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.     

Abstract considerations: disciplines and the incoherence of Newton’s natural philosophy

Historians have long sought putative connections between different areas of Newton’s scientific work, while recently scholars have argued that there were causal links between even more disparate fields of his intellectual activity. In this paper I take an opposite approach, and attempt to account for certain tensions in Newton’s ‘scientific’ work by examining his great sensitivity to the disciplinary divisions that both conditioned and facilitated his early investigations in science and mathematics. These momentous undertakings, exemplified by research that he wrote up in two separate notebooks, obey strict distinctions between approaches appropriate to both new and old ‘natural philosophy’ and those appropriate to the mixed mathematical sciences. He retained a fairly rigid demarcation between them until the early eighteenth century. At the same time as Newton presented the ‘mathematical principles’ of natural philosophy in his magnum opus of 1687, he remained equally committed to a separate and more private world or ontology that he publicly denigrated as hypothetical or conjectural. This is to say nothing of the worlds implicit in his work on mathematics and alchemy. He did not lurch from one overarching ontological commitment to the next (for example, moving tout court from radical aetherial explanations to strictly vacuist accounts) but instead simultaneously—and often radically—developed generically distinct concepts and ontologies that were appropriate to specific settings and locations (for example, private, qualitative, causal natural philosophy versus public quantitative mixed mathematics) as well as to relevant styles of argument. Accordingly I argue that the concepts used by Newton throughout his career were intimately bound up with these appropriate generic or quasi-disciplinary ‘structures’. His later efforts to bring together active principles, aethers and voids in various works were not failures that resulted from his ‘confusion’ but were bold attempts to meld together concepts or ontologies that belonged to distinct enquiries. His analysis could not be ‘coherent’ because the structures in which they appeared were fundamentally incompatible.     

The Remarkable Fecundity of Leibniz's Work on Infinite Series

The publication in 1906 of Alexander Smith's Introduction to general inorganic chemistry inaugurated a decisive change in chemical pedagogy in the US, the effects of which are still evident. The nature and extent of Smith's innovations are described through a comparison of his text to its source material and contemporaries. His authoritative command of and whole-hearted commitment to the intellectual framework of Ionist physical chemistry set his text apart from its American competitors, while his efforts to make the tools of physical chemistry immediately useful to his readers distinguished it from its most immediate source material, Wilhelm Ostwald's Grundlinien der anorganischen Chemie. Smith's curricular innovations in chemistry were a practical expression of his radically restrictive view of the social role of collegiate education, which he conceived as solely of use for its ability to prepare students for professional life. During the fifteen years prior to the publication of his groundbreaking textbook, Smith underwent two critical, formative experiences. First, he retreated intellectually from the structural organic chemistry in which he was trained, ultimately adopting a professional identity as a physical inorganic chemist. His involvement in the controversy regarding the structure of 1,3-diketones reveals much about his reasons for eventually abandoning organic chemistry. Second, he served the National Education Association as chairman of the Sub-committee on College Entrance Requirements in Chemistry, in the process making a close study of the ends and methods of secondary and collegiate education. These experiences made him unique among proponents of physical chemistry in the US, and help account for the unique nature of his contributions to the development of the chemical professions.     

Ptolemy and the meta-helikôn

In his Harmonics, Ptolemy constructs a complex set of theoretically ‘correct’ forms of musical scale, represented as sequences of ratios, on the basis of mathematical principles and reasoning. But he insists that their credentials will not have been established until they have been submitted to the judgement of the ear. They cannot be audibly instantiated with the necessary accuracy without the help of specially designed instruments, which Ptolemy describes in detail, discussing the uses to which each can be put and cataloguing its limitations. The best known of these instruments is the monochord, but there are several more complex devices. This paper discusses one such instrument which is known from no other source, ancient or modern, whose design was prompted by the geometrical construction known as the helikôn. It has several remarkable peculiarities. I examine its design, its purposes, and the merits and shortcomings which Ptolemy attributes to it. An appendix describes an instrument I have built to Ptolemy’s specifications (possibly the first of its kind since the second century bc), in an attempt to find out how satisfactorily such a bizarre contraption will work; and it explains how various practical problems can be resolved.     

Viète's Controversy with Clavius Over the Truly Gregorian Calendar

Some twenty years after the Gregorian calendar reform, towards the end of his life, François Viète published his own calendar proposal. This treatise contains a sharp attack against the Jesuit scholar Clavius, the mathematical mind behind the reform. Understandably enough, Clavius prepared a negative reply. Viète heard of it and exploded in a fit of rage, ``I demonstrated that you are a false mathematician [ . . . ], and a false theologian.'' Sadly, Clavius' rejection, added as a chapter to his monumental apology of the Gregorian reform, appeared when Viète had already passed away.Viète seriously believed that the true aim of the Gregorian reform has been betrayed and he was furious about some logical inconsistencies which he claimed to have found in Clavius' calendar. Clavius apparently confused solar day and epactal day (or ``tithi''), the thirtieth part of a lunar month. This is the very core of Viète's attack against Clavius whom he accused of having introduced a false lunar period (``falsa periodus lunaris''). But his own work has some logical inconsistencies too. For instance, he reproaches Clavius for having introduced lunar months of 31 days which, indeed, are unrealistic. Grievously, his own rules can likewise give rise to lunations of unnatural lengths.In order to understand these subtle twists reader and author must work largely through both Clavius and Viète's methods of Easter reckoning. The fruit of all those efforts might be an insight into Viète's clear mathematical thinking. His calendar, however, was never considered.     

Nicolas-Auguste Tissot: a link between cartography and quasiconformal theory

Nicolas-Auguste Tissot (1824–1897) published a series of papers on cartography in which he introduced a tool which became known later on, among geographers, under the name of the Tissot indicatrix. This tool was broadly used during the twentieth century in the theory and in the practical aspects of the drawing of geographical maps. The Tissot indicatrix is a graphical representation of a field of ellipses on a map that describes its distortion. Tissot studied extensively, from a mathematical viewpoint, the distortion of mappings from the sphere onto the Euclidean plane that are used in drawing geographical maps, and more generally he developed a theory for the distortion of mappings between general surfaces. His ideas are at the heart of the work on quasiconformal mappings that was developed several decades after him by Grötzsch, Lavrentieff, Ahlfors and Teichmüller. Grötzsch mentions the work of Tissot, and he uses the terminology related to his name (in particular, Grötzsch uses the Tissot indicatrix). Teichmüller mentions the name of Tissot in a historical section in one of his fundamental papers where he claims that quasiconformal mappings were used by geographers, but without giving any hint about the nature of Tissot’s work. The name of Tissot is missing from all the historical surveys on quasiconformal mappings. In the present paper, we report on this work of Tissot. We shall mention some related works on cartography, on the differential geometry of surfaces, and on the theory of quasiconformal mappings. This will place Tissot’s work in its proper context.     

P.S. Laplace's work on probability

Taken together with my previous articles [77], [80] devoted to the history of finite random sums and to Laplace's theory of errors, this paper sheds sufficient light on the whole work of Laplace in probability. Laplace's theory of probability is subdivided into theory of probability proper, limit theorems and mathematical statistics (not yet distinguished as a separate entity). I maintain that in its very design Laplace's theory of probability is a discipline pertaining to natural science rather than to mathematics. I maintain also the idea that the so-called Laplacian determinism was no hindrance to applications of his theory of probability to natural science and that one of his utterances in this connection could have well been made by Maxwell's contemporaries.Two possible reasons why the theory of probability stagnated after Laplace's work are singled out: the absence of new fields of application and, also, the insufficient level of mathematical abstraction used by Laplace. For all his achievements, I reach the general conclusion that he did not originate the theory of probability as it is now known. Dedicated to the memory of my Father, Boris A. Sheynin (1898–1975), the first generation of the Russian revolution Cette inégalité [Lunaire] quoique indiquée par les observations, était négligée par le plus grand nombre des astronomes, parce qu'elle ne paraissait pas résulter de la théorie de la pesanteur universelle. Mais, ayant soumis son existence au Calcul des Probabilités, elle me parut indiqués avec une probabilité si forte, que je crus devoir en rechercher la cause.(P. S. Laplace (Théor. anal. prob., p. 361))     

Pierre-Joseph Macquer an Eighteenth-Century Artisanal-Scientific Expert

Summary

Pierre-Joseph Macquer (1718–1784) is well known as one of the major chemists in the eighteenth century as a theoretician and a teacher. He is also known for his works on dyeing. This paper presents a new face of Macquer. He proposed a theory on mordants in dyeing as early as 1775. Besides his activity at the Académie des sciences, he played an important role in Government as the commissioner of dyeing from 1766 where he established close links with artisan inventors. Académicien chimiste at the royal Manufactory of Sèvres from 1757, he was also the inventor of French porcelain. His notebooks show his organization, method, courage, passion and obstinacy in the search for the paste for hard porcelain. He also proposed an interpretation of its formation. Macquer was both a theoretician and a practical expert in dyeing as well as in porcelain making. He managed to bridge the gap between science and art.     

Pluralism and anarchism in quantum physics: Paul Feyerabend's writings on quantum physics in relation to his general philosophy of science

This paper aims to show that the development of Feyerabend's philosophical ideas in the 1950s and 1960s largely took place in the context of debates on quantum mechanics.In particular, he developed his influential arguments for pluralism in science in discussions with the quantum physicist David Bohm, who had developed an alternative approach to quantum physics which (in Feyerabend's perception) was met with a dogmatic dismissal by some of the leading quantum physicists. I argue that Feyerabend's arguments for theoretical pluralism and for challenging established theories were connected to his objections to the dogmatism and conservatism he observed in quantum physics.However, as Feyerabend gained insight into the physical details and historical complexities which led to the development of quantum mechanics, he gradually became more modest in his criticisms. His writings on quantum mechanics especially engaged with Niels Bohr; initially, he was critical of Bohr's work in quantum mechanics, but in the late 1960s, he completely withdrew his criticism and even praised Bohr as a model scientist. He became convinced that however puzzling quantum mechanics seemed, it was methodologically unobjectionable – and this was crucial for his move towards ‘anarchism’ in philosophy of science.     

Before words: reading western astronomical texts in early nineteenth-century Japan

SUMMARY

In 1803, the most prominent Japanese astronomer of his time, Takahashi Yoshitoki, received a newly imported Dutch translation of J. J. Lalande's ‘Astronomie’. He could not read Dutch, yet he dedicated almost a year to a close examination of this massive work, taking notes and contemplating his own astronomical practices. How did he read a book he could not read? Following the clues Yoshitoki left in his notes, we discover that he found meanings not only in words, but also in what are often taken for granted or considered to be auxiliary tools for data manipulation, such as symbols, units, tables, and diagrams. His rendering of these non-verbal textual elements into a familiar format was crucial for Yoshitoki's reading, and constituted the initial step in the process of integrating Lalande's astronomy into Japanese astronomical practices, and the subsequent translation of the text into Japanese.     

`Nature is the Realisation of the Simplest Conceivable Mathematical Ideas': Einstein and the Canon of Mathematical Simplicity

Einstein proclaimed that we could discover true laws of nature by seeking those with the simplest mathematical formulation. He came to this viewpoint later in his life. In his early years and work he was quite hostile to this idea. Einstein did not develop his later Platonism from a priori reasoning or aesthetic considerations. He learned the canon of mathematical simplicity from his own experiences in the discovery of new theories, most importantly, his discovery of general relativity. Through his neglect of the canon, he realised that he delayed the completion of general relativity by three years and nearly lost priority in discovery of its gravitational field equations.     

The platinum pyrometers of Louis Bernard Guyton de Morveau,F.R.S. (1737–1816)

As we have seen, it was clearly Guyton's intention, in 1808, to supply details of his improved platinum pyrometer, and he did submit a drawing of the instrument at the meeting of the Class in December 1810. It would seem that on that occasion he did not supply those details which are to be found in the fourth, unpublished, part of the ‘Essay’. The existence of a text fit to be sent to the printer, and the execution of a drawing relating to the improved version of his platinum pyrometer, might be taken as evidence that Guyton intended to publish. His paper of 1810 did not appear until 1814, however, so that publication of the fourth part of the ‘Essay’ could scarcely have occurred until 1815 or later. Guyton probably hoped to be able to read it to the Class of Physical and Mathematical Sciences before publishing it in the Annales de Chimie, but his death on 2 January 1816 robbed him of the opportunity.     

Early nautical charts

Christian Wilhelm Blomstrand, Professor of Chemistry and Mineralogy at Lund University from 1862 to 1895, was one of the important chemists of the second half of the nineteenth century. His theoretical ideas and experimental accomplishments contributed to advances in several branches of chemistry. Living in Sweden during a transitional period between the older and newer chemistry and being a scientific as well as a political conservative, Blomstrand sought to reconcile Berzelius's dualistic theory with the unitary and type theories. He was opposed to Kekulé's dogma of constant valency, and he strove to establish a sound and complete theory of variable valency. This article briefly outlines Blomstrand's life and considers his best known book, Die Chemie der Jetztzeit (1869), as well as his work on mineralogy, inorganic chemistry (the earth acid elements, heteropoly acids, platinum complexes), and his theoretical views on valency, diazo compounds, and metal-ammines. His so-called ‘chain theory’, as developed and modified by his fellow Scandinavian chemist and close friend, Sophus Mads Jørgensen, was for more than three decades the most popular and successful of the numerous attempts to explain the constitution, properties, and reactions of coordination compounds.     

Joseph LeConte and the development of the physiology and psychology of vision in the United States

The nineteenth-century American scientist, philosopher and teacher Joseph LeConte (1823–1901) is well-known for his writings on geology and the reconciliation of evolutionary theory and religion, but he has not been properly recognized for his contributions to the physiology and psychology of vision. This study explores and assesses his work in the latter field, showing the nature of his original investigations into human vision and the influence of his book Sight: an exposition of the principles of monocular and binocular vision, which served as the major textbook on the subject in the United States from its publication in 1881 until after the turn of the century. Grounded in neo-Lamarckian evolutionary theory, LeConte's publications on vision had a strong impact upon subsequent studies of the phenomenon of human sight.     

Tracings of the north of Europe: Robert Chambers in search of the Ice Age

Scottish publisher and naturalist Robert Chambers pursued an amateur interest in geology through much of his life. His early measurements of raised beaches in Scotland earned him membership in the Geological Society of London in 1844, a recognition much appreciated by the anonymous author of the ‘scandalous’ Vestiges published the same year. Although familiar with emerging ice age theories, Chambers remained with most British geologists a sceptic through the 1840s, even after a trip to the glaciers of the Alps in 1848, which nevertheless prepared him for the turning point, which came in 1849 during an extensive field trip in Norway and Sweden. Here a wealth of observations left him in no doubt that vast glaciers had formerly covered Scandinavia, polishing cliffs, scouring striations, depositing old moraines and erratic boulders. This also led him to a new glacial reading of the British landscape, and with the ardent conviction of a fresh convert he became one of the most vocal supporters of glacial theory in Britain in the 1850s at a time when the iceberg drift theory for boulder transport was still favoured by most prominent British geologists. While Chambers through his popular Chambers’s Edinburgh Journal communicated his travels and ice age vision to a wide audience, and also pointed out ice age evidence on guided excursions around Edinburgh, he did not enter this new vision into subsequent editions of Vestiges, probably in order not to reveal its author. This paper explores Chambers’s contributions to the ice age debate, his field trips and the genesis of his convictions, and evaluates his impact on the scientific debate.     

The Lighthouse and the Observatory: Islam,Science, and Empire in Late Ottoman Egypt

Well-known in his day, but overlooked since, Erasmus King lectured in natural and experimental philosophy from the 1730s until 1756 at his Westminster home and twenty other venues, publicizing his frequent courses exclusively in the Daily Advertiser. In 1739 he escorted Desaguliers's youngest son to Russia, hoping to demonstrate experimental philosophy to the Russian empress. En route, he conducted trials with a sea-guage in the Baltic which were reported by Stephen Hales in his Statical Essays. Various sources testify to King's subsequent experimental research for Hales in the fields of anatomy, respiration and electricity. There is recorded evidence for the exceptional range and quality of King's scientific apparatus and models.     

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.     

Stanisław Staszic: An Early Surveyor of the Geology of Central and Eastern Europe

In the late eighteenth and early nineteenth centuries the Polish geoscientist, philosopher, and statesman Stanis?aw Staszic (1755–1826) conducted an extensive geological survey of Poland and adjacent areas. In 1815, he completed a book (in Polish), On the geology of the Carpathians and other mountains and lowlands of Poland, complemented by a well-made geological map of Central and Eastern Europe. Early in the nineteenth century, Staszic refined the idea of ‘geological mapping’, though initially he was interested in the exploration of mineral deposits, rock salt, copper and iron ores, and coal. Unlike his predecessors, his book adopted a temporal subdivision of rocks, using a somewhat modified version of Abraham Gottlob Werner's system. He delineated the surface distribution of five rock units and coloured them onto his map. His work gave expression to his view of geological history, and brought the ‘Enlightenment Period’ of geology in Central and Eastern Europe to a close.