at Braunschweig (Brunswick) University Library by the author three years ago. It is annotated at Observ. IX (pp. 47–67) only, where Hooke deals with his wave theory of light and colours. This article provides a short review of Hooke's theory, and an interpretation of Huygens's annotations, which show clearly the first steps towards the opinions he was to express in his Traité de la lumi`ere, particularly methodological ones. Furthermore, a short comparison is here drawn with Huygens's annotations in his copy of Ango's L'optique divisée en trois livres, which show similar patterns of reasoning.     

An unpublished autograph by Christiaan Huygens: His letter to David Gregory of 19 January 1694

A letter written by Christiaan Huygens to David Gregory (19 January 1694) is published here for the first time. After an introduction about the contacts between the two correspondents, an annotated English translation of the letter is given. The letter forms part of the wider correspondence about the ‘new calculus’, in which L'Hospital and Leibniz also participated, and gives some new evidence about Huygens's ambivalent attitude towards the new developments. Therefore, two mathematical passages in the letter are discussed separately. An appendix contains the original Latin text.     

Essay Review: Looking for the Rhetoric of Science

The characteristics of inductivist historiography of science, as practised by earlier scientist/historians, and Whig historiography, as practised by earlier political historians, are described, according to the accounts of Agassi and Butterfield. It is suggested that the writings of Geikie on the history of geology allow us to characterize him as a Whig/inductivist historian of science who formulated anachronistic judgements. It is further suggested that his writings have had a considerable long-term effect on interpretations of the history of geology. The character of Geikie's historiography is related to his social, political and religious views, his historicism, and his romantic enthusiasm for Nature. His methodological pronouncements are examined: he believed that the present is the key to the past, and also that the past is the key to the present. He was an empiricist and inductivist. These epistemological and methodological views impinged on his historiography of science. If one attempts to criticize Geikie's historiography, though one may try to judge his work according to the norms of his own day and age, historical anachronism cannot be avoided entirely and one may oneself be charged with acting ‘Whiggishly’. Historians of science, in the process of professionalization, have accepted the historiographical norms of general historians (perhaps for socio-economic reasons), but in so doing have inherited a problem that arises whenever they contemplate earlier historical writings. It is suggested that there may be more room for Whiggish historiography of science than is presently deemed acceptable. Alternatively, one may wish to draw a careful distinction between science and its meta-discipline, the historiography of science. Whig historiography conflates the two, and the work of Geikie (a scientist/historian par excellence) provides a good illustration of this.     

The Reception of Miller's Ether-Drift Experiments in the USA: The History of a Controversy in Relativity Revolution

This paper analyses documents from several US archives in order to examine the controversy that raged within the US scientific community over Dayton C. Miller's ether-drift experiments. In 1925, Miller announced that his repetitions of the famous Michelson-Morley experiment had shown a slight but positive result: an ether-drift of about 10 kilometres per second. Miller's discovery triggered a long debate in the US scientific community about the validity of Einstein's relativity theories. Between 1926 and 1930 some researchers repeated the Michelson-Morley experiment, but no one found the same effect as Miller had. The inability to confirm Miller's result, paired with the fact that no other ether theory existed that could compete with special relativity theory, made his result an enigmatic one. It thus remained of little interest to the scientific community until 1954, when Robert S. Shankland and three colleagues reanalysed the data and proposed that Miller's periodic fringe shift could be attributed to temperature effects. Whereas most of the scientific community readily accepted this explanation as the conclusion of the matter, some contemporary anti-relativists have contested Shankland's methodology up to now. The historical accounts of Miller's experiments provide contradictory reports of the reaction of the US scientific community and do not analyse the mechanisms of the controversy. I will address this shortcoming with an examination of private correspondence of several actors involved in these experiments between 1921 and 1955. A complex interconnection of epistemic elements, sociological factors, and personal interests played a fundamental role in the closure of this experimental controversy in the early 1930s, as well as in the reception of Shankland's reanalysis in the 1950s.     

Alexis Fontaine's ‘Fluxio-differential method’ and the origins of the calculus of several variables

Alexis Fontaine des Bertins (1704–1771) was the first French mathematician to introduce what we would now regard as results in the calculus of several variables. One example is Fontaine's theorem nF = (?F/?x)x + (?F/?y)y of 1737 for homogeneous expressions F of degree n in x and y. Many years later Fontaine indicated this particular result to have been ‘a continuation of the method of solution’ introduced by him in 1734 to solve the problem of the tautochrones. It is tempting to disregard this announcement, since the method applied to the tautochrones was a method of variations and not manifestly an exercise in the calculus of several variables. Do we have just another case of a mathematician's confusion about the origins of his earlier work? In this paper I describe Fontaine's possible intentions in his remarks.