The early history of the factorial function

Communicated by U. Bottazzini     

The early history of chance in evolution

Work throughout the history and philosophy of biology frequently employs ‘chance’, ‘unpredictability’, ‘probability’, and many similar terms. One common way of understanding how these concepts were introduced in evolution focuses on two central issues: the first use of statistical methods in evolution (Galton), and the first use of the concept of “objective chance” in evolution (Wright). I argue that while this approach has merit, it fails to fully capture interesting philosophical reflections on the role of chance expounded by two of Galton's students, Karl Pearson and W.F.R. Weldon. Considering a question more familiar from contemporary philosophy of biology—the relationship between our statistical theories of evolution and the processes in the world those theories describe—is, I claim, a more fruitful way to approach both these two historical actors and the broader development of chance in evolution.     

The wedge and the vis viva controversy: how concepts of force influenced the practice of early eighteenth-century mechanics

This article discusses the quest for the mechanical advantage of the wedge in the eighteenth century. As a case study, the wedge enlightens our understanding of eighteenth-century mechanics in general and the controversy over “force” or vis viva in particular. In this article, I show that the two different approaches to mechanics, the one that favoured force in terms of velocities and the one that primarily used displacements—known as the ‘Newtonian’ and ‘Leibnizian’ methods, respectively—were not at all on par in their ability to solve the problem of the wedge. In general, only those who used the Leibnizian concept of force or some related notion were able to get to the conventional results. This article thus rebuts the received view that the vis viva controversy was merely a semantic one. Instead, it shows that different understandings of “force” led to real and pragmatic differences in eighteenth-century mechanics.     

Electric charge in hyperbolic motion: the early history

The study of an electric charge in hyperbolic motion is an important aspect of Minkowski’s geometrical formulation of electrodynamics. In “Space and Time”, his last publication before his premature death, Minkowski gives a brief geometrical recipe for calculating the four-force with which an electric charge acts on another electric charge. The subsequent work of Born, Sommerfeld, Laue, and Pauli filled in the missing derivation details. Here, we bring together these early contributions, in an effort to provide a more modern, accessible, and unified exposition of the early history of the electric charge in hyperbolic motion.

     

Terrestrial magnetism and the development of international collaboration in the early nineteenth century

The establishment of Gauss's and Weber's Magnetische Verein in 1834, and the British Government's support of Edward Sabine's ‘Magnetic Crusade’ in 1838, marked the opening of a new era in international geomagnetic research. However, the British and German efforts, although initiating an increase in the scale of investigations of the earth's field, were also the culmination of over half a century of activity by individuals and institutions in several countries. This article traces the growth of international cooperation in terrestrial magnetism from the late eighteenth century until the 1830s, and examines the change in leadership in the field from France to Britain and Germany. The transition from individual to government-backed collaboration is described, and also the role of Alexander von Humboldt as an organiser of geomagnetic research and author of a cosmical approach to earth magnetism as one of a number of related ‘telluric’ forces.     

On the early history of Bessel functions

Communicated by Curtis Wilson     

Dumfries and the early history of surgical anaesthesia

Although the history of the word ‘geology’ has often been referred to by those interested in the development of the science, that history has never been fully traced. An endeavor is made to do so here, taking the story at least as far as 1813, by which time the basic word had unquestionably been established in its modern form and meaning. Various claims as to who first gave the science its present name are also briefly examined.     

Constraints and divergent assessments of fertility in non-empirical physics in the history of the string theory controversy

This paper examines historic appraisals of string theory to develop a less abstract understanding of the string theory controversy and assessment in non-empirical physics. This historical approach reveals several points of conflict in the controversy, each centring on a constraint. By proceeding stepwise through these constraints, I reveal the role that constraints played in determining divergent assessments of string theory. Rather than disagreement between two competing methods, a level of agreement is found amongst those critical and supportive of string theory as to the commitment to the relevant constraints, but disagreement as to the sufficiency of consistency, the path to background independence and a non-perturbative formulation, and how to interpret the significance of applications. Furthermore, the string theory community itself is shown to be divided in its commitment to the necessity of uniqueness and the legitimacy of anthropic reasoning. These varied assessments, guided by considerations of constraints, have informed divergent claims as to the past and future fertility of string theory. These are claims as to the value of string theory in guiding research in quantum gravity: claims as to whether string theory has and will be valuable as a means rather than an end.     

William Stukeley and the early history of the Orrery

Relations between J. A. C. Chaptal, pioneer of heavy chemical industry in France, and A. L. Lavoisier, reformer of chemical theory, are examined in the light of unpublished correspondence they exchanged in the period 1784–1790. The letters, together with Chaptal's early publications, allow a reconstruction of his conversion to Lavoisier's antiphlogistic chemistry. They also reveal a series of petitions that Chaptal made to Lavoisier, in the latter's official capacity as a director of the Régie des poudres et salpêtres, for relief from the controlled price of saltpetre for his acid works in Languedoc. Finally, the relationship is explored as a window on the interplay between chemical theory and industrial practice during the period of the Industrial Revolution.     

Bartolomeo Telioux and the early history of the thermometer

In the late 1810s and 1820s the Edinburgh phrenologists were largely concerned with trying to establish phrenology as the true science of mind. They challenged the accepted theories about the nature of mind and the brain; in turn, phrenology was attacked by the proponents of Scottish common-sense philosophy and by some medical men. The ensuing debate, which is discussed as an example of conflict between incommensurable world-views, involved a wide range of contentious theological, philosophical, scientific and methodological issues.     

Magnitude,moment, and measurement: The seismic mechanism controversy and its resolution

This paper examines the history of two related problems concerning earthquakes, and the way in which a theoretical advance was involved in their resolution. The first problem is the development of a physical, as opposed to empirical, scale for measuring the size of earthquakes. The second problem is that of understanding what happens at the source of an earthquake. There was a controversy about what the proper model for the seismic source mechanism is, which was finally resolved through advances in the theory of elastic dislocations. These two problems are linked, because the development of a physically-based magnitude scale requires an understanding of what goes on at the seismic source. I will show how the theoretical advances allowed seismologists to re-frame the questions they were trying to answer, so that the data they gathered could be brought to bear on the problem of seismic sources in new ways.