On Kepler's awareness of the problem of experimental error

This paper is an account of Kepler's explicit awareness of the problem of experimental error. As a study of the Astronomia nova shows, Kepler exploited his awareness of the occurrences of experimental errors to guide him to the right conclusion. Errors were thus employed, so to speak, perhaps for the first time, to bring about a major physical discovery: Kepler's laws of planetary motion. ‘Know then’, to use Kepler's own words, ‘that errors show us the way to truth.’ With a survey of Kepler's revolutionary contribution to optics, the paper demonstrates that Kepler's awareness of the problem of experimental error extended beyond discrepancies between calculations and observations to types of error which pertain to observations and instruments. It emerges that Kepler's belief in the unity of knowledge and physical realism, facilitated—indeed created—the right philosophical posture for comprehending the problem of error in an entirely novel way.     

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.     

Chemist,entomologist, Darwinian,and man of affairs: Raphael Meldola and the making of a scientific career

In 1925 a debate erupted in the correspondence columns of the British Medical Journal concerning the effectiveness of eating raw pancreas as a treatment for diabetes. Enthusiasts were predominantly general practitioners (GPs), who claimed success for the therapy on the basis of their clinical impressions. Their detractors were laboratory‐oriented ‘biochemist‐physicians,’ who considered that their own experiments demonstrated that raw pancreas therapy was ineffective. The biochemist‐physicians consistently dismissed the GPs' observations as inadequately ‘controlled’. They did not define the meaning of ‘control’ in this context, although it clearly did not have the term's present‐day meaning of a trial employing an untreated comparison group of patients. Rather, the physician‐biochemists' ‘properly controlled’ experiments involved careful regulation of their patients' diet and other environmental factors, and evaluation of the therapy's success through biochemical, rather than just clinical, criteria. However, my analysis suggests that these factors alone are inadequate to account for the biochemist‐physicians' dismissal of the GPs' work as ‘uncontrolled’. I suggest that the biochemist‐physicians were deliberately exploiting the powerful rhetorical connotations of the term ‘control’. Ultimately, they implied that only a trial which they themselves had conducted could be deemed ‘adequately controlled’.     

Henry Dresser and Victorian Ornithology: Birds,Books and Business

The metaphysical commitment to the circle as the essential element in the analysis of celestial motion has long been recognized as the hallmark of classical astronomy. Part I of this paper contains a discussion of how, for Kepler, the circle also functions in geometry to select the basic polygons, in music to select the basic harmonies, and in astrology to select the basic aspects. In Part II, the discussion centres on the question of how the replacement of circular planetary orbits by elliptical orbits in the Astronomia Nova of 1609 affected Kepler's metaphysical commitment to celestial circularity that was made manifest in the derivation of planetary radii in the Mysterium Cosmographicum of 1596. The answer is found in the new and much more accurate derivation of both the planetary radii and their eccentricities in the Harmonice Mundi of 1619. It is the relationship of the diurnal movements of single planets at aphelion and perihelion to specific musical consonances that provides the first step. Then, in the second step, these ratios are ‘tempered’ so that all six planets can provide a heavenly choir. The third and final step employs the ‘mean period’, which is obtained directly from the tempered ratios given by musical theory and diurnal (not annual) motion, in the 3/2 power law to calculate the planetary radii and eccentricities with amazing accuracy. Thus the ellipse is necessary to supply the variation in angular velocities that contain the Creator's archetypal celestial circularity.     

Maligned for mathematics: Sir Thomas Urquhart and his Trissotetras

Thomas Urquhart (1611–1660), celebrated for his English translation of Rabelais’ Gargantua et Pantagruel, has earned some notoriety for his eccentric, putatively incomprehensible early book on trigonometry The Trissotetras (1645). The Trissotetras was too impractical to succeed in its own day as a textbook, since it lacked both trigonometric tables and sample calculations. But its current bad reputation is based on literary authors’ amplifications of the verdict prefaced to its 19th century reprinting by one mathematician, William Wallace, who lacked the background to appreciate the book’s historical context. Considering that context (including seventeenth century ‘copious’ prose, and medieval logic and ‘art of memory’), the bad reputation is undeserved: the book is mathematically clear, clever (e.g. in superimposing 16 problems into one diagram), and complete. The Trissotetras may thus be viewed as simply one more of Urquhart’s polymathic projects and involvements – which included education, rise of the middle class, religious and class conflicts, development of science and mathematics, search for patronage, universal language construction, and development of English prose – which serve to make him a lively and instructive intellectual Everyman for his time.     

Europe's Infrastructure Transition: Economy,War, Nature

In his many uses of the pendulum as a model for other motions, Galileo also described several of the properties of pendular motion. All but a small number of his apparently observational reports ring true because of his use of such qualifiers as ‘almost’. His report of observations of two lead balls on equal long strings is shown by reconstruction to have been a real experiment. His report of similar observations with balls of cork and lead is shown to be an imaginary experiment. His claim that the period of a pendulum is independent of amplitude is shown to be based more on mathematical deduction than on experimental observation.     

The politics of environments before the environment: Biopolitics in the longue durée

Our understanding of body–world relations is caught in a curious contradiction. On one side, it is well established that many concepts that describe interaction with the outer world – ‘plasticity’ or ‘metabolism’- or external influences on the body - ‘environment’ or ‘milieu’ – appeared with rise of modern science. On the other side, although premodern science lacked a unifying term for it, an anxious attentiveness to the power of ‘environmental factors’ in shaping physical and moral traits held sway in nearly all medical systems before and alongside modern Europe. In this article, I build on a new historiography on the policing of bodies and environments in medieval times and at the urban scale to problematize Foucault's claim about biopolitics as a modern phenomenon born in the European eighteenth-century. I look in particular at the collective usage of ancient medicine and manipulation of the milieu based on humoralist notions of corporeal permeability (Hippocrates, Galen, Ibn Sīnā) in the Islamicate and Latin Christendom between the 12th and the 15th century. This longer history has implications also for a richer genealogy of contemporary tropes of plasticity, permeability and environmental determinism beyond usual genealogies that take as a starting point the making of the modern body and EuroAmerican biomedicine.     

Natural selection and the ‘antiquity of man’: Intellectual impacts in the Australian colonies

Two months before the publication of Charles Darwin's On the Origin of Species (1859), Scottish geologist Charles Lyell announced a consensus on ‘the antiquity of man.’ Although stemming from separate intellectual traditions, human antiquity and natural selection had such a powerful influence on nineteenth century science that the former is often thought to be an inevitable conceptual and chronological consequence of the latter. Various scholars have argued it was in fact the acceptance of human antiquity that provided a foundation for the intelligibility and eventual acceptance of evolution by natural selection. This article investigates how these two interwoven theories affected understandings of human antiquity in Australia; itself an under-examined topic in Australian scholarship. Indeed, most historians maintain Australia's human antiquity was not ‘discovered’ or broadly understood until the advent of radiocarbon dating and professional archaeology in the 1960s. This over-simplified narrative has only recently begun to be reassessed. To contribute to this reassessment, and to the broader reclamation of human antiquity as a historical subject, this article focuses on the early decades of human antiquity's dissemination in Australia, examines its complex relationship with natural selection, and ultimately challenges narratives of its ‘recent’ discovery.     

The American Philosophical Society and the rise of astronomy in the United States in the middle of the nineteenth century

Early geological investigations in the St David's area (Pembrokeshire) are described, particularly the work of Murchison. In a reconnaissance survey in 1835, he regarded a ridge of rocks at St David's as intrusive in unfossiliferous Cambrian; and the early Survey mapping (chiefly the work of Aveline and Ramsay) was conducted on that assumption, leading to the publication of maps in 1845 and 1857. The latter represented the margins of the St David's ridge as ‘Altered Cambrian’. So the supposedly intrusive ‘syenite’ was regarded as younger, and there was no Precambrian. These views were challenged by a local doctor, Henry Hicks, who developed an idea of the ex-Survey palaeontologist John Salter that the rocks of the ridge were stratified and had formed a Precambrian island, round which Cambrian sediments (now confirmed by fossil discoveries) had been deposited. Hicks subsequently proposed subdivision of his Precambrian into ‘Dimetian’, ‘Pebidian’, and (later) ‘Arvonian’, and he attempted correlations with rocks in Shropshire, North Wales, and even North America, seeking to develop the neo-Neptunist ideas of Sterry Hunt. The challenge to the Survey's work was countered in the 1880s by the Director General, Geikie, who showed that Hicks's idea of stratification in the Dimetian was mistaken. A heated controversy developed, several amateur geologists, supported by a group of Cambridge Sedgwickians, forming a coalition of ‘Archaeans’ against the Survey. Geikie was supported by Lloyd Morgan. Attention focused particularly on Ogof Lle-sugn Cave and St Non's Arch, with theory/controversy-ladenness of observations evident on both sides. Evidence from an eyewitness student record of a Geological Society meeting reveals the ‘sanit`ized’ nature of the official summary of the debate in QJGS. Field mapping early in the twentieth century by J. F. N. Green allowed a compromise consensus to be achieved, but Green's evidence for unconformity between the Cambrian and the Dimetian, obtained by excavation, can no longer be verified, and his consensual history of the area may need revision. Unconformity between the Cambrian and the Pebidian tuffs is not in doubt, however, and Precambrian at St David's is accepted. The study exhibits features of geological controversy and the British geological community in the nineteenth century. It also furnishes a further instance of the great influence of Murchison in nineteenth-century British geology and the side-effects of his controversy with Sedgwick.     

Alhazen,Leonardo, and late-medieval speculation on the inversion of images in the eye

No one before Platter and Kepler proposed retinal reception of an inverted visual image. The dominant tradition in visual theory, especially that of Alhazen and his Western followers, subordinated the intra-ocular geometry of visual rays to the requirement for an upright image and to preconceptions about the precise nature of the visual spirit and its part in vision. Henry of Langenstein and an anonymous glossator in the late Middle Ages proposed alternatives to Alhazen, including the suggestion of double inversion of the image. Leonardo da Vinci was aware of both Alhazen's theory and Henry's contradiction, but perhaps not of the anonymous hypothesis of double inversion. Leonardo's visual ‘theory’ has more the character of a critique than of a theoretical alternative, and he did not transcend the medieval concept of visual spirit.     

How Weyl stumbled across electricity while pursuing mathematical justice

It is argued that Weyl's theory of gravitation and electricity came out of ‘mathematical justice’: out of the equal rights of direction and length. Such justice was manifestly at work in the context of discovery, and is enough to derive all of source-free electromagnetism. Weyl's repeated references to coordinates and gauge are taken to express equal treatment of direction and length.     

Comments on papers by Sharlin and Wall

Wall is convincing on the Fuller court, but less so on Holmes, who may have understood Spencer's Social statics as a laissez faire rather than as a Darwinist document. Sharlin helps us to follow Spencer's attempt to universalize the concept of energy, even if Sharlin's explanation for Spencer's failure reduces to an application of the classical insight that physical phenomena are more predictable than social phenomena. Sharlin's conception of ‘scientism’ is helpful in some contexts, but less so in others; we need to remind ourselves that the role of values in scientism is active as well as passive.     

The story of ‘Scientist: The Story of a Word’

This examination of an important paper by Sydney Ross is the first in a projected series of occasional reflections on ‘Annals of Science Classic Papers’ that have had enduring utility within the field of history of science and beyond. First the messages of the paper are examined, some well known but others, particularly Ross's own contemporary concerns about the use of the word ‘scientist’, less so. The varied uses made of the paper by scholars are then traced before Ross's biography is examined in order to try to understand how a figure professionally marginal to the field of history of science came to write such a significant piece. Ross’s interest in the topic appears to have been informed by a romantically tinged scientific progressivism and a deep concern with the importance of linguistic precision in science and in public affairs. The inspirations of the author and the interests of his audience have been only partially aligned, but the paper's insights remain of broad historical interest and have wider ramifications since the denotation ‘scientist’ and its proper application are much debated today in contests over the authority of science.     

Measurement in French Experimental Physics from Regnault to Lippmann. Rhetoric and Theoretical Practice

This paper explores the legacy of the great French experimental physicist Victor Regnault through the example of Gabriel Lippmann, whose engagement with electrical standardization during the early 1880s was guided by Regnault's methodological precept to measure ‘directly’. Lippmann's education reveals that the theoretical practice of ‘direct’ measurement entailed eliminating extraneous physical effects through the experimental design, rather than, like physicists in Britain and Germany, making numerical ‘corrections’ to measured values. It also provides, paradoxically, exemplars of the qualitative theoretical practices that sustained Regnault's misguided ambition to avoid theory. By considering the largely negative reactions to Lippmann's proposals for selecting suitable electrical units and methods of measuring the ohm, this paper associates these theoretical practices with the ineffectual rhetorical strategies employed by Lippmann to promote his work, and thereby indicates that the practice of direct measurement was limited to French experimental physics. Whilst this result aligns readily with the existence of divergent nineteenth century British and German cultures of precision, it emerges from a very different disciplinary context in which the practice of precision electrical measurement developed independently of submarine telegraphy. This is because, as this paper illustrates, telegraphic engineering and experimental physics remained separate professions in France.     

Jean-Jacques Rousseau: Botanist

It is argued that Hugo de Vries's conversion to Mendelism did not agree with his previous theoretical framework. De Vries regarded the number of offspring expressing a certain character as a hereditary quality, intrinsic to the state of the pangene involved. His was a shortlived conversion since after the ‘rediscovery’ he failed to unify his older views with Mendelism. De Vries was never very much of a Mendelian. The usual stories of the Dutch ‘rediscovery’ need, therefore, a considerable reshaping.